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1.1750973.pdf | The Raman Spectra of Mono and Dichlorobenzenes
H. Sponer and J. S. KirbySmith
Citation: The Journal of Chemical Physics 9, 667 (1941); doi: 10.1063/1.1750973
View online: http://dx.doi.org/10.1063/1.1750973
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141.209.144.159 On: Tue, 16 Dec 2014 15:22:49SEPTEMBER. 1941 JOURNAL OF CHEMICAL PHYSICS VOLUME 9
The Raman Spectra of Mono-and Dichlorobenzenest
H. SPONER AND J. S. KIRBy-S~IITH*
Department of Physics, Duke University, Durham. North Carolina
(Received June 9, 1941)
Raman spectra were taken of gaseous mono-and dichlorobenzenes. Polarization measure
ments were made for the dichlorobenzenes in the liquid phase. Interpretations of the stronger
lines are given in terms of modes of vibration. The experimental results and assignments of
the frequencies are collected in Tables I-IV.
INTRODUCTION
THE Raman spectra of the different chloro
benzenes have been thoroughly studied in
the liquid state by a number of investigators.1
Polarization measurements have been carried out
in the case of monochlorobenzene by Simons.2 In
the course of an analysis of the ultraviolet ab
sorption spectra of mono-3 and the dichloro
benzenes4 it became desirable to have their
vibrational frequencies in the gaseous phase. For
this reason these compounds have been rein
vestigated in the vapor phase. To facilitate inter
pretation of the observed frequencies polarization
measurements were made for the dichloroben
zenes in the liquid state.
EXPERIMENTAL
A. Measurements in the gas
The substances used in this investigation,
monochlorobenzene, ortho-, meta-, and para
dichlorobenzene, were kindly furnished by the
Chemistry Department.t They were extremely
pure, and were carefully introduced into the
Raman tubes by vacuum distillation.
t Presented before the Division of Physical and Inor
ganic Chemistry of the American Chemical Society at
Detroit, September, 1940. .
* Present address: National Institute of Health,
Bethesda, Maryland.
1 A. Dadieu, A. Pongratz and K. W. F. Kohlrausch,
Monats. f. Chern. 61, 426 (1932); J. W. Murray and D. H.
Andrews, J. Chern. Phys. 1,406 (1933). Complete refer
ences may be found in the second book of K. W. F.
Kohlrausch, Der Smekal-Raman Effekt, Erg. Bd. (Julius
Springer, Berlin, 1938), or in James H. Hibben, The
Raman Effect and its Chemical Applications (Reinhold
Publishing Corporation, New York, 1939).
2 L. Simons, Soc. Sci. Fennica, Comm. Phys.-Math. 6,
No. 13 (1932).
3 H. Sponer and S. H. Wollman, Phys. Rev. 57, 1078A
(1940).
4 S. H. Wollman, unpublished results. t We are indebted to Dr. Eunice Moore for the courtesy
of providing us with the substances. The apparatus used, except for modifications
in the assembly of Raman tube and filter jacket,
has been previously described.5 Certain changes
have been made necessary in order to attain the
relatively high temperatures (200°C in the case
of the dichlorobenzenes) needed to give sufficient
vapor pressures for adequate scattered inten
sities, and at the same time permit suitable
filters to be employed. This condition was
attained by placing an extra glass cylinder
between the filter jacket and Raman tube.
Strong blasts of hot air were directed between
this cylinder and the Raman tube and the scat
tering section of the tube was heated to the
desired temperature. The space between the
filter jacket and the wall of the extra cylinder
served as an insulating air space and prohibited
an excessive loss of heat to the circulating filter
solution. The bottom section of the tube was
heated by resistance coils which were wrapped
around it. Temperatures were read with a ther
mocouple placed in contact with the coolest
portion of the Raman tube. With this arrange
ment temperatures up to 220°C have been
maintained at fairly constant values (±5°C)
during all exposure times.
Twelve Hg arcs were used as the light source,
excitation being by the 4047 and 4358A lines
together as well as by 4358 alone. Filters were
aqueous solutions of CoCb when excitation by
both lines was desired, and CoCl 2+quinine for
the isolation of 4358. All spectra have been ob
tained upon antihalation Eastman Super Panchro
Press or Ilford Hypersensitive Panchromatic
plates. Exposure times have been from 6 to 24
hours. The spectrograph is the Zeiss 3 prism
instrument used in previous work.
5 J. S. Kirby-Smith and L. G. Bonner, J. Chern. Phys. 7,
880 (1939).
667
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141.209.144.159 On: Tue, 16 Dec 2014 15:22:49668 H. SPONER AND ]. S. KIRBY-SMITH
GAS
200 (w)
416 (m)
608 (w)
703 (m)
1001 (st)
1024 (m)
1080 (m)
1134 (w)
1191 (w) }
1589 (m)
3079 (st b)
3180 (w) TABLE I. C6H5Cl.
DEPOLARIZATION
LIQUID FACTOR ASSIG~-
(A"AN'THAKRISH"A") (SI'IONS) Mc'KT
196 (6b)
270 (1/2)
295 (2)
420 (6)
615 (3)
702 (6)
742 (0)
790 (0)
830 (0)
925 (0)
989 (0)
1003 (lOs)
1013 (00)
1024 (7)
1084 (5)
1121 (1/2)
1158 (1/2)
1176 (1/2)
1295 (0)
1321 (0)
1372 (0)
1443 (0)
1565 (0)
1584 (4)
3008 (5)
3028 (0)
3068 (lOb)
3140 (0)
3165 (1) 0.87
0.86
0.32
0.89
0.13
0.06
0.19
0.10
0.88
0.87
0.32
B. Polarization measurements
The apparatus used here was of conventional
type, using a sensibly parallel beam of unpo
larized light as the incident radiation. The light
source consisted of two small (15 cm long) Hg
arcs similar in design to those used in the gas
apparatus. Glass cylinders filled with filter
solution focused and directed a strong beam of
filtered light into the scattering tube. The source
operated in a vertical position, and a totally
reflecting glass prism was used to direct the
scattered light into the polarizing system. This
consisted of the usual Wollaston prism, a lens
for focusing the two polarized components onto
the spectrograph slit, and a half-wave plate.
This arrangement gave good pictures in from 3
to 8 hours exposure time.
Under present conditions precise measure
ments have not been made. Density marks for the
calibration of plates and the determination of
relative intensities have not been put on all
plates. The noncparallel character of the incident
beam and imperfections in the half-wave plate
arc the other main sources of error. GAS
194 (w)
300 (m)
434 (vw)
487 (m)
664 (m)
760 (w)
1035 (st)
1133 (st)
1271 (w)
1598 (w)
3082 (st)
3150 (w)
GAS
205 (wb)
356 (w)
399 (m)
613 (vw)
665 (m)
998 (st)
1056 (m vb)
1129 (m)
1590 (m)
3090 (st)
3169 (w) LIQUID
(SWAI"E AND
MliRRAY)
154 (10)
203 (3)
239 (1b)
330 (Ob)
430 (1)
469 (1)
483 (2)
658 (5)
756 (Ob)
860 (lb)
1020 (1)
1041 (10)
1129 (5)
1160 (lb)
1274 (1b)
1577 (4)
1607 (Ob)
2994 (1)
3073 (10)
3146 (3) DEPOLARIZATION ASSIGN-
FACTOR MEKT
0.8
0.8
0.8
0.8
0.45
0.35
0.20
0.25
dep
0.8
0.40
TABLE III. m-C6H,Cl,.
LIQUID
(SWAINE AND
MURRAY) DEPOLARIZATION ASSIGN-
178 (3)
202 (3)
216 (2)
366 (1)
399 (4b)
428 (2)
530 (0)
666 (4)
999 (10)
1018 (0)
1070 (3b)
1109 (2)
1126 (4)
(1160 Kohl-
rausch)
1240 (0)
1425 (0)
1456 (0)
1544 (0)
1579 (5b)
1625 (0)
3076 (10)
3152 (2)
RESULTS FACTOR ME:"TT
0.9
0.9
0.10 "'[
0.6
0.25 "'[
0.20 "'[
0.30
0.45 "'[
The present results including the assignment
of frequencies as well as previous liquid and
polarization data are summarized in Tables I to
IV. The most recently published values have been
taken.6 Intensities have been determined from
microphotometer curves. However, due to the
6 ]. W. Swaine and]. W. Murray, J. Chern. Phys. 1, 512
(1933); R. Ananthakrishnan, Proc. Ind. Acad. Sci. 3A, 52
(1936).
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relatively greater amount of Rayleigh scattering
and general background inherent in gases these
intensities are only estimated as strong (st),
medium (m), weak (w) and very weak (vw).
While nothing has to be added to the tables
for the dichlorobenzenes, it should be mentioned
that for monochlorobenzene additional extremely
weak, broad and diffuse lines have been observed
at 275 and 500 cm-I. These lines appear only on
several plates, and then with such small intensity
that they could be spurious.
, The measurement of the frequency in the
neighborhood of 200 cm-I was taken as an anti
Stokes transition from Hg 4047. As a Stokes line
from Hg 4047 it is masked by the strong Hg 4077
and from Hg 4358 by the Hg II line at 4398.6A.
The 200 frequency is usually measured from the
Hg 4358 line in the liquid, as under these condi
tions the spark line is too weak for detection.
A definite diffuse wing on the low frequency
edge of the strong 3079 cm-I line has been ob
served on all plates. Attempts to resolve any
structure were unsuccessful.
DISCUSSION OF RESULTS
For convenience in discussing the frequencies
of the investigated benzene chlorides Fig. 1 has
been included which represents the different
types of vibration in the benzene molecule.7 The
TABLE IV. p-CeH,CI 2•
LIQUID
(SWAINE A"n DEPOLARIZA TIO~ ASSIGN-
GAS MURRAY) FACTOR :\lENT
302 (4)
326 (w) 333 (8)
386 (w) 355 (1) 0.8 {32" 0.5 ala
627 (5)
710 (00)
742 (st) 748 (lOb) 0.8 {32g
0.2 alg
885 (0)
942 (0)
1050 (m) 1070 (3)
1087 (2) 0.5 (a1")
1110 (st) 1109 (10)
1170 (1) 0.4 ala
1217 (0)
1300 (vw b) 1294 (0)
1331 (0)
1440 (vw b) 1379 (0)
1570 (m) 1576 (8) 0.8 {32il
1630 (1)
3090 (st) 2953 (0)
3079 (10) 0.4
3153 (2)
7 Vibration types after Langseth and Lord, reference 9. symmetry D6h of benzene is reduced to Vh in
p-dichlorobenzene, and to C2v in 0-and m-dichlo
robenzene and monochlorobenzene. The sym
metries of the different vibrations of the sub
stituted benzenes are represented in Tables V
to VII.
The symmetry symbols are listed in Placzek's
notation.8 C2Y, etc. refer to twofold axes in the
y, etc., directi::m, ()? denotes a plane of reflection
perpendicular to the z axis (molecular plane), and
i refers to the center of symmetry. The + and
-signs indicate respectively that a given sym
metry class is symmetric orantisymmetric to
the noted symmetry element. The asterisk at the
symbol of C2v for the ortho-compound indicates
that the twofold symmetry axis passes here
between the two carbons having the substituents.
Small Greek letters have been used for the sym
metry symbols to distinguish them from the
same symbols with capital Latin letters for elec-
)?: - , * if '*'* - ~ -+ l-
1 'J II-~~_rY.-,"* °*1* t--~----~ »: * ~Q_--~ »: 7a E' 7b f'+ 180 f.t -'=}-~---~-,--~
* * *+* + -I --
~Oa £q llOb ' E~ + 86 £~ 9a £: 9b ~
* * * X:c!~A'
+ • ] II'~ + - -
~oc..u. 12 r3,~ 13 il, .. 14 1.\.", 15 !l.
*' '*' '* :** -, + + -+
+ - + + + -
+ -> + - +
f6a E,+ 16b '+ €u. f7a t.:' 17b + £;. f8a £~
* * * * * 18b ~~ f9a t.:" 19b £;;,. 20a £:.. 20b €'-""
FIG. 1. Types of vibrations in benzene.
8 G. Placzek, Handbuch d. Radiologie, Bd. VI/2 (Leipzig,
1934), p. 283; L. Tisza, Zeits. f. Physik 82,285 (1932).
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141.209.144.159 On: Tue, 16 Dec 2014 15:22:49670 H. SPONER AND ]. S.KIRBY-SMITH
TABLE V. Symmetries of vibrations for para-C,H 4CI2 in
group Vh•
ESSENTIAL SYMMETRY
ELEMEN"TS NUMBER OF
SVMl\JETRY C2Y C2z VIBRATIONS
ala + + + 6
alu + + 2
fllu + + 1
fl1 u + 5
fl,y + + 5
fl2u + 3
fl3g + 3
fl3u 5 SELECTION RULES
. INFRA-
RAMAN RED
+
+ + + + + +
tronic terms. Langseth and Lord9 have discussed
in the case of the deuterated benzenes which
symmetry classes of the group D6h go over into
the respective classes of C2v and Vh•
Monochlorobenzene
As can be seen from Table I, only the strong
lines of the liquid have been observed in the
gaseous phase. Most of them are totally sym
metrical vibrations as is indicated in the last
column under "Assignment."
The frequencies 416 and 608 correspond to the
Ea + vibration of 606 cm-I in benzenelo (No.6 in
Fig. O. According to polarization measurements2
the 416 is totally symmetrical and the 608
non-totally symmetrical. As already pointed out
by Kohlrauschll the non-totally symmetrical
vibration is very nearly independent of the
substitution because here the motion of the
carbon atom with the substituent is small and
perpendicular to the C -Cl bond. The totally
symmetric vibration, however, is strongly in
fluenced because the carbon atom attached to the
chlorine participates in the vibration.
The 703 represents the vibration of the
chlorine atom towards the ring. It is totally
symmetrical and originates out of the four 3000
cm-I hydrogen vibrations in benzene alg, {3lu,
E+g and E-u (Nos. 2, 13, 7,20 in Fig. 1). The last
two split in the monosubstituted benzenes into a
totally symmetrical (al) and a non-totally sym
metrical ({31) part. We have, of course, to con
sider here only the al vibrations. It has no
9 A. Langseth and R. C. Lord, Kg!. Danske Vid. Sels.
Math.-fys. Medd. 16, No.6 (1938).
10 In his second volume, Der Smekal-Raman Effekt, Erg.
Bd., 1938, p. 163, Kohlrausch ~om;lates the Raman l!nes
416 and 470 with the 606 vibratIOn In benzene. Our assign
ment corresponds to his previous one, cf. reference 11.
11 K. W. F. Kohlrausch, Physik. Zeits. 37, 58 (1936). meaning to correlate the 703 to a particular one
of the four totally symmetrical vibrations since
it will in reality have contributions from all of
them. The observed frequency 3079 cm-I has to
be assigned to the remaining hydrogen vibra
tions. It is sharp on the short wave side and
diffuse on the other, and may well cover two
lines. The frequency of 3180 cm-I is probably
due to an overtone.
The strong lines at 1001, 1024, and 1080 cm-I
are all totally symmetrical according to polari
zation measurements.2. They are believed to
correspond to the carbon vibrations alg, {3lu
and probably Cu in benzene (Nos. 1, 12, 19 in
Fig. 1). One should expect one of the three
carbon frequencies {32u, e+o and c u (Nos. 14, 8
and 19 in Fig. 1) to decrease considerably in
monochlorobenzene and this is probably the E-u.
A detailed correlation of the observed frequencies
cannot be made because they will be linear com
binations of all three modes of vibrations alg,
{3lu and E-u, particularly since the frequencies are
almost identical.
The line at 1589 cm-I is probably one of the
components that arise from the carbon vibration
E+g= 1596 in benzene (No.8 in Fig. 0 when the
degeneracy is released. As the line is found highly
depolarized it must represent the non-totally
symmetrical mode of vibration.
The line at 1134 cm-I belongs quite likely to a
hydrogen vibration, as does perhaps the 1191
line. The latter may correspond to the depolarized
line 1158 or the 1176 in the liquid. To find an
interpretation we consider the six hydrogen
vibrations of benzene azg, {32u, E+g and E-u (Nos.
3, 15,9, 18 in Fig. 1). They all have frequencies
between 1000 and 1200 em-I. In CsH6CI one of
them and in C6H4Clz two of them must drop
down to a very low value. In all compounds there
must originate at least one totally symmetrical
vibration around 1100 cm-I and two non-totally
TABLE VI. Symmetries of vibrations for C,H.Cl and meta
C6H4Cl, in group C2v•
ESSENTIAL SYMMETRY
ELEMENTS NUMBER OF
SYMMETRY C2Y lIz VIBRATIONS
+ + +
+ 11
3
10
6 SELECTION RULES
INFRA-
RAMAN RED
+ + + + +
+ +
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symmetrical vibrations in the same region. It is
quite possible that in C6H5Cl the line at 1134
cm-l is an al (with large contribution from e+g)
and the 1190 cm-l a {31. The vibration with the
low frequency mentioned above is perhaps the
200 em-I. It would be then a {31 in accordance
with the depolarization factor. Another possi
bility is that it is the 294 cm-l observed in the
liquid.
Dichlorobenzenes
Here too only the strong lines of the liquid
have been found in the vapor. The 606 cm-1 e+g
vibration in benzene is split into al=416 and
{31 = 615 cm-l in monochlorobenzene. The same
types occur in the meta-and ortho-derivatives,
but here both will be influenced by the substi
tution, the values for the frequencies probably
not being much apart from each other. Indeed,
no line has been observed in the neighborhood
of 600 cm-1 for meta-and ortho-C 6H4Cl2• There
are several lines between 300 and 500 cm-1 in
the meta-and ortho-compounds which may be
chosen for the assignment in question. Polariza
tion measurements indicate that the 399 in
m-C6H4Cl2 is totally symmetrical and hence
quite likely is the al in question. In o-C6H4Cl2
the strong line at 483 has according to our
measurements a rather low depolarization factor
and therefore may be the corresponding al.
Kohlrauschll has also made empirically a similar
correlation. We make no proposal for the non
totally symmetrical component. In p-C 6H4Cl2 the
606 E+g of benzene splits into an ala and a {32g
vibration. The results in the deutero-benzenes9
make it probable that the ala is rather low, lower
than in C6H5CI. Hence the most reasonable
assignment seems to be alg=326 em-I. This is
further confirmed by the polarization measure
ments. The {32a should be higher and is perhaps
similar to the corresponding {31 in C6H5CI which
leads to the possible assignment {32g = 627 em-I,
again in agreement with the depolarization
factor.
The benzene hydrogen vibrations of high fre
quency alg, {3lu, E+a and E-u (Nos. 2, 13, 7, 20 in
Fig. 1) which give rise in C6H5Cl to one chlorine
valence vibration of 703 cm-l produce two such
vibrations in the di-derivatives. One of these has
been observed with certainty in all three cases TABLE VII. Symmetries of vibrations for ortho-C,H.Cl 2 in
group C*2v.
ESSEI"TIAL SYMMETRY
ELEMENTS NUMBER OF
SYMMETRY C2L tTl VIBRATIONS
+ + +
+ 11
5
10
4 SELECTION RULES
INFRA-
RAMAS RED
+ + + + +
+ +
in the lines 742 (para), 665 (meta), and 664 cm-l
(ortho) as has been noticed by previous authors.
Each line is polarized as it should be for a totally
symmetrical vibration. The vibration has a
larger contribution from E+g for the para
compound.
The lines at 3082 (ortho), 3090 (meta), and
3090 cm-1 (para) have to be assigned, as in
monochlorobenzene, to totally symmetric hy
drogen vibrations. Polarization measurements
support this conclusion. The frequencies of 3150
(ortho) , 3169 (meta), and 3153 (para, observed
in the liquid) probably represent overtones.
As in C6H5CI the benzene carbon vibrations
ala and {3lu (Nos. 1 and 12 in Fig. 1) should give
frequencies in the neighborhood of 1000 em-I,
the {3lu being Raman inactive in the para-com
pound. It is furthermore possible that the E-u
(No. 19 in Fig. 1) carbon vibration of benzene
drops to a value in the 1000 cm-I region. The six
hydrogen vibrations of benzene a2u, {32u, E+g and
en (Nos. 3, 15, 9, 18 in Fig. 1) will also give,
besides two very low frequencies, four frequen
cies in the 1100 cm-I region. In the case of
p-C6H4CIz two lines of appreciable intensity have
been found in the gas at 1050 and 1110 em-I. The
latter is the stronger of the two. It is very likely
a totally symmetrical carbon vibration. This is
supported by polarization measurements and the
analysis of the ultraviolet spectrum.4 The 1050
cm-l line is probably also totally symmetric
according to the fairly low depolarization factor.
No preference can be offered as to the assign
ment to a carbon or hydrogen vibration. The
1170 cm-I line is perhaps connected with the e+g
in benzene.
In meta-C 6H4CIz three fairly strong polarized
lines have been observed with frequencies of 998,
1056, and 1129 em-I. We would like to consider
the 998 and 1129 cm-l as belonging to totally
symmetrical carbon vibrations. This assignment
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gets support again from the ultraviolet spec
trum.4 The explanation of the 1056 em-I line
seems too indefinite at the moment although its
low depolarization factor points to a totally
symmetrical vibration.
In ortho-C 6H4Cl2 two lines were found at 1035
and 1133 and a weak one at 1271 em-I. \Ve
propose to ascribe the two strong polarized lines
to totally symmetrical carbon vibrations, again in
agreement with the analysis of the ultraviolet
absorption spectrum.4 The interpretation of the
1271 em-I seems ambiguous without additional
information. We are, however, inclined to believe
that the depolarized 1160 em-I line observed in
the liquidl2 of ortho-and meta-C 6H4Cl2 cor
responds to the depolarized line 1158 em-I in
C 6H 5Cl and hence represents in both cases the
non-totally symmetrical component originating
mainly from the hydrogen bending vibration
~+o = 1178 in benzene.
I t has been mentioned before that out of the
hydrogen vibrations a2g, /3211' ~+g and ~-" (]\;"os.
3, 15, 9, 18 in Fig. 1) there must originate two
low frequencies which represent chlorine bending
vibrations in the molecular plane. l.n the case of
para-C 6H4Cl2 only one of them will be observable
in the Raman effect which we believe to be
{32a = 302 em-I originating chiefly from ~+ 9 and
a2g and found in the liquid. In meta-C 6H4Cl2 and
in ortho-C 6H4Cl2 there have been observed in
the liquid three low frequencies of 178, 202, 216
em-I and of 164, 203 and 239 em-I, respectively,
while we could detect with certainty only one at
205 em-I (meta) and one at 194 em-I (ortho) in
the gas. Since in the ortho-and meta-compounds
one of the above-mentioned two low vibrations
must be totally symmetrical (al) and the other
one non-totally symmetrical ({31), we were sur
prised to find only high depolarization factors for
the observed low lines. A detailed assignment
cannot be given.
In para-, meta-, and ortho-C 6H4Cl2 lines have
been found at 1570, 1590, and 1598 em-I,
respectively. As they are depolarized they cor
respond in all probability to the 1589 em-I in
C6H5Cl and have likewise to be interpreted as
the non-totally symmetric one of the two com-
12 This line has not been observed by Swaine and
Murray in the meta-compound, but Kohlrausch and col
laborators give it as a weak line. We have confirmed their
observation. ponents into which the ~+g = 1596 em-I in
benzene (No.8 in Fig. 1) splits in these molecules.
The vibrations which we have considered so
far all take place in the molecular plane, either
as valence or as bending vibrations. We have
not mentioned any modes which occur perpen
dicular to the molecular plane. Of these the
carbon vibrations {32g and ~+u (Nos. 4 and 16 in
Fig. 1) in benzene will be influenced only slightly
by the substitution. They are both Raman
inactive in benzene, and the ~+ u is also forbidden
in the para-derivative. They are allowed in the
other derivatives considered here. Very few of
them have been observed in the deuterobenzenes
and these with very weak intensity. Weak lines
in the neighborhood of 300 em-I in the cor
responding chlorobenzenes could be due to these
vibrations.
There are four hydrogen bending vibrations
a211, {32g, ~+u and ~-g perpendicular to the molecular
plane in benzene (Nos. 11, 5, 17, 10 in Fig. O.
They lie between 670 and 1000 em-I. Out of
these should result one low frequency for
monochlorobenzene and two low ones for the
dichlorobenzenes. The a211 is Raman inactive in
benzene but is known from the infra-red to occur
at 670 em-I. In monochlorobenzene a strong
band has been observed in the infra-redl3 at
680 em-I which is almost certainly the {32 result
ing mainly from a2u in benzene. The ~-g gives
weak to medium Raman lines in benzene and
the deuterobenzenes. We suppose that one of the
lowest frequencies, 200-294 em-I in C6H6Ci, and
at least one of the three lowest in liquid m-and
o-C6H4Cl2 represent vibrations of the type dis
cussed here.
The suggested assignments include most of
the lines in the gas. Many more have been re
ported in the liquid phase. It seems too doubtful
a procedure, however, to try an explanation of
these. Some of the interpretations presented here
have already been suggested by Kohlrausch,l1
while others differ from his. Since the whole
problem is attacked here from a different point
of view we believe it worth while to give our
considerations and conclusions.
In conclusion we want to acknowledge a
grant-in-aid from the Duke University Research
Fund which made this research possible.
13 J. Lecomte, J. de Phys. et Rad. 8, 489 (1937).
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1.1723759.pdf | Energy Levels and Color of Polymethine Dyes
A. L. Sklar
Citation: The Journal of Chemical Physics 10, 521 (1942); doi: 10.1063/1.1723759
View online: http://dx.doi.org/10.1063/1.1723759
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130.88.90.110 On: Fri, 19 Dec 2014 05:59:03AGGUST. 1942 JOURNAL OF CHEMICAL PHYSICS VOLUME 10
Energy Levels and Color of Polymethine Dyes
A. L. SKLAR
Chemical L!lboratory, The Catholic University of America, Washington, D. C.
(Received April 29, 1942)
The secular determinant for the energy levels of the unsaturation electrons of a polymethine
dye is discussed in both HLSP and LCAO approximations. The roots of the secular determi
nant, which were obtained in the preceding paper by Herzfeld, are applied to a discussion of the
longest wave-length electronic band of symmetrical and unsymmetrical polymethines. The
LCAO approximation gives good numerical values for the dependence of both the transition
energy and oscillator strength on the length of the p::>lymethine chain in symmetrical dyes,
but cannot handle the questions which depend sensitively on a sm'lll difference between the
groups attached to the two nitrogen atoms at the extreme ends of the chain. Although the
HLSP method yields correct qualitative results for symmetrical dyes, it does not give good
numerical values. The HLSP method, however, is sensitive to a difference between the two
ends of the dye molecule and affords a simple explanation for a number of properties in which
unsymmetrical dyes differ from symmetrical ones.
THE spectra of the polymethine dyes have
been discussed briefly from the atomic
orbital point of view by Paulingl and from the
molecular orbital viewpoint (LCAO) by M ulIi
ken2 and Forster.3 The connection between the
molecular structure and the low lying energy
levels of these dyes will be discussed qualitatively
in a forthcoming paper;4 here it will be treated
more quantitatively in order to arrive at a firmer
basis for the purely qualitative considerations.
The lower energy levels of the plane ion I will be
approximated by both the atomic orbital (HLSP)
and molecular orbital (LCAO) methods. Ion I
represents a large class of polymethine dyes, if
the T groups are
understood to mean either individual groups or a
nucleus which bends around and joins to the
conjugated chain, as in the ion II.
I L. Pauling-Gilman, Organic Chemistry, Vol. 2, p. 888.
2 R. S. Mulliken, J. Chem. Phys. 7, 570 (1939).
3 T. Forster, Zeits. f. physik. Chemie B47, 245 (1940);
48, 12 (1941).
4 A. L. Sklar and L. G. S. Brooker (to be published). S
("'( "'C-(CH=CH)n_l-CH=
"'/"'+/ N S
I / "'/'" C2H6 =C I I. II '" /"'/ N
\ C2H6
Since the excitation of the in plane (J electrons
yields the molecular Rydberg series below 2000A,
we may restrict our discussion concerning the
visible and near ultraviolet absorption to the
energy values of the un saturation electrons (11' or
Pz) which do not interact with the (J electrons.
In the LCAO method, as is well known, we
write a linear combination of atomic orbitals for
the molecular orbital of each unsaturation elec
tron in the field of the multiply-charged residue
formed by stripping ion I of its unsaturation elec
trons. Ion I has (2n+4) un saturation electrons
but we will consider that two of these are perma
nently localized, one on each nitrogen atom. Our
system, then, consists of (2n+2) electrons in a
potential field made up of a chain of (2n+3)
singly charged nuclei. If we write the one-electron
orbitals as a linear combination of the (2n+3)
atomic orbitals and neglect all overlaps and also
interactions between electrons on non-neighbor
ing atoms, the energies of a single electron are
521
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130.88.90.110 On: Fri, 19 Dec 2014 05:59:03522 A. L. SKLAR
given by the roots of the (2n+3) rowed secular determinant III, whose solution has been dis
cussed in the preceding paper. 5
el-W;
al
0
0
o
o
o al ;
j-W;
a
0
o
o
o 0
a
j-W;
'" a
o
o
o o· ,
o· ,
a;
'" '" '"
In this determinant W is the one-electron en
ergy; a is the in teraction energy between two
electrorts on neighboring carbon atoms; al and
a2 are, respectively, the interactions between two
electrons on a carbon atom and on either the left
or right-hand nitrogen atom; and j, el, and e2 are,
respectively, the ionization potentials of an un
saturation electron localized on either a carbon
atom, the left-or right-hand nitrogen atom. In
this approximation the 1's will be somewhat
different for the various carbon atoms in the
chain. It will, however, be sufficiently accurate
for our purposes to take all the 1's as equal,S
especially since the variation in j in this approxi
mation is due primarily to the fact that the inter
action between the unsaturation electrons is
neglected. In the ground state of the ion I the
(2n+ 2) electrons will fill the lowest (n+ 1) orbi
tals and the longest wave-length electronic band
will be associated with the transition of an elec
tron from the (n+ 1)st to the (n+ 2)nd orbital.
In going over to the HeitIer-London-Slater
Pauling method it is to be noticed that the ground
structure I is doubly degenerate in that the posi
tive charge may be shifted to the other nitrogen
atom and the double bonds readjusted. Ion I is
thus analogous to benzene which has the two
Kekule structures as doubly degenerate ground
structures. A difficulty, however, arises in carry
ing over from benzene to ion I the view that the
5 K. F. Herzfeld, ]. Chern. Phys. 10, 508 (1942).
• We also neglect energy differences due to the replace
ment by other groups of the hydrogen atoms attached to
the conjugated carbon chain. ·0; 0 0 0
·0; 0 0 0
·0; 0 0 0
1
1
1 =0. III
1 ",I
a; j-W; a o
0; a
0; o
longest wave-length electronic absorption is asso
ciated with a transition between the two molecu
lar states which arise from a resonance splitting
of the degenerate ground structures.7 The elec
tron distributions in the two I structures, which
differ in that an electron has moved from one end
of the molecule to the other, do not overlap ap
preciably. The split of these two structures would
thus be expected to be negligible instead of the
observed value of the order of a few volts.
Pauling,8 however, has pointed out that one
must consider, in addition to the two structures
I, the following set of intermediate structures
X 2p+l (p = 0 to n). Since the overlap of electrons on
atoms separated by even two interatomic dis
tances is very small, we will also have to include
the set of structures Y2p(P = 1 to n)
Tl
"" N-(CH=CH)p_l-CH-
/ T/ + / -CH-CH-(CH=CH)n_p-N
"" T2
T2'
7 A. L. Sklar, ]. Chern. Phys. 5, 669 (1937); H. Sponer,
G. Nordheim, A. L. Sklar, and E. Teller, ]. Chern. Phys.
7, 207 (1939).
8 L. Pauling, Proc. Nat. Acad. Sci. 25, 577 (1939).
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130.88.90.110 On: Fri, 19 Dec 2014 05:59:03POLYMETHINE DYES 523
For every structure in the set consisting9 of I,
X, and Y there is a second structure which differs
from the former in that an electron has been
moved to the neighboring atom on the left. Thus,
al though the two I structures do not overlap
appreciably directly, one I structure interacts
with Xl, Xl with Y 2, Y 2 with X3, and so on until
X2n+1 interacts with the other I structure. The
two ground structures I can split through this
chain of interactions with the intermediate struc
tures X and Y.
Although it is not easy to estimate numerically
the relative energy of I and X, it is clear from
chemical considerationslO that the I structures are
considerably lower in energy than the X and Y
structures. The Y structures are energetically
higher than the X structures since the former
have one less double band. Acting against this
TABLE I.
HLSP LCAO
. " 2" 8m N +1 (26)
R=I 4" sin' [,,;2(N +2)J (30) 4" cos N :2 sin 2(N"+2) (31)
R»I . 3 " 4" sm :1 N +3 (36) 2" sin N :'3 (37)
9 The set of structures X and Yare chosen in preference
to the following set, Zk(k= 1 to 2n+l), on energetic
grounds.
TI
"-+ -
/
TI' N =CH-(CH=CH) n-p-CH- 1'. +/ -
-(CH=CH)p_I-CH=N
"-Z2P' 1'2'
It is not obvious, though, that the interaction energy
among the Z structures is not sufficiently larger than that
among the X, Y structures to compensate for the higher
energy of the former. This question is, however, immaterial
for the purpose of this paper since we will not try to
evaluate the interaction energy but only its variation as n
is increased or as the character of the T groups is changed.
10 The essence of the chemical arguments is the fact that
whereas ammonium ions N+ are frequently encountered,
carbonium ions C+ are never met in any quantity, although
they probably do occur in minute amounts in the course
of reactions. As an example, we may compare the basicity
of ammonia (NH.+HzO-NH,++OH-) with that of
ethylene (CH2=CH 2+H20-CH.-CH 2++OH-). Except
for the very small difference between the strength of a CH
and NH bond, the second reaction requires more energy
than the first by about the same amount that is required
to change structure I into an X structure. (The hydration
energies balance out to a first approximation.) The fact
that ethylene is enormously weaker as a base than ammonia
would, then, suggest that X is considerably higher in
energy than I, since there is no reason to suspect the
entropy to be vastly different in the two cases. effect is the additional possibility of resonance
possessed by the Y structures due to the fact that
the C+ breaks the carbon chain into two odd
segments which may be written several ways, as
for example:
-(CH=CH) k-CH-p-CH-(CH=CH) k-
To each Y, then, corresponds a group of struc
tures and we may consider that, in writing one
structure for this group, we have written the
stabilized result of the resonance among the
whole group. Since two compensating factors
enter in the relative energy of the X and Y struc
tures, and since a small difference in their energy
will not affect our discussions, we will assume, for
mathematical simplicity, that all intermediate
structures, X and Y, are of equal energy.
In all we have 2n+3 structures, two I, (n+ l)X,
and n Y structures. If we neglect all Coulomb and
exchange integrals which are smaller than the
product of the first power of the overlap integral
of electrons on neighboring atoms times the or
dinary Coulomb and exchange integrals, respec
tively, and also neglect terms containing overlaps
of electrons on non-neighboring atoms, the mo
lecular energies resulting from resonance among
the 2n+3 structures are given by the roots of a
secular determinant which is formally the same
as that reached in the LCAO method, namely
determinant III. The meaning of the quantities
in the determinant is, of course, now quite differ
ent. a, ai, a2 are, respectively, the interaction
energies between an intermediate structure, and
either a second intermediate or one of the two
ground structures; Cl and C2 are the energies of
the two ground structures I; and f is the energy
of an intermediate structure, X and Y. Since W
is the energy of all the unsaturation electrons in
the molecule, the transition energy in question is
the difference between the two smallest val ues
of W.
The roots of determinant III have been dis
cussed as a function of the number of rows in the
preceding paper by Herzfeld5 for various ranges of
the parameters R=a/(cl-f) and R'=a/(e2-f).
The results will now be applied to a discussion of
the qualitative conclusions which were reached
in reference 4, since purely qualitative considera
tions of complex situations, even when applied
with caution, are occasionally misleading.
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130.88.90.110 On: Fri, 19 Dec 2014 05:59:03524 A. L. SKLAR
1000 "
900 0 -
,..
'"' 800
A
"700 O-
~oo 0
500 Or-
400 0 I
/ /
II
/
/ V
/
j
}
!
:/
/ L
V
/'
2 3 4 5 cD 7
n+1
FIG. 1. The solid points in the figure give the wave
length of the absorption peak for ion II as a function of
the number of double bonds between the nitrogen atoms
(NH). The empty circles give the same data for an ion
which differs from ion II only in having an acetoxy group o /' (CHa-C-O-) in place of the hydrogen atom on the
sixth carbon atom of the polymethine chain.
SYMMETRICAL IONS
We will first treat those dyes in which the same
groups are attached to both nitrogen atoms as,
for example, in ion II. For such symmetrical ions
the secular determinant is simplified since al = az
and el = ez. Since a and al are of the same order
of magnitude and since a small difference be
tween them would not be expected to affect the
general questions treated in this paper, except
for very smaIl values of n, we wiIl further sim
plify the mathematical treatment by setting al
equal to a. Table I gives the transition energies to the
first order found in reference 5 from the roots of
the secular determinant, for various ranges of
the parameter R=a/(e-f). In Table I the num
bers in parentheses are the numbers of the equa
tions in reference 5 and N = (2n+ 1) is the num
ber of carbon atoms in the chain between the two
bounding nitrogen atoms.
I t is clear from the formulas in Table I that
the magnitude of R plays a determining role in
the HLSP but not in LCAO approximation, ex
cept for very smaIl values of N. This becomes
clear, physically, if we regard a as constant and
vary R by varying e -f. In the HLSP method the
energy of the degenerate ground structures, e is
the zero approximation to the energies of the
two lowest states of the molecules. Therefore,
the transition energy depends on the magnitude
of the split of the degenerate energies of the
ground structures. Since these two structures
interact only through a chain of second-hand
interactions with the intermediate structures X
and Y, which are higher in energy than the
former by an amount (i-e), it is clear thatll the
greater is (i-e), the smaller is the transition
energy. Table I of reference 5, obtained by a
numerical solution of Eqs. 17 and 18, shows this
dependence if a is considered to be constant; the
transi tion energy increases as (i -e) decreases
(R increasing) and approaches for small values
of (f-e) the limiting value, independent of R,
required by Eq. 36.
In the LCAO method, on the other hand, e is
the zero approximation, not to the energy of the
molecule, but to the lowest energy state of one
electron of the molecule. Since the states associ
ated with e, as well as a number of states whose
energies in zero approximation are f, are full,
both in the ground and excited states, there is no
longer any reason to expect (i-e) to playa large
role in the transition energy.
It is clear from Table I that in both approxi
mations and for all ranges of R, the transition
energy should decrease monotonously with in
creasing chain length N as is found to be the case.1Z
11 f -e may be changed experimentally by changing the
character of the groups T j which are attached to the
nitrogen atom. For example, the ionization energy of a
electron from methyl amine, (CHa)· NH2 is smaller than
that of aniline. (C6H5hNH.
12 L. G. S. Brooker et al .• J. Am. Chern. Soc. 62, 1116
(1940).
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130.88.90.110 On: Fri, 19 Dec 2014 05:59:03POLYMETHINE DYES 525
The algebraic relationship between the peak
wave-length and N differs in the two methods
and, in the HLSP approximation, depends on R.
The usual linear dependence of peak wave-length
on chain length shown in Fig. 113 agrees with the
results found for large values of N by the LCAO
approximation for all ranges of R. In the HLSP
approximation the dependence on N is quadratic
for R,); 1, but is exponential for very small values
of R; only in the region of R slightly smaller than
unity is there a possibility of a linear dependence.
The value of the absorption frequency for fixed
N is directly proportional to the interaction
energy a for constant R, but the ratio of the fre
quencies of a dye with a given value of Nand
that with an N larger by one, is not explicitly
dependent on a. The value of this ratio affords a
test for the two methods. In the LCAO method,
the ratio does not depend sensitively on the value
of R and is therefore completely determined by
N; in HLSP approximation, the ratio does de
pend on R. We can compare the theoretical
values with the experimental14 value of 1.17 (d.
Fig. 1) for the ratio of the peak absorption of a
dye with a chain of seven carbon atoms (n= 3) to
that of one with a chain of nine carbon atoms
(n=4). The LCAO approximation, in excellent
agreement with experiment, yields the value 1.19
for this ratio when R is very large; 1.20 when R
is unity, and 1.24 for very small values of R. In
the HLSP approximation, however, the above
ratio varies between 1.2 and 1.4 as R varies
between one-half and ten.15
In addition to yielding too high a value for the
above ratio, the HLSP method demands an ab
normally high value for the exchange energy a
to explain the absolute values. The transition
energy for a five-membered carbon chain (n=2),
which is actually about three volts, is only two
tenths a in the region R= 1, which seems to be
the most likely region in this method. In the
LCAO approximation the transition energy,
13 The data in Fig. 1 were obtained at the Eastman
Kodak Laboratories and communicated to the author by
Dr. L. G. S. Brooker.
14 It has been pointed out (reference 12) that the wave
length of the peak of most symmetrical polymethine ions
increases by about 1000 angstrom units when n increases
by one. The constancy of this value is to be expected
according to Table I except in the HLSP approximation
when R«1.
15 Reference 5, Table I. roughly independent of R, for a five-membered
carbon chain, is about nine-tenths a, which is
much more reasonable.
It is seen that although both methods tell us
that the absorption frequency should decrease as
the chain lengthens, the quantitative features of
this decrease are not given very well by the HLSP
method, but are given very well indeed by the
LCAO approximation.
We may also inquire into the dependence of
the intensity on chain length. Although the chain
is a bent one, we may assume that each increase
of n in ion I by unity lengthens the chain by a
constant amount. The coefficients of the orbitals
in the LCAO approximation are given, except for
a normalization factor, in Eqs. 13 and 14 of
reference S. With them we can calculate the
transi tion mom en t, which, as M ulliken2 has
pointed out, is polarized along the chain. In first
order, the transition moment turns out to be
proportional to N when N is large. Since the in
tensity is proportional to the product of the
frequency and the square of the transition mo
ment, and since the frequency in the LCAO ap
proximation is inversely proportional to N, the
intensity should vary linearly with N. The in
tensity of the shorter members of the series
represented by ion II (small values of n) is shown
in Table II.16 Although the first member is out of
line, the last three fo values vary linearly with the
chain length as indicated by the last two succes
sive differences. Since the theoretical discussion
on the variation of intensity with chain length
was limited to large values of N, the excellent
agreement of the last three values is probably in
part fortuitous. It would, accordingly, be useful
to obtain f values for the higher members of this
series but these, unfortunately, are not very
stable and rapidly change with time.
In addition to yielding the correct dependence
N
3
5
7
9 TABLE II.
f.
fo is the oscillator of the longest wave-length electronic band of ion
II and N =2" +1 is the number of carbon atoms in the chain.
16 The data in Table II were calculated from the absorp
tion curves of Fig. 2.
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130.88.90.110 On: Fri, 19 Dec 2014 05:59:03526 A. L. SKLAR
x
W
FIG. 2. The absorption curves of ion II for n=1 to 4; N=3 to 9.
of intensity on chain length, the LCAO method
also has yielded interesting results concerning the
relative intensities of the set of absorption bands
of a given dye. On the basis of the LCAO method,
Mulliken has reported2 that in a series of N-7 V
transitions, as are our transitions, in a maximally
elongated chain, the longest wave-length transi
tion is by far the strongest. Since the ions II have
bulky nuclei on the ends, their chains may be
expected to be in an elongated configuration.
Figure 2 shOWS,17 in accord with Mulliken's pre
diction, that the higher energy transitions are
very weak compared with the lowest energy
transition. For example, the oscillator strength
of the band having a peak at 3600A eN = 9) is
0.23, the long wave band having an oscillator
strength of 1.89,
UNSYMMETRICAL IONS
If the nuclei T2 which are attached to the right
hand nitrogen atom in ion I, differ from those
attached to the left-hand one, the ionization
energies of the two nitrogen atoms are no longer
equal and el is, in general, different from ez in
both methods. In the HLSP approximation, we
would expect a sensitive dependence of the color
on the difference between the two e's since the
resonance splitting of the energies of the two I
structures is both affected by, and superimposed
17 The absorption curves of Fig. 2 were taken at the
Eastman Kodak Laboratory and communicated to the
allthor by Dr. L. G. S. Brooker. on, the energetic difference (el-e2). In the LCAO
approximation, on the other hand, this difference
clearly plays a minor role in the transition energy.
The special sensitiveness of the HLSP method to
(el-e2) is due to the fact that in this method er,
ez are the zero-order approximations to the ener
gies of the two levels involved in the transition;
whereas, in the LCAO approximation, the two
one-electron levels approximated in zero order
by el, e2 are filled in both the ground and excited
state of the molecule.
That differences in kind between symmetrical
and unsymmetrical ions do exist may be seen
experimentally by comparing the absorption
peak of an unsymmetrical ion with the mean of
the absorption peaks of the two parent sym
metrical ions of which the unsymmetrical ion
may be considered a hybrid. The existence of
important differences between the absorption
peak of unsymmetrical ions and the mean of
those of its two parents has been emphasized by
Brookerl8 and called the "deviation." Isolated ex
amplesls of the deviations are given in Table III.
As discussed above we can only hope to get an
explanation of the significant differences between
unsymmetrical and symmetrical ions through the
HLSP approximation. However, before any con
fidence can be placed in results which are yielded
by the HLSP but not by the LCAO method, one
18 L. G. S. Brooker and Sprague, J. Am. Chern. Soc. 63,
3202 (1941).
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130.88.90.110 On: Fri, 19 Dec 2014 05:59:03POLYMETHIN"E DYES 527
TABLE III. ii is the wave number of the absorption peak of the ion in column I, iiL(iiR) is that for the symmetrical ion
having the nucleus on the left (right) in common with the unsymmetrical ion, and the last column is the deviation. All
ions occurring in this table have N = 5. Me is a CH3 group, Et a C2H5 group, and Ph a phenyl group. It is to be noted
that in the ions given in the last two lines of the table the end groups containing conjugated double bonds are joined to
an inner member of the chain. It is not clear how far the present formulae apply to this case. However, the table shows
that the rules discussed do apply and that the deviation is particularly large.
Ion
(Meh C S 0/ ~C-CH=CH-CH=C/ ~O
~+/ ~ / N N
I I Et Et
O/~' S N02
t-CH=CH-CH=C/ ~O/
"+f ~ /
S N N
I I Et Et
/ C-CH=CH-C=C
I ~ Me
I /N-Ph
o
/ ~ Me
HC /
II C-CH=CH-C=C
HC~~ I ~N-Ph
~t 0
must ask whether the results are artefacts of the
HLSP approximation, especially since the LCAO
method gave better numerical results on sym
metrical dyes.
That one can trust, in a qualitative manner,
the conclusions which the HLSP'method gives
concerning the effect of the difference (el-e2) can
be seen by comparing the direction of the errors
made by the two methods. As discussed before,
elo e2 affect the transition energy sensitively in
HLSP because they are zero-order approxima
tions to the energies of the two molecular states
involved in the transition; whereas, in the LCAO
approximation, the difference (el-e2) has no ap
preciable effect on the molecular states. The true
molecular state, however, is somewhere between
those described by the two methods, being some-Dev.
18,150 17,710 17,930 +330
17,240 16,560 17,140 +390
23,950 22,470 22,270 +1580
22,730 17,510 22,270 +2840
what closer to the LCAO as judged by the
numerical results concerning the dependence of
the transition energy on chain-length. Since the
actual situation is intermediate between that de
scribed by the two methods, the approximation
which overemphasizes a given effect is certainly
more reliable for finding, in a qualitative way,
the consequences of that effect than is the ap
proximation which practically neglects the effect
in questionY
Our discussion of unsymmetrical ions, el + e2,
19 Since, in the HLSP approximation, e" e2 are important
primarily because the two structures I have more chemical
bonds, one might hope that the dependence of the molecu
lar energies on (el-e2) will reappear in the molecular
orbitals method if anti symmetrical molecular orbitals,
including spin, are used and the interaction of electrons
explicitly included in the Hamiltonian. See M. Goeppert
Mayer and A. L. Sklar, J. Chern. Phys. 6, 645 (1938).
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130.88.90.110 On: Fri, 19 Dec 2014 05:59:03528 A. L. SKLAR
will accordingly be limited to the HLSP approxi
mation and the results will depend on the magni
tude of R.
The same factors which cause el to differ from
e2 also introduce a difference between the inter
action energies al and a2. However, a distinction
between the roles played by an inequality of el
and e2 and that played by an inequality of al
and a2 appears if one compares an unsymmetrical
dye with' the two parent symmetrical dyes of
which the unsymmetrical dye may be considered
a hybrid. Both ground structures are degenerate
of energy el in one parent symmetrical dye and
of energy e2 in the other parent; whereas, in the
unsymmetrical dye the ground structures are no
longer degenerate, but have the energies el and
e2 in first order. Since the e's are zero approxima
tions to the energies of the molecular states in
volved in the transition, we might anticipate, as
will be shown later, that the transition energy of
the unsymmetrical dye will be larger than that
of either parent symmetrical dye. That is, on the
basis of a difference in el and e2, we should expect
the unsymmetrical dye to differ from any mean
of its parent symmetrical dyes. On the other
hand, if el were equal to e2, even if al were not
equal to a2, we would expect the properties of
the unsymmetrical dye to be intermediate be
tween those of its symmetrical parents. Further
theoretical investigation will be required to de
cide which type of mean one should expect if
al differed from a2 but if el were essentially
equal to e2.
The properties, then, which are peculiar to un
symmetrical dyes, and which distinguish them in
kind from symmetrical dyes, may be found ex
perimentally by comparing the absorption peak20
of the unsymmetrical dye with those of the sym
metrical parents, and may be found theoretically
by setting al = a2 but keeping el different from e2.
We will, then, set al equal to a2,21 but keep el
different from e2, in the secular determinant III,
and thereby obtain a transition energy for the
unsymmetrical dye which is to be contrasted
with a mean of the transition energies of its two
20 Since the absorption curves are obtained in solution
the significance of the wave-length of peak absorption is
open to question. This can perhaps be settled by a study,
now under way of the structure of the absorption bands at
low temperatures.
21 As in the case of symmetrical dyes, we also equate ""
and a. symmetrical parents. The results depend upon
the order of magnitude of R = a/ (ej -f) and
R'=a/(e2-f)·
Case I. R«l and R' «1
The easiest case to discuss qualitatively is that
of small values of Rand R' which is the case when
the intermediate structures, X and Y, are con
siderably higher in energy than the ground struc
tures I; the qualitative discussions of reference 4
were limited to this case. Equation 46 of reference
5 gives the transition energies when Rand R' are
small as:
2!.lEN= ((ej-e2)2+(WTN)2)t + ((el-e2)2+(MN')P, (46)
where UN2=4R2N(1-R2)(1- RR').
UN' has Rand R' interchanged. aUN, aUN' differ
from the transition energies of the parent sym
metrical dyes only in that the factor (1-RR1)
replaces a factor (1-R2) which is a difference of
higher order for the case of small R under
discussion.
A number of interesting results follow from
Eq. 46. First, it is clear that the effect of a small
non-degeneracy (el-e2) causes the transition
energy !.lEN to be larger than (UN+uN')a/2,
which is essentially the mean of the transition
energies of the parent symmetrical dyes. Thus,
it is seen that unsymmetrical dyes should absorb
at shorter wave-lengths, that is, be "lighter" in
color, than related symmetrical dyes. This has
been found by Brooker22 who, in a series of papers,
gives values of the "deviation," which are always
found to be toward short waves except in one or
two cases when they are extremely small. Ex
amples of the deviation are shown in Table III.
Although the transition energy is larger, the
resonance stabilization in the ground state is for
unsymmetrical dyes smaller than the mean of
their related parent dyes. This may easily be
seen from Eqs. 20 and 45 of reference 5, by com
paring the difference between the energy of the
lower ground structure and that of the ground
state for the various cases. One should accord
ingly expect that unsymmetrical dyes, by virtue
of their larger resonance stabilization, should be
22 L. G. S. Brooker et al., J. Am. Chern. Soc. 62, 1116
(1940); ibid., 63, 3192 (1941); ibid., 63, 3203 (1941); ibid.,
63,3214 (1941); ibid., 64, 199 (1942).
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130.88.90.110 On: Fri, 19 Dec 2014 05:59:03POLYMETHINE DYES 529
FIG. 3. "Converging" and
"non-converging" series. The
dye in the center of the figure
differs from the one at the top
only in that the acetate radicle Et
CX~~H~~k.~~--~i--+-'~i--T~~~~~--+-~~--+-~~~ n;, n=2 r=3
" -....., ...... -
[CH~-<l Et,
CX~9~IKIl),.-tlPh.
H
is replaced by a hydrogen atom. 3000
more stable than unsymmetrical dyes. They
should, for example, be less readily decomposed.
An interesting confirmation has been called to
the author's attention by Brooker. The cyanine
dyes act as indicators both in an acid and alka
line range. Now, either the addition or subtrac
tion of a proton will be resisted by the resonance
stabilization of the cyanine chain since the reso
nance is present only before either of these
processes. On this basis of a larger resonance
stabilization of symmetrical dyes, one should
expect the applicability to the polymethine dyes
of a rule which has been found by Schwarzen
bach23 and which states that the difference be
tween the pK values24 (pH at half-transformation)
is larger for symmetrical than for unsymmetrical
dyes.
It may also be seen from Eq. 46 that as N in
creases, <1N, and accordingly 6.EN, decreases. Now
in a symmetrical dye 6.EN would go to zero as N
is increased indefinitely, but in an unsymmetrical
dye, 6.EN decreases to the magnitude of the
energy difference (el-e2). It has, indeed, been
found by Brooker22 that for many series of un
symmetrical dyes the members of which differ
only in the value of N, the absorption peaks ap
pear to converge to a finite wave-length limit as
N increases, whereas the peaks for a correspond
ing series of symmetrical dyes do not converge
to a finite line when plotted on a wave-length
23 G. Schwarzenbach, Zeits. f. Electrochemie47, 40 (1941).
Schwarzenbach's examples are not strictly analogous to
our case but will he shown in a later paper to have the
same basic explanation.
"Since the difference in the pK's is a measure of the
free energy change involved in the reaction {2I-HI+++B I
where B is the neutral molecule obtained by taking a
proton away from ion I, one would not expect the entropy
change in the case of unsymmetrical dyes to differ markedly
from that of symmetrical dyes, except perhaps for an effect
due to the symmetry number. The symmetry number
comes into question because both HI++ and B may be
unsymmetrical whether I is symmetrical or unsymmetrical.
This effect, however, is at most small (of the order of a few
tenths of a pH unit), and even in the wrong direction. --
" ---,
I ,-
I " "." ,---
4000 5000 6000
A
scale. Many unsymmetrical dyes form series
which behave like series of symmetrical dyes; the
former presumably have small values of the
difference (el-e2). Figure 3 shows an example of
a "non-converging" series (middle case) and two
examples of "converging" series. The dye at the
bottom of Fig. 3 is not an ion but its analogy to
the present case is discussed in the last section.
Equation 46 also affords an explanation of the
"sensitivity rule" found by Brooker,22 which
states that the deviation produced by introduc
ing a given alteration in the molecular structure
of a symmetrical molecule is much smaller than
the change in 'deviation produced by making the
same structural alteration in a highly unsym
metrical molecule. This may be seen to be a con
sequence of the fact that the resonance inter
action and the energetic difference (el ez) enter
into the transition energy as a sum of squares.
When the difference (el-e2) is small compared
to a<1N, a given increase in (el-eZ) affects 6.K"
much less than would the same increase if (el -ez)
were of the order of magnitude of a<1N or larger.
One set of examples from Brooker's papers is
given in Table IV to illustrate the "sensitivity
rule. "
Case II. RR' = 1
In order to see whether the results discussed in
Case I are valid even if the intermediate struc
tures are not very much higher in energy than
the ground structures, we may consider an un
symmetrical dye in which RR' = 1. This case can
be solved exactly; Eq. 55 of reference 5 gives the
following transition energy when RR' = 1:
l::.EN=a{R+R'-2 cos_1r
_}. (55) N+2
One should expect, even in Case II, a finite
convergence limit for the absorption peaks of a
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130.88.90.110 On: Fri, 19 Dec 2014 05:59:03530 A. L. SKLAR
TABLE IV. ji is the wave number of the absorption peak in methyl alcohol of the dye in column I, ilL, ilR are those of
the parent symmetrical dye, which have both ends like the left (right) side of the ion in column I; Dev. is the deviation
and tJ.D is the change in deviation produced by introducing a nitro group. All ions in Table IV have five CH groups be
tween the nitrogen atoms. Note that the ion in the second row differs from that in the first row only in that a hydrogen
atom is replaced by a nitro group; the fourth ion differs from the third in exactly the same way, but because the third
ion is unsymmetrical (deviation 55), the effect of the introduction of the N02 is much greater than for the symmetrical
ion in the first line.
Ion ji Dev. 6D
S S 0/ ~C-CH=CH-CH=C/ ~O 17,930
~+/ ~ / N N
I I C2H5 C2H.
S S N02 0/ ~C-CH=CH-CH=C/ ~O/ 17,500 17,930 17,140 35 35
~+/ ~ / N N
I I C2H. C2H.
17,300 16,560 17,930 55
. I / ~ /' 0/" S N02
C-CH=CH-CH=C 0 17,240 16,560 17,140 390 345
'-.+1 ~ /' N N
I I C2H. C2H5
homologous series of dyes as N increases in
definitely, though a smaller one than in Case I.
This may be seen from equation 55' which applies
to Case II.
For values of (el-e2) which are small compared
to (el-f) this limit reduces to:
(el-e2)2j4(el- j),
which is smaller than (el-e2), (Case I).
The finite convergence limit implies that one
should expect that unsymmetrical ions, even in
Case II, should exhibit a "deviation," at least for
large values of N.
That the "sensitivity rule" should hold even
in Case II may also be seen by considering the
convergence limit rather than the deviation. The
energy difference (el-e2) is a function of el since RR' = 1. If we now differentiate the convergence
limit (R+R'-2) with respect to eJ, we find that
the derivative is proportional to the energy differ
ence (el-e2). That is, we should expect that
there exists a "sensitivity rule" for convergence
limit which would seem to imply the same for the
deviation, at least for large values of N.
The discussions concerning resonance stabiliza
tion cannot be treated in the same way as in the
preceding section because only the symmetrical
case in which R= 1 has been solved exactly. Since
the cases when R is slightly above or below unity
have not been treated exactly, it is not simple to
compare the behavior of the unsymmetrical ion,
RR' = 1, with the mean behavior of the two sym
metrical parent ions.
That the resonance stabilization is less for un
symmetrical than for symmetrical ions, even in
Case II, can be seen, however, in the following
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130.88.90.110 On: Fri, 19 Dec 2014 05:59:03POLYMETHINE DYES 531
way, at least when R does not differ too much
from R'. In this case, although the behavior of
an unsymmetrical ion cannot be compared with
the mean behavior of its symmetrical parents, it
can be compared to the behavior of a symmetrical
ion having an R equal to the mean of those of its
symmetrical parents since if RR' = 1 and the R's
are almost equal, the mean of Rand R' is unity.
The resonance stabilization, EI -el, is equal to a
in the symmetrical case, R = 1 (d. Eq. 54, refer
ence 5), and equal to R'a in the unsymmetrical
case, RR' = 1 (d. Eq. 54, reference 5) where R' is
the smaller of the two R's and hence less than
unity. Since the resonance stabilization of un
symmetrical ions is less than that of symmetrical
ions when Rand R' are not very different, one
would expect this same to be true, a fortiori,
when the R's do differ considerably.
Case III. R» 1 ; R'» 1
In case both Rand R' are large, the intermedi
ate structures are close to the ground structures
and one should expect this case to differ in kind
from Case I. From chemical considerationslO one
would not expect this case to obtain in the poly
methine dyes.
Equation 61 of reference 5 gives the transition
energy in Case III as:
6.EN=3a(-7r )2{1_(~+~ __ 2 )
N+3 R R' RR'
X(I_~_~+_1 )-1}2
R R' RR' (61)
In this case, Eq. 61 shows that there is no
finite convergence limit to the wave-length as N
increases indefinitely. This is not surprising since
the ground structures, whose energetic difference
caused the convergence limit in Cases I and II,
are now very bad approximations to the two
lowest states of the molecule.
Case IV. R«l, R'»l
This case is useful in considering the neutral
dye molecule in which the lowest structure is IVa:
TI
"" N-(CH=CH)n-CH=N-T 2• IVa
/
TI' A number of intermediate structures exist of
which the lowest in energy is probably IVb:
TI
""+ N=CH-(CH=CH)n-N-T 2• IVb
/
Tl'
The remaining (2n+ 1) intermediate structures
are:
Since the set of (2n+3) structures IVa, IVb,
and Wi interact among themselves in the same
way as the set of (2n+3) structures for ion I, the
neutral dye molecule may be considered as a
limiting case of a highly unsymmetrical ion in
which one of the ground structures, IVa, is of
very much lower energy than the intermediate
structures, but the other ground structure IVb is
just a little lower in energy than the intermediate
structures, W2(p+I). This case is handled, then,
by treating R as small and R' as large compared
to unity. The results have already been discussed
for the special case that RR' = 1. Equation 70 of
reference 5 gives the transition energy for Case
IV as:
1 (1) 7r -6.EN= R+--2cos--
a R' N+l
{(R+R') 7r + sin2--
N+2 N+2
(I-R2)2} _R2N+2 (RR' -1).
R'-R (70)
As N increases indefinitely, 6.EN for the neutral
molecule approaches a finite limit just as in the
case of a highly unsymmetrical ion.
In conclusion the author would like to express
his appreciation for numerous discussions with
Professor K. F. Herzfeld and Dr. L. G. S.
Brooker, and also for the courtesies shown him
by the Eastman Kodak Laboratories.
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1.1750951.pdf | Evidence for a Rigid Multilayer at a SolidLiquid Interface
W. G. Eversole and Paul H. Lahr
Citation: The Journal of Chemical Physics 9, 530 (1941); doi: 10.1063/1.1750951
View online: http://dx.doi.org/10.1063/1.1750951
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/9/7?ver=pdfcov
Published by the AIP Publishing
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129.49.23.145 On: Wed, 17 Dec 2014 21:09:07JULY, !94! JOURNAL OF CHEMICAL PHYSICS VOLUME 9
Evidence for a Rigid Multilayer at a Solid-Liquid Interface
W. G. EVER.SOLE AND PAUL H. LAHR
Division of PhysICal Chemistry, State University of Iowa, Iowa City, Iowa
(Received March 20, 1941)
The assumption of an immobile hydrous multilayer at a wall of fixed potential was used in
deriving equations relating zeta potentials, concentrations of univalent salt solution, wall
potential, and thickness of the immobile layer. Calculations were made using data taken from
published papers of various experimenters. Values of SA to 63A were obtained for the thickness
of the immobile layer. The values of wall potential and film thickness were considerecl suf
ficiently consistent for each set of data to justify the original assumption.
THE theory of Freundlich! on the variation of
electrokinetic (S) potentials with concen
tration of electrolyte involved the hypothesis of
an immobile layer of electrolytic solution at the
solid-liquid· interface. More recently, Miiller2
has considered the Freundlich rigidity layer as
"probably monomolecular" and treated the inter
face involved in t potential phenomena as only
an adsorbed monolayer containing ions.3 It is the
purpose of this paper to show evidence in favor
of a rigid multilayer.
The t potential may be defined as the electrical
potential at an interface which is responsible for
the experimental phenomena of streaming poten
tial, cataphoresis, and electro-osmosis. Zeta po
tentials are obtained from the experimental data
by means of a formula by Helmholtz and von
Smoluchowski.4 The formula for streaming po
tential (E) is E=tDPR/47r'YJ where D is the di
electric constant, P the pressure forcing liquid
through a capillary, R the specific resistance of
the liquid, and 'YJ the viscosity.
Abramson and M iiller3 derived an equation
<T=2a(c)!sinht/{3 for the charge, <T, at the
interface required to produce the t potential in a
concentration, c. (a and (3 are constants.) A simi
lar derivation utilizing different boundary con
ditions results in equations for charge density
and interface potentials based upon the postulate
of a rigid multilayer.
Let1/; be the potential at a distance X from a
1 H. Freundlich, Kapillarchemie (Akaclemische Veriags
gesellshaft m.b.H., Leipzig, 1922), p. 342.
2 H. MiiIler, Cold Spring Harbor Symposium Quant. BioI.
(1933), Vol. 1, p. 7.
3 H. A. Abramson and H. MiiIler, Cold Spring Harbor
Symposium Quant. BioI. (1933), Vol. 1, p. 29.
4 Graetz, Handbuch der Elektricitat und des Magnetismus
(Barth, Leipzig, 1921), Vol. II, p. 366. flat surface in contact with a dilute solution of
simple salt (see Fig. 1). 1/;0 is the potential of the
wall with its adsorbed ions. 1/;N is the Nernst
potential of the wall. 1/;0 will be influenced by
changes in 1/;N and by adsorption of non-potential
determining ions having high specific adsorption
potentials. It will be assumed that monatomic
ions of low polarizability have a negligible
specific adsorption potential and therefore 1/;N
and 1/;0 are not changed by the addition of small
amounts of alkali halides. Outside the 1/;0 plane
only Coulomb forces will be considered.
The potential,1/;, will decrease with distance,
X, from the wall as a result of a diffuse double
layer or Gouy "ion atmosphere" in a manner as
shown in Fig. 1. Let t be the potential at a
distance, t, from the wall, t being the thickness
of the solution which is assumed not to take part
in viscous flow during streaming potential deter
minations. Then, according to the Boltzmann
distribution equation, the excess charge density
II of ions in solution near the charged wall will be:
II= -nz€[exp (z€1/;/KT) -exp (-z€1/;/KT)], (1)
where n = number of ions per unit volume of
solution
z=valence of the ions (only symmetrical
valence considered)
€ = unit charge
K = Boltzmann's constant
T = absolute temperature.
More compactly,
II = -2nz€ sinh €z'if;/ KT. (2)
II can be eliminated from the equation by the
use of Poisson's differential equation (for a flat
530
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129.49.23.145 On: Wed, 17 Dec 2014 21:09:07SOLID-LIQUID I::-JTERFACE 531
surface),
Then
and iJ2if; 47r --II.
iJX2 D
a2if; 87rnz€ €zif; --=--sinh -
iJX2 D KT
aZif; aif; 167rnz€ czif; aif; 2----=--- sinh -----.
aX2 ax D KTaX
Integrating,
(aif; ) 2 167rnKT €zif;
-=---cosh--+I,
ax D KT
where I is the constant of integration, or
iJif; (167rnKT €zif; )1 =± ----cosh-+I . ax D -KT (3)
(4)
(5)
(6)
(7)
If aif;/ax is negative, approaching zero at infinite
distance where if; is zero,
aif; =_[167r~KT(cOSh:...zif; -1)]!. (8)
ax D KT
Letting (S7rnz2e2/DKT)!=Debye's K and
a €z/KT
aaif; -----= -v'1KaX.
(cosh aif;-l)! (9)
This equation can be rearranged into a standard
form for integrating.
a sinh aif;aif;
(10)
(cosh aif;-1)t(cosh2 aif;-l)!
fa sinh aif;aif; f ----------= -V2KaX. (11)
(cosh aif;-l)(cosh aif;+ 1)!
(cosh aif;+1)!-v'l 1
-2Kx=ln -- +In -. (12)
(cosh aif;+ 1)!+v'l p
When X =0, if; = if; 0 and
(cosh aif;o+l)!-v'l p=------
(cosh afo+1)!+v'l
or
cosh aif;o/2 1 cosh aif; /2-1
2KX In -In (13)
cosh aif;o/2+1 cosh aif;/2+1 When X =t, if;=r and
cosh aif;o/2 -1 cosh at /2 -1
2Kt=ln -In-----. (14)
cosh aif;o/2+1 cosh at/2+1
Cf, the charge density on the wall is the negative
of the integral of the excess charge density from
the wall to infinity. Or, from Gauss' law,
aif; 411" -= --Cf and Eq. (S) (15) ax D
4;Cf =C67r
;KT (cosh ~i-l) J. (16)
4nz€ aif;o Cf=--sinh-,
K 2 (17)
or
Cf = 35,300c! sinh 19.5if;0 (IS)
for water solutions if T=298.2 and D=78.8.
Formula (1S) is strictly true only if the charge
giving rise to the potential if;o lies in the if;o plane.
Now if if;o is not a function of concentration, it
may be eliminated from Eq. (14) in terms of t
for two concentrations.
2t(Kt-Kl)
(cosh ard2 -1) (cosh ard2+ 1)
= In --------------------. (19)
(cosh arJ/2+ 1)(cosh atd2 -1)
I
I
I
I
I
I
I
I I
~t"":
I I : \
I I
I I
I I
I I
I I
o 0 x-
FIG. 1. Variation of potential with distance from a soIid
liquid interface.
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129.49.23.145 On: Wed, 17 Dec 2014 21:09:07532 \V. G. EVERSOLE AND P. H. LAHR
TABLE I. Calculations from published zeta potential data
ELEC- MOLARITY
EXPERIMENTER TROLYTE METHOD SOLID cXlO'
Schonfeldt' KCl Electro-osmosis Ceramics 0.03
" " " .05
.07
Velisek and 10
Vasicek2 1
.316
NaCl 31.6
10
3.16
1
KI 10
1
.1
Baborovsky and KCl Streaming 1
BurgP Potential .75
.5
.25
.1
.05
.01
.005
Monagham and Electro-osmosis Pyrex 1
White' (sph,~res) .1
.01
Pyrex 1
(capil- .1
laries) .01
DuBois and Glass .1
Roberts· .05
.01
Streaming .1
Potential .05
.01
1 N. Schonfeldt, Zeits. f. Elektrochernie 37, 734 (1931). VOLTS VOLTS
i 0/.
0.0327 0.0391
.0309 .0390
.0298 .0390
.015 .053
.035 .054
.042 .054
.010 .042
.024 .056
.036 .060
.040 .053
.006 .052
.029 .061
.041 .051
.0057 .028
.0066 .026
.0104 .032
.0113 .025
.0156 .026
.0189 .027
.0228 .027
.0262 .029
040 .135
.066 .097
.095 .111
053 .107
.083 .108
.098 .107
.049 .130
.052 .104
.079 .113
.040 .048
.044 .050
.045 .048 0'0 IN
e.s.u.
510
658
779
13700
4320
2470
24300
13700
7680
4320
13400
4200
1340
1980
1710
1390
988
624
441
198
139
3040
1860
1100
4330
2700
1160
1230
1060
780
960
855
350 tIN
cm XIO'
0.29
.115
.075
.2
.469
.257
.15
.626
.16
'J. Velisek and A. Vasicek, Collection of Czechoslovak Chern. Cornrnun. 4, 428 (1932).
3 J. Baborovsky and B. BUrgI, Collection of Czechoslovak Chern. Cornrnun. 3, 563 (1931) .
• Monagharn and White, J. Phys. Chern. 39, 935 (1935).
5 R. DuBois and A. H. Roberts, J. Phys. Chern. 40, 543 (1936).
Using Eq. (19) and published data of various
experimenters, the value of t was calculated. The
average value of t was substituted back in Eq.
(14) to determine 1/;0, The average value of 1/;0
was then used in Eq. (18) to calculate 0'. The
results are shown in Table I.
As is evident from the table, it is possible by
proper choice of a value for t to fit these equations
to experimental zeta-concentration data. The
failure of experimental data to fit exactly the
derived equation may be due in part to errors in
the data itself and partly to the assumption of a
constant 1/;0 in deriving the equations used.
It is of interest to note that in data from
Monagham and White's work,1/;o is the same for
both methods of measurement while both t' and t
are different. It may be that the flow of liquid
had a more destructive effect upon the water
layer in the capillary than in the diaphragm of Pyrex spheres. Also, the data from Velisek and
Vasicek for a ceramics diaphragm show nearly
the same value (0.05 volt) for sodium chloride,
potassium chloride and potassium iodide, while
again rand t differ for the three salts.
At least to some degree, the assumption of a
rigid multilayer which incloses part of the
counter ions of the ion atmosphere at an interface
makes it possible to account for observed varia
tions of r with concentration of simple ions.
Evidence which would seemingly contradict such
an assumption may be found in a paper by
Abramson and Miiller.3 They applied the formula
(20), 0'=2a(c)! sinh r/{3, which corresponds to
Eq. (17), to determine the charge at the interface
of solid and solution necessary to produce the r
potential. For a large variety of electrolytes,
their curves relating surface charge (0') to con
centration (c) for concentrations up to 0.01
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129.49.23.145 On: Wed, 17 Dec 2014 21:09:07SOLID-LIQUID INTERFACE 533
molar closely resemble a Langmuir adsorption
isotherm for adsorption of gas molecules on an
inert surface. The adsorbed charge on the nega
tive glass surface proves to be negative, whereas
counter ions in a layer near a negative surface
would have a predominantly positive charge.
However, several observations throw some
doubt on the validity of this evidence. As
Abramson and Muller pointed out, at concentra
tions above 0.01 molar "er might conceivably
decrease." According to the formula for er, the
charge would be zero for zero r at any finite
concentration. Such a decrease in er at higher
concentrations is foreign to a Langmuir iso
therm. Moreover, in the specific case of potassium
chloride adsorption on glass, Abramson and
l\liiller's er-c curve shows an increasing negative
charge on the negative glass surface whereas a
large difference in specific adsorption potentials
of two ions so nearly alike in ionic weight and
volume is not to be expected. Finally, a careful
analysis of the equation for er will reveal that er
may consist very largely of charges other than
ions of the added electrolyte.
The equation er=2a(c)! sinh S/(3 involves the
assumption that the entire charge on the wall
is in the single r potential plane. Verwey5 con
siders the charges on the wall to be scattered in a
finite layer, consisting of potential-determining
ions in the wall, adsorbed ions on the wall and,
perhaps, counter ions inclosed in an immobile
water layer along the wall. If the only force
holding ions in or near a glass surface were elec
trostatic (obviously not strictly true), if the
dielectric constant of the solution were un
changed near the surface, and if all the potential
determining ions of a glass electrode were in one
plane, an equation similar to Eq. (17) could be
derived to give erN=4nz~/K sinh aifiN/2. Using
Abramson and Muller's constants, this would
become erN = 2act sinh ifiN/(3. In this case ifiN would
be the Nernst potential of the glass as an elec
trode, erN would be the charge in the potential
plane, and c would be as before the concentration
of ions of all kinds in the bulk solution. The
Nernst potential of glass in pure water would be
expected to be the same sign and perhaps larger
in magnitude than the r potential of glass 10
5 E. J. W. Verwey, Chern. Rev. 16,363-411 (1935). pure water. It follows from the above equation
that an increase in concentration of the solution
must result in an increase in erN if ifiN is to remain
constant. Unless the electrolyte added in r
potential measurements contains potential-de
termining ions, ifiN should remain nearly constant.
According to the equation, the er -c curve for a
constant ifiN would be a parabola of increasing
negative charge resulting from a transfer of
potential-determining ions. The reason for an
increase in erN in this case is clear if the electrode
and its double layer are considered to be two
plates of a charged condenser. If the plates are
moved closer together, a greater charge on the
plates is necessary to maintain the original
potential. An increase in the concentration of a
solution results in a greater K, the reciprocal of
which is Debye's measure of the effective thick
ness of a double layer. That is, an increase in c
results in a decrease in the effective thickness of
the double layer.
Even though the assumptions necessary to
derive an equation for erN are not strictly valid,
it is evident that the er in the r potential plane
which could represent all the charges in the
o o
Data from
Baborov.ky and BurgI
ti.18, tr=3Sl00rc: sirlhI9.5\f.
,¥.=.Ol8vo 1h
c -in mo'.~ per lih,.
.001 .OOlS ,005 .0075 .0'
FIG. 2. Variation with concentration of effective
charge density.
finite wall surface is in a large measure repre
sentative of the adsorbed potential-determining
ions rather than ions of the added electrolyte.
The first approximation of the charge of ad
sorbed potassium and chloride ions might be
obtained by subtracting Abramson and Muller's
curve (Eq. (20)) from a true parabola (Eq. (17)),
(see Fig. 2). The resulting er for adsorbed counter
ions would be positive instead of negative and
would comprise the part of the positive ion
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129.49.23.145 On: Wed, 17 Dec 2014 21:09:07534 W. A. ZISMA~
atmosphere in the immobilized layer between the
1/10 and s planes. This (J' might not necessarily
follow a Langmuir adsorption isotherm.
SUMMARY
(1) Equations have been derived for the rela
tions between wall potential, zeta potential, and
concentration of univalent salt solutions, assum
ing an immobile hydrous layer of finite thickness
was attached to a wall of fixed potential.
(2) When published s potential-concentration
data for simple salt solutions are substituted in an equation relating film thickness to s potential
for a constant wall potential, values of SA to 63A
are obtained for the rigid layer thickness.
(3) The results show that s potential-concen
tration curves for simple univalent ions can be
explained without attributing such large specific
adsorption potentials to the ions as the (J' -C
curves of Abramson and Muller might indicate.
(4) The hypothesis of a rigid or viscous water
multilayer at a solid-water interface, though not
proved. is at least tenable in the light of its
ability to fit certain s-potential data.
JCLY, 1941 JOURNAL OF CHEMICAL PHVSICS VOLCME 9
The Spreading of Oils on Water
Part I. Ionized Molecules Having Only One Polar Group
W. A. ZISMAN
Naval Research Laboratory, Anacostia Station, Washington, D. C.
(Received March 31, 1941)
The spreading phenomena on water of drops of mineral
oils containing a wide variety of .organic acids and amines
having but one polar group have been studied under con
ditions where dissociation at the oil-water interface could
most readily occur. Particular emphasis is placed on the
homologous series as an aid in separating the variables
involved. Various phenomena of edge diffusion are
described and a qualitative theory is presented. Edge
diffusion is shown not to be a serious source of error
in measuring the cross-sectional areas of the adsorbed
molecules if there are over 13 carbon atoms per straight
chain. The different types of film spreading and break-up
effects are described and the various physical and chemical
factors involved are discussed. The changes in the spread
ing effects due to varying the pH and to the presence in
the water of Ca++, Cu++, Pb++, Fe+++, AI+++, La+++, and
1. INTRODUCTION
IT has long been known that highly purified
mineral oils such as medicinal petrolatum do
not spread on the clean surface of water but form
lenses having well defined contact angles with the
water. Such lenses were studied by Hardy,1
Coghill and Anderson,2 Lyons,3 and more recently
1 W. B. Hardy, Proc. Roy. Soc. A86, 610 (1912).
2 W. H. Coghill and C. O. Anderson, Tech. Paper 262,
U. S. Bureau of Mines, 1924.
3 C. G. Lyons, Trans. J. Chern. Soc. (London) 623
(1930). Th++++ on the interfacial film are described. It is shown
that only the long chain monobasic saturated acids form
rigid films when affected by metallic ions, while other
acids are either condensed somewhat or are unaffected.
Short chain metallic salts of these fatty acids are often
oil soluble and have brief lifetimes of adsorption. An
experimental proof is given that dissociated long chain
acids and amines have infinite lifetimes of adsorption.
Evidence is given for concluding that the lifetime is short
for molecules having less than 14 carbon atoms. The effect
of Ca++ on the spreading of oleic-stearic acid mixtures is
given in some detail and also a theory of the results.
Reasons are given for concluding that the adsorbed acid
molecules form two-dimensional film complexes with
hydrocarbon molecules derived from the oil.
by Langmuir.4 Harkins and Feldman5 have
shown that a drop of a pure liquid would not
spread on water if its spreading coefficient Fs
were negative; and in agreement with this,
values of F s for mineral oils, calculated from
surface tension data, range usually between -11
and -14 dynes per centimeter.
When such oils are either heated or radiated
with ultraviolet light in the presence of air they
41. Langmuir, J. Chern. Phys. 1, 756 (1933).
5 W. D. Harkins and A. Feldman, J. Am. Chern. Soc. 44
2665 (1922). '
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129.49.23.145 On: Wed, 17 Dec 2014 21:09:07 |
1.1916075.pdf | Sound Prevention Mechanism of Nonporous Materials. Part I
Sadao Kawashima
Citation: The Journal of the Acoustical Society of America 12, 75 (1940);
View online: https://doi.org/10.1121/1.1916075
View Table of Contents: http://asa.scitation.org/toc/jas/12/1
Published by the Acoustical Society of America
Articles you may be interested in
Sound Prevention Mechanism of Nonporous Materials. Part II
The Journal of the Acoustical Society of America 12, 327 (1941); 10.1121/1.1916107JULY, 19 40 J . A . S. A . VOLUME 1 2
Sound Prevention Mechanism of Nonporous Materials. Part I
SADAO KAWASHIMA
Department of Architecture, Waseda University, Tokyo, Japan
(Received December 6, 1939)
INTRODUCTION
N response to the modern requirements for satisfactory sound insulating materials, nu-
merous investigators have been engaged in the
search for such materials. As a result of such
efforts, both of theoretical and experimental
nature, the following generalization, namely,
that the sound insulation of building materials
is proportional to the logarithm of their weight
per unit area, is accepted as substantially
correct.
This generalization, although quite helpful
from the practical point of view, cannot be
applied to all kinds of building materials, varying
widely in their physical properties, which pro-
duce differences in the mechanism of sound
transmission. The so-called building materials
may be classified as either porous or nonporous
depending upon their physical composition, and
the differences in the mechanism of sound
transmission would depend upon the nature of
material under consideration.
Another objective, much desired and needed
by the engineering profession, is the attainment
of satisfactory sound insulation by using light
materials. In response to such a demand, the
analysis of sound prevention mechanism must
be made.
In this connection, the author has analyzed
the following two problems; first, the trans-
mission loss of elastically restrained nonporous
material and second, that of nonporous and non-
elastically built-in materials. This paper is re-
stricted, however, to the discussion of the results
obtained in the study of the first-mentioned
problem, namely, the relation between mechani-
cal vibration and transmission loss of non-
porous plates.
THEORETICAL CONSIDERATIONS
When the plate is considerably rigid and thin
compared with the wave-length of the exciting
pulstances, the actual wave transmission of
sound through the plate is not of great im- portance, and it becomes possible to regard the
plate as an infinitely thin massive diaphragm.
In practice, however, the plate is clamped at
the edges, and may vibrate as a whole.
The theoretical consideration of this mecha-
nism of transmission loss of thin, nonporous,
rigid materials under elastic restraints was pub-
lished by A. H. Davis. According to his theory,
when the sound wave /3=/}0e (t-x/*) is incident
normally upon a partition which may be con-
sidered as an infinitely large diaphragm, having
a mass m per unit area, then the diaphragm will
vibrate in the manner represented by the
expression /32 =/302e t.
Then the following equations may be written'
For the first medium,
! oei,(t_c/c)q_. t i,(t+x/c) = l!/0 e , (1)
where the second term represents the reflected
wave.
For the plate,
2= 02e it (2)
and for the wave transmitted on the other side
of the plate,
a = 0ae '('-/), (3)
where /, /2 and a represent particle displace-
ments in the first medium, the plate and the
second medium, respectively.
At the boundary, consider the plate as per-
fectly rigid;then between the first medium and
the plate, or plate and second medium, velocities
must be continuous. Therefore applying the
boundary condition such that
0+0 '=02, /}0a =02. (4)
The pressure variations causing the motion of
the plate arise from the sum of the effects of the
pressure variations associated with the incident,
reflected and transmitted waves. The total force
on unit area of the plate may be written 6p0
A. H. Davis' "Transmission of sound through parti-
tions," Phil. Mag. 15, 309 (1933).
75 76 SADAO KAWASHIMA
q-bPo'--aPoa or since ap=-+-ct>}, with attention
to the sign of c, it becomes pc(}0-30'-303)e t.
Then the equation of the plate becomes
m+r+s2=g1(o1--o'--oa)e it, (5)
where m is the mass per unit area, r the dissipa-
tive resistance, s the coefficient of elastic re-
straint of the plate and R the specific acoustic
resistance of the air represented by c, where is
the density and c the velocity of sound in air.
Solving this equation, the ratio of the square
of the velocities is given by
0= (0 (r+2R)+(mw-s/w) / X0/ = 4R (6)
and the transmission loss in db by the foilroving
equation
[ (r + 2R ) + (mw - s /w) ] T.L.(db) = 10 1og0 . (7)
4R
By writing w0 for the natural pulstance (s/m)
of the plate, 2 the following expression is obtained
T.L.(db) = 10 log0[ (r+2R)2 4R
4 . (8)
4R =
When there is no appreciable dissipation in the
plate itself, r0, and the equation becomes
T.L.(db) = 10 log0 1 q . (9)
4R =
It can be readily seen that the transmission
loss is due to the effect of mass and the relative
relation between the natural and excited pul-
stances.
It is possible that the plates may have several
modes of vibration but in our experiment, with
the exception of a thin iron plate, only a single
mode of vibration appeared.
It is evident that o=(s/m) is a decisive
factor in determining the transmission loss, where
the coecient s is related to and influenced by
the boundary conditions of the plate. For a
= Actual angular velocity of the oscillation is w0'=
(s/m--r=/4m =) but in general, as s/m<<r=/4m , we can pu
WoWo t. certain material, when the boundary conditions
are fixed, the natural frequency assumes a
constant value, and as may be seen from Eq. (8),
the amount of the transmission loss is decisively
affected by whether the natural frequency coin-
cides with the exciting frequencies. The factors
relating to the natural frequency are mass and
stiffness. The stiffness is considered a function
of the "geometrical shape" and the boundary
conditions, and m is determined by the quantity
representing the nature of the material itself.
Therefore, the transmission loss of plate-like
materials is determined by the following two
factors, geometrical shape and boundary condi-
tions as well as by inherent physical properties.
A similar situation arises in the case of the
strength of elastic materials where the moment
of inertia depends upon the shape of the body
and the modulus of elasticity is an inherent
physical property of the body.
As a logical consequence, it is meaningless to
express the transmission loss of elastically re-
strained nonporous materials on the basis of the
physical properties alone.
DESCRIPTION OF EXPERIMENT AND DISCUSSION
OF TEST RESULTS
The tests vere conducted in order to ascertain
the factors mentioned above and appearing in
Eq. (8), but before proceeding to the description
of the test and the discussion of the test results,
a word in regard to the transmission loss meas-
urement may not be out of order.
In our sound laboratory at Waseda University,
all interior surfaces of the test room were
covered with highly absorbent materials (see
Fig. 1). The reduction factor is sometimes defined
as the square of the ratio of the sound pressure
of the generating and receiving rooms, respec-
tively, when they are separated by the test plate.
However, this method of conducting the test,
as previously pointed out by other investigators,
is unsatisfactory for the reason that the measured
values of the transmission loss include the ab-
sorption power of both rooms. Next consider the
comparative intensities of progressive waves at
points A and B (see Fig. 1), namely points in
front and back of the test window without the
ß test plate in place. SOUND PREVENTION MECHANISM 77
SPECIM
SOUND IECIIVING' gOOM
ß
4.50 m
FIG. 1. Plan of sound laboratory.
In spite of the absence of the test piece in the
window, owing to the abrupt change in the cross-
sectional area of the room to that of the test
window, a slight transmission loss of about
I1.8 db due to open-mouth resistance, ap-
peared in the experimental measurements.
From the foregoing, it is evident that the test
must be conducted under the following condi-
tions in order to satisfy Eq. (8):
(a) The receiving room to be covered with
highly absorbent units to similate open air
conditions.
(b) The distance between the sound source
and the test plate to be kept as large as
possible, and absorbent units to be hung pro-
fusely in the sound generating room so that
the reflected waves from the plate are absorbed
before returning to the sound source.
The fulfillment of condition (a) will, in a
large measure, eliminate the reflected waves,
thereby satisfying one of the conditions expressed
in Eq. (4), and the meaning of condition (b) is
that the measurement must be made under the
condition of plane waves;that is, the intensities
of sound at point A and B (at least 60 cm apart)
are to be identically equal. Further, when the
plate is placed in position, reflected waves will
be produced which will tend to create negative
pressure at the loudspeaker. The reflected wave, however, will propagate from the plate making
a wide angle so that the amount of sound picked
up by the speaker is negligible, not only by this
fact alone but also by the absorption of energy
by the absorbent unit hanging from the ceiling.
In spite of the fact that such elaborate pre-
cautions were taken, a slight wave pattern could
not be eliminated in the receiving room, and the
measured transmission loss of so-called pro-
gressive wave at point A and B amounted to
somewhat less than 1 db; such small discrep-
ancies in the transmission loss, expressed in db
can properly be disregarded. Considering the
pressure at point A and B to be substantially
the same, in our present experiment, the sound
pressures at point B were measured both with
and without the test plate in place.
As previously stated, the purpose of the
present experiment being the investigation of
sound transmission mechanism of plate-like ma-
terials-in other words, the relation between
mechanical vibration and transmission loss--we
first attempted the use of Rochelle salt of the
deflection type to pick up the mechanical vibra-
tion, but we experienced great difficulties in
keeping compliance between the plate and the
needle edge always in a constant condition. For
this reason, the method hereinafter described
was used. Fixing the coil on the plate by paraffin,
the magnet was placed over the coil independent
of the plate. When the plate is acted on by the
sound pressure, the coil moves with it which
induces an e.m.f. which is amplified and meas-
ured. A view of this movable type coil vibration
pick-up is shown in Fig. 2. While picking up the
relative amplitude of mechanical vibrations, the
velocity microphone was placed at the point P
(see Fig. 1) in the sound generating room,
taking precaution to avoid the reflected wave
from the back wall, to ascertain whether the
acoustical output for all range of frequencies
was being maintained constant. The induced
e.m.f. is proportional to the velocity of motion
of the plate and not to the actual displacements.
Consequently, in order to represent the relative
displacement of mechanical vibration, it is neces-
sary to compute these displacements. In order to
determine the natural frequency of the plate,
the latter was struck slightly by a soft hammer
and the induced oscillations of the plate and the 78 SADAO KAWASHIMA
.$
Fx. 2. Vibration pick-up.
sound wave were obtained simultaneously on an
oscillograph record. Meanwhile the sound pres-
sure was measured by band microphone and
Schalldruckmesser of Siemens and Halsk A.G.
A general view of this measuring equipment is
shown in Fig. 3.
As a representative specimen of the non-
porous materials, glass plate was selected. A cir-
cular glass plate, 3 mm in thickness and 50 cm in
diameter, was placed in the opening. (See Fig. 3.)
The recorded natural vibration and sound wave
for this specimen are shown in Fig. 4. From this
figure it is evident that the sound wave forms
follow that of the mechanical vibration where
the mechanical vibration is of the order of
f0 = 68 cycles per second and calculated resistance
from the damping is r=27.5 g/cm 2 sec. The
results for the transmission loss and relative
amplitude of mechanical vibration are shown in
Fig. 5, where the curve for transmission loss
represents the transmission loss as calculated
from the Eq. (8) and the plotted points are the
measured value of the transmission loss. (The
amplitude curve for mechanical vibration is
obtained from the experimental results.) On the
basis of the results of this test, it may be said
that at the frequency of 68 cycles per second,
the amplitude of plate vibration becomes a
maximum and the transmission loss a minimum,
but on the contrary, in the domain of high
frequencies, the amplitude of the mechanical
vibration decreases gradually which results in
large values of the transmission loss. This phe-
nomenon occurs when the exciting frequency differs considerably from the natural frequency
and only the mass of the plate contributes to the
reduction factor. As may be seen at the point of
f=68 cycles, the amount of energy dissipation
due to resistance is so small that it can be said
that the sound prevention mechanism of similar
nonporous materials elastically restrained is
mostly due to mechanical reactance.
The above relations obtained in the case of
plate-like thin specimens. However, what will be
the relation of the transmission loss when the
thickness of the materials is gradually increased ?
To investigate these probable differences in
behavior, 50-cm square gypsum plaster plates of
various thickness were investigated. The con-
dition of the specimens--for instance, the
presence of bubbles and the condition of drying
of the plate--will have an important effect upon
the transmission loss. For this reason, all the
F6. 3. View of experimental set-up looking from the
receiving room toward the generating room.
F6. 4. Damped oscillation of a glass plate. SOUND PREVENTION MECHANISM 79
60 100 200 500 1000 2000 4000
FREQUENCY IN CYCLES PER SECOND
FIG. 5. Mechanical vibration and transmission loss of a glass plate. 80OO
specimens were prepared at one time and these
were naturally dried extending over a period of
about a month. The physical dimensions of
these 50-cm square specimens as well as their
respective natural frequencies are all listed in
the following Table I.
The weight of unit area of each plate is rather
uniform and the reason for the irregularity of
the natural frequencies with respect to the thick-
ness is most probably due to the boundary
conditions of the plate, i.e., the differences in the
tensile force acting. The results from the experi-
ment and the computed value from Eq. (8) are
graphically shown in Figs. 6-10. From these
results, it can be said that the greater portion
of the reduction factor of a plate is caused by
mechanical diaphragm action since the amplitude
of vibration decreases for high frequencies.
Broadly speaking, the transmission loss of a
nonporous material is proportional to the loga-
rithm of its weight per unit area, but as the
transmission loss is also a function of the ex-
citing frequencies, the value becomes somewhat
different near f0.
Consider Eq. (9) for definite value of w0 and w,
TABLE I.
No. THICKNESS
14
21
30
40
50 VrEIGHT
(G/Ct 2)
1.50
2.18
3.15
4.10
5.15 NATURAL
FREQUENCY
(c.p.s.)
95
101
101
93
85 DISSIPATIVE
RESISTANCE
(C/SEC.)
72
111
146
228
262 putting
ws(1 -woS/w2) 2
=k, (10)
4R 2
then Eq. (9) rewritten as
T.L.(db): 10 log10 (1 +kmS), (11)
if krn2>> 1, then the former equation becomes
T.L.(db): 10 log10(km s) or
T.L.(db): 10 log10 k-+- 10 log10 ms. (12)
The condition krnS>>l is satisfied when the
exciting frequencies are far from the natural
frequency. Taking f0-100 cycles and f- 1000
cycles, the relation between the transmission loss
and weight per unit area calculated from Eq.
(12) is shown in Fig. 11. If the curve of
10 log10 krn s is analyzed, it is evident that this
curve is the summation of the curves 10 log10 k
and 10 log10 m s and the value 10 log10 k is the
amount of reduction which is primarily due to
the exciting frequency, and 10 log10 rn 2 is the
reduction factor due to the mass.
Next consider the case when krn becomes com-
parable to 1, this being the case when m becomes
very small or when w approaches w0, then the
approximate calculation of Eq. (12) indicates
negative transmission losses, an evident contra-
diction which is due to the approximate calcula-
tion, and the dotted line showing 10 log0 (1 q- krn )
is the real transmission loss.
In our present experiment m changes from
1.55.15 g/cm s and f0 from 68101 cycles.
For convenience of computation it has been 80 SADAO KAWASHIMA
J
)__5, --
)--4 ... TTMISSION LOSS ./AMPLITUDE . rr" .
0
60 100 200 500 10o0 2000 4000 8000
FREQUENCY IN CYCLES PER SECOND
Fro. 6. Mechanical vibration and transmission loss of a plaster plate (thickness 14 mm).
7O
(0- -6
40-- -4 - ß
ß
.< DE
:r ø 60 1 200
FREENCY IN CYCLES PER SECOND
Fro. 7. Mechanical vibration and transmission loss of a plaster plate (thickness 21 mm).
qRANSMISSION LOSS
30--3
20--2
<
, 1 0 60 100 2:) 5(2' 1000 2000 4000 8000
FREQUENCY IN CYCLES PER SECOND
FIG. 8. Mechanical vibration and transmission loss of a plaster plate (thickness 30 mm). SOUND PREVENTION MECHANISM 81
70
z m z J-TRANSMISSION LOSS z 50 5
o 40 4
30 3
m 20--2 m
½ ½ ITU
0 6b lOO 260 lO 2000
FREOJJENCY IN CYCLES PER SECOND
Fro. 9. Mechanical vibration and transmission loss of a plaster plate (thickness 40 mm).
z 60-- -6 -.
z N LOSS
z 50-- 5
o40 4-
o
30 20---2 z
0 I 100 2 5 10 2 8000
FREQUENCY IN CYCLES PER SECOND
FIG. 10. Mechanical vibration and transmission loss of a plaster plate (thickness 50 mm).
6O
%: 20
i- 10
0001 0.02 004- 0.06 01 02 04 06 1 2 4 6 8 10
WEIGHT PER UNIT AREA(
FI6. ! 1. Transmission loss versus weight per unit area. 82 SADAO KAWASHIMA
FIG. 12. Filtration
overtones. of
(a) (b) (c)
assumed that all of the plates have a constant
natural frequency of f0 = 100 cycles for all thick-
nesses and that the exciting frequency is 1000
cycles; then the computed values of 10 log10 m 2
are shown in the lower right hand part of Fig. 11,
while the plotted points are the values obtained
by deducing 10 log10 k from the experimentally
measured values shown in Figs. 6-10. (See also
Table I I.)
The reduction factor due to a certain mass,
however, will bear a constant relation to the
transmission loss, while the values of 10 log10 k
are affected by the boundary conditions. There-
fore, the slope of 10 log10 m 2 as shown in the
right-hand lower part of Fig. 11 represents the
trend of transmissibility of all nonporous ma-
terials when the natural frequency differs from
the exciting frequencies. But if this slope is
compared with those based on the experimental
results of other investigators, it is a slightly
steeper slope. This is reasonable as the experi-
mental values contain attenuation or dissipation
values, but this trend becomes meaningless in
the case when the exciting frequencies approach
the value of the natural frequency.
The question of the filtration of noises will
now be briefly discussed. As shown in Figs. 6-10
the amount of the sound reduction varies over
a wide range of frequencies causing the filter-
ing out of sound containing the overtones. For
TABLV. II.
NO. WEIGHT[ 1000
(G/CM') ] (DB) '.s0 2.18 [ 40
3.15 [ 46
4.10148
5.15 I 51 10 LOG10 k
37
37
37
I37 37 10 LOG m - =T.L. --10 LOG10 k
1
3
9
11
14 instance, for a 30-ram thick plaster plate, the
wave forms of complex sound before and after
transmission are shown in Fig. 12. This figure
shows (a) the actually recorded wave form of
the sound source, (b) the mechanical plate
vibration and (c) the sound wave after being
transmitted.
From the above, it is clear that the quantities
of high frequencies in the receiving room are
considerably reduced while those of lower fre-
quencies are not appreciably reduced. This
means that the gypsum plaster plate acts as a
low pass filter, and the reason for the distortion
of sound which we actually experience becomes
apparent.
CONCLUSION
On the basis of the present experiment, it is
evident that in the case of elastically restrained
nonporous thin materials, the principal part of
sound transmission mechanism is traceable to
diaphragm action. It is clearly evident that this
transmission mechanism is composed of the
following two parts: (a) the effect due to the
relation between the natural and exciting fre-
quencies, (b) the effect due to mass. Therefore,
in the expression of the transmission loss of
building materials, not only the weight per unit
area of the material but also the boundary
conditions play a very important role which
should be given full consideration.
ACKNOWLEDGMENTS
Acknowledgment is made to the Japan Society
for the promotion of Science for the financial
assistance in conducting this research, to Pro-
fessor Dr. T. Satow for stimulating advice and
criticism, and to Mr. S. Nagata for performing
most of the experimental work. |
1.1712732.pdf | Qualitative Spectrochemical Analysis in Agriculture and Geochemistry
Stanley S. Ballard
Citation: Journal of Applied Physics 11, 750 (1940); doi: 10.1063/1.1712732
View online: http://dx.doi.org/10.1063/1.1712732
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in Agriculture and Geochemistry
By STANLEY S. BALLARD*
University of Hawaii, Honolulu, Hawaii
OF the several physical instruments that are
employed in the chemical analysis of
materials, the spectrograph is perhaps the most
firmly intrenched and the most widely used.
The current literature of analytical chemistry
contains an increasing number of references to
what is known as spectrochemical analysis.
Quantitative methods are now being emphasized
particularly, but this should not cause one to
overlook the value of a good qualitative technique.
It is the purpose of this article to outline quali
tative analytical methods applicable to the fields
of agriculture and geochemistry and to give
illustrations of their use.
The general advantages of spectrochemical
analysis are well known-the speed, the ade
quacy of very small samples, and the high
sensitivity for many elements. Marked advan
tages of a spectrochemical technique for quali
tative analysis are the following: first, a single
analysis serves to determine many elements,
including all the metals, and the nonmetals
silicon, phosphorus, boron, arsenic, and fluorine
(in the presence of calcium); second, the tech
nique is adaptable to any type of sample, be it
liquid or solid, metallic or nonmetallic; third,
permanent records in the form of the original
spectrograms are obtained, which can be con
sulted later for additional information not
desired at the time of making the original
analysis. An example of this occurred recently,
regarding the presence of lead in Hawaiian soils;
all spectrograms of soils taken since the estab
lishment of the laboratory in 1931 could be
consulted readily, and lead was found to be a
rarely occurring trace soil constituent. The
fourth, and final advantage is that semi-quanti
tative estimates can be made with little added
* Assistant Profes~or of Physics. The present paper is an
outgrowth of the activities of the writer as Consultant in
Spectroscopy in the Experiment Station of the Hawaiian
Sugar Planters' Association, 1937-40.
750 work, giving results that are much more valuable
than those of the "present or not present" type
of qualitative analysis. The estimates are made
on a logarithmic scale and should be accurate
to the nearest factor of 10.
The fact that only small samples are used in
spectrographic analysis is a great advantage
when working with samples difficult to obtain.
But, curiously enough, the smallness of the
portion needed for testing may be a disadvantage
if a large amount of material is at hand, when a
difficult problem of sampling results. Since the
maximum amount of material that can be used
in an analysis is about SO milligrams, consider
able difficulty is encountered in obtaining a
representative sample of this size from a ten-acre
soil plot or a lava flow that may cover a fraction
of a mountain side!
The analytical methods about to be described
have been found most useful in two types of
investigations. The first is the determination of
the approximate composition of a totally un
known sample. In the course of one hour to one
working day, depending on the complexity of
the sample, the spectroscopist can determine the
identity of the major, minor, and trace arc
sensitive elements present. This information
should be of considerable value to the chemist
who may wish to obtain quantitative data on
certain constituents. An example which can be
quoted here concerns a white, crystalline in
crustation deposited in areas of solfataric activity
on the crater floor of Kilauea volcano. This
incrustation had been designated as "gypsum"
to the writer by geologists. The spectroscope
immediately revealed, however, that there was
entirely too much silicon present for this to be a
pure gypsum. In Table I is given the composition
estimated spectrographically, and the accurate
quantitative elemental composition recomputed
by K. T. Mau from the subsequent gravimetric
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was too low for calcium, and included traces of
magnesium, manganese and sodium that were
npt detected chemically. Chemical analysis re
vealed the presence of a small amount of phos
phorus, an amount below the spectrographic
threshold (for the technique employed). The
chemical results also revealed 36.52 percent S03,
and 13.60 percent H20. These data, combined
with the results of a mineralogical examination,
indicated that the substance was a gypsum
(CaS04·2H20)-opal (Si02·nH20) combination
along with some other silicate mineral containing
the excess of 503• These results are discussed
elsewhere by Mau and Payne.!
The second field of especial usefulness of the
spectrographic technique is the determination of
the identities and estimation of the amounts of
minor and trace elements in samples whose
major constituents are known. Indeed, a com
parison among the amounts of trace elements in
substances of similar major composition can
readily be made. Good examples of this can be
drawn from geochemistry, since 99 percent of
the earth's crust is made up of only ten elements.2
The spectrograph appears to be an ideal instru
ment for learning the composition of the re
maining one percent.
Experimental Technique
The experimental work described in the
present paper was carried on in the spectroscopic
laboratory of the Chemistry Department of the
Experiment Station of the Hawaiian Sugar
Planters' Association, in Honolulu. In this
laboratory, spectra are excited by the direct
current arc and are produced and photographed
by a large quartz Littrow spectrograph (Bausch
and Lomb). This technique is perhaps the best
for most agricultural analyses, since the direct
current arc method is particularly applicable to
the nonconducting powders so often encountered,
and an instrument of high resolving power is
necessary due to the abundant iron in Hawaiian
soils.
Direct current is supplied by a 3-kva motor
generator. The striking potential for the arc is
250 volts. Sufficient resistance is put in series
to hold the arc current at a desired value within
VOLUME 11, DECEMBER, 1940 TABLE I. Elementary metallic composition of a white in
crustation, as estimated spectrographically and as determined
chemically.
ELEMENT
Silicon
Calcium
Iron
Magnesium
Manganese
Sodium
Phosphorus SPECTROGRAPHIC ESTl
MAHON, PERCENT
more than 10
more than 1
approximately 0.1
approximately 0.01
approximately 0.01
approximately 0.01
less than 0.1 CHEMICAL DETERMI
NATION, PERCENT
15.31
12.2
0.14
not found
not found
not found
0.07
the range 4 to 10 amperes, whereupon the
voltage drop across the arc is of the order of 30
to 50 volts. The arc current selected depends
upon the volatility of the sample and the
exposure time desired. In work of this sort,
electrodes of the highest obtainable purity should
be used. It is now possible to obtain graphite
electrodes that contain only occasional impurities
-copper, boron and silicon. Copper electrodes
free of boron and silicon, but with traces of
lead, tin, iron, nickel and silver can be obtained.
Therefore, only copper remains as a possible
contaminant, and is of importance only when it
is present in the sample in concentrations of
less than one part per million. Electrodes must
be prepared with extreme care to avoid inad
vertent contamination. The steps employed in
this laboratory are described elsewhere.3 A bare
electrode strip is photographed on the plate for
each pair of electrodes used, in order to be sure
that no accidental impurity is present. Lower
electrodes are now prepared with a conical
cavity, the ratio of the diameter to the depth of
the cone being 2 to 1, 1 to 1, or 1 to 2 for small,
medium, or large samples, respectively.
Experiments showed that the arc ran more
steadily when the lower electrode was of positive
polarity. This arrangement has the added ad
vantage (at least when refractory samples are
being arced) that the positive electrode gets
much hotter than the negative. For these two
reasons the lower electrode is always made the
positive. Figure 1 shows the plateholder end of
the spectrograph, and various accessories.
Two different techniques are available, and
the one chosen depends upon the sensitivity and
reproducibility desired. For the highest sensi
tivity a short arc of 2-mm length is used, and
751
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spherical quartz condensing lens. The effective
instrumental speed is regulated by the use of
rectangular apertures over the condensing lens.
As described elsewhere,3 this allows the speed to
be changed during the course of the exposure,
as is important in the detection of traces of the
volatile elements, whose sensitive lines may be
lost unless the photographic speed is high during
the first few seconds of exposure. When com
paring samples of similar general constitution in
order to note minor differences of composition,
a technique of lower sensitivity but better
reproducibility is employed. A longer arc, 4-5
mm, is focused on the collimator lens of the
spectrograph by the condensing lens. Speed
regulation is effected by the use of rectangular
apertures placed over the collimating lens.
These apertures cannot be changed during the
course of the exposure. When high reproduci
bility is desired, it is important that each sample
shall be entirely volatilized, as emphasized by
Slavin4 and others.
In order to photograph sensitive lines of all
arc-sensitive elements with the large Littrow
instrument, it is necessary to take two spectro
grams, one in the wave-length range 5900 to
3100A and the other in the range 3100 to 2360A.
In the former range, Eastman spectroscopic
plates type I-D are used, and in the latter, type
1-0. Plates are developed in Eastman high
contrast developer D-19 and are fixed, washed
and dried in the conventional manner.
Analysis of Spectrograms
Plates are analyzed by comparing the unknown
spectrograms in a Judd Lewis comparator
(Adam Hilger, Ltd.) with standard plates upon
which are marked the ultimate and other sensi
tive lines of the various elements. We have a
file of some 60 of these plates, each of which,
of course, was taken with one or the other of
the two regular instrumental settings. The use
of comparison spectrograms of Hilger's "R. U.
Powder" that show the "raies ultimes," or
ultimate lines, of three or four dozen of the
common arc-sensitive elements has not been
found practical in this laboratory, since sensitive
lines of trace elements may so easily be confused
with weaker lines of the more abundant elements.
752 Much time is saved by using a pair of "elimina
tion plates," on which are photographed and
identified all the stronger lines of the elements
common in agricultural materials, namely,
calcium, magnesium, sodium, potassium, alumi
num, manganese, copper, boron, silicon, phos
phorus, and iron. To this list might well be
added strontium and barium, in trace quantities.
Lines are dotted with colored ink as they are
identified, and the symbols of the appropriate
elements are written in the margin. Of course,
for provisional analysis the plates can be in
spected while still washing, and the presence or
absence of the sensitive lines of a dozen or more
elements can often be noted without delay.
Because of the occurrence of seeming coinci
dences of spectrum lines, to the non-uniform
wave-length sensitivity of photographic plates,
to the wave-length range available, and to the
virtual obliteration of certain regions by cyanogen
bands, the "raies ultimes" are not always the
most sensitive lines, from the point of view of
TABLE II. Estimated composition of a meteorite-like
metallic specimen, and the average composition of iron
meteorites, as given by Watson.!3
ELEME::-.lT
Iron
Nickel
Silicon
Cobalt
Phosphorus
Calcium
Copper
Magnesium
Manganese
Chromium
Zinc
Molybdenum
Sodium
Tin
Aluminum
Sulphur
Carbon SPECTROSCOPIC
ESTIMATION
approx.90%
approx. 1 %
approx. 5%
strong trace
weak trace
trace
strong trace
trace
strong trace
not found
weak trace
trace
trace
trace
trace
not detectable
not detectable CHE:MICAL AVERAGE,
IRON METEORlTES.
PERCENT*
88.3
8.15
0.76
.53
.15
.05
.05
.03
.03
.03
1.70
0.04
* Watson (reference 13, p. 430) states: "Many elements present only
as traces in meteorites have been omitted as being relatively un ..
important. tt
practical spectrochemical analysis. We have
found that in general the "best lines for trace
analysis" are those listed by Milbourn.5
Semiquantitative estimates may sometimes
be made by com paring the unknown spectrum
with that of some substance of analyzed compo-
JOURNAL OF ApPLIED PHYSICS
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graphite electrodes in place), the arc height indicator, the rack with copper and iron electrodes, the prepared graphite
electrodes (protected by inverted test tubes), and the reversing switch in the arc electrical supply line.
sltIon. For example, it was desired to analyze a
piece of iron pipe for copper and molybdenum.
The spectrum of this sample was compared with
that of Hilger's "H.S." brand analyzed iron
electrodes, and it was reported that copper was
present in the sample in amount exceeding 0.1
percent, while molybdenum was present in
amount exceeding 0.01 percent. Subsequent
chemical analysis showed 0.2 percent copper and
less than 0.05 percent molybdenum.
If no analyzed substance of appropriate
composition is available it is still possible to
make semiquantitative estimations, on a some
what a priori basis. The two steps are: first, to
estimate the relative amount of the element
present, in terms of the strength of its sensitive
lines and the degree of development of its
spectrum; and second, to weight this information
in view of the known spectroscopic sensitivity
of the various elements. In arriving at a judg-
VOLUME 11, DECEMBER, 1940 ment of the first point, one must have a knowl
edge of the behavior of the spectrum of each
element as increasing amounts of the element
are present. This, therefore, requires considerable
practical experience founded on a knowledge of
the fundamental theory of spectrum analysis.
Thus equipped, the experienced spectroscopist
will have no difficulty in making these judg
ments, reporting them on a fivefold scale such
as "high, medium, low, trace, not detected."
The writer has found that he can reproduce such
judgments with only minor changes after months
or years have elapsed. The relative arc-sensitivity
of the various elements has been given by Ryde
and Jenkins. 6 It has been found that each step
in sensitivity of a factor of 10 corresponds
approximately to one of the steps in the scale-of
five given for the development of the spectrum.
Combining the original estimate and the weight
ing in terms of spectral sensitivity, the final
753
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Table I gives an example of the results obtained
by the application of this method, as do Tables
II and Ill.
Applications to Agriculture
Chemical methods are used regularly and
succe,?sfully in agriculture to determine the
major plant nutrients: nitrogen, phosphorus,
potassium, calcium, magnesium, and so forth.
The use of the spectrograph is, therefore, rele
gated ordinarily to the determination of the
so-called minor elements: those that are essential
to normal plant growth but are needed in only
minute amounts. Hoagland7 has recently given
a good review of this subject. He favors the
term "micronutrient elements." Boron, copper,
manganese, and zinc are now accepted as
"minor" essential elements, and others such as
molybdenum have been suggested. Traces of
cobalt are essential for animal nutrition, so its
presence in plant material is of interest. It should
be noted that the beneficial effect of certain of
the minor elements changes to a toxicity when
they are present in only 5 or 10 times the
concentration necessary for normal plant growth.
Therefore, not only the lower but also the upper
limit of concentration should be determinable.
In an article entitled "The role of the spectro
graph in the analysis of agricultural materials"8
the writer has set forth the principal advantages
of the spectrograph in this field, and has given
a number of examples of its use. An all-important
point, when analyzing such materials for trace
elements, is to reduce the chance of accidental
contamination by giving the sample the mini
mum amount of treatment. The methods of
preparation of various types of materials for
spectrographic analysis will hence be outlined:
(1) SOILS
Fusion analysis of soils to determine the total
amounts of the various nutrients present is
almost a thing of the past, since it is now
known that the availability of the element is far
more important. However,an exception to this
general rule is found in the case of the minor
elements, where total amounts are still deter
mined. In addition to determining these "micro-
754 nutrient elements," the agriculturist often wishes
to have data on certain other elements, such as
arsenic, lead, and fluorine, that may be toxic if
present in too large amounts.
The soil sample is first air-dried, then broken
up with a wooden mallet until it wil1 pass
through a 2-mm screen. It is then spread out
on a large piece of wrapping paper, is mixed
thoroughly, and is quartered repeatedly, until a
representative sample of about 10 grams has
been withdrawn. The IO-gram sample is ground
in an agate mortar until it will pass through a
lOO-mesh screen. A representative sample of a
few milligrams can then be taken from this
finely ground material.
(2) FERTILIZERS
The spectrochemical analysis of fertilizers is
useful in detecting the presence of minor and of
toxic elements, and traces of major nutrient
TABLE III. Spectroscopic estimations and subsequent
chemical determinations for four lava samples. All figures are
percent of total.
BLACK YELLOW GRAY RED
ELEMENT SPEC. CHEM. SPEC. CHEM. SPEC. CHEM. SPEC. CHEM. --------------
Silicon 10 24.21 10 33.52 15 23.73 5 12.06
Aluminum 1 8.12 0.1 0.33 5 7.51 1 13.66
Iron 5 6.79 0.01 0.07 5 8.01 1 14.49
Calcium 10 7.51 0.1 0.074 10 7.59 0.01 0.11
Maq;nesium 1 3.58 0.01 0.006 1 4.05 0.1 0.048
Sodium' 0.01 1.53 N.F. 0 0.01 1.56 0.001 0.19
Potassium 1 0.32 <0.1 0 <0.1 0.72 <0.1 0.10
Titanium 0.5 1.53 10 6.53 1 1.26 0.5 2.16
Zirconium N.F. 0 0.1 0.10 0.05 0.04 N.F. 0
Phosphorus <0.1 0.09 <0.1 0 <0.1 0.10 <0.1 0.12
Chromium 0.1 0.039 om 0.025 0.05 0.050 0.05 0.138
Vanadium 0.1 0.037 N.F. 0 0.01 0.040 N.F. 0
Nickel 0.01 0.035 N.F. 0 0.01 0.013 0.01 0.018
Copper 0.1 0.079 0.01 0 0.1 0.053 0.1 0.055
Manganese 0.5 0.112 N.F. 0 0.5 0.255 0.1 0.107
Strontium om 0.017 N.F. 0 0.01 0.025 N.F. 0
Barium N.F. 0 N.F. 0 0.01 0.009 N.F. 0
Cobalt 0.001 I 0 N.F. 0 0.00,5 0 0.005 0
, See discussion in text of low sodium sensitivity.
elements. In many cases the soil may receive
certain minor elements only from fertilizer
applications, and, therefore, it is a matter of
some importance to know their trace composi
tion. This situation has been of greater impor
tance in recent years, since synthetic fertilizers
of rather high chemical purity are being substi
tuted for the natural products that have a large
trace element content. The writer has analyzed
a dozen of the common commercial fertilizers
used in Hawaii in order to determine the identity
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stituents.9 Fully twenty-one elements were de
tected in this investigation, although the spectro
scopic methods were not the most searching.
The method of preparing fertilizers for analysis
is similar to that for soils, except that the
sampling procedure is ordinarily not so laborious.
(3) PLANT MATERIALS
In order to concentrate the mineral portion of
plant materials, they are ordinarily ashed, there
by destroying the organic matter. This ashing
is done in platinum dishes, and at low tempera
ture so that the more volatile elements will not
be driven off. Wet ashing may be faster, but it
involves the use of reagents, whose trace im
purities must be carefully determined, and
should be checked from time to time. In quali
tative spectroscopic analysis the use of reagents
should be kept down to the minimum, since the
impurities in the reagents may be the very
elements concerning which information is desired.
Examples of the analysis of sugar cane have
been given elsewhere8.n by the writer. One series
attempted to determine the distribution of
mineral elements throughout the sugar cane
plant by comparing ash samples of leaves and
various parts of the stalk. A preliminary surveyl0
indicated that the lower part of the stalk
contained the highest concentration of minerals.
It was then realized that this state of affairs
was doubtless more apparent than real, due to
the variation in ash content of different parts of
the plant. The older stalk material is heavier in
sugar and, therefore, gives a much smaller ash
than does any other part of the plant. In an
effort to overcome this difficulty, the spectra of
ash samples of different weights were compared,
the weights being those representing equal
weights of oven-dry material. Data furnished by
A. S. Ayres, Assistant Chemist, Experiment
Station H. S. P. A., were used in making these
computations, and final analyses were made on
samples taken from a single stalk of 16 months
old sugar cane. 1.0 mg of dry leaf cane ash
(24 hours at 300°C), was compared spectro
graphically with the following ash weights:
1.6 mg of green leaf cane, 4.4 mg of nonmillable
top, and 6.2 mg each of green leaves and dead
VOLUME 11, DECEMBER, 1940 leaves. Chemical results for the major elements
phosphorus, potassium, calcium, magnesium and
silicon, and spectrographic results for nine minor
and trace elements, are presented and discussed
elsewhere.!l This type of comparison, which
involves different weights of the various samples
and hence quite different arc-burning conditions,
doubtless pushes the present technique to its
very limits.
(4) MISCELLANEOUS AGRICULTURAL MATERIALS
Analyses of a number of these are given in
the article already referred to.8 Liquids require
no preparation for analysis, for they can be
tested directly by soaking the ends of the
electrodes in the solution, or by transferring a
droplet into the lower electrode cavity with a
pipette. Aqueous solutions can be concentrated
by evaporation in platinum over a hot plate or
a water bath. The mineral content of a more
viscous liquid, such as a sugar sirup, can often
be concentrated by low temperature ashing,
perhaps preceded by caramelization over a
hot plate.
Applications to Geochemistry
Rock samples are ordinarily analyzed by the
chemical methods recommended by Washington,
Hillebrand, and others. The ten elements oxygen,
silicon, aluminum, iron, calcium, sodium, potas
sium, magnesium, hydrogen and titanium ac
count for over 99 percent of the earth's crust,
according to Clarke and Washington.2 In order
to achieve sufficient accuracy, these elements
must be determined chemically, as must phos
phorus, which is not sensitive spectroscopically.
The less abundant elements chlorine, carbon,
sulphur, and perhaps fluorine cannot be deter
mined with the present spectroscopic technique,
hence other methods must be used. The chemical
method for manganese is straightforward and
accurate. However, the minor metallic elements
barium, chromium, zirconium, vanadium, stron
tium, nickel, copper, etc., are present in amounts
of less than 0.1 percent in the "average igneous
rock," and hence lie within the accurate ana
lytical range of the spectrograph. Chemical
determinations for these elements are laborious,
and larger samples must be used. It is here
755
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since with a single 20-mg sample of finely
powdered material the spectroanalyst can estab
lish within a few hours the identity of all of the
metallic trace constituents. Entirely unsuspected
constituents are as likely to be found as are the
well-established ones. The knowledge of what
elements are present in trace amounts should
certainly shorten the work of the chemist, and
he need not run his samples at all for the metals
not found by the spectroscopist. Furthermore,
the semiquantitative spectrographic information
will allow him to adjust his methods in order
more accurately and readily to make these
sometimes difficult quantitative determinations.
Indeed, if the amount estimated spectroscopi
cally is equal to or less than 0.001 percent, the
actual amount present will probably not have
to be determined at all, since even with an
allowable error in estimation of a factor of 10,
the amount present would not exceed 0.01
percent, and the element would ordinarily be
termed a chemical "trace." It is the writer's
considered opinion that one who has performed
a number of such spectrochemical analyses on
samples that have previously been analyzed
chemically for major, minor and trace elements
could give for similar samples semiquantitative
estimations on trace elements which should not
be in error by more than a factor of 5. In fact,
rough quantitative spectrographic methods, in
which the average error should not exceed 15 to
20 percent, could be introduced with only a small
amount of additional work. (Certain major
elements already determined chemically could
serve as "internal standards.") However, this
matter is outside the scope of the present
paper, which is concerned only with qualitative
and semiquantitative methods.
It should be remembered that "not detected"
may have different meanings for different ele
ments, since the "detection threshold quantities"
differ considerably. For many elements this
threshold is far below the common 0.01 percent
"trace" designation. Quoting Hillebrand12 re
garding the advisability of the determination of
trace elements: "If present in little more than
traces, that knowledge alone may suffice, for it
is often more important to know whether or
not an element is present than to be able to
756 say that it is there in amount of exactly 0.02
or 0.06 percent."
An added advantage to the analytical chemist
of the present rapid spectrographic technique is
the possibility of testing precipitates for traces
of elements concentrated therein. The chemical
tests may have failed to reveal them because
such small amounts were present, or because
their presence was unsuspected and they were
not sought. Or they may have been incompletely
removed in previous steps of the chemical
procedure.
Of course no geological sample will have
exactly the "average composition of the litho
sphere"! Nor will it always be true that the
identity of all the major constituents will be
known. An example of benefits of determining
what major elements are present is the case of
the "gypsum" mentioned above (Table I).
Another example of the identification of the
major elements occurred when the writer was
asked to analyze a ferrous material which
appeared to be a meteorite. The estimated
composition of this sample is shown in Table II,
along with the average composition of iron
meteorites as given by Watson.13 The analyzing
of such a sample, with iron strongly predominant,
is quite different from that discussed above for
soils and plant materials, where silicon, calcium,
aluminum and the like were the dominating
elements. In the first place, the iron may have a
different effect on the burning of the arc, so that
a priori estimates of amounts of other elements
present in the sample cannot be reported with
confidence until experience has been gained
through the use of chemically analyzed samples.
In the second place, the complexity of the iron
spectrum gives the spectrograms a quite different
appearance, and many of the familiar lines of
other elements are masked by some of the
thousands of iron lines. Analyses must be made
by using the few lines that are not blends with
iron lines, and so judgments of "the degree of
development of the spectrum" become very
difficult.
Table II shows that the spectroscopic estima
tion for the sample and the chemical average for
iron meteorites agree fairly well, except for
silicon and nickel. It might be instructive to
determine the specific gravity of the sample, as
JOURNAL OF APPLIED PHYSICS
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under the metallographic microscope might also
give interesting information, but this is outside
the writer's field. Estimates of amounts of the
various trace elements are not given, due to
lack of experience with ferrous samples. The
spectrograms indicated that the five elements
not reported by Watson were present in amounts
ranging from 0.001 to 0.01 percent.
I t was noted that when this specimen Was cut
or ground so as to expose a fresh metallic surface,
there appeared slowly on the surface a viscous
liquid exudate, which turned into a brownish
powder. This powder was spectrographed, and
seemed to be of about the same composition as
the parent metal, with the exception that the
metal was stronger in phosphorus, magnesium,
and manganese, while the powder appeared to
be much stronger in zinc.
Another example of the value to the chemist
of preliminary spectroscopic analysis is the study
recently completed by Mau and Payne! of the
accelerated decomposition of Kilauea lava by
solfataric gases. A visual examination of the
various specimens, namely the parent rock, the
rock tha twas decom posing in the presence of
steam and carbon dioxide, and the rock decom
posing in the presence of steam, carbon dioxide
and sulphur dioxide, showed clearly that wide
spread changes were taking place and that the
502 gave a different result from the CO2 and
steam alone. Preliminary spectrographic exami
nations of the various samples were made by the
writer, and these showed the process of disinte
gration to be accompanied by the concentration
of certain elements and the depletion of others,
many of them behaving in a totally unexpected
fashion. The amounts of all constituents present,
as shown by the spectrograph, were estimated,
and these data were found to be of great use to
the chemists in selecting and adjusting the
quantitative analytical methods. As an example
of the accuracy that can be expected from such
estimation, these spectroscopic estimates are
given in Table III along with the accurate
values (reduced to element percentages) found
subsequently by Mau and Payne. The "black"
and "gray" samples are the parent, undecom
posed material, and are almost identical in
composition. The "yellow" is the decomposition
VOLUME 11, DECEMBER, 1940 product of "black" lava attacked by steam, CO2
and S02, while the "red" resulted from the
decomposition of "gray" by steam and CO2 only.
The "gray and red" samples were spectro
graphed approximately six months after the
"black and yellow" ones, and with a somewhat
modified technique. Nevertheless the spectro
scopic estimates for the constituents of the
similar undecomposed samples agree more closely
than by a factor of 10 in practically every case.
Only the arc-sensitive elements are listed in
Table III, so the various columns will not total
100 percent. The total time consumed in ana
lyzing the pair of spectrograms for the "gray"
and "red" samples, and making the estimates
given in Table III, was four hours.
Some twenty other minor elements, in addition
to those listed in Table III, were specifically
sought, but their sensitive spectrum lines were
not found. The chemists did not report amounts
less than 0.01 percent, but labeled these "0,"
which gives no indication of the sensitivity of
the various chemical methods. In the spectro
scopic columns the abbreviation "N.F." signifies
"not found." As conservative estimates of the
threshold sensitivities for these experimental
conditions, "N.F." for sodium, nickel and cobalt
means "less than 0.001 percent," while for
zirconium, manganese, vanadium, strontium and
barium it means "less than 0.01 percent."
Judging by the figures for phosphorus, the
limiting spectroscopic sensitivity has been set a
bit too low. On the other hand, it is probable
that the thresholds just stated for cobalt and
nickel are conservatively high, since 0.0001
percent, or one part per million, of these elements
can ordinarily be detected with certainty spectro
graphically. However, the technique employed
in the present analyses was of low sensitivity,
at least for such volatiles as sodium and potas
sium. The instrumental speed was very low, and
therefore such fast burning elements did not
register proportionately; it appears that in
subsequent low speed analyses of refractory
samples the estimated percentage for sodium
should be multiplied by 100. The fact that
potassium was detected in the "black" but not
in the "gray" sample is explained by the heavy
background on the "gray and red" plate. A dark
background effectively conceals many of the
757
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Downloaded to ] IP: 128.240.225.44 On: Sat, 20 Dec 2014 10:19:55weaker lines, and in this case invalidated the
"gray" analysis for potassium.
Fortunately, a number of elements each have
some sensitive lines in one instrumental range
and other sensitive lines in the other range.
Thus the uneven or incomplete burning of a
sample in the exposure in one range is discovered
and can be allowed for. If all the lines of the
elemen t lie in one range, as do those of potas
sium, exposure variations will not be detected,
and duplicate plates or duplicate exposures with
fresh electrodes should be taken. The present
analysis was not run in duplicate, and poor
burning of the arc in the case of the "red"
sample for the visible range plate is suspected,
since the spectra of the major (and refractory)
elements, silicon, aluminum, iron, titanium, and
particularly calcium, were very weak.
In conclusion, attention is drawn to an
application of spectroscopy to petrology. Stand
ard chemical methods have proven the presence
of various trace elements in lavas but have
given no indication whether they are distributed
uniformly throughout the rock or are concen
trated in certain of its mineral constituents.
Information on this distribution is of particular
importance to a petrologist who is studying the
process of magmatic differentiation. The spectro
graph is an ideal analytical instrument for use in this connection, because of its extreme sensi
tivity for many metals and its ability to handle
minute amounts of material, such as fragments
of phenocrysts laboriously separated by hand
from a crushed rock specimen. An example of
the successful use of the spectrograph for this
purpose is a series of analyses performed recently
on samples of the groundmass and of various
phenocrysts of a Haleakala lava. Nickel was
shown by semiquantitative spectrographic anal
ysis to be highly concentrated in the olivine
phenocrysts. Vanadium is restricted to the
pyroxene, but was found in both larger pheno
crysts and smaller groundmass crystals.
Acknowledgments
Thanks are d~e K. T. Mau and Dr. J. H.
Payne for permission to use their analytical data
in Tables I and III. The writer wishes to ac
knowledge the aid of P. L. Gow, Assistant
Chemist, Experiment Station H. S. P. A., who
was in part responsible for the development of
many of the features of the analytical technique
reported here. The enthusiasm and encourage
ment of Dr. F. E. Hance, Chemist, Experiment
Station H. S. P. A., under whose cognizance the
experimental work was carried on, have been
greatly appreciated.
Bibliography
1. K. T. Mau and J. H. Payne, article to be submitted
to J. Geol.
2. F. W. Clarke and H. S. Washington, Proc. Nat. Acad.
Sci. 8,108-115 (1922).
3. S. S. Ballard and P. L. Gow, J. App. Phys. 10, 556-
557 (1939).
4. M. Slavin, Ind. Eng. Chern., Anal. Ed. 10, 407-411
(1938).
5. M. Milbourn, J. Soc. Chern. Ind. 56, 205T-209T
(1937). .
6. F. Twyman and D. M. Smith, Wavelength Tables for
Spectrum Analysis (Adam Hilger, London, 1931),
p. 130.
758 7. D. R. Hoagland, Science 91, 557-560 (1940).
8. S. S. Ballard, Hawaiian Planters' Record 44, 35-48
(1940).
9. S. S. Ballard, Hawaiian Planters' Record 42, 185-195
(1938).
10. S. S. Ballard, Phys. Rev. 53, 689A (1938).
11. S. S. Ballard, Hawaiian Planters' Record 44, 183-186
(1940).
12. W. F. Hillebrand, The Analysis oj Silicate and Carbon
ate Rocks (Bull. 700, U. S. Geol. Sur., 1919), p. 23.
13. F. G. Watson, Jr., J. Geol. 47, 426-430 (1939).
JOURNAL OF APPLIED PHYSICS
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1.1750584.pdf | Lifetime of Fluorescence in Diacetyl and Acetone
G. M. Almy and Scott Anderson
Citation: The Journal of Chemical Physics 8, 805 (1940); doi: 10.1063/1.1750584
View online: http://dx.doi.org/10.1063/1.1750584
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IP: 155.33.120.209 On: Thu, 04 Dec 2014 05:53:19OCTOBER, 1940 JOURNAL OF CHEMICAL PHYSICS VOLUME 8
Lifetime of Fluorescence in Diacetyl and Acetone
G. M. ALMY AND SCOTT ANDERSON
Department of Physics, University of Illinois, Urbana, Illinois
(Received July 3, 1940)
The mean lifetime of the fluorescence of diacetyl vapor
has been determined by direct measurement with a
phosphoroscope to be 1.65 X 10-3 sec. Quantitative meas
urement of the diffusion of the excited molecules from a
beam of exciting illumination, at different pressures, has
also been made and the results are compatible with this
lifetime. Integration of the absorption coefficient over the
band associated with the fluorescence leads, on the other
hand, to a lifetime of the excited state of 10-5 sec. To
explain this discrepancy and other facts known about the
fluorescence various mechanisms are considered, of which
the most satisfactory seems to be this: Following light
absorption, X ---A, the diacetyl molecule goes without
radiation into a long-lived state M, lying near A. Fluores-
THE study of the fluorescence of polyatomic
molecules may lead to information about
their behavior after absorption of light which is
of fundamental importance in understanding
photochemical processes. The fluorescence of the
diacetyl molecule offers such an opportunity for
several reasons. First, the fluorescence of diacetyl
occurs in water solution as well as in the vapor.1
Second, similar fluorescence occurs in several
I I
compounds containing the O=C-C=O group,
e.g., benzil in solution,2 indicating that properties
of diacetyl obtained from a study of the fluores
cence may be to some extent common to a large
class of molecules. The same fluorescence is
found to occur in the vapor of other compounds
containing acetyl radicals (CHaCO), e.g., ace
tone, when they are radiated with light which
will decompose the molecules.1·3 Third, the
fluorescence is strongly quenched by oxygen,!
the oxygen being consumed. Thus a process of
photo-oxidation can be studied by means of the
fluorescence. Fourth, there is the practical
reason that the green diacetyl fluorescence is
especially easy to study. It is excited intensely
by the Hg arc groups of strong lines near
AX3650, 4047, 4358 and it can readily be observed cence occurs only upon return to A. M may correspond
to a tautomeric rearrangement of the molecule. Acetone,
radiated with ),3130, shows fluorescence identical with that
of diacetyl radiated with >.4358, but the fluorescence
grows with time. It can be produced immediately with high
intensity by adding diacetyl. The growth curve has been
determined and is of form, 1,=10 (l-e-kt). Diffusion
experiments show the lifetime of the fluorescence in
acetone to be equal to that in diacetyl and that the life
time, or rate of decay, is independent of exciting intensity.
The conclusion is that the same molecule, presumably
diacetyl, is responsible for the fluorescence in both cases.
Possible mechanisms for the excitation of diacetyl in
acetone are discussed.
by visual, photographic or photoelectric methods.
In a previous study! several properties of the
fluorescence were observed and could be ac
counted for by the assumption of a simple
fluorescence process. Rough estimates of the
lifetime of the excited molecule were compatible
with this model. Further experiments, which are
the subject of the first part of this paper, have
led to more accurate determinations of the
lifetime of the fluorescence, which proves to be
much longer than the rough estimate, and also
much longer than one would estimate from the
probability of the transition between the states
involved in the absorption leading to the fluores
cence. Various possible implications of these
facts have been considered and the most satis
factory interpretation is the introduction of a
long-lived state, with approximately the same
energy as the state reached on absorption, into
which the excited molecule can go for a time,
before returning to the original excited state to
emit the fluorescence.
In the second part of the paper some experi
ments are described which have to do with the
fluorescence of acetone and acetone-diacetyl
mixtures. They establish further the identity
of the emitting molecule, very probably diacetyl,
1 Almy, Fuller and Kinzer, J. Chern. Phys. 8, 37 (1940). in the fluorescence of diacetyl and acetone
2 P. R. Gillette, Master's Thesis, University of Illinois, vapors. They throw some light on the question
1939.
3 Matheson and Noyes, J.Am. Chern. Soc. 60, 1857 (1938). of the process of excitation in acetone.
805
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IP: 155.33.120.209 On: Thu, 04 Dec 2014 05:53:19806 G. M. ALMY AND S. ANDERSON
FIG. 1. Phosphoroscope arrangement to measure the
lifetime of the fluorescence. A, high pressure water-cooled
mercury arc. 52 and 53, radial slots in the disk D. C, fluores
cence chamber, PI, reversing prism. V, visual photometer.
DIRECT MEASUREMENT OF LIFETIME
WITH PHOSPHOROSCOPE
To obtain a direct measurement of the mean
lifetime of the fluorescence we employed the
phosphoroscope shown in Fig. 1. It consisted of
a disk D, 30 cm in diameter, with radial slots
1 mm wide spaced every 4° around the cir
cumference, rotated by a direct-current motor
whose speed was varied by a resistance in the
primary. The speed of the disk was measured
with a tachometer. The arc at A was a General
Electric high pressure water-cooled arc with a
quartz envelope. This was focused through a
filter onto the slit 51 which had its image focused
upon a slit in the disk. An image of the latter
was formed in the Pyrex chamber C into which
the vapor was introduced. The fluorescence oc
curring at F was focused on a slit 53 opposite 52
by means of the prisms PI (for reversing the
image), P2, and the lens L4• This lens was pro
vided with a calibrated scre~ adjustment. The
point of focus could be arranged so that when
the disk was turning at a constant velocity, one
could view the fluorescence through 53 a measur
able time after the exciting light was cut off at
52. Thus by measuring the intensity of the
fluorescence coming through 53 with the visual
photometer V, the intensity of the fluorescence
still left at measured times after excitation could
be determined. The photronic cell at M enabled
us to check the variation in the intensity of the
exciting arc, which proved .to be negligible. The
voltage on the bulb in the visual photometer was
kept constant. Employing this phosphoroscope we measured
the decay of the fluorescence in diacetyl at room
temperature (26°C). It was found that the decay
was exponential in time; when log It! 10 was
plotted against delay time a straight line was
obtained, of which the negative reciprocal of the
slope is the mean lifetime (7). The data for six
runs gave a mean lifetime for the fluorescence
of 1.65±0.2X10-3 sec. at 26° C. There was no
perceptible variation with pressure.
To study the variation of the lifetime with the
wave-length of the exciting light we inserted
filters at Fl. For light of the longer wave-lengths
we employed a Corning N oviol glass which
transmits about 5 percent of 3800A increasing
to 70 percent at 4400A. The Corning 986 glass
was inserted to transmit wave-lengths less than
about 4000A. There was no appreciable difference
in the two lifetimes measured and they were
each in agreement with the measurement
previously made with the full arc. It should be
noted here that in both of these cases the
intensity of the incident light was much less
than when employing the full arc as in all the
previous measurements. This indicates that the
lifetime is independent of intensity; a point
which is verified in experiments on diffusion of
the fluorescence to be described later.
The lifetime for the fluorescence of diacetyl
in an aqueous solution was also determined. The
results of one attempt, with a concentration of
1 part in SO, revealed a much shorter lifetime
of the order of 6 X 10-· sec. '
DIFFUSION OF FLUORESCENCE
An altogether different means of gammg
information concerning the lifetime of fluorescing
molecules is a quantitative study of the diffusion
of excited molecules before fluorescing. Heil4 and
Almy, Fuller and Kinzerl performed such an
experiment to secure qualitative values of the
lifetime for fluorescence of N02 and diacetyl,
respectively. We have refined this experiment
by making a quantitative measurement of the
fluorescence intensity and hence of the distribu
tion of the excited particles since the intensity
is proportional to concentration of the excited
particles. From an analysis of the diffusion
4 Heil, Zeits. f. Physik 77,563 (1932).
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IP: 155.33.120.209 On: Thu, 04 Dec 2014 05:53:19FLUORESCENCE IN DIACETYL AND ACETONE gO,
pattern, the product of the diffusion coefficient
(D) and the lifetime (r) is obtained. Thus, as
suming a reasonable value of D, we can calcu
late r or, conversely, using the value of r meas
ured directly with the phosphoroscope, D and
thus the collision cross section of excited against
unexcited particles, is determined. These meas
urements were carried out on diacetyl.
The experimental arrangement is shown in
Fig. 2. The high prt!ssure mercury arc was placed
at A. A uniformly illuminated slit at S was
focused in the center of the Pyrex chamber C.
The beam of light in the chamber as seen by the
camera had the dimensions shown in the inset at
(A). At low pressures of diacetyl the excited
molecules diffused out into the shadow before
fluorescing. The resulting fluorescence pattern
was photographed. The distribution of intensity
in the diffusion pattern was obtained by photo
graphic photometry.
The interpretation of these diffusion patterns
is as follows. Consider a beam of excited mole
cules initially between the infinite planes x = 0
and x= -b. The rate at which the concentration
will vary in space if these molecules are per
mitted to diffuse out of the beam is given by the
usual diffusion equation
(1)
subject to the boundary conditions that at t=O
c-fa for -b<x<O -lO for x>O and x< -b,
where C is the concentration of excited mole
cules. These boundary conditions correspond
physically to the situation in the chamber about
10-2 sec. after illumination begins, i.e., the con
centration of excited particles in the beam has
come to equilibrium but no diffusion has oc
curred. A solution of this equation under these BANTAM CAMERA (A)
1-~-cNl
]~T
1--3.6 CN-i
DIMENSIONS OF IMAOE AT 1
FIG. 2. Apparatus for studying the diffusion of the
fluorescence. A, high pressure arc. C, Pyrex chamber.
F2, Wratten 12 filter. The inset (A) gives the actual dimen
sions of the image at I with high diacetyl pressure in
the tube.
conditions is seen to be
(2)
Therefore, if t represents the elapsed time since
the molecules were excited and q represents the
number per cc that are excited per second in
the beam, then under equilibrium conditions
the contribution (dC) to the concentration at x
from molecules having been generated in the
previous interval of time between -t and
-t+dt is given by the expression (2) if a is set
equal to qdt. If the excitation of the molecules
takes place only when they are in the beam, the
fraction that will still be excited at time t is
e-t/T, where 'f is the mean lifetime of the excited
molecules. Now in the steady state the molecules
at x may have received their excitation at all
previous times between 0 and CIJ. Therefore the
concentration of excited molecules (C*) at x
after the equilibrium is attained is given by the
equation
q foo {1eXH)/2eDt)i 1"/2eDt)! } C*=- e-t/T e-fJ'd{3- e-fJ2d{3 dt.
Y'll" 0 0 0 (3)
Performing the integration with respect to {3 by parts, we have
qr 100 e-x2/4Dt-t/T qr(x+b)foo e-ex+b)2/4Dt-t/T
C*=-x dt- - dt. Y'll" . 0 4yDt! Y7T 0 4yDti (4)
If m the first integral we let t/r=A2w-2, where A2=X2/4Dt and in the second let t/r=B2ur2,
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where B2= (x+b)2/4Dr we get
(5)
Therefore qr, , C* =_e- x/(DT)'(l_e- b/(DT)'). (6)
2
Since the intensity of the fluorescence at any
point is proportional to the concentration of
excited particles at that point, we can write
log C*/Co*=log 1/10= -x/CDr)!, (7)
where Co* is the concentration at the edge of the
beam, 10 the intensity of fluorescence there, and
I the intensity of the fluorescence at any point x.
If we reduce this to atmospheric pressure we have
log 1/10= -x(P/760D or)!, (8)
(A)
15.11.
0.13 ••
OJ5 •• 0.02 WII
~
0.01 ••
0.15 ••
FIG. 3. Microphotometer traces of diffusion pattern of
fluorescence in diacetyl at the pressures indicated. A, pat
tern at high pressure; B, C, D, used to determine DOT in
Fig. 4. E and F used to show T independent of exciting
intensity. F (IS-second exposure) obtained with nine times
intensity used in E (3-minute exposure). where p is the pressure of the vapor, and Do is
the diffusion coefficient at atmospheric pressure
at the temperature of the experiment (26°C).
Thus, plotting (760/p)t log 1/10 against x, we
should get a straight line, the negative reciprocal
of whose slope should equal (Dor)!. If by an
independent measurement one or the other of
these two quantities is known, the other is
determined.
Microphotometer traces of" the diffusion pat
terns for four diacetyl pressures are shown in
Fig. 3. In Fig. 4, (760/p)! log 1/10 is plotted
against x, the distance from the edge of the
illuminated beam, which is sharply defined at
high pressures. The data at three pressures are
used and all fit reasonably well on the same
straight line, as predicted. The slope of the line
is l/(Dor)!, according to Eq. (8). From the
estimated slope one finds Dor=5.34X10-6 cm2•
No value of Do for diacetyl is available, for the
diffusion of either excited or unexcited molecules.
Neither has the coefficient of viscosity been
measured from which D, equal to 1// p could be
estimated. For several somewhat similar mole
cules 1/ is about 10-4 c.g.s. units; for acetone it is
0.95 X 10-4• Assuming 1/=10-4, Do is 2.7XI0-2
and r=2.0XlO-3 sec., in good agreement with
the lifetime measured with the phosphoroscope.5
Conversely, assuming r = 1.65 X 10-3 sec., the
value found by the phosphoroscope method, we
calculate the value for Do to be 3.2 X 10-2
cm2/sec. as the diffusion coefficient of excited
diacetyl molecules among unexcited ones. Using
the kinetic theory relation between the diffusion
coefficien t and collision cross section (S), 6 we
calculate a value of S=11.2X10-15 cm2 which
for spherical molecules is equivalent to a col
lision diameter of 5.9A. This is roughly what one
would expect for unexcited molecules of this
mass and structure.
This apparatus was well suited for detecting
any change in lifetime for fluorescence under
different intensities of excitation. Since the
diffusion pattern is determined by the product
Dor, any change in r would be reflected in the
• From visual observation of the fluorescence pattern
(reference 1) the lifetime had been estimated to be 10-· sec.,
or longer. The quantitative measurements show the visual
method to be unreliable.
6 See, for example, Kennard, Kinetic Theory of Gases
(McGraw-Hill, 1938), p. 194.
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diffusion pattern. With a given pressure of
diacetyl in the chamber we took pictures of the
fluorescence with different intensities of the
exciting light. Since the intensity was lowered
by the interposition of screens at Fl, the time of
exposure of the films was increased by such an
amount that the maximum blackening was the
same on all plates. Fig. 3 shows the micropho
tometer traces of two such plates for which the
intensity of the exciting radiation differed by
ninefold. It is obvious that the two traces are
almost identical, showing that the lifetime does
not depend upon the intensity of the exciting
light.
LIFETIME ESTIMATED FROM INTEGRATED
ABSORPTION COEFFICIENT
To shed more light on the processes associated
with the fluorescence of diacetyl, the lifetime of
the state reached on absorption was determined
from the absorption coefficient integrated over
the band which is connected with the fluores
cence. In a molecule the complete band system
arising from a single electronic transition corre
sponds to a single line in an atomic spectrum.
If the spectrum is continuous or consists of
lines so close together as to overlap throughout
the absorption band, the integrated absorption
coefficient, fkvdv, can be obtained by measuring
ku at various wave-lengths, plotting it as a
function of wave number, and integrating
graphically over the band. The lifetime is
calculated from the relation7
n 1
T =--g' / g"---,
871"cv2 fkudV (9)
where n=2.7X10l9 molecules per cc; kv=ab
sorption coefficient, defined by Iu=Ivoe-kul, l
being the path in cm of gas at O°C and one at
mosphere pressure; v = wave number, cm-l;
g', g" = statistical weights of upper and lower
states.
To obtain the absorption spectrum of diacetyl
vapor we employed the same high pressure
mercury arc used in the other experiments. The
various regions of the spectrum were selected
by the use of a quartz monochromator whose
7 See Mulliken, J. Chern. Phys. 7, 14 (1939) for a
summary of intensity relations. O~--------------------------~
Ll .0IMM
Q.02MM
X .13MM
Q," '534 X lo-bl
. -" -50
:; -100
.J
-150 A
o~
A
o
-200~--------~~--------~~~----~IA
X IN eM
FIG. 4. Plot of data from the diffusion of the fluorescence.
Data taken with three pressures of diacetyl, 0.01 mm,
0.02 mm, and 0.13 mm, all at temperature of 26°C. Slope
of straight line equals -lj(DoT)!. .
exit slit was focused through a Pyrex cell con
taining the vapor onto a potassium hydride
photo-cell. Each setting of the monochromator
admitted a spectral range of approximately 100A.
The plot of kv against v is given in Fig. 5.
The area under the curve is 7340 cm-2• The
assumption was made that the spectrum could
be treated as continuous. This assumption was
tested (1) by showing that Beer's law holds over
a pressure range of 43 mm to 0.01 mm and (2)
by comparing the integrated absorption coeffi
cient with that obtained from data taken by
Lardy8 for diacetyl in hexane solution, in which
case the lines of the band system should be
considerably broadened. The area under the
curve from Lardy's data is 7265 cm-2• This is
subject to an increase of about twenty percent
on account of a correction factor (no2+2)2/9no,
. where no=the index of refraction of the solvent,
which must be applied in the case of absorption
spectra of solutions. 9 The agreement is certainly
close enough to justify the use of f kvdv of the
vapor in calculating the order of magnitude of T.
8 Lardy, Dissertation, Zurich (1924).
9 Chako, J. Chern. Phys. 2, 644 (1934).
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Substituting our value of fkvdv in Eq. (9), T
comes out to be 8.5 X 10-6 second, if we assume
g' / gil = 1. There may be a large error in this
last assumption but in any event the order of
magnitude of the lifetime of the upper state of
the absorption transition required by the in
tegrated absorption coefficient is 10-5 sec. This
is a hundred times smaller than the directly
measured mean life of the fluorescence.
DISCUSSION OF DIACETYL FLUORESCENCE
The most important facts concerning the
fluorescence of diacetyl vapor from the present
and previous work can be summarized as follows.
The fluorescence is produced by absorption
within the band extending from }"3500 to },4650.
The fluorescence consists mainly of three bands,
with fine structure, with maxima at }"}"5120,
5610, 6135. There is a gap between fluorescence
and absorption in which both are very weak, if
present at all.
The spectrum of the fluorescence of diacetyl
vapor is independent of pressure (0.1 mm to
60 mm), temperature (10° to 100°C), exciting
wave-length (X3650 -A4358) and the pressure
of added gases.
The quantum yield of the fluorescence is
about 0.035 at A4358, 0.03 at X3650. The yield
at },4358 is independent of the exciting intensity
and pressure. Henriques and Noyes!O find that at
X3650 the yield is enhanced by increasing the
pressure.
The mean lifetime of the fluorescence in the
vapor is 1.65 X 10-3 sec. On the other hand, the
lifetime corresponding to the integrated absorp
tion coefficient over the band associated with
the fluorescence is about 10-5 sec. The lifetime
of the fluorescence is independent of pressure
and exciting intensity as shown by both phos
phoroscope and diffusion experiments.
The lifetime and the quantum yield both
decrease as the temperature is increased, but
with different temperature coefficients.
The radiation which excites the fluorescence
(at least up to A4358) is also capable of decom
posing the molecule, eventually into CO and
hydrocarbons.
10 Henriques and Noyes, J. Am. Chem. Soc. 62, 1038
(1940). In view of the available experimental facts,
what is the most likely mechanism of the fluores
cence emission? Three sorts of process have been
considered. (1) Simple fluorescence, that is to
say, absorption, followed by vibrational redis
tribution and then, reemission. (2) Delayed
fluorescence, in which absorption (call it X~A)
is followed by transition into a long-lived state
(M) lying near· state A. Fluorescence occurs
only when the molecule is returned by collisions
to a state, presumably A, which can combine
with the ground state. The long-lived state
might be a tautomeric form of the diacetyl
molecule. (3) Processes involving the recombina
tion or reaction, of radicals, or radicals and
molecules.
Of these three types of mechanism, (1) and
(3) can be shown to be very improbable. Simple
fluorescence, while adequate to account for
many of the observed facts,! will not admit
the results of measurements of lifetime. The
mean life of the fluorescence is 1.65 X 10-3 sec. ;
the quantum yield is only 0.035 which means,
on this mechanism, that while the molecule
IS in the excited state a competing process is
~~------------------------------,
2, -HEXANE SOLUTION(LARDY)
. __ ••• VAPOR
2,1 2.2 2.3 2.4 2.5 2,6 2.7 2.8 2.9 3..0
-u IN CM-1 X 10·'
FIG. 5. Absorption spectrum of diacetyl. Solid line
plotted from data taken by Lardy on diacetyl in a hexane
solution. Broken line determined for diacetyl vapor.
kv, absorption per cm path at atmospheric pressure.
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about 30 times as probable as the fluorescence.
I t is, therefore, the competing process which is
mainly responsible for the observed rate of
decay; the lifetime against fluorescence must be
30 times that observed, or about 0.05 sec. On
the other hand, the lifetime against the same
transition, estimated from the absorption coeffi
cient, is 10-5 sec. This large discrepancy rules
out this simple process.
The third type of mechanism involving the
recombination of radicals or the attack of
molecules by radicals might conceivably occur
in many different ways. Of these, emission ac
companying a recombination of radicals IS
excluded by the following arguments:
(1) It has been shownl that the density of
radicals under the conditions used cannot be
great enough to account for the observed rate
of decay.
(2) In such a bimolecular process, the rate of
decay of the fluorescence should be smaller the
lower the initial concentration of radicals, that
is to say, the lower the exciting in tensi ty. It
was observed, however, especially in the diffusion
experiment, that the rate of decay was inde
pendent of intensity. A ninefold change in
intensity caused no change in the form of the
diffusion pattern, hence no change in the rate
of decay. In such a process, moreover, the decay
curve should not be exponential, as observed.
(3) Dilute aqueous solution (e.g. 1 : 200) of
diacetyl fluoresces strongly. Under these condi
tions the recombination of radicals (except of
those just separated) should be greatly hindered.
(4) The slow growth of the identical fluores
cence in acetone (described below), as contrasted
with its immediate appearance in diacetyl is
difficult to understand if the emission is a
recombination spectrum. It should not require
minutes or hours in one case, about 10-3 sec.
in the other, to establish equilibrium between
production and recombination of the same
radicals.
The first three of these arguments apply also
against a process of chemiluminescence, in
which the energy released in a bimolecular
reaction between radicals excites a third mole
cule. Argument three (occurrence of fluorescence
in dilute aqueous solution) also applies against
chemiluminescence caused by the energy re-leased in a radical-diacetyl reaction going to
excite another diacetyl molecule. This argument
is against any process which involves the diffu
sion of radicals before reaction.
Still another possibility of this type is the
formation of an excited molecule by a sticking
collision of a radical and a diacetyl molecule,
which compound molecule later emits the
fluorescence. If the slow rate of decay measures
the rate at which effective collisions of this type
occur the rate should depend upon the pressure
of diacetyl; no variation of lifetime with pres
sure is observed (Fig. 4). If, on the other hand,
the effective collision requires only a short time,
say 10-7 sec. at 1 mm pressure, the problem
of accounting for the long observed lifetime has
merely been transferred to another molecule.
The second mechanism suggested, delayed
fluorescence, is capable of accounting for all of
the observations. In this process diacetyl ab
sorption (X~A) is followed by a transition
without radiation into a long-lived state M,
which may be a tautomeric form of the molecule,
separated by a potential barrier from state A.
The chemical reactions which have been ob
served, decomposition and photo-oxidation if
oxygen is present, may occur while the molecule
is in either state A or M. Fluorescence occurs
when the molecule returns to a state, presumably
A, which can combine with the ground state X.
The state A reached on absorption is the one
described by McMurry and Mullikenll as
forbidden by electronic selection rules to com
bine with the ground state. The lifetime of
10-5 sec. against this transition, which we com
pute from the absorption coefficient, is com
patible with this assignment.
This mechanism is similar to the one proposed
by Henriques and Noyes.1° They introduce
three excited states: BO, corresponding to state A
here, the state reached on absorption; BI,
analogous to our metastable state M; and B2
from which fluorescence occurs and which in our
model is a low vibrational level of electronic
state A. At }.36S0 they find the fluorescence
intensity increases with increasing pressure.
This may be due primarily to the rapid removal
of vibrational energy by collisions, reducing the
11 McMurry and Mulliken, Proc. Nat. Acad. Sci. 26, 312
(1940).
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FIG. 6. Plate showing growth
of green fluorescence in acetone
under X3130 radiation. Spectra
1-6, density marks. Spectra 7-15,
consecutive one-minute expo
sures during first nine minutes
of excitation of static acetone.
Spectrum 16, taken during 10th
minute of radiation with glass
plate transmitting only X>3400A
before arc. Spectra 1-16 on
Eastman 40 plate. Spectrum 17,
mixture of 14 mm diacetyl and
99 mm of acetone, five-minute
exposure with X3130 excitation.
Spectrum 18, same as in 17 with
glass plate as in 16. Spectrum 19,
flowing acetone with mean pres
sure of 108 mm, five-minute ex
posure with X3130 excitation.
Spectra 17, 18, and 19 all on
Eastman 50 plate.
probability of chemical processes, such as
decomposition, and thereby enhancing the
chance of fluorescence. When the molecule is
excited with M358 the initial vibrational energy
is much less and the effect of pressure in shifting
the relative probabilities of chemical processes
and fluorescence may be negligible.
The simplest adequate form of our proposed
mechanism is one in which it is assumed that the
processes competing with the fluorescence for
the excitation energy all occur in state A,
rather than M. In this case the fluorescence
quantum yield is given by Itlh=kv/(kv+kc)
where kv is the probability of fluorescence and
kc is the probability of the occurrence of a
competing process. The lifetime is then de
termined primarily by KMA, the rate of return
from M to A. This mechanism allows the intro
duction of two activation energies: Ec in kc and
EMA in kMA, which control the temperature
dependence of the competing chemical process
and lifetime, respectively. From the roughly
measured dependence of yieldl2 and lifetime
12 Unpublished measurements of Almy and Gillette.
Also measured by Henriques and Noyes (reference 10) who
found a somewhat more rapid change with temperature. (l/kMA) on temperature, from the observed
quantum yieldl3 (0.035) and kv (l05 sec.-I), one
can calculate, Ec= 2100 cal. per mole, EMA =3900
cal. per mole, kc = 28 X 105 sec.-I.
One can easily write down the kinetic equa
tions for the case in which chemical changes
occur in both states A and M, with rates de
pending on temperature. No simple interpreta
tion, as in the above case, can be inferred from
the more complicated expressions for yield and
rate of decay.
EXPERIMENTS WITH ACETONE
It has recently become clear that the green
fluorescence observed when acetone is radiated
with X3130 is identical with the fluorescence of
diacetyl when radiated with X4358. Not only do
the same three broad bands appear in the spec
trum in both cases, but the finer superimposed
structure is identical.I Matheson and Zaborl4
have also shown that several compounds con
taining the radical CH3CO, e.g., acetaldehyde
and methyl ethyl ketone, have a similar fluores
cence spectrum. In addition there is chemical
evidence that diacetyl is present in acetone after
radiation with X3130.I5,16
If the fluorescence in acetone is due to the
accumulation of diacetyl under the action of
light the fluorescence should grow from zero
intensity with continued radiation, To de
termine the course of growth of the fluorescence,
~ ______________ ~o.o
4
TOTAL EXPOSURE TIME IN MINUTES -10
= -20 ..i
:;;.
-3.0 ~
-4.0 o -'
FIG. 7, Typical growth curve of green fluorescence in
acetone radiated with X3130. Points determined from
Fig, 6 by taking the integrated intensity of each successive
interval as the intensity for the midpoint of that interval.
Full curve: intensity of fluorescence, If, Dotted curve:
log (1-IJI 10), 10= final intensity.
13 Fuller, Phillips and Almy, J. Chem, Phys. 7, 973
(1939),
14 Matheson and Zabor, J. Chem. Phys. 7, 536 (1939).
1. Spence and Wild, J. Chem. Soc, 352 (1937).
16 Barak and Style, Nature 135, 307 (1935).
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~ (Al
165MM
.27MM (8)
.26MM
FIG. 8. Microphotometer traces of diacetyl, and diacetyl
acetone mixtures. (A) 150 mm of acetone plus 15 mm of
diacetyl, one-second exposure; (B) 0.26 mm pressure
(1 part diacetyl, 10 parts acetone), ten-minute exposure;
(C) 0.27 mm of diacetyl, fifteen-second exposure; (D) same
vapor as in (B) with exciting intensity reduced to 1,
thirty-minute exposure. A, Band D, ,,3130 radiation;
C, M358 radiation.
thoroughly outgassed acetone was flowed through
a Corex fluorescence chamber where it was
radiated with light from a quartz mercury arc,
filtered by an aqueous solution of the iron-free
sulphates of nickel and cobalt which transmitted
principally the ),,3130 line. The fluorescence
spectrum was photographed with a Steinheil
spectrograph equipped with one glass prism
and an f: 3.5 camera. After getting a spectrogram
of the fluorescence of the flowing acetone, the
flow was arrested and a series of consecutive ex
posures was taken of the fluorescence of the
static acetone. A series of such exposures is
shown in Fig. 6.
From a study of a number of such plates the
following facts appear:
(1) With rapidly flowing acetone radiated
principally with ),,3130, a negligible amount of
green fluorescence is produced. Practically all
the fluorescence is in the blue beginning at
about 4700A and extending toward the ultra
violet.
(2) When the flow of acetone is stopped the
intensity of the green fluorescence grows from
a very low value towards a maximum as is
shown by the successive exposures. With the aid of the density marks the intensity of the
fluorescence in the successive exposures in
Fig. 6 was determined and plotted against time
in Fig. 7. The justification for plotting the curve
through the origin is obtained from a comparison
of exposures 7 and 19. The former is an exposure
taken during the first minute of radiation of
static acetone; the latter is an exposure of five
minutes with flowing acetone at a pressure
about i of the first and on a plate much faster
in the green. This comparison shows that the
average intensity of the green fluorescence in the
first minute of radiation of stationary acetone
is ten to one hundred times stronger than in a
flowing system and that, therefore, one is justi
fied in plotting a point of sensibly zero intensity
at zero time in Fig. 7. In the same figure the
straight line shows that the fluorescence grows ac
cording to the relation 1/=1o(1-e-kt) where 10
is the final intensity, approached asymptotically.
(3) When a little diacetyl is added to the
acetone the green fluorescence appears immedi
ately with full intensity upon radiation with
)"3130 (exposure 17). Furthermore, this fluores
cence is not due to the direct excitation of
diacetyl by a small amount of blue light which
might pass the filter. This is demonstrated by
the disappearance of the fluorescence when a
glass plate transmitting only light of wave
lengths longer than 3400A is interposed.
(4) The blue fluorescence present in a system
of flowing acetone grows weaker on continued
radiation of the static vapor (exposures 1-9).
We attempted in a second experiment to
detect the formation of diacetyl in acetone
radiated by }'3130 by measuring the absorption
of light of wave-length 4358A which is absorbed
by diacetyl but not by acetone. The few rough
trials gave positive evidence of absorption at
),,4358 suggesting that a small amount of di
acetyl was formed, but at most no more than a
partial pressure of a few tenths of a mm. Further
more, apparently an equilibrium between its
creation and decomposition was soon established
for one could get as much absorption of ),,4358
after fifteen minutes of radiation as after several
hours.
In addition to these experiments, we measured
the lifetime for the fluorescence in acetone by
the method of the diffusion of the fluorescence.
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This we did by comparing the diffusion patterns
of an acetone-diacetyl mixture radiated with
X3130 and diacetyl radiated with X4358 at equal
pressures. As seen from Fig. 8 the mictophotom
eter traces of the photographs are identical.
This shows that the lifetime in the two cases is
nearly the same since their diffusion coefficients
surely are not greatly different. We also de
creased the intensity of the exciting light by a
factor of three and compensated by increasing
the exposure time by three and found that the
diffusion pattern is unaltered, indicating (1)
that the lifetime in the case of acetone, as in
diacetyl, is unaltered by the variations in the
intensity of the exciting light and (2) that, as
suming photographic reciprocity, the intensity
of the green fluorescence in the acetone-diacetyl
mixture is proportional to the intensity of the
exciting light. In this experiment there was
present much more diacetyl than occurred in
radiated acetone, even on long radiation.
In conclusion, what can be said about the
origin of the green fluorescence in acetone?
What is the molecule which emits it and by
what process i's it excited? The fluorescence
spectrum is identical in acetone excited by X3130
and diacetyl excited by XX3650, 4047, 4358.
I t does not appear in pure acetone flowing
rapidly. It appears when diacetyl is added or
when, on continued radiation, diacetyl has
accumulated in the tube. The presence of diacetyl
appears to be necessary for the production of
the fluorescence and the simplest assumption
is that the diacetyl molecule is the emitter.
Further relations between acetone and diacetyl
fluorescence are seen in the diffusion experiments.
At the same total pressures the diffusion patterns
of pure diacetyl and acetone plus a small amount
of diacetyl are identical. This means that, as
suming the same diffusion coefficients, the life
times are identical; a ten-percent difference
could easily be detected. This constitutes a
further check on the identity of the emitter or
emitting process in the two cases. RecomQina
tion or chemiluminescence processes are ruled out by arguments given in the discussion of
diacetyl fluorescence. The fluorescence must be
due to a long-lived molecule, presumably di
acetyl, excited while in the illuminated region.
The process by which the diacetyl molecule is
excited must involve a reaction between an
excited molecule and diacetyl. Diacetyl does not
fluoresce with appreciable intensity when radi
ated with X3130 unless acetone is present. Hence,
the simplest picture of the excitation of diacetyl
is a collision of the second kind between excited
acetone and diacetyl. It cannot be that a diacetyl
producing reaction between excited acetone and
another molecule or radical leaves the diacetyl
produced in a condition to emit the fluorescence,
for in that case the fluorescence in pure acetone
should be present almost immediately with full
intensity.
The simple nature of the growth curve of the
fluorescence should shed some light on the
processes of production, excitation, and dis
appearance of the diacetyl. However, just be
cause several steps are involved between ab
sorption by acetone and the appearance of the
fluorescence, there is no series of processes
which will uniquely account for the growth.
QUENCHING EFFICIENCY OF OXYGEN
The fluorescence of diacetyl is apparently
strongly quenched by oxygen,l but recovers in
time, indicating that the oxygen is consumed.
It was shown that an oxygen pressure of 0.013
mm brought the fluorescence to one-half in
tensity. Assuming a collision diameter of 3 X 10-8
cm, a lifetime of the' excited molecule of 10-5
sec. was required to make fluorescence and
quenching collisions equally probable. We now
find, however, that the molecule actually re
mains in an excited state 10-3 sec. Therefore,
abou t 100 collisions (to wi thin 3 X 10-8 cm) be
tween excited diacetyl and oxygen occur, on the
average, before a quenching collision takes place.
The quenching process thus owes its apparent
high efficiency to the long lifetime of the excited
molecule.
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1.1712799.pdf | Growth Conditions for Single and Optically Mosaic Crystals of Zinc
C. A. Cinnamon and Albert B. Martin
Citation: Journal of Applied Physics 11, 487 (1940); doi: 10.1063/1.1712799
View online: http://dx.doi.org/10.1063/1.1712799
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/11/7?ver=pdfcov
Published by the AIP Publishing
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Downloaded to ] IP: 130.70.241.163 On: Tue, 23 Dec 2014 18:51:52for quantitative spectrum analysis shows that
the radiation of all of them is determined by
only one quantity which is either the gas tem
perature or the electron temperature, the latter
of which is in some cases higher, in others equal
to the gas temperature of the discharge. The
excitation energy is therefore distributed among
the excited states of the atoms statistically, and
the number of atoms in the various energy levels
is determined uniquely by the electron or gas
temperature. Consequently the intensity ratio
of two lines is related to the intensity ratio of
two others. A "correlation method" is described, which permits one to work at nonstandardized
conditions (variation of the shape of the elec
trodes, influence of extraneous elements, etc.)
while reducing the measurements to "normal"
(standard) conditions. The method may also be
profitably used under standard conditions to
improve the accuracy of an analysis while
eliminating errors due to accidental fluctuations
in the light sources.
In conclusion, the author would like to express
his sincerest thanks to Professor Mark W.
Zemansky for many helpful discussions and
suggestions.
Growth Conditions for Single and Optically Mosaic Crystals of Zinc
C. A. CINNAMON AND ALBERT B. MARTIN*
Physics Department, University of Wyoming, Laramie, Wyomitig
(Received January 30, 1940)
A modified Kapitza method used in the study of conditions favorable to the growth of single
crystals of zinc (99.99+ percent pure), shows that the ratio of the temperature gradient (across
the interfacial boundary between the liquid and solid phases) to the rate of growth of the crystal
must be maintained within an optimum range of values, depending on the angle of orientation.
Optically mosaic crystals give no indication of a preferred region of growth and can be ob
tained over a much wider range of conditions.
INTRODUCTION
THE modified Kapitza method of growing
single crystals of zinc as described by
Cinnamon! and used by other investigators 2-4 has
met with a fair degree of success. However, a .
more recent application of this method has
resulted in the production of a large number of
optically mosaic crystals5 compared to the num
ber of single crystals.6 In this respect difficulties
arise quite similar to those experienced by investi-
* Now at Yale University, New Haven, Connecticut.
1 C. A. Cinnamon, Rev. Sci. Inst. 5, 187 (1934).
2 W. J. Poppy, Phys. Rev. 46, 815 (1934).
3 H. E. Way, Phys. Rev. 50, 1181 (1936).
4 G. E. M. Jauncey and W. A. Bruce, Phys. Rev. 50, 408
(1936).
5 A description of optically mosaic crystals of zinc and
photomicrographs of natural cleavage surfaces are given
by H. K. Schilling, Physics 5, 1 (1934).
6 A single crystal, when properly cleaved, is characterized
by a single, flat and mirror-like cleavage surface in contra
distinction to the optically mosaic crystal having a
"broken" cleavage surface consisting of discontinuities
caused by two or more slightly inclined areas.
VOLUME 11, JULY, 1940 gators7•8 employing the Czochralski-Gomperz
method.
The study of factors influencing the growth of
single-crystalline zinc, as initiated by Cinnamon,
was but partially completed, in that only the
lower limit to the region of favorable growth had
been determined. The existence of a lower limit
region was later qualitatively confirmed by
Poppy2 and Way,3 who used the same method
and procedure for crystals of approximately the
same size and degree of purity. The growth con
ditions imposed by J auncey and Bruce4 also agree
reasonably well, considering the difference in
cross-sectional area and the possibility of differ
ences in impurities. Poppy, also, found indica
tions of an upper limit to the favorable conditions
as predicted by Cinnamon; however, his data
were not extensive enough to set a definite
7 H. K. Schilling, Physics 6, 111 (1935).
8 J. S. Kellough, "Growth conditions for some zinc-rich
alloys," Thesis, University of Iowa, 1937.
487
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to investigate the upper limit and to determine as
far as possible the complete range of favorable
growth for single and mosaic crystals of zinc.
MATERIALS
The material from which the crystal specimens
were-grown was obtained from two SO-lb. slabs of
Horsehead Special zinc (99.99+ percent Zn). A
spectrographic analysis of the two lots, made by
the New Jersey Zinc Company9 to determine the
relative amounts of the iron and cadmium
present, gave the following results: Lot I con
tained 0.0018 percent cadmium and 0.0017
percent iron; lot II contained 0.0010 percent
cadmium and 0.0010 percent iron.
PROCEDURE
The procedure was the same as that used by
Cinnamon with the following modifications. It
was found more convenient to substit!lte for the
transite cover a thickness of 3 to 4 mm of
asbestos paper placed under a thin sheet-iron
strip of 0.7 mm thickness. This assembly of the
same width and length as the mold could be held
firmly thereto by means of a few single turns of
fine iron wire. The thermocouples were placed at
S-cm intervals along the mold and stem. On the
basis of this length, from preliminary observa
tions, a calculation of the probable error in the
measurement of the ratio of temperature gradient
to rate of growth gave ± 1.3 percent. With this
degree of precision a S-cm section was considered
sufficient to represent the crystal unit under test.
The temperature gradient and rate of growth
were controlled over each S-cm section. These
quantities were measured over the section that
included the interfacial boundary between the
solid and liquid phases. The temperature gradi
ents impressed across different sections extended
from 3.4°C/cm to 12°C/cm. The rates of growth
imposed on the different sections extended from
0.07 cm/min. to 0.34 cm/min.
The crystals grown were approximately one
sq. cm in cross section 10 and varied in length from
9 The authors acknowledge with gratitude the kindness
of the New Jersey Zinc Company in rendering this service.
10 During the course of the investigation two molds were
used; the first, 0.7 em' and the second, 1.2 em'. An examina
tion of the data indicated that the effect of such a variation
488 Scm to 60 cm. A lS-cm length required constant
attention and control for 8 hours; a 60-cm length
required 14 hours.
An improvement in technique was accom
plished by etching the specim~n in a 10 percent
concentrated HCl solution for a period of 2 to 2t
hours. The etching made evident any change in
the angle of orientationll of the crystal as well as
the origin of any superficial mosaic structure.
This technique proved very helpful in the location
of mosaics in crystals of high orientation. Al
though the presence of striations on the etched
surface could be taken as proof that the specimen
was mosaic, the absence of such markings was not
conclusive evidence that mosaic structure was
lacking. This was found to be the case for the
crystals of low orientation, where it became
difficult to observe variations in the character of
the etch. As a final confirmation, all of the single
crystal specimens were cleaved and examined
both optically and by the sun test, as described
elsewhere.1 The cleavage technique was improved
by first cooling the specimen in a mixture of dry
ice and alcohol.
ANALYSIS OF DATA
In the course of the investigation 81 specimens
were grown. Of this number, 39 startea growing
in the main groove of the mold as good single
crystals, while 42 were optically mosaic through
out their length. Four of these 39 crystals experi
enced an abrupt change in the angle of orientation
and continued as single crystals of higher
orientation. Four continued as single crystals for
the entire length of the groove, while the re
maining 31 crystals changed to various types of
optically mosaic, as described by Schilling.5 Oc
casionally some of these mosaics later changed in
orientation. This occurred in approximately 20
percent of all the mosaics grown. Almost in
variably the resulting mosaic was of higher
orientation.
An analysis of these results was obtained, by
taking as the crystal unit, the S-cm section of the
specimen included between the adjacent thermo-
in the cross section of the specimens amounted to less than
the scattering of points along the boundary due to the
slight variation in the impurities of the materials.
11 The angle between the normal to the basal plane and
the length of the specimen.
JOURNAL OF APPLIED PHYSICS
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140
'" 0
+ /
/
+ + / 0
+V~ 00
0 120
v 0
0
+ (
0 <'P ~ r'\
+ 0 let v <co 0 f" @ 0 (
~ 00 ~o ~: ---0 -I:> ~ v ...... C
0 8 o <
8°~ 0 0 0 + 0+ + rn-
+ u~ 40
+ +++ + (!) ~. +
+ + + zo
+
o o ZO 40 60 80 ItJO
O,.ienlolion-(deqree.s)
Osinq/e crljstol(Jcn.); + chal7<fC from sil7'1/e 10
mo",alc;.o. chQl'ICfe of oriientt:llJDn.
FIG. 1. Graph showing the effect of the temperature
gradient (G) and the rate of growth (R), on the propagation
of single-crystalline structure.
couple junctions. If the entire 5-cm section re
sulted in a single crystal, this unit was said to be
"good" and the temperature gradient and rate
of growth imposed over this length were said to
be "favorable." A section in which the single
crystal experienced an abrupt change in orienta
tion was said to have "failed." The temperature
gradient and rate of growth imposed over this
unit were said to be "unfavorable" to the crystal
of the original orientation. Such failures were
identified as type (1). Also, each section in which
a single crystal changed to mosaic was said to
have "failed" and the corresponding temperature
gradient and rate of growth over this unit were
considered "unfavorable." Failures of this kind
were identified as type (2).
The effect of the temperature gradient (G) and
the rate of growth (R), on the propagation of
single-crystalline structure was revealed by
plotting different functions of these two variables
VOLUME 11, JULY, 1940 against the angle of orientation. The most sig
nificant function proved to be of the form, Gm I Rn.
Plotting the simplest form, GIR, against the
angle of orientation for each 5-cm section of
"good" single crystal, together with the corre
sponding data for each section that had failed,
there resulted a distinct separation of points. The
plot is shown in Fig. 1. Each circle represents a
section of "good" single crystal; each triangle, a
section in which the crystal experienced a failure
of type (1), and each cross, a section wherein the
crystal experienced a failure of type (2). The
smooth solid lines shown were placed by inspec
tion and indicate the approximate boundaries to
the region of successful growth.
Other forms of the function, G2 I Rand G I R2,
also gave a distinct region of favorable growth
(graphs not shown), but were not markedly
distinguishable from the plot of G I R. The first
form gave a slightly better definition of boundaries
than was obtained for GIR, while the latter gave
boundaries slightly less defined. Although the
distinction appeared genuine, it is evident that a
far greater range in the values of G and R will
need be imposed, than were used here, in order to
make this difference markedly pronounced and of
practical significance. The boundaries to the
GI R function are sufficiently exact for practical
work and can be readily used as a guide during
the process of growing a crystal. Functions that
gave no indication of a regional separation of
points were (G), (R) and the product (GR).
All the data for the single crystals, together
with that of resulting failures, are represented in
Fig. 1. The data show that temperature gradient
and rate of growth are significant factors in the
growth process of single crystals. They also show
a region of preferred growth, depending on the
angle of orientation. Crystals of high orientation
can be grown over a much greater range of values
in GIR than those of a lower orientation.
Plotting the corresponding data of GIR for
mosaics (crystals that originally started mosaic
from the seed nucleus or in the stem and the
mosaics originating from the failures of type 2)
resulted in no indication of preferred growth con
ditions (graph not shown). Failures appeared at
random, with a maximum frequency of failures
for mosaics orientated between 25° and 60°. The
results indicate that mosaic crystals are not
489
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orientations can be grown over a wider range
than for single crystals. In this respect, mosaics
are more similar in behavior to polycrystalline
zinc than to monocrystalline zinc. This incon
sistency is in agreement with their erratic thermal
and electrical resistivity properties.2•12
CONCLUSIONS
In agreement with the experience of others7• 8.13
the present investigation shows that single crys
tals must be grown under special conditions. The
structure sensitive properties of such crystals are
known to be consistent with definite crystal
lographic relations2.3. 12.14 and thereby indicate
that single crystals approach in reality the
crystal lattice continuum in agreement with the
contention of Buckley.1s Furthermore, these
crystals appear to be free of the lineage structure
proposed by Buerger.16
It is evident that the factors, effective in propa
gating the single-crystalline structure, change
with the angle of orientation and depend on the
relation of the temperature gradient across the
solid-liquid phase boundary to the rate of growth
of the crystalline formation. For a particular
angle of orientation the optimum conditions fall
between a definite maximum and minimum value
of G I R. Such restrictions on the growth of single
crystalline zinc, as compared to the relatively
greater range for mosaics, show definitely that
unless the optimum conditions are imposed, the
crystals obtained are very likely to be mosaic and
thereby lacking in the properties that charac
terize single crystals.
It is to be understood that the results obtained
are for zinc crystals of the size and degree of
purity stated and under the conditions imposed
by this method of growth. A modification in
method, as used by Hasler,11 apparently yields
12 C. A. Cinnamon, Phys. Rev. 46, 215 (1934).
13 A. G. Hoyem and E. P. T. Tyndall" Phys. Rev. 33, 81
(1929).
14 E. P. T. Tyndall and A. G. Hoyem, Phys. Rev. 38, 820
(1931); A. G. Hoyem, ibid., 38, 1357 (1931).
15 H. E. Buckley, Zeits. f. Krist. 89, 221 (1934); 93, 161
(1936).
16 M. ]. Buerger, Zeits. f. Krist. 89, 195 (1934).
17 M. F. Hasler, Rev. Sci. Inst. 4, 656 (1933).
490 different limitations on temperature gradient and
rate of growth.
An investigation of the scattering of points
about the lower and upper boundaries (See Fig.
1) revealed in all cases, with two exceptions,18
that the crosses falling out of place represented
specimens grown from one slab of zinc while the
corresponding circles represented crystals grown
from the other slab. Apparently, the cause of the
scattering is due to the slight differences in the
purity of the two slabs of zinc.
The increase in the iron content over that in
the zinc used by Cinnamon appears to be
responsible for the predominance of mosaics that
originated in the stem of the mold where the
same technique was used as formerly. 1 It also
appears to be responsible for the great number of
failures of type (2) compared to the relatively
few failures of type (1). The lower boundary in
Fig. 1 is entirely determined by failure~ of type
(2), while the lower boundary obtained by
Cinnamon was solely determined by failures of
type (1). It is interesting to note that the two
boundaries fall in approximately the same region
of the graph.
Although observations on growth conditions in
general are incomplete, the present findings
warrant at least two speculations on the probable
significance of temperature gradient and rate of
growth. (1) The temperature gradient and rate
of growth, jointly or separately, must have a
direct internal influence on the system of atomic
forces at the interfacial boundary between the
liquid and solid phases. (2) These factors, jointly
or separately, must have an external effect by
changing the direction of the temperature
gradient across the interfacial boundary. Crystals
of low orientation would be more influenced by
such changes due to the smaller magnitude of the
atomic forces along the direction of growth, while
crystals of high orientation would be less
influenced due to the greater atomic forces in this
direction.
18 The cross in the upper limit in the proximity of 42°
and the triangle in the proximity of 60° constitute two
failures that cannot be definitely explained.
JOURNAL OF APPLIED PHYSICS
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1.1916076.pdf | The Effect of Wall Materials on the Steady-State Acoustic Spectrum of Flue
Pipes
C. P. Boner and R. B. Newman
Citation: The Journal of the Acoustical Society of America 12, 83 (1940); doi: 10.1121/1.1916076
View online: http://dx.doi.org/10.1121/1.1916076
View Table of Contents: http://asa.scitation.org/toc/jas/12/1
Published by the Acoustical Society of AmericaJULY, 1940 J. A. S. A. VOLUME 1 2
The Effect of Wall Materials on the Steady-State Acoustic Spectrum of Flue Pipes
C. P. BONER AND R. B. NEWMAN
University of Texas, Austin, Texas
(Received March 2, 1940)
HE role of the naterial of musical instru- ments in determining tone quality has long
been a source of argument among musicians,
instrument makers, physicists, and the public.
Much has been said and written on the subject,
often without foundation. On the one hand,
strong claims have been made for certain
materials, on the ground that those materials
gave the tone certain desirable characteristics.
On the other hand, others have claimed, as did
Lavignac in his book, Music and Musicians, that
the only function of the body of the instrument
is to contain the air.
The authors of this paper have been interested
in this problem for several years, the interest
originating largely as a result of field contacts
with men of the pipe organ industry. Many of
these men, including pipe voicers, manufacturers,
and maintenance men, are of the opinion that
the material used in an organ pipe has a profound
effect on the tone quality. For example, pipes of
wood are popularly supposed to give a tone
that may be described as "woody," "warm,"
"mellow," and the like. Tones of metal pipes
with a high percentage of lead (common metal)
are generally described as "solid," "founda-
tional," "massive." If the metal has a high
percentage of tin and the walls are thin, the tone
is often thought of as "keen," "stringy," "biting,"
or "incisive." The fact that general descriptive
terms that are used to describe timbre are
indefinite has, perhaps, led observers to persuade
themselves that their conclusions regarding the
effect of materials are valid, even in the absence
of logical bases for the conclusions. Thus, one
need only read the comments of Schafhautl, as
he described the tone of a paper trumpet as
"papery" and the tone of a lead trumpet as
"heavy," to discover a foreshadowing of opinions
on the effects of materials that continue down to
the present.
Experimentally, the problem is definite. The
C. v. Schafhautl, Allgemeine Musikalische Zeitung 14,
593 (1879). problem calls for outdoor analyses of the acoustic
spectra emitted by the individual pipes, with
proper controls of spurious reflections and of
variables in the pipes other than the nature of
the material used in the walls. This paper de-
scribes the measurements taken in an attempted
an, swer to the question, the precautions observed,
and the results obtained.
HISTORY OF THE PROBLEM
Miller 2 gave a rather complete account of work
done and opinions rendered prior to 1909; and
his account serves admirably for a summary of
early work done. Thus, Blot (1817) proposed
that the quality of each substance might be due
to varying relative harmonic intensities. Boehm
(1871) stated that hardness and brittleness of
the material used had a major effect on tone
quality. He was of the opinion that pewter tubes
gave a soft, weak tone;German silver a brilliant,
shrill tone;silver a brilliant and sonorous tone;
and wood a "literally wooden" tone. On the
other hand, Mahillon, in his treatise entitled
Elements d'A coustique, Musicale et Instrumentale,
criticized Boehm for his statements regarding the
effect of materials. Mahillon believed that only
the air vibrated in wind instruments; in fact, he
built a wooden cavalry trumpet that sounded like
the ordinary brass trumpet. Lavignac (1899)
agreed with Mahillon and referred specifically to
pasteboard organ pipes that had been used by
certain organ builders.
Helmholtz 3 expressed the opinion that wooden
pipes produced tones of different quality from
metal pipes, when he declared: "Wooden pipes
do not produce such cutting windrush as metal
pipes. Wooden sides also do not resist the
agitation of the waves of sound so well as metal
ones, and hence the vibrations of higher pitch
seem to be destroyed by friction. For these
D.C. Miller, "The influence of the material of wind
instruments on the tone quality," Science 29, 161 (1909).
a L. Helmholtz, Sensations of Tone, Ellis translation
(1930).
83 84 C. P. BONER AND R. B. NEWMAN
reasons wood gives a softer, but duller, less
penetrating quality of tone than metal."
Savart 4 constructed numerous resonating bod-
ies of different materials and found that when he
made the bodies of paper or parchment the tone
was usually more agreeable and lower in pitch
than when harder materials were used. He also
found that if the tension and stiffness were
gradually diminished the frequency was reduced.
Impregnating the material with water vapor
produced this effect. He pointed out that the
analogies between the musical instruments and
the membranous cavities of the human voice
mechanism is poor. He said' "In the musical
instruments the air contained in a cavity is set
into vibration by the solid walls surrounding it;
on the contrary, in membranous cavities, it is
the air which is the body set directly into
vibration and which communicates then its
vibrations to the containing walls."
Liskovius 5 found that if the material used was
parchment, tightening or stiffening of the walls
raised the pitch.
Miller 2 used pipes of wood and of zinc of the
same internal dimensions. He found that the
zinc pipes were more than two semitones lower
in frequency than the wood pipe and that the
tones of the zinc pipe were sensitive to pressure
on the walls from the outside. When water was
filling the space between one of the pipes and an
outer cylinder, the pitch, quality, and vibrational
mode excited all varied. Miller discussed at some
length the role of materials from the standpoint
of his experiments and from the traditional
point of view of the manufacturer; and he
expressed the opinion that the material had a
decided effect on tone quality.
Gronwall 6 showed theoretically that, in the
case of longitudinal vibrations of an elastic tube
filled with liquid, the velocity of wave propaga-
tion is reduced due to vibration of the walls of
the tube.
Richardson 7 declared that if the walls of the
instrument are yielding or absorbent, the pitch
is lowered and the tone is weak and strongly
4 F. Sayart, Ann. chim. phys. 30, 64 (1825).
5 K. F. S. Liskovius, Pogg. Ann. 57, 497 (1842).
6 T. H. Gronwall, Phys. Rev. 30, 71 (1927).
? E.G. Richardson, Acoustics of Orchestral Instruments
and of the Organ (Edward Arnold & Co., London, 1929). damped. As a basis for his conclusion he stated
that when a papier mach( horn is grasped firmly,
the tone becomes louder. This observation, if
intended to be general in application, is in
conflict with that of Miller. 2 Richardson stated
that increased rigidity causes increased efficiency.
He also stated that the natural frequencies of
the walls might be such as to cause reenforce-
ment of certain notes of the instrument.
Barnes s states that: "The thickness of the
metal has also much to do with the development
of the harmonics, or the reverse. Thick metal
causes the tone of pipes made with it to be more
foundational. Pipes made with thin walls have
greater harmonic development."
Jones 9 states that: "The material of the walls
has little effect on pitch or quality so long as the
walls are hard and smooth and are fairly rigid.
But if the walls are thin or flexible the material
does become important."
Press 1ø treated the problem of energy flow
through the walls of a tube. He found that this
flow requires the generation of a progressive wave
along the walls of the tube and a change in the
phase velocity.
Cotton 11 found: (1) That the resonant fre-
quency of a soft-walled cavity is higher than in
the case of rigid walls; (2) that the partials in
soft-walled cavities are inharmonic; (3) that
soft walls reduce radiation from the resonator.
Lottermoser 1 found extra maxima in the
spectrum from organ pipes of metal, these addi-
tional maxima being due to excitation of weakly
damped resonance modes of the metal tube.
These modes, he stated, modulate the tone from
the air column and produce audible beats. The
particular harmonic that is thus modulated,
according to Lottermoser, will ordinarily be a
high harmonic since the material is such that
resonance of the metal is at a higher frequency
than that of the lowest partials of the air column.
8 W. H. Barnes, The Contemporary American Organ (J.
Fischer & Bro., N.Y., 1933).
9 A. T. Jones, Sound (D. Van Nostrand, 1937).
0 A. Press, "Theory of sound in voice tubes with radiat-
ing walls," Physik. Zeits. Sowjetunion 5, 616 (1934).
11j. C. Cotton, "Resonance in soft-walled cylinders,"
J. Acous. Soc. Am. 5, 208 (1934).
15 W. Lottermoser, "The influence of the materials of
metal organ pipes on their tonal structure," Akustische
Zeits. 3, 63 (1938). EFFECT OF WALL MATERIALS ON ORGAN PIPES 85
...--- 5 4 cm 4
FIG. 1.
These metal tones also affect the transient state
of the pipe, in his opinion.
Jones, 3 in discussing the paper of Lottermoser,
pointed out that the modulating frequencies
necessary to produce the lines in the spectrum
presented by Lottermoser are far below any
modes of the pipe wall. Certain results of the
present paper will bear on this point.
SCOPE OF THE PRESENT STUDY
In making a study of the effect of materials on
the acoustic spectrum, it is extremely important
to maintain all factors other than material
strictly constant. Thus, all dimensions of the
pipe in the vicinity of the mouth must be un-
changed, especially mouth dimensions and posi-
tion of the languid (Fig. 1). A change of a few
hundredths of a millimeter in the height of the
languid will make a decided difference in the
3 A. T. Jones, "Recent investigations of organ pipes,"
J. Acous. Soc. Am. 11, 122 (1939). spectrum. For example, raising the languid nakes
the pipe slow in speech and decreases the ampli-
tudes of the partials. Mouth height, wind
pressure, inside diameter of the tube, and other
physical factors all influence the tone of the
pipe. Any test of the effect of materials that calls
for several pipes geometrically identical is likely
to lead to erroneous conclusions because of
almost unavoidable differences in factors other
than materials. Only by microscopic setting can
the languid be set at the same relative positions
in all pipes with sufficient accuracy for an
accurate measurement. If the material of the lip
is changed, the curvature of the edge will change
and the tone will be different. Consequently, in
the present work the structure and material at
the mouth of the pipe was kept the same by
using only one pipe, while the spectrum was
measured as a function of the material of
cylinders joined to the lower portion, as shown
in Fig. 1. Analysis before and after placing the
collar showed that the collar had negligible
effect.
METhOD OF AN^L¾SS
Free-field analyses were made, by the method
previously described. 4 It is particularly im-
portant to note, in a test of the effect of a single
variable, that the sound field at a point is the
resultant of all emissions from the pipe, and
that the intensity will, therefore, vary from
point to point. If emission is solely from mouth
and top of the pipe, then the interference pattern
in the sound field can be roughly predicted by
considering the mouth and the top as single
sources of sound. For odd-numbered harmonics,
emissions from mouth and top should differ in
phase by approximately mX (m=0, 1, 2, 3, etc.),
because the distance between the two sources is
approximately nX/2 (n-harmonic number). For
even-numbered harmonics, emissions from top
and mouth should differ in phase by approxi-
mately (n- 1)X/2. Thus, at a point on a line per-
pendicular to the axis of the pipe, passing
through the pipe midway between "mouth" and
"top" sources, the intensity of odd-numbered
harmonics should be a maximum and the in-
tensity of even-numbered harmonics should be a
4 C. P. Boner, "Acoustic spectra of organ pipes," J.
Acous. Soc. Am. 10, 32 (1938). 86 C. P. BONER AND R. B. NEWMAN
I 2 3 5 6 7 8 I0 II 12 13 Id, 5
HARMONIC NUMBER
Fro. 2.
minimum. Measurements lnade in this labora-
tory have shown this to be the case for the first
four harmonics, although higher harmonics obey
a more complex rule. Measured amplitudes near
mouth and top are of the same order of magni-
tude; hence, amplitudes of second and fourth
harmonics at the measuring point described are
smaller than would otherwise be expected. It has
been experimentally shown in this laboratory
that if radiation from the mouth of the pipe is
suppressed, the amplitudes of even-numbered
harmonics are markedly increased at the meas-
uring point, as would be expected, and the tone
of the pipe is thereby made totally different from
that of the unaltered pipe. The resulting spec-
trum can be made much more regular, by this
device, than those of normal flue pipes as pre-
viously described. TM
In the light of this interference effect, analyses
made at a point as described above will be
sensitive to amplitude and phase effects and, in
addition, to effects of wall vibration and emission
through the walls. As the material of the tube
is changed it might be expected that emission
from the tube walls would change, as well as
amplitudes and phases of emissions from mouth
and top. MATERIALS USED
Seven cylinders were used, as follows'
NUMBER MATERIAL
Common pipe metal
Galvanized iron
Steel
Shellacked paper
Light copper
Medium copper
Heavy copper
Pine WEIGHT
IN
POUNDS
2.20
O.7O
2.20
0.15
0.30
O.5O
0.90
O.88 THICKNESS IN
THOUSANDTHS
OF AN INCH
50
25
7O
8
5
13
29
312
EFFECTS OBSERVED
Some of these cylinders exhibit curious effects.
The paper cylinder, for example, was of ordinary
wrapping paper and was therefore porous. When
first formed, the resulting pipe refused to speak,
except in that it emitted unstable noises. As the
shellac that was later placed on the paper began
to dry, continued improvement in speech was
noted over a period of three or four days. At the
end of that period, the speech was apparently
perfectly normal, as compared with the cylinder
of regular pipe-metal (largely lead). Clearly, the
shellac gradually sealed the pores and, as EFFECT OF WALL MATERIALS ON ORGAN PIPES 87
I 2 3 4 .5 6 7 6 9 I0 II 12 13 14 1.5
HARMONIC NUMBER
Fro. 3.
Lavignac would possibly have said, the pipe
began to "contain the air." If the finished paper
pipe is grasped by the hand, vigorous vibrations
of the cylinder are felt and the tone rapidly
changes as the grasping pressure is increased.
Any sensible deformation of the pipe from a true
cylinder cause large tonal changes. If a de-
pression is made in the cylinder the tone ceases;
increased blowing pressure will then produce a
tone of considerably higher frequency than the
original tone. These results are in accord with
the observations of Miller and others.
The light-weight copper pipe exhibits an inter-
esting transient effect. When the blowing pres-
sure is suddenly cut off, the pipe continues to
emit sound for a second or two, the tone having
two basic frequencies: one very close to the
original, steady-state frequency and one at a
slightly lower frequency. Beats are clearly audible
during the decay period, and the effect is some-
what like an organ Flute Celeste. This effect
might be pleasing in an actual organ stop, par-
ticularly since the beats are not present in the
steady state. The effect is possibly related to the
effect described by Lottermoser, TM but his expla-
nation (see Jones 13) could hardly suffice for the
effect noted in the present paper. If this thin copper pipe is tapped with the
finger (the pipe not being blown), the same
beating tone is heard as in the case of the
removal of the blowing pressure. There are, in
addition, other tones produced, one of them
having a frequency of approximately 200 vibra-
tions per second. Each of these modes appears,
in most cases, as a doublet, and the beats heard
are beats between the members of the doublet.
When the pipe is speaking normally, by being
blown in the usual manner, only the customary
harmonic series (singlets) is found, provided the
blowing pressures are normal for the particular
pipe. When the blowing pressure is suddenly cut
off, the doublet series of the wall-and-air-column
acoustic system is excited and a beating series of
tones is heard. During normal blowing, this
doublet series is too weak to be heard. The
doublet series, further, is less highly damped
than the normal vibration of the blown system.
Contrary to the experience of Lottermoser, in-
crease of blowing pressure fails to elicit the beat-
ing tones in the steady state. The beating effect
under strong blowing, as described by Lotter-
moser, is characteristic of slightly overblown flue
pipes and is produced, as will be shown by the
authors in a paper now in preparation, by beats 88 C. P. BONER AND R. B. NEWMAN
between members of a doublet or triplet series
of partials. It is, therefore, possible that the
result of Lottermoser was, in part, due to excess
pressure and was not completely determined by
resonance of the tube.
EFFECT OF MATERIALS ON STEADY-
STATE SPECTRUM
In Figs. 2 and 3 is plotted the r.m.s. sound
pressure in db (zero db equals 1 dyne per square
centimeter at the measuring point previously
described, 17 feet from the pipe under test)
against harmonic number. To aid in presenting
results, the points are joined by straight lines,
although there is obviously no energy at fre-
quencies other than the harmonic frequencies
labeled.
One striking result is the fact that lst-har-
monic amplitudes produced by all materials are
nearly the same. The paper pipe has the lowest
value, but it is only 1 db below the wooden pipe
and 3 db below the steel pipe. Second, fourth,
and extreme upper harmonics of the paper pipe
are materially lower than for other materials,
but harmonics of the paper pipe other than these
are nearly as strong (less than 5 db difference) as
those of the metal pipes. The wooden cylinder,
instead of producing what some would anticipate
as a "woody tone," is virtually as strong in
harmonic development as the metal cylinders.
The common-metal (largely lead) exhibits the
most intense lower harmonics, while the steel
tube exhibits the most intense upper harmonics.
The galvanized iron pipe is intermediate between
steel and common-metal. However, maximum
differences among these three are of the order
of 3 db.
For convenience, the spectrum may be divided
into three groups: Group A--harmonics 1-7,
inclusive; Group B--harmonics 8-11, inclusive;
Group C--harmonics above 11.
GROUP A
In Group A the common-metal pipe shows
greatest harmonic development. It is surpassed
by the wooden pipe on harmonic numbers 6 and
7, by the heavy copper pipe on harmonic No. 6,
and by the light copper pipe on harmonic No. 7.
The differences, however, are very small. Galva- nized iron is superior to steel, is substantially
equal to heavy copper, and is superior to light
copper. If copper is used by a manufacturer to
secure higher harmonic development in Group A,
it would seem that his efforts are not particularly
fruitful.
Arranging the cylinders in descending order of
harmonic development in Group A gives the
following tabulation:
1. Common pipe metal, 5. Steel,
2. Wood, 6. Paper,
3. Galvanized iron, 7. Medium copper,
4. Heavy copper, 8. Light copper.
GROUP B
In this group of harmonics, steel is supreme,
except at the 9th, where wood excels and at the
8th, where copper excels. The paper pipe is
uniformly low in this group, although its de-
ficiencies are less than 4 db except at the 11th.
A rating, similar to that in Group A, gives:
1. Steel, 5. Medium copper,
2. Wood, 6. Light copper,
3. Heavy copper, 7. Common-metal,
4. Galvanized iron, 8. Paper.
GROUP C
The order in this group would be:
1. Steel, 5. Heavy copper,
2. Medium copper, 6. Light copper,
3. Galvanized iron, 7. Common-metal,
4. Wood, 8. Paper.
With the exception of the paper cylinder, it
must be concluded that the material of the
cylinder above the upper lip of a flue pipe has
very little effect on the steady-state spectrum of
the pipe. The amplitude deficiencies of the paper
pipe are, in fact, not particularly great. Listening
tests made on these pipes showed very small
audible differences. It is, moreover, particularly
shocking to hear a good diapason tone from a
pipe with its cylinder made of wrapping paper.
Grasping a thin-walled pipe and putting dents
in a pipe both cause considerable reflection at
the resulting discontinuity and a corresponding
change in the acoustic impedance at the mouth.
This change exhibits itself in marked changes in
frequency and spectrum. Frequently, in practice,
a pipe that is tending toward overblowing may EFFECT OF WALL MATERIALS ON ORGAN PIPES 89
have its speech steadied by applying an external
constraint at the proper point.
The physical lengths of these pipes, to give
the same frequency, are as follows:
Steel 57.8 cm, Heavy copper 57.5 cm,
Common-metal 57.7, Medium copper 57.5,
Galvanized iron 57.7, Light copper 57.3,
Wood 57.5, Paper 56.9.
These variations, although small, are in agree-
ment with the general observations of Savart 4
and Richardson, 7 but are much smaller than
variations reported by Miller. 2 The small amount
of frequency variation found indicates a minor
effect of cylinder material on the reactive com-
ponent of pipe impedance, even though the thin-
walled cylinders exhibited large amplitudes of
vibration in comparison with the thick-walled cylinders. Thus, one would expect a minor
effect of cylinder material on phase differences
between emissions from mouth and top. Hence,
since the amplitude differences at the observation
point in the sound field were small, in most
cases, particularly at the 2nd and 4th harmonics
for which there is partial cancellation, it may be
concluded (except for the paper pipe) that
cylinder material has a negligible effect on
generation and emission of sound at mouth and
top of the flue pipe and that emission from the
walls is probably small in comparison with that
from mouth and top. Further studies of the paper
pipe should reveal the exact cause of the low
values of the 2nd and 4th harmonics, by making
measurements on phase difference between mouth
and top, emission amplitudes at mouth and top,
and sidewall emission. |
1.1769827.pdf | An Apparatus for the Measurement of AlphaParticle Range and Relative
Stopping Power of Gases
M. Y. Colby and T. N. Hatfield
Citation: Review of Scientific Instruments 12, 62 (1941); doi: 10.1063/1.1769827
View online: http://dx.doi.org/10.1063/1.1769827
View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/12/2?ver=pdfcov
Published by the AIP Publishing
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Downloaded to IP: 129.105.215.146 On: Mon, 22 Dec 2014 19:48:15FEBRUARY. 1941 R. S. 1. VOLUME 12
An Apparatus for the Measurement of Alpha-Particle Range and
Relative Stopping Power of Gases
M. Y. COLBY AND T. N. HATFIELD*
University of Texas, Austin, Texas
(Received October 8, 1940)
A description is given of an apparatus which has been developed for measuring the extra
polated ra~ge of .alpha-particles in gases by the method of specific ionization. The improved
apparatus IS designed after the Curie-Naidu apparatus but increases the specific ionization
current about one hundredfold without increasing the thickness of the alpha-particle source.
INTRODUCTION A VARIETY of methods has been devised
for determining experimentally the range
?f alpha-particles in gases. These may be grouped
mto three general classifications: (1) the method
of individual particle counts, (2) the cloud-track
method, and (3) the ionization method. Holloway
and Livingston1 have made a comprehensive
investigation of range methods and they have
pointed out that range determinations should be
based on ionization measurements. The two
general methods of making ionization measure
ments are (1) the measurement of the total
ionization by the Geiger, or sphere, method and
(2) the measurement of the specific ionization
with a thin chamber. It is with this latter
measurement that the present work is concerned.
The extrapolated range as determined from
specific ionization measurements is the most
reproducible characteristic of the ionization
curves and there are two types of thin chambers
used in determining this range. The perpendicular
thin chamber, as used by Bragg and Kleeman2
and later by others, includes a wire grid as the
front face of the chamber, the grid being perpen
dicular to the beam of alpha-particles. The
parallel type chamber as used by 1. Curie,3
Naidu,4 and others has thin electrodes parallel to
the alpha-particle beam. The advantage of the
latter type is that errors due to particles reflected
from the wire grid are avoided. The specific
ionization current obtained by investigators with
* 9? leave from Louisiana State University, University
LOUISiana. '
1M. G. Holloway and M. S. Livingston Phys Rev 54 18 (1938). ' . .,
2 W. H .. Bragg and R. Kleeman, Phil. Mag. 8, 726 (1904).
31. Cur~e, Ann. de physique 3. 299 (1925).
4 R. Naldu, Ann. de physique 1, 72 (1934).
62 the parallel type thin chamber is of the order of
10-15 amp., while the total ionization current
obtained with the sphere method is of the order
of 10-12 amp. Because of the difficulty of meas
uring accurately the specific ionization current
much of the recent work on range measurement~
has been-carried out by the sphere method. The
apparatus described here gives a specific ioniza
tion current of the order of 10-13 amp. The
advantages of using a thin source and having the
alpha-particle beam well collimated were pointed
out by Naidu and both these are retained in the
present apparatus.
DESIGN OF THE ApPARATUS
Since the results of the work of 1. Curie and
R. Naidu are considered the most accurate data,
to date, on alpha-particle ranges, their type of
~pparatus was used as the basis for the apparatus
m the present work. A diagram of the general
form of the apparatus used by Naidu is shown'
in Fig. 1. The alpha-particles leaving the source
S are collimated by the slits cc and the beam,
on reaching the ionization chamber, produces
ions which are collected on e. The ionization
chamber u~ed was 2.6 cm .high and 7 cm deep,
the collectmg electrode bemg 3 mm wiqe. The
measured ionization current was that produced
by the alpha-particles in the 5.46 cc of gas above
the collecting electrode. The general form of the
FIG. 1. General form of the Naidu apparatus.
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Downloaded to IP: 129.105.215.146 On: Mon, 22 Dec 2014 19:48:15MEASUREMENT OF ALPHA-PARTICLE RANGES 63
FIG. 2. Diagram of
the chamber: 1-Glass
ring; 2-Bakelite post;
3-collecting electrode;
4-guard rings; 5-
glass plate; 6-amber
post; 7-sylphon bel
lows; 8-source and
collimator; 9-upper
electrode. Scale Ii? em
present apparatus is that which would be
generated by rotating the Naidu apparatus
through 3600 about an axis through the source
and in the plane of the paper (Fig. 1). The
collecting electrode thus becomes a circular ring
about the source and the straight collimating
slits form circular slits which give a disk of
collimated alpha-particles. The volume of the
gas above the collecting electrode is thus greatly
increased and the small source is stretched ou t
into a circular band. The source-to-electrode
distance is no longer variable but the effective
distance is varied by varying the pressure of the
gas in the chamber.
The chamber, a diagram of which is shown in
Fig. 2, consists of a glass ring of 29.7 cm inside
diameter and 3.85 cm height capped on the ends
by half-inch plates of Duralumin. The composi
tion bushings shown in the upper plate insulate
it from the bolts and lower plate. The collecting
electrode is an aluminum ring approximately
4 mm wide and 11 cm inside radius mounted on
·three amber posts in the lower plate. It is held
in position by small pins in the posts, one of the
pins making contact with an outside lead
through the post. The guard rings are mounted
directly onto the lower plate. The space between
the guard rings and collecting electrode does not
exceed one-quarter mm at anyone place. The
upper electrode is mounted on three Bakelite
posts and the distance between the upper and lower electrodes is 2.56 cm. With this electrode
spacing and the wide guard rings, the field is
sensibly uniform at the collecting electrode and
perpendicular to it. The collimator consists of
two half-inch brass plates 6 cm in diameter
machined out so as to form two rings of diameters
3 cm and 6 cm, respectively, which, when fitted
together as shown in Fig. 2, form two circular
slits. The lower collimating plate rests on three
leveling screws and the upper plate is fitted with
three slit adjustment screws which rest on the
lower collimating plate. The slit edges are made
sharp (less than half a mm) to avoid errors due
to "tube collimation." A photograph of the
chamber with the upper plate removed is shown
in Fig. 3.
The alpha-particle source consists of polonium
deposited on a thin band of silver which has been
chemically deposited on a 6-mm glass tube.
L. Miller' has investigated the deposition of
polonium from half-normal hydrochloric acid
solutions onto metals, obtaining the best results
by depositing on silver which has been chemically
deposited on glass. The tube on which the
polonium is deposited is one cm long and is held
by a shallow cup cut into the lower collimating
plate as shown in Fig. 2. The brass cap shown
fits over the source to avoid contaminating the
5 L. Miller, "The range of alpha-particles from polonium
in various gases," Master's Thesis, The University of
Texas, 1939 (unpublished).
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Downloaded to IP: 129.105.215.146 On: Mon, 22 Dec 2014 19:48:1564 M. Y. COLBY AND T. N. HATFIELD
FIG. 3. Chamber with top removed: A-Slit adjustment
screws; B-source cover; C-collimating slit; D-collect
ing electrode; E-Dershem electrometer; F-standard
condenser.
chamber when the apparatus is not in use. The
sylphon bellows arrangement allows one to
uncover the source by raising the long pin which
runs through the tube and is attached to the
brass cap.
In view of the work by Naidu6 on diffusion of
the alpha-particles, range measurements in air
were made with the present apparatus using
various slit widths to determine whether the
measured range was influenced by the geometry
of the apparatus. The slit widths used were
0.028, 0.052, 0.074, and 0.1 cm. No variation
was found that could be attributed to the use
of too wide a slit up to the one-mm width.
However, to be certain that the range measure
ments were not affected by diffusion, a slit width
of 0.085 cm was adopted for the apparatus.
This gives an alpha-particle beam-thickness of
1.02 cm at the collecting electrode (assuming
geometrical projection), lacking 1.54 cm of being
as thick as the distance between electrodes.
Since all alpha-particles are not emitted
normaIly from the source, the source-to-electrode
distance cannot be taken merely as the radius of
the electrode minus that of the source. The
average distance traveled by all the particles
must be calculated.
First consider the variation of the source-to
electrode distance with the angle which an
emitted particle makes with the horizontal.
From the geometry of the apparatus it is easily
shown that the emitted particle making the
largest possible angle with the horizontal will
6 R. Naidu, Ann. de physique 1, 77 (1934). have a source-to-electrode distance which is less
than one-tenth of a percent greater than that of
the particles traveling horizontally through the
slit. Considering this smaIl variation and the fact
that fewer particles travel in the "penumbra,"
(i.e., make the larger angle)the variation from
the horizontal source-to-electrode distance can
be neglected here.
Assuming, then, that the particles are emitted
horizontally from the source (forming a colli
mated disk), the source-to-electrode distance for
a particle emitted at an angle cp with the normal
to the source is represented by PA =x in Fig. 4.
In this figure ss is a section of the source, and
ee is the collecting electrode center. The radius
of the source is taken as r and the distance to
the center of the coIlecting electrode as R. We
desire to calculate the average value of x. From
the figure, we have:
x= (R2_r2 sin2 cp)!-r cos cpo (1)
The number of particles emitted in the angle dcp
is proportional to dcp under our assumption of no
vertical spread. Thus, for the average distance
we have:
7r/2 71"/'2
X = i xdcp / i dcp
o 0 (2)
e
s
'~---l'--...l.-_~ B FIG. 4.
e
or
x= 2:[i~/2 (1-:>in2cp YdCP-~J (3)
In the present apparatus, R= 11.238 cm and
r = 0.305 cm, giving
x= 11.042 cm. (4)
The ionization current is measured by the
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Townsend7 compensation method, a Kohlrausch
slide wire and a Dershem electrometer being used
in the circuit with a 50p,p,f cylindrical condenser.
The advantages of using this method are pointed
out by Naidu. The larger currents obtained with
the present apparatus, however, eliminate the
necessity of using a Compton electrometer and
the special resistances used by Naidu. The gas
pressure in the chamber is measured with a
closed manometer and a cathetometer.
EXPERIMENTAL PROCEDURE
The chamber is first washed with the gas to
be used. Then as the gas is introduced at various
pressures, readings on the ionization current are
taken. Best results are obtained by applying the
compensating voltage for 30 to 50 seconds. This
is done by having a potential difference of 0.6
volt across the slide wire, and turning the slide
through a counted number of turns. If the
capacity of the condenser is C, and the compen
sating voltage V is applied in t seconds, then the
current is given by
I'=CV/t. (5)
However, since the mass of the gas ionized is
proportional to the pressure, this current must
be corrected to some reference pressure. Thus
1= (CV/t)· (76/P), (6)
where P is the pressure, and I is the current
which would be produced if the mass above the
collecting electrode were that which would be
present at a pressure of 76 cm Hg. Figure 5
shows examples of I plotted against P. The
straight line portion of the curve has been
extended to the axis to give the "extrapolated
pressure range" p' at the temperature T.
Plotting the latter portion of the curve to a
larger scale affords a better determination of p'.
GAS TABLE I. Straggling parameter and range of air,
argon and H.S.
y
.424 em
.366 em
.31 em .23 cm
.17 em
.12 em r (PRESENT WORK)
3.850 em
4.16 em
2.58 em r (NAIDU)
3.868 cm
4.20 em
7 J. S. Townsend, Phil. Mag. 6, 598 (1903). The extrapolated ionization range r at 15°C and
76 cm Hg is then calculated by
r= 11.042 X (p'/76) X (288/T). (7)
The apparatus in its present form is probably
not suitable for precision measurements of
absolute range. The instrumental straggling is
large and empirical range formulae as given by
Holloway and Livingston and others may not
apply here. The authors are at present investi-
{{J ----
-I # -~
'" ,.. ~.--1----~ -l/-- t--
):t
J2 V ~ W N f1i
---4-_ .. 1I l---' ~ t-""
~ idt'
~\ ~ I I t--~ ~ -~ '--I~ t--
<> ...,
--I -
~: ~~ z -~ f--~'
16~ -.~ ~
lZ~ ~-
~ I-;~ .-j--If r--
t-I~
OJ. 1-I~ ~. ~YIi~
I~, t\ rl" )::( fli I .. 41-./ I"
246 8maH~MMllUSM.~~
PreJ.Jure In em H9
FIG. 5. Examples of the specific ionization curve obtained
with the apparatus.
gating the use of a source of smaller diameter
and a narrower collecting electrode which, it is
hoped, will result in steeper ionization curves
and increased accuracy in range measurements.
Although the straggling parameter, a, is larger
than the range straggling parameter generally
reported (0.052 to 0.067 for air), the extrapolated
ionization range as measured with the present
apparatus is in general agreement with that
reported by others. The results of measurements
on air, argon and H2S are given in Table I. The
value of y given is that obtained from the curve
as shown in Fig. 4 (reduced to cm at 760 mm
and 15°C), and the value of the straggling
parameter a is that calculated by the Livingston
and Holloway formula:8
a=0.917y-0.160. (8)
The value of the range given is that obtained
from an average of several measurements.
By making several measurements on a given
8 Reference 1, p. 35.
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gas, some of the measurements being taken as
long as 10 days apart, the precision of the appa
ratus has been checked. It is found that the "ex
trapolated pressure range" as measured by this
apparatus checks to better than one-half of a
percent for the gases measured. By measuring
the range in two different gases, and then in
mixtures of these gases, a check is obtained on
the validity of the measurements. The stopping
power of a gas relative to air is calculated from
the ratio of the ranges: Or, since the source-to
electrode distance is constant, the relative
stopping power may be calculated from the "extrapolated pressure range." Thus the appa
ratus affords the measurement of the relative
stopping power of gases by a method which is
quite easy to carry out.
The authors have used the apparatus described
in measuring the relative stopping power of
several gases. The additive law is verified for all
gases measured, including nitrous oxide, a gas
for which Schmieder9 has reported that the law
does not hold.
9 Karl Schmieder, "Bremsvermogen und Tragerbildung
der Alpha Strahl en in Gasen," Ann. d. Physik 38, 445
(1939).
FEBRUARY. 1941 R. s. 1. VOLUME 12
An Interferometric-Dilatometer with Photographic Recording
F. C. NIX AND D. MACNAIR
Bell Telephone Laboratories, New York, New York
(Received November 12, 1940)
An interferometric-dilatometer for the temperature range from + 750° to -190°C with photo
graphic recording. The method is illustrated by results obtained on quartz perpendicular to the
optic axis.
RECENT studies on the nature of order
disorder transformations in alloys have
shown the need for a dilatometer with great
sensitivity, permitting measurements of volume
changes, accompanying the transformation, to be
made at very slow rates of heating or cooling, in
order to achieve thermodynamical equilibrium in
the interesting region near the critical ordering
temperature. The slow rates in turn demand a
dilatometric apparatus with automatic recording.
Both requirements have been met by an
interferometric method which in a cruder form
dates back to Fizeau.l The interferometer (de
picted in Fig. 1) is of the same general form as
described by Merrit,2 and used in more recent
investigations by Austin.3
In this instrument three pieces of the material
whose expansion is to be measured rest between
two optically polished fused silica disks. The
1 V. Valentiner, Handbuch der Experimental Physik 8.
Part 2. p. 1.
2 G. E. Merrit, Sci. Pap. Bur. Stand. 19,357 (1924).
3 J. B. Austin, Physics 3, 240 (1932). lower and upper disks are 27 and 10 mm in
diameter, respectively. The material to be
studied is cut into the form of small pyramids
some 3 or 4 mm in height, with a diameter of 2 or
3 mm. The three specimens of almost iden tical
height are then placed on the lower disk as indi
cated in the section view of Fig. 1, and on top of
them is placed the second disk. This disk is cut in
l. .................................. __ -' FIG. 1. The plan
view shows typical ap
pearance of the two
sets of interference
fringes. The vertical
view shows the speci
mens between the fused
silica disk. The cross
and arrow serve as
fiduciary marks.
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1.1712899.pdf | SteadyState Solutions of Electromagnetic Field Problems. I. Forced
Oscillations of a Cylindrical Conductor
J. A. Stratton and L. J. Chu
Citation: J. Appl. Phys. 12, 230 (1941); doi: 10.1063/1.1712899
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Published by the American Institute of Physics.
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Downloaded 10 Sep 2012 to 139.184.30.132. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsSteady-State Solutions of Electromagnetic Field Problems
I. Forced Oscillations of a Cylindrical Conductor
J. A. STRATTON AND L. J. CHU
Massachusetts Institute of Technology, Cambridge, Massachusetts
(Received December 9, 1940)
The object of this investigation is a study of the current distribution in or on the surface of a
conductor and its associated field under the influence of a localized e.mJ. Steady-state solutions
of the field equations are found for conductors of simple geometric form. The results clarify
many electromagnetic problems involving localized sources, especially in the u-h-f region,
for which ordinary circuit theory fails to give a satisfactory quantitative explanation. Part I
treats the p~oblem of a straight cylindrical conductor and shows the relation of the principal and
complementary waves to the nature of the exciting field. A driving point impedance is calcu
lated for the case of an external field applied over a vanishingly short section of conductor. The
driving point impedance is infinite for a conductor of infinite length and perfect conductivity.
Likewise the case of a conductor of finite length bounded at either end by an infinite, perfectly
conducting plane is discussed. This problem bears a direct relation to that of a hollow pipe
excited by a linear antenna.
THE object of this investigation is a study of
the current distribution in or on the surface
of a conductor and its associated field under the
influence of a localized e.m.f. Solutions of electro
magnetic field problems are ordinarily con
structed from wave functions satisfying a homo
geneous set of equations, which in rationalized
m.k.s. units can be written
VXE+iw/-,H=O,
VXH-(O+iWE)E=O. (I)
(II)
It is assumed here that all quantities contain the
time in the form of a factor exp (iwt). The field
intensity E is measured in volts/meter, H in
ampere-turns/meter, and conductivity CF in
mhos/meter. In free space J.!o =411" X 10-7 henry/
meter, EO= 10-9/3611" farad/meter. When the usual
boundary conditions are applied in an appropri
ate coordinate system, (I) and (II) reduce to a
set of homogeneous algebraic equations whose
determinant must vanish. The. complex roots of
this determinantal equation fix the frequencies
and damping of the allowed or free modes of
oscillation. The amplitudes, however, are com
pletely arbitrary and will be determined by the
nature of the exciting source, to which (I) and
(II) give no clue.
Exact steady-state solutions of eleCtromagnetic
problems have been found in a number of simple
cases, such as that of a plane wave incident upon
230 a cylinder or sphere. The equations relating the
coefficients of the various particular solutions are
now inhomogeneous; hence the amplitudes of the
excited modes are uniquely determined and the
system oscillates with the frequency of the
impressed field. In such problems the diffracting
body is entirely enveloped in the incident wave.
Quite as numerous as these problems of purely
optical interest are those in which the impressed
field is applied as a local e.mJ., confined es
sentially to a small domain of the conductor. The
applied field intensity will be designated by the
vector E' measured in volts/meter. E' is a
specified function of position and time but is not
necessarily analytic. It represents the intensity
of any external force, of whatever origin, acting
on the free charges of the conductor. It may be
introduced by a mechanical or chemical agency,
by the motion of an external magnet, or by a
shielded transmission line. In the latter case,
which is the common and practical one, it is
obvious that the entire problem is modified to
some extent by the presence of the line. It is
reasonable to assume, however, that in most
cases the effect of the leads on the current
distribution in the principal conductor or upon
the field at a distance is small and that the
perturbation can be taken into account by a
second approximation.
I t will be assumed in the foIlowing that a
JOURNAL OF ApPLIED PHYSICS
Downloaded 10 Sep 2012 to 139.184.30.132. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsconducting body is embedded in a homogeneous
dielectric medium and that the external e.m.f. is
applied within or on the surface of the conductor
only. The grounds for the latter assumption are,
perhaps, open to some question, since an applied
field at the surface of a conductor must inevitably
extend into the neighboring dielectric and thereby
effect its polarization; but the effect on the total
field of such additional dielectric ,displacement
currents is small relative to that of the con
duction current, and its neglect seems entirely
warranted. Hence the field within the dielectric is
governed by Eqs. (I) and (II). If the conductor
is metallic the displacement current term is
negligible, and since the current density J is
proportional to the resultant field intensity,
J=cr(E+E'), we have to satisfy in this domain
the inhomogeneous system
V'XE+iW/-LH=O,
V'XH-crE=crE'. (I)
(II-a)
Analytic continuation of the solutions from one
domain to the other is insured by the boundary
conditions which call for a continuous transition
of the tangential components of E and H. Note,
however, that the transition of E' across a bound
ary is arbitrary and in general discontinuous. It was shown by Sommerfeld that the system
admitted a principal wave propagated with
negligible damping and a velocity approaching
that of light, together with an infinite series of
complementary waves associated with damping
factors so great as to result in immediate extinc
tion. In dielectric wires or hollow pipes, on the
other hand, no principal mode occurs and for
sufficiently high frequencies the complementary
waves are propagated with relatively little
attenuation. These are free modes of oscillation
whose amplitudes are determined by the initial
conditions and which are responsible for reso
nance phenomena. A "surface impedance" was
also defined by Rayleigh and used as a basis for
the discussion of the alternating-current resist
ance of linear conductors. It differs from the
driving-point impedance to be observed at the
point of application of an external e.m.f.
We shall assume that E' is parallel to the axis
of the conductor and is uniform over the cross
section. In Fig. 1 the axis of the conductor is
shown coinciding with the z axis of the coordi
nate system and the impressed e.m.f. is intro
duced in the neighborhood of z = 0. Particular
solutions of (I) and (II) in cylindrical coordinates
r, cp, z appropriate for the dielectric domain
r>a can be taken directly from Sommerfeld's
discussion.2
nX(E 2-E1)=0, qX(H 2-H1)=0, (III) Thus for r>a
where n is a unit normal vector drawn from
medium (1) to medium (2). The normal will
always be drawn outward from a metallic surface
into the dielectric.
There is, of course, nothing new in these
equations and they are discussed in most of the
older texts on electromagnetic theory.l The pur
pose of the present work is to show that in many
cases they are easily integrated and that the
solutions can be of greater practical interest than
those giving simply the transient oscillations. As
a first example we consider the propagation of
waves along a single, infinite conductor of circular
cross section. The classical treatments of this
problem are due to Rayleigh and to Sommerfeld.
1 M. Abraham, Theorie der Elektrizitiit (Teubner, seventh
edition, 1923); O. Heaviside, Electrical Papers (Macmillan,'
1892).
VOLUME 12, MARCH, 1941 Ez=AH~2)(p2r) }
Er= (iU/P2)AH~2) (P2r) ei",t-iuz,
• (2) Hq,=(1,WE2/P2)AHl (P2r) (1)
h= (k22-U2)!, k22=W2E2!J.2' (2)
where H~2) (P2r) is a Hankel function of the
second kind insuring proper behavior of the field
at infinity.
Inside the conductor
Ex' =Ey' =0, Ez' =E'(z), (3)
where E' is a prescribed function of z and t.
2 A. Sommerfeld, Ann. d. Physik 67, 233 (1899); also in
Riemann-Weber, Differentialgleichungen der Physik, Vo!' 2,
(Vieweg, 1935) eighth edition.
231
Downloaded 10 Sep 2012 to 139.184.30.132. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions==:: -------E' ~Z
FIG. 1. Section of infinite conductor of circular cross section
a embedded in dielectric medium E2, 1'2.
Equations (1) and (II-a) now reduce to
aET aE. ----+iWJ.l.IHq,=O, az ar
aHq, --+O"IEr=O, az
Eliminating Er and Hq, one obtains
If now we place a2E'
=iwl-lwIE' ---. az2
F=E.+E' (4)
(5)
(6)
and note that the field is finite on the axis, !t is
apparent that for r<a particular solutions of (5)
must be constructed from the functions
F=BJo(Plr)eiwt-iuz, (7)
PI= (kI2-U2)~, k12= -iWJ.l.IO"I, (8)
where JO(Plr) is a Bessel function of the first
kind.
The impressed field E' is a prescribed function
of z. For the moment we shall assume only that
E'(z) and its first derivative are piecewise con
tinuous and that the integral
exists. Under these circumstances the impressed
field can be represented by the Fourier integral
E' = G(z)eiwt
= (eiwt/27r) L:dU l:dCi G(a)eiu(a-.). (9)
The coefficients A and B of the particular
solutions (1) and (7) are now considered to be
functions of a parameter a. Upon integrating
with respect to u and Ci the field at any point is
232 represented as a superposItIOn of cylindrical
waves. Thus for r>a
while for r < a
(11)
These equations are next subjected to the
boundary conditions (III) at the surface r =a.
There results the algebraic system
(2) B Jo(pla)-A Ho (p?p)=G(a),
(12)
0"1 ~WE2 (2) . -B JI(PIa)--A HI (p2a)=0
PI P2
from which we obtain
(2) x Jo(x) y Ho (y) Z(u) =---' ------ (13)
O"la JI(x) iWE2a H(2)(y)'
I
x=PIa, y=P2a.
In the absence of a driving force G, the natural
modes of propagation are given by the roots of
Z(u) = 0, exactly the conditi.on found by Sommer
feld. This condition has an interesting physical
interpretation. By definition the wave impedance
of a cylindrical wave in the radial direction is
-E./ Hq,. The rule for the algebraic sign is that of
the Poynting vector. The ratio is positive when
the components of E and H follow in cylindrical
order.3 It is clear that apart from a sign the first
term of Z(u) is the radial impedance of the
cylindrical field within the conductor, while the
second term expresses this impedance in the
external medium. Z(u) is the difference of the two
impedances at the boundary. The free oscillations
3 S. A. Schelkunoff, Bell Sys. Tech. J. 17, 17--48 (1938).
JOURNAL OF APPLIED PHYSICS
Downloaded 10 Sep 2012 to 139.184.30.132. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsof any system of bodies embedded in a homo
geneous medium follow from the condition of
equality, or "matching," of the normal com
ponents of wave impedance across the bounding
surfaces, expressed in the present instance by the
vanishing of Z(u).
Let us now calculate the current passing
any cross section of the conductor. Since
Jz=u1(E z+E'), we find for the current I at any
point z
ioo g(u) I =aeiwt(27r)i --e-iuzdu,
-00 Z(u) where (14)
g(u) = (1/(27i")!) i:G(u)eiUada (15)
is the Fourier transform of the applied field G(z).
The zeros of the impedance function Z(u)
occur at the values of u corresponding to the
propagation constants of the principal and com
plementary natural modes, and all are complex
provided U1 is finite. Z(u) is symmetric in u and
the roots lie in the first and third quadrants, with
none falling on the real axis. It follows, moreover,
from the asymptotic behavior of the Bessel and
Hankel functions that as U---HXJ, Z(u)-t 00 as
(1/1T1+1/iwf2)U. Hence the path of integration
along the real axis may be closed by a semicircle
of very large radius in the upper or lower half
plane according as z is greater or less than zero.
This is illustrated in Figs. 2(a) and 2(b), the
dots indicating schematically the location of the
zeros.
We assume the transform g(u) to be ana
lytic everywhere within the closed contour and
properly bounded at infinity. Let Un designate the
roots of Z(u) =0. Then
1= ±a(27r) !eiwt27ri :E bn, (16)
n
where bn is the residue at the pole Un and the plus
or minus sign holds as z is less or greater than
zero.
To determine the residues we need only the
first term in the Taylor expansions of Z(u) about
the poles.
Z(U)=(U_Un)(dZ) +"', (17) du u=u,.
and hence
g(un)e-iun
I=a(27r)!e iwt27ri:E -----------. (18)
n (dZ/du)u=un
VOLUME 12, MARCH, 1941 Thus the source excites all modes and these
travel along the line with the propagation factors
determined by Sommerfeld's analysis. The ampli
tudes are uniquely determined by the form of the
exciting function g(u). It will be recalled that if
the radius of the conductor and its conductivity
are not too small, the propagation factor of the
principal wave is given approximately by
The effect of a finite conductivity is to introduce
a very small imaginary part and a corresponding
attenuation. The attenuation of the comple
mentary modes, on the other hand, is exceedingly
large and so for all practical purposes (18) reduces
to
(20)
To calculate the denominator in (20) note that
If we write k1=al-i{h it follows from the
asymptotic representations of the Bessel func
tions that
while from the first term of the series expansions
of the Hankel functions in the neighborhood of
y = 0 it is easily shown that
(2) (2) • Ho (y)/H 1 (y)-ty In ('Yy~/2) as y-tO, (23)
where 'Y = 1. 781. From this it follows that
dZ/du-t2ia(JJ.df2)lln ('Yyi/2) as U-tk2' (24)
2<0
(a) 2>0
(b)
FIG. 2. Closed contours of integration in u plane.
233
Downloaded 10 Sep 2012 to 139.184.30.132. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsand the current at any point on the line is The ratio of V to the current at the midpoint is
now g(k2) . . 1= 27r(7rEd2.u2)I e,wt-,k2Z•
In ('Yyi/2) (25) Vll(O) = 120 (dkdsin dk2) In ('Yyi/2), (33)
In case the external dielectric is air, the first
factor reduces to 211"(EO/ ,1.10) 1 = 1/60.
For the sake of example consider the case of an
applied field whose form is represented by the
"impulse function."
2 2 Eo e-Z /2d G(z)=-----
(27r)! d
with the property
L:G(Z)dZ=Eo, (26)
(27)
where Eo is a constant and d a parameter. Its
Fourier transform is
Eo 2 2 g(k ) =-- e-d k2 /2.
2 (211")1 (2.8)
By definition the applied voltage is
1"'0
V= E'dz=Eoeiwt•
-00 (29)
The ratio of this voltage to the current at the
point z=o depends in general on the parameter
d, which measures effectively the length of the
segment to which the driving force is actually
applied. In the present instance
2 2 • V /1(0) = 120 ed k2/21n ('Yy~/2). (30)
In the limit as d~O the region of application
reduces to a point and the ratio represents the
true driving-point impedance of the line.
Zi=lim V/l(O) =120 In ('Yyi/2) ohms, (31)
d-+O
assuming the external medium to be air. Practi
cally, it is only necessary that the region of
applied field be small relative to the wave-length
to justify the concept of a voltage V applied at a
. definite driving point z=O. In this limit the
impedance is independent of the exact functional
form of the applied field. This is easily verified for
the case of a "rectangular" distribution defined
by
234 G(z) =Eo when
G(z)=O when Izl <d,
Izl >d. (32) which reduces to (31) in the limit d=O.
One will note that u is exactly equal to k2 and y
equals zero only in the case of a perfectly con
ducting wire. In these circumstances the driving
point impedance of the system is infinite, a result
entirely comprehensible from the fact that the
wire is of infinite length. Sommerfeld's solution
has shown how currents, established in an
unspecified manner, are propagated. We now see
how these currents are related to the source and
it appears that a finite current in a perfect con
ductor of infinite length cannot be established by
a finite voltage. If the conductivity of the wire is
finite, the input impedance is large but bounded.
A current enters the wire and the inflowing
energy is eventually dissipated in heat.
It is of some interest to consider the case of a
wire of finite length, although it has no direct
bearing on the free antenna problem to be dis
cussed later. The procedure followed above will
give us, by a slight modification, the driving
point impedance at the center of a linear, vertical
antenna bounded at either end by horizontal,
perfectly conducting planes. The problem is thus
related indirectly to the establishment of waves
in hollow pipes.
The applied field is now represented by a
Fourier series in place of an integral. Let the
transverse, perfectly conducting planes be located
at z=l and z= -l. The tangential component Er
must vanish over these surfaces and hence in
place of (1) when r>a we construct a solution of
the form
00 (u nw Ez=eiwt L: An Ho (P2r) cos -(z+l),
n=O 21
(34)
where A is the wave-length in the dielectric. The
JOURNAL OF ApPLIED PHYSICS
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'" n1r E'=ei"'t L Cn cos-(z+l), (35)
n=O 21
so that the field within the wire is represented by
The boundary conditions at r=a lead to
X Cn 1 B,,=---
U1a J1(x) Zn (36)
(37)
in which Zn is formally identical with (13) but
with u restricted to the discrete set of values
n1r/2l. The current at any point on the line is now
DO Cn n1r 1= haei"'t L -cos -(z+l). (38)
n=oZn 21
Assume next the rectangular distribution of
applied field defined in (33). E' is then a sym
metric function of z, so that all odd coefficients of
(36) are zero, while for the even coefficients one
obtains
d
Co=--Eo 1 ' 2( -1)n . n1rd
C2n = Eo Sill --,
n1r 1
(n=1,2,···). (39)
The input impedance at the central point of the
wire is again found by taking the ratio of the
applied voltage to the current at z = 0 and passing
to the limit as z-'>O.
1 '[ 1 00 1 1 Zi=-1/ -+2 L --,
1ra Zo n=1Z2n (40)
or for the admittance
(41)
VOLUME 12, MARCH, 1941 where Yn=1/Z n• Let us assume for the moment
that the conductivity of the radiating cylinder is
infinite. Then Yn reduces to
~
Y2n= -(1_tl,,2)}(e dJL2)!
Hi2
)[ (ha/X)(1- fln2) I]
X (42)
H~2l[ (ha/X) (1-tln2)!J'
where fjn = nX/21. If tin> 1, the ratio of Hankel
functions is a pure imaginary. Hence if X> 21, all
admittance terms with the exceptions of Yo have
susceptance components but no conductance.
The complex power associated with these terms
is purely reactive. If now X is decreased, a critical
wave-length is reached .at which Y2 assumes a
nonvanishing conductance. Further decrease of X
introduces successively in step-wise fashion the
conductances of higher modes, and with each
entry there is a corresponding increase in real
power input representing outward radiation of a
higher order wave. It will be noted in passing
that the sum of these terms fails, in the present
instance, to approach a limit, due to the as
sumption of a voltage concentrated at a mathe
matical point rather than over a small but finite
segment of the cylinder. This matter will be
referred to later.
The term Yo has a nonvanishing conductance
at all wave-lengths and represents the principal
wave. Its field is strictly two dimensional, there
being no variation along the z axis. The com
ponent Er is zero everywhere and energy flows
radially outward from the cylinder. Such a mode
is possible because of the absence of any further
boundaries transverse to the conducting planes.
It will be recalled that the principal wave is
completely suppressed in hollow wave guides of
finite cross section. .
In case the conductivity of the cylinder is
finite the term xJO(x)/J1(x) in (13) contributes a
small conductance to each admittance com
ponent at all wave-lengths, accounting for the
dissipation of a certain amount of energy in heat.
235
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1.1712798.pdf | A Correlation Method for the Elimination of Errors Due to Unstable
Excitation Conditions in Quantitative Spectrum Analysis
Saul Levy
Citation: Journal of Applied Physics 11, 480 (1940); doi: 10.1063/1.1712798
View online: http://dx.doi.org/10.1063/1.1712798
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/11/7?ver=pdfcov
Published by the AIP Publishing
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A Correlation Method for the Elimination of Errors Due to Unstable Excitation
Conditions in Quantitative Spectrum Analysis
SAUL LEVY*
Perth A mboy, New Jersey
(Received January 10, 1940)
THE quantitative determination of the com
position of substances by spectroscopic
means (quantitative spectrum analysis) is not
very old. Its development required not only the
improvement of spectroscopic equipment but
also a better understanding of the phenomena
which accompany the emission of spectral lines.
At the present time, quantitative spectrum
analysis has achieved a high degree of perfection
as far as ~peed and accuracy are concerned. The
methods employed in this field are finding more
and more applications in industrial laboratories
and still greater application is to be expected in
the future.
Quantitative spectrum analysis, however, is
still attended by some difficulties which retard
its development and expansion. The difficulties
at the present time are not so much in the field
of intensity (or density) measurements, the
technique of which is near to perfection, but in
a certain instability and insufficient reproduci
bility of line-excitation. In other words, the
difficulties lie in the light sources.
Workers in this field have suggested various
improvements in equipment to overcome these
difficulties, the best known of which is the so
called Feussner1 method with synchronous inter
rupted discharge.
Although increasing the stability and improv
ing the standardization of excitation conditions
are very desirable, nevertheless improvements in
equipment alone can hardly remove the diffi
culties in a radical way. The reasons for the
instability of "burning" of the arc or spark are
various. All the electrical parameters: voltage,
current, self-inductance, capacitance, and resist
ance have an essential influence on the intensity
* Formerly member of the Physical Institute of the
Universitvof Moscow.
10. Feussner, Archiv. f. Eisenhuettenwesen 6, 551 (1933).
480 relations of spectral lines. But while it is not
difficult to maintain the constancy of these
parameters, there are many other factors, not so
easy to control, which influence the discharge
and, therefore, the intensity relations.
Particularly important is the influence of the
shape and structure of the electrodes on the dis
charge. A solid electrode gives a different result
than do chips or powder; moreover, with solid
electrodes of definite shape, the analysis is not
always accurate. Sharp edges or l~ttle defects in
the electrodes, such as holes or insertions of
particles of other metals, can cause a noticeable
change in the discharge; in fact a spark dis
charge can, in this way, be transformed into one
similar to an arc discharge. The length of spark
or are, which is not always equal to the distance
between the electrodes, has also an influence on
the intensity relations. The discharge is moving
from one place to another, and its length is
changeable. This cannot and should not be
avoided, because it is desirable in most cases to
make use of a considerable surface for getting a
good average.
There are many cases, too, when it is im
possible to give a definite shape to the electrodes,
as for example when they are very small and
cannot be made up in a mechanical way (grain
of gold, etc.), or when they are ready-made
objects.
The application of standard working curves
(relations between concentration and intensity
ratio under standard conditions) is in all these
cases questionable, for they are obtained usually
with electrodes of other shape. On the other
hand, the preparation of standard working
curves for different shapes of electrodes would be
too laborious.
The influence of extraneous impurities has to
be mentioned separately. This problem has been
JOURNAL OF ApPLIED PHYSICS
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and the influence determined in many cases.
Twyman, Duffendack, Breckpot, Brode and
many others2 investigated the influence of ex
traneous metals on relative line intensities. Such
influences have to be tested in every given case
separately, and if stated, many working curves
have to be made for different concentrations of
the extraneous impurity. Each working curve,
however, requires a series of repeated spectro
grams, and takes much time. Besides, one has
to know what kind of extraneous impurities there
are and in what quantities.
These considerations show that improvements
in equipment alone cannot remove some of the
difficulties of quantitative spectrum analysis.
Therefore an attempt is made in the present
paper to indicate another way of eliminating
these difficulties. This procedure is essentially
the same that was applied by Naedler3 in the
determination of platinum and rhodium in silver
where the change of excitation conditions was
caused through the various shapes of small
electrodes. It is the opinion of the author under
whose supervision this method was elaborated
(in the laboratory of Professor Landsberg of
Moscow University) that it should be useful in
many other cases, including the influence of
extraneous impurities. Although the method has
its greatest application to widely varying excita
tion conditions, it may also be profitably used
under "normal" conditions to improve the
accuracy of an analysis.
The method is a simple and natural develop
ment of the fundamental principles of quantita
tive spectrum analysis as given by Gerlach and
Schweizer. 4 Let us first outline the method of
Gerlach and Schweizer:
1. The concentration of the "impurity" is
determined by measurements, in the same spec
trogram, of the intensity (or density) ratio of a
line of the impurity and one of the main sub
stance. These two lines are chosen to satisfy the
condition that they react approximately in the
2 See W. Brode, Chemical Spectroscopy (John Wiley &
Son, 1939).
3 W. W. Naedler, Comptes rendus de l'Acad. des
Sciences, U. R. S. S. 4,23 (1935); Tech. Phys. U. S. S. R. 4,
553 (1936).
4 W. Gerlach and E. Schweizer, The Foundations and
Methods of Chemical Analysis, etc. (Adam Hilger, London,
1930).
VOLUME 11, JULY, 1940 same way when excitation conditions are changed.
They were therefore called by Gerlach the
"homologous" pair. 2. The constancy of excita
tion conditions is checked by means of observa
tion (without actual measurement) of a "fixation
pair" ; i.e., of a pair of lines of the main substance
whose intensities are equal under the desired
working conditions, but which react in a different
way when the conditions change. When the two
lines show different intensities, it is a proof that
the excitation conditions have deviated from the
standard, and the spectrogram is to be rejected.
The method of Gerlach and Schweizer is suffi
cient for an accurate analysis, if and when it is
possible to maintain constant conditions, but this
is not always possible, as we have seen above.
The method which will be described below in
detail, consists of a combination of actual meas
urements on two pairs of lines, the working pair
and the fixation pair. We choose as the working
pair any two arbitrary lines, one from the main
substance and one from the impurity, which may
or may not react in the same way when excitation
conditions are changed. For the fixation pair,
two lines from the main substance are chosen
which react in a different way when excitation
conditions are changed. As we shall see, there is
a definite correlation between the intensity ratios
in both pairs, which does not depend on that
particular factor which has caused the change of
excitation; i.e., on the change of electric param
eters, or the shape of electrodes, or the distance
between them, or the influence of extraneous
elements. This correlation can be easily de
termined by deliberately changing one of those
factors, for instance by varying the self-induct
ance of the spark circuit. The analysis is then
made with the aid of both the correlation curve
and the working curve. The method is based on
some known facts concerning electrical discharges
in gases, which are briefly summarized in the
following paragraphs.
Low PRESSURE DISCHARGE
The investigations of Langmuir5 and his col
laborators have demonstrated that, in the posi
tive column of a discharge, even at relatively low
5 I. Langmuir and E. Mott-Smith, Gen. Elec. Rev. 26,
731 (1923); Phys. Rev. 28, 727 (1926).
481
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distribution of electron velocities is formed which
depends on the gas pressure. Between the
quantity T., which has in the Maxwell ex
pression the same meaning as the temperature
in the corresponding gas kinetic formula, and
the average velocity of the electrons V (in volts)
is the relation:
eV=!kT.,
where e is the electronic charge, k is the Boltz
mann constant, and Te is called the electron
temperature of the discharge. Te at low gas
pressures is of the order of 20,000o-40,000oK,
and decreases when the pressure increases.
The reason for the formation of a Maxwellian
distribution of electron velocities is the collisions
between the electrons and the atoms. It can be
expected, therefore, that the inelastic collisions
which excite the atoms will lead to an analogous
distribution of the potential (excitation) energy
of the atoms. In fact, as Kopfermann and
Ladenburg6 have shown, the numbers of excited
atoms in the various energy levels correspond to
a Maxwell-Boltzmann distribution, the tempera
ture of which is equal to the electron temperature
(about 20,0000K) while the gas temperature of
the discharge (from Doppler-effect) 7 is 300-
400oK. The measurements were taken in a neon
discharge tube at about 1 mm pressure and
about 1 amp. per cm2 current density. Kopfer
mann and Ladenburg also deduced theoretically
that the assumption of a Maxwellian distribution
of electron velocities in conjunction with "col
lisions of the second kind"8 leads to a Maxwell
Boltzmann distribution of the atoms among the
energy levels.
Let Nk be the number of excited atoms in an
upper state k, Ni the number in a lower state j,
which may also be an excited state. Then for
statistical equilibrium,
Nk/ Ni=Ae-",/kT"
where hI' is the energy difference between the
two states, Te is the electron temperature, and
6 H. Kopfermann and R. Ladenburg, Naturwiss. 19,513
(1931); R. Ladenburg, Rev. Mod. Phys. 5, 243 (1933).
7 R. Ladenburg and S. Levy, Zeits. f. Physik 65, 189
(1930).
8 See A. C. G. Mitchell and M. W. Zemansky, Resonance
Radiation and Excited Atoms (University Press, Cambridge,
1934), p. 57.
482 A is a constant equal to the ratio of the statistical
weights of both states. In other words, the energy
levels are occupied by the atoms in the same
relative number as in the case of thermal excita
tion at the corresponding temperature.
FREE ARC
Similar conditions exist in the positive column
of a free arc discharge (at a pressure of 1 atmos.),
as was shown by Mannkoppf. 9 The difference is
only that in the arc because of the high pressure,
the electron temperature is practically equal to
the gas temperature. Therefore we can say that
the excitation in that part of the arc is a thermal
excitation.
In the cathode layer of the arc the conditions
are very differen t from those of the other part.10
I t is usually acceptedll that the excitation there
corresponds to a high electron temperature, but,
as far as the author is aware, no investigations
have been made concerning the distribution of
the excitation energy of the atoms in that layer.
It is possible that there is no statistical equi
librium due to the lack of time (few collisions).
Therefore the cathode layer has to be treated
separately. However, as Mannkoppf and Peters
have shown, the excitation in this layer is
remarkably stable-much more so, in fact, than
in the positive column.
FREE SPARK
Photographs by Kaiser and Wallraff,12 taken
with the aid of a rotating mirror in a manner
first described by Fessenden, show with par
ticular clarity that the radiation of a spark in
air at atmospheric pressure consists essentially
of two parts: the radiation of the purely periodic
discharge with a lifetime of from 10-6 to 10-5
sec., and the radiation of the hot vapors with a
lifetime up to 10-3 sec. This latter part of the
radiation is the more important one and repre
sents the greater part of the total light. It is
pure temperature radiation. Kaiser and Wallraff
demonstrated further by means of an oscillo-
• R. Mannkoppf, Zeits. f. Physik 86, 161 (1933).
10 R. Mannkoppf and E. Peters, Zeits. f. Physik 70,
444 (1931).
11 See W. Rollwagen, Spectrochimica Acta 1, 66 (1939).
12 H. Kaiser and A. Wallraff, Ann. d. Physik 34, 297
(1939).
JOURNAL OF ApPLIED PHYSICS
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.300
2M /
260 /
2¥0
220
.., :too /
V
~ .. 180
(...
~ 160 ,.
"<:: /
/
II
I
~ 11/0
120 /
I
100 J
/
80
00
¥O V /
'1800
Te",~eMfqre ill rler ..t
FIG. 1. Graph of e-hp/kT against T with hp equal to 4.24
X 10-12 erg, corresponding to p equal to 6.5 X 1014 sec.-!.
graph that the spark discharge is really a high
frequency arc of low voltage (about 50 v). It is
highly probable that the radiation of the first
part of the spark discharge is also temperature
radiation, like the radiation of a free arc, where
the electron temperature is equal to the gas
temperature. However, even if it is not so, we
can be sure that the excitation energy in the
first part of the discharge is also distributed
statistically because of the high pressure of
the gas.
DEGREE OF IONIZATION
The degree of ionization, as is well known,
can be calculated from the equation of Saha,13
which gives the ionization as a function of the
temperature and pressure. Langmuir showed
that in a discharge at low pressure there is no
one temperature for particles of various kinds,
13 M. N. Saha, Zeits. f. Physik 6, 40 (1921).
VOLUME 11, JULY, 1940 but many "temperatures" for each kind. The
ionization therefore cannot be calculated in a
simple way, unless complete thermal equilibrium
exists. We see now that this calculation is possible
in a free spark or arc, and not possible in a
Geissler tube at low pressure. Therefore we can
say that the neutral and the ionized atoms in
a spark or in an arc at atmospheric pressure are
in a thermal equilibrium, which may not be true
in case of a discharge at a lower pressure.
The curve e-hp/kT showing the relative numbers
of atoms which occupy two energy levels with
energy difference hll=4.24XlO-12 erg (11=6.5
Xl014 sec.-1), as a function of the temperature
in the interval between 4000 and 54000K is
shown in Fig. 1. The relative atom number for
T=4500oK is 1 : 1000. We see that over a
relatively large temperature interval this ratio
changes almost linearly with temperature. A
change of temperature of 1000K causes a change
in the ratio of about 20 percent.14
So long as the intensities of spectral lines are
proportional to the number of atoms, the in
tensity ratios are proportional to the Boltzmann
factor plotted in Fig. 1. This is true for radiation
from a small volume element of the gas in which
reabsorption does not take place. Intensity rela
tions are altered when one is dealing with the
radiation from a finite volume (large concentra
tion of the atoms in the lower states, great
probability of transition). The ratios are not
represented by the Boltzmann factor any more,
but are still a function of the temperature.
The influence of a change in thickness of the
emitting layer will be discussed later on. Strictly
speaking, there is no one temperature that may
be associated with an arc or spark, but rather a
distribution of temperature, for the outer parts
of the discharge are cooler, and we have in a
cross section of the discharge a superposition of
many Boltzmann distributions.
Summarizing we can say that the intensity
relations of the lines in a spark and in an arc
(except maybe for the cathode layer) are deter
mined by the temperature. This is true as well
for the radiation of neutral atoms as that of
14 The change of temperature of 2000K at 90000K causes
only a 4 percent change in the ratio. This is one of the
reasons why the spark, whose temperature is much higher
than that of the arc, is more stable.
483
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FIG. 2. Concentration of an impurity in percent of the
main substance. A typical working curve. Ratio of the im
purity line to that of the line of the main substance plotted
against concentration of the impurity.
ionized atoms. In a Geissler tube it is true only
for the radiation of neutral atoms at high current
density.l5 Therefore, we can change the intensity
relations only through variation of the temperature.
Mannkoppf has expressed this very clearly with
regard to the influence of an extraneous element
on the arc by pointing out that the only influence
of an extraneous element is a change of tempera
ture, and that therefore the "sensitized fluores
cence," discovered by Franck, i.e., a selective
mutual influence of certain energy levels, is
impossible in an arc at atmospheric pressure.
We can add now that this is also impossible
in a free spark. As to the Geissler tube, the same
statement may be made at least with regard to
the radiation of the neutral atoms at high current
density. The fluctuations in the light sources
caused by any factor are accompanied by the
change of temperature.
These considerations justify the application of
the following procedure:
DESCRIPTION OF THE CORRELATION METHOD
The working pair may consist of arbitrarily
chosen lines (of the impurity and the main sub
stance) which are convenient for photometric
measurements. The choice of the fixation pair is
determined only through the condition, that the
energy difference of the two excited states should
be large enough to cause a noticeable change of
15 The higher the excitation potentials, the higher is the
necessary current density. The excitation potentials for
neon are about 16-18 volts, whereas, for metallic elements
they are 5-10 volts.
484 intensity ratio while the temperature is changing.
This condition can be always satisfied if one of
the lines belongs to neutral atoms and the other
to ionized atoms, although this is not necessary.
In an arc or spark the use of "spark" lines for
one of the lines is justified; in a discharge tube at
lower pressure it is questionable.
The working curve is to be found in the usual
way. Let h= Fa/ Fm be the intensity ratio of the
working pair (h pair), which is a function of
the concentration k of a in m (see a typical
working curve in Fig. 2), and f= Fd F2' the
intensity ratio of the fixation pair (f pair). It
does not matter whether we work with the actual
intensity ratios or with some function of them
which is better to measure. The f ratio has to be
kept constant while taking the whole series of
spectrograms for the working curve:f = fo = const.
It is convenient to choose an fo value for that
purpose which is approximately in the middle of
the values corresponding to the extremes of
temperature which can be expected.
The determination of the relationship between
the intensity ratios in both working and fixation
pairs while the temperature is changing has to be
made in the following way: Let us vary one
(or many) of the parameters which have an
influence on the discharge and therefore on its
temperature, for instance, the self-inductance of
the spark circuit, preserving at the same time
the concentration of the impurity in the elec
trodes, say k = k1. To each value of the varying
parameter we will get a pair of values of f and h.
f. f, f-r,;
FIG. 3. Correlation curves for various concentrations.
Intensity ratio of the working pair plotted against the
intensity ratio of the fixation pair under continuous varia
tion of excitation conditions.
JOURNAL OF APPLIED PHYSICS
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f values and get in this way the "correlation
curve" for the concentration kl (Fig. 3). For
other concentrations k2' k3, etc. we obtain curves
which naturally differ from one another. Then we
take from one of the correlation curves, say for
the concentration kl' a pair of corresponding
values of f and h, say II and hI. We see by means
of the working curve in Fig. 2 that, because of
the change of temperature indicated by fl' we
would obtain the value hI instead of ho• This
value of hI corresponds to the concentration
kl +~kl instead of kl' making a relative error
D.kdkl which may be positive or negative. Hence,
in order to obtain the right result, we have to
divide our result by a reduction factor R where
R= 1+~kdkl. Since to each f value (i.e., to
each temperature value) belongs a certain R, we
can plot R= 1 +~k/k as a function of J. In this
way we get the "reduction curve" (Fig. 4).
I t has to be stressed that the reduction curve
for a certain working curve does not depend on
that particular concentration by means of which
the correlation curve was made (see section, Dis
cussion of the Method). Nevertheless, in order
PIO
/.20
~~ {z% ... /.00 .....
A
11:
1"'/0
O.60L--_-L._---I. __ .l.-_-.L._--I':- __
0.8 0.9 UJ 1./ t~
FIG. 4. Example of a reduction curve. Reduction factor
R = 1 +Llk/k plotted against the intensity ratio of the
fixation pail.
to increase the accuracy of the reduction curve
it is useful to plot it by means of many correla
ti(;>n curves. Since the correlation curves are
practically straight lines,16 it is sufficient to take
only two points in order to plot the whole curve.
The correct determination of the concentration
of an impurity in an unknown sample is made as
follows: the hand f ratios are measured on the
16 The ratio of two spectral lines (see Fig. 1) is within
certain limits an almost linear function of the temperature,
consequently the connection between! and h is also linear.
VOLUME 11, JULY, 1940 +
•• '11)
~ C.20 ..
~
~
~ 0 f=%
~
~
~ 0.20
~
0.'11)
0.8 <>.9 /.0 1./ /.2
FIG. S. Correction curve from Naedler's paper. Llk/k
(equivalent error produced by a change in excitation
conditions) plotted against the intensity ratio of the fixa
tion pair. The dots are the actual measurements for plotting
the correction curve.
spectrogram, then the concentration determina
tion k (in the first approximation) is made by
means of the h ratio and the working curve in
the usual way, and then R is determined by
means of the f ratio and the reduction curve.
The correct result is k/ R.
As an example, a typical curve is shown in
Fig. 5 taken from Naedler's work on the determi
nation of platinum and rhodium in silver. The
light source was a spark and the photometric
measurements were made with a logarithmic
sector. The silver electrodes were very small and
of different shapes. f= Ft! F2 is the intensity
ratio of two Ag lines 2744A and 2722A ("fixation
pair"), ~k is the corresponding correction to the
analysis in percent for platinum. The curve was
used in conjunction with the working pair
3043A Pt and 3099A Ag. The mean error of a
single determination of Pt before the correction
was ± 18 percent; after the correction (using the
same spectrogram) ±9 percent; whereas for Rh,
the mean error before correction was ±21 per
cent and after correction ± 13 percentY
DISCUSSION OF THE METHOD
The correlation curves obtained at different
concentrations have different slopes because of
reabsorption, which depends on the concentra
tion. Therefore the change of the relative number
of atoms does not cause a proportional change of
the intensity ratio. But the slope of the corre-
17 The remaining rather large error was mostly due to the
-unsatisfactory quality of the photographic plates and un
sufficient accuracy of the measurements with the logarith
mic sector.
485
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practically the same reabsorption. IS If the slope
of the correlation curve corresponding to the
concentration k2 is smaller than that correspond
ing to the concentration kl' then the corre
sponding I:lk/k will still be practically the same,
because of the smaller slope of the working curve
at k2• Therefore, the value of I:lk/k corresponding
to a certain f value is the same for all concentra
tions. This is rigorously true so long as I:lk/k is
small, i.e., so long as the slope of the working
curve in the interval I:lk does not change very
much. A value of I:lk/k equal to 0.3 or 0.4 can
usually be regarded as "small." This is the range
of values brought about by the influence of the
temperature variation that usually occurs in
spectroscopic practice. Otherwise, when I:lk/k is
very large, one reduction curve for all concentra
tions can no longer be used, and one has to use
the corresponding correlation curves.
The intensity ratios are in fact not only a
function of the temperature, but also of the
"thickness" of the emission layer (because of
reabsorption), when one is dealing with a con
siderable concentration of atoms in the lower
states or with great transition probabilities of
the lines. Furthermore, a substantial change of
the conditions (great variation of current density,
etc.) can cause a change in vapor density which
also influences the reabsorption. It is important
to know the extent to which the correlation
curves are affected by a change of reabsorption,
in other words, to know the limits of the method.
This question can be answered only through experi
ment in every doubtful case. The method is
applicable so long as the correlation curves do
not change appreciably. In general, the change
of the vapor density on the correlation curves
will be an effect of the second order.
It is not necessary to measure the intensity of
four lines in order to plot and to use the working
and the correlation curves. One can avoid the
fourth measurement and use only three lines.
For instance, Fm. can be equal to Fl or F2•
Moreover, two lines of the impurity can also be
used for the "fixation pair."
For the concentration determination one
usually uses more than one working pair. An
18 The temperature influence on the reabsorption is
negligible.
486 average is usually taken from the results from
two or more h pairs from the same spectrum.
This procedure is correct, if the divergence of
the determination by both pairs is caused only
through accidental errors of the measurements.
I t is not correct, when the divergence is caused
by a change of excitation conditions. The corre
lation curve can be taken in this case with the
aid of two lines of the impurity. The average of
the results should be taken only after the correc
tion. The advantage of using the lines of the
impurity for getting the correlation curves is that
no more measurements are required than before.
Application to a "normal" analysis
The correlation method permits one to work
under nonstandardized conditions with satis
factory results. It will also diminish the mean
error while working under standard conditions
by eliminating the fluctuations of the light
source. As well known, the mean square error R
of the result depends on the partial mean errors
rl, r2, ra, ... according to the equation
R2=rI2+r22+ra2+ ....
Assuming that the irregularities of the photo
graphic plate cause an error of analysis rl of
about ±1.5, and a photometric error r2 of about
±1.5, then with a total error R= ±5 percent,19
we get for ra, the error due to irregularity of the
source, about ±4.5 percent. We see therefore
that the main error of the analysis in this case
is caused by a change of temperature in the
source and perhaps through insufficient homo
geneity of the sample. The correlation method
permits us in this case to eliminate ra and sepa
rate it from r4, the error due to inhomogeneity.
After ra is found as the mean correction from the
reduction curve, we determine r4, which charac
terizes the influence of the inhomogeneity on
the accuracy of the particular method of analysis.
SUMMARY
It is pointed out that some difficulties associ
ated with quantitative spectrum analysis cannot"
be removed through improvements in equip
ment only.
A survey of the most important light sources
19 See for example J. A. C. McClelland and H. Kenneth
Whaley, Spectrochimica Acta 1, 21 (1939).
JOURNAL OF ApPLIED PHYSICS
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the radiation of all of them is determined by
only one quantity which is either the gas tem
perature or the electron temperature, the latter
of which is in some cases higher, in others equal
to the gas temperature of the discharge. The
excitation energy is therefore distributed among
the excited states of the atoms statistically, and
the number of atoms in the various energy levels
is determined uniquely by the electron or gas
temperature. Consequently the intensity ratio
of two lines is related to the intensity ratio of
two others. A "correlation method" is described, which permits one to work at nonstandardized
conditions (variation of the shape of the elec
trodes, influence of extraneous elements, etc.)
while reducing the measurements to "normal"
(standard) conditions. The method may also be
profitably used under standard conditions to
improve the accuracy of an analysis while
eliminating errors due to accidental fluctuations
in the light sources.
In conclusion, the author would like to express
his sincerest thanks to Professor Mark W.
Zemansky for many helpful discussions and
suggestions.
Growth Conditions for Single and Optically Mosaic Crystals of Zinc
C. A. CINNAMON AND ALBERT B. MARTIN*
Physics Department, University of Wyoming, Laramie, Wyomitig
(Received January 30, 1940)
A modified Kapitza method used in the study of conditions favorable to the growth of single
crystals of zinc (99.99+ percent pure), shows that the ratio of the temperature gradient (across
the interfacial boundary between the liquid and solid phases) to the rate of growth of the crystal
must be maintained within an optimum range of values, depending on the angle of orientation.
Optically mosaic crystals give no indication of a preferred region of growth and can be ob
tained over a much wider range of conditions.
INTRODUCTION
THE modified Kapitza method of growing
single crystals of zinc as described by
Cinnamon! and used by other investigators 2-4 has
met with a fair degree of success. However, a .
more recent application of this method has
resulted in the production of a large number of
optically mosaic crystals5 compared to the num
ber of single crystals.6 In this respect difficulties
arise quite similar to those experienced by investi-
* Now at Yale University, New Haven, Connecticut.
1 C. A. Cinnamon, Rev. Sci. Inst. 5, 187 (1934).
2 W. J. Poppy, Phys. Rev. 46, 815 (1934).
3 H. E. Way, Phys. Rev. 50, 1181 (1936).
4 G. E. M. Jauncey and W. A. Bruce, Phys. Rev. 50, 408
(1936).
5 A description of optically mosaic crystals of zinc and
photomicrographs of natural cleavage surfaces are given
by H. K. Schilling, Physics 5, 1 (1934).
6 A single crystal, when properly cleaved, is characterized
by a single, flat and mirror-like cleavage surface in contra
distinction to the optically mosaic crystal having a
"broken" cleavage surface consisting of discontinuities
caused by two or more slightly inclined areas.
VOLUME 11, JULY, 1940 gators7•8 employing the Czochralski-Gomperz
method.
The study of factors influencing the growth of
single-crystalline zinc, as initiated by Cinnamon,
was but partially completed, in that only the
lower limit to the region of favorable growth had
been determined. The existence of a lower limit
region was later qualitatively confirmed by
Poppy2 and Way,3 who used the same method
and procedure for crystals of approximately the
same size and degree of purity. The growth con
ditions imposed by J auncey and Bruce4 also agree
reasonably well, considering the difference in
cross-sectional area and the possibility of differ
ences in impurities. Poppy, also, found indica
tions of an upper limit to the favorable conditions
as predicted by Cinnamon; however, his data
were not extensive enough to set a definite
7 H. K. Schilling, Physics 6, 111 (1935).
8 J. S. Kellough, "Growth conditions for some zinc-rich
alloys," Thesis, University of Iowa, 1937.
487
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1.1712790.pdf | Temperature Radiation Emissivities and Emittances
A. G. Worthing
Citation: Journal of Applied Physics 11, 421 (1940); doi: 10.1063/1.1712790
View online: http://dx.doi.org/10.1063/1.1712790
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/11/6?ver=pdfcov
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and Emittances *
By A. G. WORTHING
University oj Pittsburgh, Pittsburgh, Pennsylvania
Introductory
THE word emissivity comes from the Latin
"emittere" meaning to send out. In accord
with that primary meaning, an emissivity for a
given material is a measure of the ability of a
body made of that material to send out radiant
energy. Such an ability might be expressed in
'terms of the rate of emission per unit of surface
area. Some use the word emissivity in this sense
and speak of an emissivity of 50 watts/cm2, for
instance; but general usage now expresses this
ability differently. A comparison is made instead
with a like ability of a complete or perfect
emitter, a blackbody, at the same temperature.
In the interior of an opaque body of uniform
temperature throughout, at distances from its
surfaces yielding practically complete absorption
for entering radiation, blackbody conditions are
found. If the body is a blackbody, the rate of
emission of radiant energy from its surface will
correspond to the unhindered passage of radiant
energy from such an interior. If the body is a
nonblackbody, the rate of emission will be
lessened because of the 'hindrance, in the way of
reflection, occurring at the surface. With these
facts in mind, it is natural to express a sending
out ability, that is an emissivity, for nonblack
material as a ratio, that for an opaque body
composed of the nonblack material to the corre
sponding ability for a blackbody at the same
temperature.
In accord with the usage that an ivity ending
shall denote a characteristic of a material, the
term emissivity is limited to a comparison with a
blackbody under conditions where the individual
characteristics of bodies composed of the material
under consideration, are eliminated. Since the
radiating characteristics of a body depend in part
... Presented at the American Institute of Physics Sym
posium on Temperature, Its Measurement and Control in
Science and Industry, New York, November 2, 1939.
VOLUME 11, JUNE, 1940 upon its opaqueness and the roughness of its
surface, these features must be considered in the
forming of an acceptable emissivity definition.
Ease of specification and of reproduction are the
obvious reasons for requiring that the emissivities
of materials shall refer to comparisons made with
opaque specimens whose surfaces are polished.
Accordingly the emissivity of a material is
defined as the ratio of a rate of emission of
radiant energy by an opaque body with polished
surface composed of that material as a conse
quence of its temperature only, to the corre
sponding rate for a blackbody at the same
temperature. Thus a rate of emission of radiant
energy per unit area by tungsten at 20000K is
23.7 watts/cm2, the corresponding rate for a
blackbody is 91.8 watts/cm2, and the total
hemispherical emissivity of tungsten at 20000K is
0.258. There are several types of emissivity.
Two other terms, namely emissive power and
emission factor, have been and are still used to
some extent to indicate what we now mean by
emissivity. It is also true that, to some extent, as
stated above, the term emissivity has been and is
used to designate the quantity now called
radiancy.
In accord with the usage that an ance ending
shall denote a characteristic of a body or of a
portion of a body rather than of the material
composing it, an emittance for a body at some
constant temperature is defined as the ratio of a
rate of emission of radiant energy by the body in
consequence of its temperature only to the
correspondi~g rate for a blackbody at the same
temperature. The condition of the surface of the
body, polished or not, oxidized or not, and the
condition as to opaqueness are immaterial. For a
tungsten filament at 20000K whose surface has
been roughened greatly a hemispherical total
emittance of 0.5 in contrast with the corre
sponding emissivity of 0.258 is not impossible. If
421
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emissivity as its lowest limiting value. For a glass
rod at lOOOoK, however, due to its nonopaqueness,
one expects emittances less than the emissivities.
In place of a normal spectral emissivity for
visible light of about 0.96, one may obtain a
corresponding emittance of say 0.10. Often the
emittances of composite bodies, as of a shellacked
piece of steel, are of interest. Their probable
values range from zero to unity.
Types and Definitions
There are various standpoints from which a
nonblackbody's radiating ability may be con
sidered. The two most common are the total
heating effects per unit area taking account of all
wave-lengths of radiation, and the spectral
heating effects taking account of only a very
limited range of wave-lengths. Corresponding
thereto we have total and spectral emissivities.
If the standpoint is one of visual effects rather
than of heating effects produced by the radiation,
we obtain a luminous, or visible, emissivity.
Corresponding to a comparison with a blackbody,
not at the same temperature but at the same
visual color instead, we speak also of a color
emissivity. Other emissivities such as an ery
themal emissivity might be defined but the writer
is not aware of their actual use.
For each of the foregoing types of emissivity,
at least two subdivisions are to be recognized, a
normal and a hemispherical emissivity. The
cause for this is the departure from Lambert's
cosine law exhibited by the radiation from
nonblackbodies. Illustrations of such variations
are shown in Fig. 1 spectrally for tungsten44 and
in Fig. 2 totally for platinum. 2 One might, if one
wished, speak also of an emissivity at any
prescribed angle with respect to the normal.
Such emissivities are not commonly listed,
however.
In giving precise definitions for the various
emissivities, we need, in describing radiation
sources, to make use of three well-recognized
terms and a fourth which is not well recognized.
They are8 radiancy, steradiancy, brightness, and
"luminous radiancy." The radiancy of a source of
radiation is its rate of emission of radiant energy
per unit of area. It is commonly expressed in
watts/cm2. The steradiancy of an element of a
422 source of radiation in a given direction is its rate
of emission of radiant energy in that direction per
unit area and unit solid angle. It is commonly
measured in watts/(cm 2 steradian). The bright
ness of an element of a source of radiation in a
given direction is its rate of emission of light in
that direction per unit area and unit solid angle.
I t is analogous to steradiancy and is commonly
expressed in lumens/ (cm2 steradian) or in
candles/cm 2. The "luminous radiancy" (the not
well-recognized term) of a source of light is its
rate of emission of light per unit of area. It is
analogous to radiancy and is expressed in
lumens/cm,2.
We are now ready to give precise definitions
for the various emissivities, each of which is
defined for an element of polished surface of an
opaque body at constant temperature.
A hemispherical total emissivity, Eht, for the
polished surface of art opaque portion of material
12
-- -~ ---
" /"
l-/' v-' B>+8, M~ I--------- -p
~~
B> -
/ 1-
B / II
/ /
.7 /
/ J 1./ p
'" /v /
S< _t--/ r------
.¥ ---", /
~ ll"
J V ~B"
2 / I'j,
/ "-
-, V " "'. r---v I~ ", 0 '0 0 10 0
ANGLE IN D£GRHS
FIG. 1. Showing for tungsten, at temperatures ranging
from 17500K to 2470oK, relative spectral brightnesses
(X=O.66S}") for the principal polarized light components
B~ and BII and the natural light B~ +BII and the polariza
tion of the natural light P. The variation from Lambert's
cosine law is shown by the B ~ + B II curve, as well as the
variation of the emissivity <eA with angle of emission. The
B ~ and B II curves show similar emissivity variations for the
two corresponding polarized components.
JOURNAL OF APPLIED PHYSICS
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radiancy to that of blackbody material at the
same temperature.
A normal total emissivity, Ent. for the polished
surface of an opaque portion of material at
constant temperature is the ratio of its normal
steradiancy to that of blackbody material at the
same temperature.
A hemispherical spectral emissivity, Eh~, for the
polished surface of an opaque portion of material
at constant temperature is the ratio of its
spectral radiancy to that of blackbody material
at the same temperature.
A normal spectral emissivity, EnX, for the
polished surface of an opaque portion of material
at constant temperature is the ratio of its normal
spectral steradiancy to that of blackbody material
at the same temperature.
A hemispherical luminous emissivity, EM, for the
polished surface of an opaque portion of material
at constant temperature is the ratio of its
"luminous radiancy" to that of blackbody ma
terial at the same temperature.
A normal luminous emissivity, En!' for the
polished surface of an opaque portion of material
at constant temperature is the ratio of its normal
brightness to that of a blackbody material at the
same temperature.
A hemispherical color emissivity, Ehe, for the
polished surface of an opaque portion of material
at constant temperature is the ratio of its
"luminous radiancy" to that of blackbody ma
terial having the same color as viewed visually.
A normal color emissivity, Ene, for the polished
surface of an opaque portion of material at
constant temperature is the ratio of its normal
brightness to that of blackbody material having
the same color as viewed visually.
In use there has been considerable confusion
due to a failure to distinguish between hemi
spherical and normal emissivities. This has been
particularly true of total emissivities.
Emissivities, both spectral (Fig. 1) and total
(Fig. 2), vary with the emission angle. The
definitions for the various types belonging to this
group are obvious. They may be designated by
EOX, EOI, EO., and EOe• Types of emittances are equal
in number to the types of emissivities, and we
properly speak of the hemispherical total
emittance of a body and of its normal spectral
VOLUME 11, JUNE, 1940 emittance. Emittances will be distinguished by
primes, thus En/, Eh/, fhA', etc.
Closely connected with the terms emissivity
and emittance, in theory and practice are
the terms reflectivity and reflectance, and ab-
2.0
>-
~ ..: 1.8
C; ..: a: w I
<J1
~ 1.6
g
w ::: I-
::s 1.4 w a:
o :z ..:
~
~ 12
l
I
<!) cr
<D
W >-f= ..: -' It! o __
o 1\ / \
I I
1 ,
/ I
I
I
I
I
/ I
I
I ,
I
I
/ ,
I
I
I
I
I
I I
I L ~ , I
, I
\ I
\ I
\ I -,I
"
" ,I
II
J.
20 40 60 80
ANGLE OF EMISSION IN DEGREES
FIG. 2. Showing for platinum, at incandescence, the vari
ation (a) of total steradiancy, and (b) of spectral brightness
in the red with angle of emission.
sorptivity and absorptance. A reflectivity is de
fined for an opaque, polished portion of material
as the ratio of a rate of reflection of radiant
energy from its surface to the corresponding rate
of incidence of radiant energy upon it. An
absorptivity is defined for an opaque polished
portion of material as the ratio of a rate of
absorption of radiant energy by it to the corre
sponding rate of incidence of radiant energy upon
it. Since all of the radiant energy which is
incident on an opaque element of. surface is
necessarily either absorbed or reflected, the sum
of a reflectivity and its corresponding absorp
tivity is necessarily unity. As with emissivity, we
speak of spectral and total, normal and hemi
spherical reflectivities and absorptivities.
For an opaque-walled cavity which has a uni
form temperature throughout and is therefore in
equilibrium, it is easy to show that a body in the
423
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Downloaded to ] IP: 130.64.175.185 On: Tue, 09 Dec 2014 20:57:41interior is emitting radiation from its surface at
just the rate that it is absorbing radiation from
the walls which is incident on its surface. Not
only is this true for total hemispherical rates of
emission and absorption, but it is also true for
the normal and the spectral rates for the con-
P Q M": s'
·HH --ffr--0J -n-B-E--'" (9.--0---------m __ ----EJ
f d III. ~\:{ ~
,-",
S /
~(
FIG. 3. Arrangement of apparatus for obtaining spectral
emissivities by a reflectivity method in the visible region.
S is a nearly enclosed light source, M a lamp containing a
ribbon filament whose reflectivity is to be measured, Q a
Rochon double image prism, L a lens imaging S on the rib
bon filament, P a disappearing filament pyrometer with
pyrometer lamp at I, absorbing screen at a, limiting di
aphragm at d, and colored pyrometer glass filter atf. S, L,
and M are supported on a rotatable mount with a vertical
axis at the center of M. S' and L' are positions correspond
ing to Sand L for the determination of the unreflected
brightness of the image of S.
ditions described, generally known as blackbody
conditions. We may therefore write
(1)
the subscript T at the right indicating that not
only the ~, the a, and the r are for the tempera
ture T, but that the incident radiations also are
such as occur in a blackbody cavity at the temper
ature T. The equation then holds separately for
each type of E, a and r.
If, however, the incident radiation has a
spectral distribution different from that charac
teristic of a blackbody at the temperature of the
element of surface in question, the simple rela
tions given in the equation no longer hold for the
total emissivities. The corresponding spectral
values for E, a and r are, however, as one will
perceive, independent of spectral distributions
and are therefore completely interrelated at all
times by Eq. (1) as shown. To illustrate, for
tungsten at 2000oK, EnX at 0.665M is 0.435 and the
corresponding absorptivity and reflectivity values
are 0.435 and 0.565. The value of Ekt for the same
temperature is 0.260, but what the values of aht
and rht are cannot be stated unless the spectral
distribution of the incident radiation is known.
If it is that of blackbody radiation corresponding
to 2000oK, akt and rht are 0.260 and 0.740.
424 Measurement oj Spectral Emissivities
OPTICAL CONSTANTS METHOD
In texts on physical optics, there are shown
(1) the dependency of the reflectivity and the
emissivity of a material on its optical constants,
that is upon its index of refraction and its
absorption coefficient, and (2) how these con
stants may be determined experimentally. For
further details regarding the optical constants
method, such texts should be consulted.
REFLECTIVITY METHOD FOR OBTAINING EnX
This method for obtaining a spectral emissivity
depends upon the relation
(2)
or upon the corresponding relation in case EhX is
desired. In either case, the experimental pro
cedure involves three determinations of spectral
brightness or of spectral steradiancy.
To illustrate, suppose that one wishes to de
termine EnX for tungsten, say at 1500oK, in the
visible region. As the tungsten specimen, let him
select a uniform, polished ribbon mounted in a
glass lamp bulb which is either evacuated or
contains an atmosphere which does not react
chemically with the tungsten, and, as an arrange
ment of apparatus, that of Fig. 3, except that the
double-image Rochon prism Q may be eliminated
if one is not interested in polarized components.
Let BX1 be the spectral brightness of the mirror
resulting from its own high temperature, BX2
that of the source S in position S' as seen, with M
slightly displaced, through the bulb containing
the polished tungsten ribbon, and BX3 that of the
source in position S as seen reduced by reflection
from the mirror ribbon, superposed on the
spectral brightness which results from the mirror's
own high temperature. The reflectivity rnX, as a
first approximation, is then given by
(3)
Strictly speaking, one obtains thus an rex where 0
is half of the angle between the iine SM of Fig. 3
and the axis of the pyrometer. The correction to
be applied to yield rnX when not negligible may be
obtained by extrapolation. Eq. (2) serves for
obtaining EnX. Inspection shows that no correc
tions need be made for absorption of light by the
JOURNAL OF APPLIED PHYSICS
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accuracy it is desirable that Bn shall be con
siderably less than Bxa.
The method described has been much used by
the writer44 not only for determining EnX, but also
Eex for various angles of emission and for the two
normal polarized components of emitted light as
well as the light taken as a whole.
Langmuir,19 applied this method to tungsten
at its melting point. In a molten terminal of a
metal arc, there may be seen mirrored images of
several orders, the first being that of the op
posing terminal, the second that of the first
terminal mirrored in the second, etc. Spectral
brightnesses just inside and just outside such a
first-order image for terminals just alike and at
the same temperature, yield as above the rXn and
then eXn.
M3 ~ I' I'
I 'I '
I ~ \
\ 1\ \
I I , \
1\ \ \ I, ,\
I I ,\ I \ ,
I I \ \ B
I I '\ fill I' \ \ , \ \ , I
11 \ \ "
I I \ \ I'
1\ \ \ ,I " ' \ " II \ \ 1:
\1. \ \ I,
II \ II L' M II \ ,W II
". \, ~I / :\
'v' II ,\ \ I 1\ II
, \\\ "I \ I I
\ ~ '\ \ \ \ I I '\ \. \cr '-'-, : :
\, '\ \~'I\ \\,\, II :,
'\ T "I
\ 't "II ~ \\' \ \
. \' '--1\ \' \' I'
'~ '\" \ I \' ,\ ,
~ ,,:::..., \1 \\ \ \ I I \, ~{:\ \' \ ,I ,
'\ \\ ,I~' \\ \ ~\I . \\ II '::',\\ \I~_ \\ \ ,-'" :.---\' I, '~
\ \~,\ 'HI; M+
'y.-
~ M~
L
FIG. 3a. Diagram showing apparatus used by Weniger
and Pfund, reference 42, in the determination of normal
spectral emissivities EnX in the infra-red.
VOLUME 11, JUNE, 1940 s,
* n L, l
~~. 5,
*
FIG. 4. Apparatus for the determination of a hemi
spherical emissivity in the visible region. U, Ulbricht sphere,
T, polished hemispherical target, M, plane mirror, SlS2
light sources, L1L2lenses, N, opaque screen with opening to
just include the image of T formed by L2• P, photometer
head, F, filter for yielding approximately monochromatic
light of the desired wave-length.
Shackelford,aa using a somewhat open helical
coil of polished tungsten ribbon which was
heated electrically to a uniform temperature,
measured likewise the spectral brightness of the
ribbon within the coil just inside and just
outside an image. Values for EnX, as in the case of
Langmuir's measurements, followed simply.
Obviously the procedure outlined may be used
in the infra-red region as was done by Weniger
and Pfund42 (Fig. 3a). Of course a receiver
responding to the thermal effects of radiation was
substituted for the pyrometer.
REFLECTIVITY METHOD FOR OBTAINING EhX
To obtain a hemispherical spectral emissivity
by a reflection method is equally simple in
theory, though not so in practice. A most direct
method for the visual region employs the Ulbricht
sphere of spherical photometry with its inner
coating of highly reflecting and highly diffusing
paint. A small polished hemisphere T, (Fig. 4)
of the material being studied with the convex
surface symmetrically oriented with respect to
the photometric axis replaces the ordinary target.
The source S supplying the light within the
sphere should be so located that initially as much
as possible of its utilized luminous flux shall be
incident on a small portion only of the inner
surface of the sphere back of the target T on the
axis of the system at o. Insofar as the paint is
perfectly diffusing, the remainder of the inner
surface, except for the two small openings, will
then be uniformly bright and will illumine the
hemisphere uniformly. Under these conditions,
the ratio of an average spectral brightness of the
small hemisphere as viewed by the reflected light,
less its own natural spectral brightness, to the
corresponding spectral brightness of the inner
425
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Downloaded to ] IP: 130.64.175.185 On: Tue, 09 Dec 2014 20:57:41surface of the large sphere, yields a corresponding
rh"A and finally by means of Eq. (2) the €h"A sought.
An appropriate filter, F, of Christianson or other
type, yields the wave-length desired. An aver
aged spectral brightness for the hemisphere, IBhA
is assured by having its image just fill the opening
in screen N. Comparisons are made in the
standard manner with the auxiliary source 52.
An ordinary optical pyrometer cannot be used
FIG. 5. Mendenhalls open-V, blackbody wedge.
because the hemispherical surface ordinarily will
not be uniformly bright. However, a photoelectric
cell with a sufficiently large aperture placed back
of N may be safely used. A determination of the
brightness of the Inner surface of the large sphere
involves replacing the hemispherical mirror by a
plane mirror of knownrn"A with axis slightly tilted
with respect to the photometric axis. The screen
opening at N is then completely filled with light
reflected from the inner surface of the sphere. A
comparison of this image at N of spectral bright
ness, 2Bh"A with the auxiliary source 52 is made as
before. It follows that
€hA = 1-rh"A = 1-IBhX/2Bh),. (4)
The foregoing method has not actually been
used so far as the writer knows. Perhaps there has
not been sufficient need for the emissivity thus
measured. An approximation to this method how
ever, has been used by Prescott and Morrison32
in a determination of the surface temperature of
an oxide-coated filament. Because of the varia
bility of oxide coatings for filaments in practice
426 and because of the low thermal conductivity of
the oxide layer, measurements with an optical
pyrometer of the temperature of a coated tubular
filament with its wall pierced by a small hole are
not satisfactory. In place of the sphere, Prescott
used a cylindrical tube lined with white fluffy
cotton which was lighted up by two automobile
headlight lamps at opposite ends of the tube. A
lamp with the oxide-coated filament was mounted
with filament along the axis of the tube. An
optical pyrometer was used to measure the
spectral brightnesses (t) of the oxide surface
with the headlight lamps unlighted, (2) of the
oxide surface with the headlight lamps lighted,
and (3) of the cotton lining with the headlight
lamps lighted. The further procedure for ob
taining an rH and an €h"A is evident. Strictly the
emissivity obtained was neither normal nor
hemispherical since the average brightness was
for a cylindrical surface.
To obtain in a similar way a hemispherical
spectral emissivity wherever desired in the infra
red, using receivers responding to the thermal
effects of radiation, would seem quite practicable.
Inner surface coverings for the sphere such as a
diffusing aluminum paint which are generally
highly reflecting and highly diffusing throughout
the infra-red, and selectively reflecting materials
for filter purposes are both available.
DIRECT BRIGHTNESS AND STERADIANCY
COMPARISONS
In accord with the definition of an emissivity,
these methods employ direct comparisons of a
spectral brightness or a spectral steradiancy of
the body (a nonblackbody) with that of a
blackbody at the same temperature. Often but
not always the material of the non blackbody also
forms that of the blackbody and in such instances
the condition of a common temperature for the
two bodies is easily attained.
Le Chatlier according to Burgessb was the
first to use the blackbody characteristic of a
cavity in determining the brightness temperature
5"A, true temperature T, relations for a non black
body. Since 5A and T are connected with €"A by the
relation
(5)
JOURNAL OF APPLIED PHYSICS
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function of T.
It was Mendenhall,26 however, who in 1911
first proposed the open-V wedge device as a
practical method for assuring equality of temper
ature for the black and the nonblackbodies which
were to be compared. The procedure was simple
and a considerable impetus to the study of high
temperature radiations was given thereby. For
polished material, as is evident from Fig. 5, the
brightness viewed along OA is a composite
brightness, being the sum of the natural bright
ness of A for the direction AO, the natural
brightness of B once reflected, that of C twice
reflected, that of D three times reflected, that
from C directed toward D four times reflected,
etc., in all seven terms. In equation form this
yields for the spectral brightness of the wedge
opening wBx
«.Bx = nBx(1 +rx +rx2+ ... rx 6), (6)
where nBX is the natural spectral brightness of the
wedge material. Though strictly speaking nBX
varies with the angle of emission, that variation
is immaterial here. Were the series of Eq. (6)
infinite, the right-hand member would represent
the spectral brightness of a blackbody at the
temperature of the wedge, bBX. In the case of a
lOa-wedge, the departures of the wedge opening
from blackness ebBX -wBx) I bBX amount, re
spectively, to 0.0001, 0.0016, 0.018, 0.16 and 0.40
for spectral reflectivities of 0.60,0.70,0.80,0.90
and 0.95. Such a wedge is seen to be suitable for a
blackbody, if the spectral reflectivity is of the
order of 0.75 or less; and, where such is the case,
the spectral emissivity EnX may be taken as the
ratio nBX/ wBx, the nBX being measured in the
direction PQ (Fig. 5). This method was con
siderably used by Mendenhall and Forsythe,27
Spence,3! McCauley25 and others.
The open-V wedge fails if the surface is not
polished, but polishing ordinarily does not repre
sent a serious difficulty. There are certain real
difficulties, however. If the wedge is formed from
a single sheet of material, a bulge will form on the
inside at the sharp edge. If formed from two
sheets instead, a slot is quite likely to be produced
when the wedge is heated. Both effects are very
serious so far as blackbody conditions are
concerned.
VOLUME 11, JUNE, 1940 The best method for obtaining blackbody
radiation whose temperature is the same as or
very nearly the same as that of the material under
study, where the heating is done electrically,
seems to be that of shaping the material into a
FIG. 6. Diagram showing how radiation through it small
hole in the side wall of a uniformly heated tube builds up
to form blackbody radiation.
uniform tube with small holes through its side
wall. This was done first by the writer45 (Fig. 6)
in a study of the radiation characteristics of
tungsten. In this case the tungsten tube was
formed by extruding through an annular die,
tungsten powder which had been mixed with a
binder. The holes were punctured shortly after
the extrusion. The blackening of the radiation
for a somewhat slantwise angle of emission from
such a hole is nearly complete and independent of
the polish which mayor may not be present on
the inner surface of the tube. If the thermal
conductivity of the material is known, correction
may be made for the diffe.rence in temperature
between the internal and external surfaces of the
tube wall. An emissivity, obtained by comparing
an external surface brightness with that of an
adjacent hole, would seem to be free from error
of method. In some instances, as for Pt, Pd, Au,
and steel, small tubes may be purchased from
supply houses. With small holes properly drilled,
these tubes are equally as satisfactory as those
just described.
The methods described for obtaining tubes
with small holes in the sidewalls are not always
convenient or possible. In that case, one may
use a ribbon with small holes drilled through it, as
has been done by Wahlin39 and his co-workers,43
and roll it around a mandrel to form a complete
tube with opposite edges of the ribbon touching
427
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tubes would seem to be nearly if not quite as
satisfactory as the tubes which have been
described. Still another method of obtaining a
tube consists in winding a narrow ribbon, such as
may be obtained by rolling down a circular wire,
on a mandrel to yield a tightly closed spiral.
02 a
5
0 VI
/ ~J /
5 // 1 1/
/
.500 V ) c
~ ~/ to /
V> " // ~/
~/ V
/;7
1000
TEMPERATURE IN OK 1500 !Y
~/-a
2000
FIG. 7. A composite plot showing total emisslvltles,
normal En. and hemispherical Eh. for platinum; (a) theoret
ical curve for En' derived by Foote, reference 11; (b) curve
representing average of two sets of observed values of En.
obtained by Foote; (c) curve representing values of En.
obtained by Lummer and Kurlbaum, reference 22b; (d)
theoretical curve for Eh. derived by. Davisson and Weeks,
reference 9; (e) curve representing observed values obtained
by Geiss, reference 12, and separately by Lummer, refer
ence 22; (f) curve representing observed values obtained
by Davisson and Weeks, reference 9.
Previous to the winding, the edges of the wire
should be notched slightly to yield the desired
holes leading to the interior. This method was
used by the writer46 in a study of the emissivities
of Mo. Such blackbody tubes are definitely
inferior to those previously described.
When .the spectral emissivity of one metallic
substance is known, that of a second metallic
substance may be obtained by direct comparison.
In making such a determination for Ta by com
parison with Mo, the writer fused end to end two
equally sized filaments, one of Mo and one of Ta,
mounted them as a lamp filament, heated them
to incandescence, observed their spectral bright
nesses as functions of the distances from their
428 junction, extrapolated such brightnesses for short
distances to the junction, and computed the
emissivities for the tantalum on the basis that the
extrapolated spectral brightnesses corresponded
to a common temperature. This is not recom
mended as a primary method because of the
alloying action of the metals while being fused as
well as afterwards when the junction is at a
high temperature. The results obtained for Mo
by this method checked well with those obtained
otherwise.
Thus far tubular blackbodies have been used
chiefly for visual studies probably because of the
larger holes in the sidewalls, the larger tube and
consequently the larger heating currents that
would be demanded for receivers other than the
eye.
Spectral emissivities for a material are also
obtainable from comparisons of spectral radiancy
curves of the substance at a given temperature.
Assuring, where incandescent temperatures are
concerned, that the two temperatures involved
are precisely the same is the main drawback to
this method. Could one rely upon the Mendenhall
open-V wedge to yield blackbody radiation, as
was hoped for by McCauley25 in his studies, such
methods would be highly satisfactory. For tem
peratures which can be measured and regulated
precisely with the aid of thermocouples, the
general method is acceptable now.
HEMISPHERICAL SPECTRAL EMISSIVITIES
BY AVERAGING
Given for a material at some one temperature,
a normal spectral emissivity En). and the variation
with angle of emission (J for spectral emissivities
of the same wave-length Ee)., one can compute the
corresponding hemispherical spectral emissivity
Eh)'. By zonal integration, taking account of the
fact that the projection of an element of area
varies as cos (J, one obtains
1,,/2
E&).271" sin (J cos (Jd(J
o Eh).=----------
11(12
271" sin (J cos (Jd(J
o (7)
The first precise measures of variations of Ee).
with 0, seem to have been made by Bauer and
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Similar measurements have been made by the
writer, on the variations of EO}" for tungsten,
(Fig. 1) molybdenum, tantalum and carbon.
From these studies, it has been found that the
ratios of Eh}"/ En}.. for Pt, W, Mo, Ta, and C in order
are 1.045, 1.044, 1.062, 1.042, and 0.92~ While
certain general conclusions seem indicated, the
results are really too few in number to justify
their statement.
Measurement of Total Emissivities
METHOD OF COMPUTATION BASED ON E}..=j(A)
I t is obvious that if EnA = j(A) is known, one may
obtain Ent by the relation made the predicted values were generally slightly
too low.
O.6,----,-----,---~---r----r-----,
O.5r-~;2'I;::__--t---t_---j---t-----j
, ,
',-O.Ir---t---"" ........ :::l---t---"i''<:""""--t-----j ----2100'K
1700 'K
1300'K
300'K
01>0 ---'---;1.;'0 ---'----t.20,----'-----;3.0
WAVEUNGTH IN MICRONS
Ent=---------(8) FIG. 8. Observed normal spectral emissivities for tungs-
It is equally obvious that, if EhA=j(A) is known,
one may obtain Eht in an exactly similar manner.
Drude, assuming Maxwell's electromagnetic
theory, deduced the well-known relation
(9)
where p is the resistivity of the material and A 1 a
constant having the value 0.365 ohm-i. Using
this relation, Aschkinass 1 derived for the total
emissivity of a metal the relation
(10)
This equation was tested for platinum by
Lummer22 and by Weber.41 Deviations were
assumed as due to the failure of the theoretical
relations to take account of the variation of
platinum from the Lambert cosine law.
In 1915 Foote,ll using the more accurate
radiation constants then available, extended
Aschkinass' relation to include the second-order
approximation term. He obtained for platinum
Ent=Aa(Tp)t-A4(Tp), (11)
A3 and A4 having the values 0.5736 (ohm
em KO)-! and 0.1769 ohm em KO. In the region
lOOOoK to 15000K where measurements were
VOLUME 11, JUNE, 1940 ten as a function of wave-length for several temperatures,
and expected variations ( ... ) as a function of wave
length were the Drude relation general.
Sti11later Davisson and Weeks9 taking account
of the variation in EOA, expected in accord with
electromagnetic theory, arrived at the following
expression for the Eht for platinum
(TP)! (Tp) Eht=0.89920hm-!;; -0.90470hm-1;;
(TP)! (Tp) +1.1490hm-!;; -1.2450hm-2;;, (12)
of which C2 is the second radiation constant for
which 1.432 em KO was accepted. As shown in
Fig. 7, computed values for Eht for platinum are
greater than the observed values for tempera
tures below 70o.°K, and less for temperatures
above 700oK, the difference increasing with
increase in temperature. Fig. 7 also shows that
both the computed and observed values for Ekt
are greater than: the corresponding Ent. Davisson
and Weeks concluded that the deviation between
computed and observed results at the higher
temperatures could readily be explained by the
well-known failure of the Drude relation in the
region of the near infra-red the visible and
the ultraviolet, evidence for which is shown in
the observations for tungsten (Fig. 8).
429
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This method of measuring eht is particularly
applicable to metals which can be mounted and
heated as incandescent lamp filaments in vacuum.
It is also applicable to substances which, in the
form of thin opaque coatings, can be applied to
such filaments. Temperature measurements in
such instances represent the greatest sources of
uncertain ty.
a b
FIG. 9. Showing (a) a single filament mount with poten
tial leads and (b) a two-filament mount with filaments of
different lengths, for use in the filament-in-vacuum method
of measuring E ht.
The filament-in-vacuum method requires, for
the particular temperatures concerned, that one
shall be able to associate a definite heating
current, and a definite potential drop with a
definite length of filament whose known tempera
ture from one end to the other is sensibly uni
form. Two methods of mounting filaments for
this purpose are shown in Fig. 9. In the method
shown at (a), the portion of the filament chosen
is that between the places of attachment of the
fine potential leads. In the method shown at (b),
the central portion of the longer filament is so
chosen. Its length is the difference between those
of the two filaments. The potential drop used is
the difference between the two drops for the
filaments taken separately. One has always to
assure one's selfby some means that the filaments
are sufficiently long so that uniformity of temper
ature may be secured for the central portion of
the longer filament.
Given a filament of length I, of circular cross
section of radius T, maintained at a uniform
430 temperature T, by energy supplied electrically at
the rate IV in an evacuated space whose dimen
sions are large in comparison with r and whose
boundaries are at the temperature To, one can
determine an EM for the filament material at
the temperature T. The condition of a steady
state yields
In order the terms represent, per unit of surface
area of the filament, the rate of supply of energy
to the filament electrically, the rate of supply of
energy to the filament by absorption of radiant
energy incident on its surface, and the rate of
emission of radiant energy from the surface of
the filament. It is often assumed that ah/ is
equal to EM, but such is not the case. The radiant
energy incident, since To the temperature of the
surroundings will be different from T, will have a
different spectral distribution from that charac
teristic of a blackbody at temperature T. How
ever, if T differs but little from To, one may
assume equality and solve for an approximate Ekt
which later may be adjusted if additional deter
minations at other neighboring temperatures
show that such is necessary. If, on the other
hand, T is considerably in excess of To, the term
containing ah/ tends to become negligibly small
and a precise value for it becomes unnecessary.
In many instances that term may be neglected
altogether. Generally for metals, if not always,
the aht' will be less than the €ht for any particular
case.
The foregoing method has been used con
siderably in determining hemispherical total
emissivities of metals through wide ranges of
temperature. Corresponding emittances of bodies,
whose surfaces are not polished or whose partially
transparent surface layers differ from the under
lying layers, may be determined by this method.
TOTAL RADIATION PYROMETER METHOD
There are various forms of total radiation
pyrometers. Which one is used is not material
here. For this work, however, it is essential that
the calibration of the instrument shall show
directly or through computation the instrument
response as a function of the net rate of receipt of
radiant energy. If the temperature of the
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k(E/uP-uTo4), of which u is the Boltzmann
radiation constant and k a constant depending on
the detailed dimensions of the set-up.
To obtain the En! of some material at some
specified temperature T, one needs first to expose
the pyrometer to the radiation from a properly
prepared body of that material held at the
temperature T. The body should be opaque, have
a plane polished surface oriented with its normal
directed toward the pyrometer, and in size be
such as to fill completely the opening in a
radiation-limiting disk which is fixed with respect
to the pyrometer. The instrument response d,
possibly a galvanometer deflection, is noted.
Next with conditions in all respects the same,
except that a blackbody also at te"mperature T
replaces the body whose Ent is desired, a corre
sponding response do is noted. In accord with the
above given expression for the net rate of
reception of radiant energy, it follows that whole of the hemisphere and no more onto the
blackened disk of a thermocouple receiver or a
total radiation pyrometer. By a slight shift of the
hemisphere sidewise, the mirror, in effect, will
image instead a portion of the wall on the total
radiation receiver.
FIG. 10. Diagram of apparatus for the measurement of
hemispherical total emissivities at low temperatures using
the method of total reflection.
and that
Et=~+(1_!_)(To)4
do do T If the receiver and its surroundings are also at
(13) temperature To and if the reflectance of the
hemisphere for blackbody radiation characterized
by the temperature T is sensibly the same as for
(14) blackbody radiation characterized by tempera
ture To, it may be shown that
In case (ToIT) is small compared with" one or
dido approximately equals one, the ratio dido
may be taken as the total emissivity. If the solid
angle subtended at the receiving element of the
pyrometer by the aperture of the limiting disk is
small, the observed Et is an Ent. If the solid angle is
approximately hemispherical, it becomes an Eht.
Emittances are measured by this method as
well as emissivities. In industry normal total
emittances are very often measured.
METHOD OF TOTAL REFLECTION
This method does not seem to have been used,
though it possesses certain features tending
toward precision. As shown in Fig. 10, the
material under study is shaped as a hemisphere,
water cooled to a temperature To, and mounted
at the center of a large sphere kept at a higher
temperature T. A concave mirror outside, re
ceiving radiation from the hemisphere through a
small hole in the large sphere, serves to focus the
VOLUME 11, JUNE, 1940 where d is the receiver response for the conqition
where the hemisphere is centrally located and do
that for the condition where the hemisphere is
somewhat displaced. It has been tacitly assumed
that the reflectivity of the concave mirror and the
absorptivity of the receiver are both unity.
However, taking into account the deviations
therefrom in no way affects the equality between
the first and the last members of (15).
PARALLEL PLATE METHOD
This method described recently by the writer48
is based on the proposition that the rate of
transfer of energy by radiation between two
paral1e\ plates is a function of their hemispherical
total emissivities It seems not to have been used
for actual measurements though the underlying
equations are well known and have been con-
431
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box (Fig. 11) held at temperature To and with
dimensions large in comparison with those of the
contained device, there is mounted an electrically
heated metal plate A with surface kept at a
temperature T' as determined by thermocouples.
Let its surface have a known hemispherical total
emissivity, fht which is preferably high and a
reflectivity which is as nearly perfectly diffuse as
possible. Near to this plate and parallel to it on
one side, there is mounted a smaller circular plate
B with one surface covered with the material to
be studied and protected by a guard ring. The
mass, the dimensions, and the specific heat of
plate B must be known. The temperature of its
surface as well as that of the guard ring must be
measurable, preferably by a resistance ther
mometer or a thermocouple. The space between
the plates and presumably inside the box should
be evacuated.
The procedure follows. Initially by means of a
cooling device not shown in the figure, plate B is
brought to a temperature lower than To while
plate A is maintained at temperature T'. Then
with the cooling device removed, one observes
the temperature T of plate B as a function of
time. From a plot of such data, one is able to
determine the time rate (dT/dt)o at the instant
that T becomes To. From this, the mass of the
plate, its specific heat, and the area presented
toward plate A, one determines the net rate of
transfer per unit of area, of energy from plate A
at T to plate B at To by radiation. Call this rate
W. Consideration of the various processes of
emission, absorption and reflection between
plates A and B for the above specified charac
teristics for the surface of A, together with the
assumption that the absorptance of B for the
radian t energy inciden t on the A side is essen tiall y
equal to its emissivity-this would be very nearly
true if T' differs but little from To-leads to the
relations
1 W= , (qT4-qT o4)
1/ lEht+ 1/ 2Eht-l (16)
and to
(17)
All of the terms on the right-hand side of the
432 equation are directly measurable. If precise
measurements for the hemispherical total emis
sivity of a material of the corresponding emittance
of a body in industry is desired the above would
seem to be a fairly simple and precise method for
the determinations.
The factor
1
is used in industrial calculations for the transfer
of radiant energy between surfaces. McAdams24
refers to it as an "emissivity factor."
Luminous Emissivity
This term has often been called visible emis
sivity. It applies to luminous radiations and can
have significance only for materials raised to
incandescence. An EZ may obviously be obtained
(1) by comparing with a photometer the bright
ness of the material at some temperature with
that for a blackbody at the same temperature.
FIG. 11. Diagram of apparatus for the parallel plate method
of measuring hemispherical total emissivities.
The ratio of the two brightnesses is the EZ
sought. An EZ may also be obtained (2) by
computations based on known measured values
of EA' The formula is
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o El=-----------
J"'LxA-S(ec2/xT -1)-ldA
o (18)
where Lx is the spectral luminosity or luminosity
factor of radiation. Evidently an El is a weighted
average of EX'S. To the writer's knowledge lumi
nous emissivities have been determined only for
such substances as tungsten, tantalum, and
molybdenum.
Color Emissivity
Like luminous emissivity, this term can have
significance only for materials at incandescence,
and then only when their radiations may be color
matched with those from a blackbody at some
temperature. Strictly speaking an Ec is not an
emissivity at all, since radiations for the material
at one temperature are compared with those for a
blackbody at another temperature. It is, how
ever, a convenient term. An Ec may obviously be
obtained (1) by comparing with a photometer the
brightness of the material at some temperature
with that of a blackbody at a temperature such
that its color matches the material being studied.
An Ec may also be obtained (2) with the aid of an
optical pyrometer whose color filter can be
changed so as to yield at one time an effective
wave-length Ar, in the red, say, and at another
time as desired an effective wave-length Ab, in the
blue, say. When obtaining the Ec for a given
material at a temperature T, one seeks for a
blackbody at temperature Tc whose spectral
brightness in the red bears to the corresponding
spectral brightness for the material a ratio which
is exactly the same as that for the blue light. This
ratio is the Ec sought. An Ec may also be obtained
(3) by computations based on known spectral
emissivities for two wave-lengths in the visible
say EXr and EXb for wave-lengths AT and Ab. For
this computation, it is customary to substitute
the Wien spectral radiancy equation for the
Planck equation. For most practical cases the
error is very small. By definition
EXe-C2/XT
Eo =---- = EXe-(c 2/X)(1/T-I/T c) = const. (19)
e--c2/XT,
VOLUME 11, JUNE, 1940 1"-
"-.3 6 "-
6
~ r---
~ I'" HtH/
I' f·C V-
i'-. ~ ~K V
2 "-1/ I~
V t'---w. +- w 0 +- ,",5
1"1'<1 ,... r---
I 1-1-.211
1000 1000 I_
1600 Temp.erature 1600 2000 K
Curve Author Year A
Hand K Holborn and Kurlbauml1 1903 0.651'
WandB Waidner and Burgess40 1907 .66 LandM Laue and Martens20 1907 .63
F and C Fery and Cheneveau10 1909 .629
H Henning 14 1910 .665*
M Mendenhall" 1911 .658
Me McCauley" 1913 .658
S Spence34 1913 .658
HandH Henning and Heuse11i 1923 .647
W Worthing47 1925 .665
SI Stephens" 1939 .665
* Interpolated from results for 0.6801' and 0.627,..
FIG. 12. Published spectral emissivities of platinum for
red light at incandescent temperatures as obtained by
various experimenters.
The constant must not vary with the wave
length in the visible region. Choosing two wave
lengths AT and Ab, we may write therefore
or
EAT
In -=c2(1jT-1jTe)(1jAT-1jAb). (21)
EXb
For tungsten at 2500oK, 0.665JL and 0.467 JL as
selected values for Ar and Ab, and 0.425 and 0.462
as the corresponding EXT and £Ab, we obtain with
the aid of Eq. (19), 2557°K as T" and with the
aid of Eq. (19), 0.356 as Ee. Color emissivities
have been determined mainly for metals such as
tungsten, molybdenum, and tantalum in the
field of i11umination.
Measurement of Emittances
I t is obvious that emittances are measured hy
exactly the same methods as are emissivities.
There is the exception that the reflectivity
methods are applicable only when the body
whose emittance is being sought is opaque. This
is in accord with the fact that, when the body is
opaque, has a polished surface and is composed of
a single material, an emittance of the body is the
corresponding emissivity of the material.
433
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perature values are given in a few instances where they, along with values at higher temperatures, form a connected series and
where the values given for the higher temperatures depend on those given for low temperatures. *
AUTHOR
Prescott, and Hincke31
Whitney"
Stubbs"
Bidwell'
Burgess and Waltenberg<
Burgess'
Holborn and Henning!'
Stubbs and Prideaux37
Bidwell' ,
Burg"". and Waltenberg'
Worthing47 METHOD
Tube
Tube
Spectrophotometer
Spectrophotometer
Couple and pyrometer
Contact with Pt
pyrometer
pyrometer
Spectrophotometer
Spectrophotometer
Couple and pyrometer
Contaet with Pt
Contaet with Pt
Tube, reflectivity RED GREEN BLUE IR AND UV
T IN OK A IN }L, En"-A IN Il. EnX X IN p., En>.. }.. IN IL, En>.
1600 0.66 0.89
2500 0.66 0.84
1600-2500 0.66 0,374
0.66 0.11
0.66 0.15
900-2100 0.66 0.105
1275 0.66 0.105 Carbon
Columbium
Copper
1350 0.66 0.120 0.55 0.38
1375 0.66 0.15 0.55 0.36
1450 0.66 0.14 0.55 0.32
1500 0.66 0.13 0.55 0.28
Gold
0.66 0.127 < 1336 0.665 0.120 0.535 0.410 0.495 0.531 > 1336 0.208 0.405 0.473
1100-2020 0.66 0.125
1275 0.650 0.145 0.550 0.38 > 1336 0.650 0.219 0.550 0.38
1275 0.665 0.140 0.535 0.448 0.460 0.632
Iron
Bidwell' Couple and pyrometer 1000 0.66 0.27
1480-1500 0.66 0.29
Burgess and Waltenberg' Contact with Pt 1480-1500 0.65 0.37
MiIIi." Pyrometer
Mendenhall and Forsythe" Open-V wedge
Burgess and Waltenberg'
Worthinp;'6 f tube, reflectivity, con-}
\ tact with tungsten
Whitney" tube
Reflection 1200 0.665 0.43
1300 0.658 0.44
2000 0.38
2750 0.39
2300 0.650 0.43
300 0.665 0.420
1300 0.378
2000 0.353
2750 0.332
1300-2100 0.667 0.382
Henninfl14
Bidwell' Coupleand pyrometer 1200 0.660 0.250
1700 0.660 0.215
0.660 0.215 Konnl
Molybdenum
Nickel
Contact with Pt 1200-1700 0.66 0.36 0.55 0.44
, 0.66 0,37 0.55 0.46 0.467 0.425
0.395
0.380
0.365
Burgess and Waltenberg'
Worthing" 1200-1650 0.665 0.375 0.535 0.425 0.460 0.450
Palladium
Waidner and Burgess" 1275 0.66 0.35
1725 0.31
Burgess and Wallenberg' Contaet with Pt 1805 0.650 0.33 0.55 0.38
1830 0.37
• For many recommended emissivities see Int. Crit. Tab. 5, 242. Highly Outgassed
Solid
Liquid
Solid and liquid
Solid Solid
Liquid Liquid
Liquid
Solid
Liquid
Solid and Liquid
Solid
Liquid
Solid
Solid
Solid and liquid
Solid and liquid
Highly outgassed
Solid
Solid
Liquid
Solid
Liquid
Solid
Solid
Liquid REMARKS
When the surface of a body is polished, there
is no doubt as to how one shall determine the
surface area that enters into radiancy and
steradiancy measurements and hence into emis
sivity and emittance determinations. What shall
be done in the case of roughened surfaces is not so
obvious. The general rule seems to be that when
the roughened dimensions are small compared
with distances to the receiving instruments and
its dimensions, the area that is taken as source
area is a projected smooth area which follows the
general outline of the body. This is the case which is generally of importance. For opaque bodies, of
some one material, the emittances in such
cases are never less than, but instead always
greater than the corresponding emissivities of
the material. In some instances, as in the
case of projection lamps containing crimped or
zigzag-shaped ribbon filaments of tungsten,
advantage is taken of this principle to attain an
emittance considerably in excess of the emissivity
of the tungsten.
434 How the normal total emittance Ene' of a
polished piece of copper is changed in the region
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Whitney"
Henning 14
Bidwell'
Burgess and Waltenberg'
Stubbs" METHOD
Tube
Spectropyrometer
Couple and pyrometer
Contact with Pt
Spectrophotometer
Mendenhall and Forsythe" Open-V wedge
McCauley"
Worthing47 Spectrobolometer
Reflectivity. tube, con
tact with Wand Mo
UtterbachandSanderman 38 Open-V wedge
Malter and Langmuir" Tube
Whitney" Tube
Pirani 29 Open-V wed!!e
Mendenhall and Forsythe" Open-V wedge
Burgess and Waltenberg'
Pirani and Meyer'"
Langmuir1'
Shackelford'"
Hulburt"
Worthing45
Weniger and Pfund"}
and Co blent.7
Henning and Heusel'
Lax and Pirani2l
Zwikk .... • Hamaker l3
Wahlin and Whitney39 Contact with Pt
Helix
Helix
Helix
Helix
Photoelectric compo
Tube
{Spectrobolometer}
Reflectivity
Cavity in sphere
Tube
Reflectivity
Tube TABLE I.-Continued.
RED GREEN BLUE IR AND UV
T IN OK A IN p... En>.. ).. IN fJ.. EnX }.. IN IL, En>.. ).. IN 1./., En>..
1300-2000 0.667 0.242
0.66 0.077
1000-1700 0.66 0.055
1215 0.650 0.044
1255 0.072
0.66 0.072
1400 0.658 0.61
2100 0.49
2800 0.47
1400 0.658 0.59
2100 0.47
2800 0.46
300 0.665 0.493
1400 0.442
2100 0.415
2800 0.390
1400 0.667 0.49
2100 0.40
1200 0.665 0.459
2100 0.417
2800 0.394
1300-2000 0.667 0.380
1200 0.64 0.46
1700 0.48
1375 0.658 0.45
3175 0.66
2044 0.65 0.39 Platinum
(See Fig. 12)
Rhodium
Silver
Tantalum
Thorium
Tungsten
0.532 0.44
1400-3000 0.664 0.46 0.537 0.485
1900 0.656 0.456 0.467 0.565
0.505
0.460
0.493 0.470 Highly outgassed
Solid and liquid
Solid
Liquid
Liquid
Highly outgassed
Obnously in error
I~arge variations
2300 0.445
1800 0.54 0.465
0.452 0.46 0.488 0.34 0.501
0.496
0.492 2200
2800
300
1200
2200
{:~~t1 1700
2100 0.665 0.470 0.452
0.431
0.411 0.438 0.476
0.424 0.45.;
0.467 0.505
0.482
0.466
0.452
2000-3200 0.647 0.49 0.536 0.49
0.650 0.45 1.27 0.335 2.00
0.335
0.335
0.335 0.100 2.50
0.162
0.187
0.212
5% uncertainty REMARKS
0.062 0.129
0.155
0.179
{ 3001 0.650 0.453 0.550 0.469 0.450 0.492 0.230 0.423 0.300 0.505 0.350 0.476 0.800 0.466 1.000 0.424
1200f 0.444 0.458 0.477 00411 .493 0.471 .434 .388
2000J 0.436 0.448 0.463 0.400 .483 0.467 .405 .355
1200-2200 0.669 0.46 Highly outgassed
of low temperatures by the addition of thin coats
of lacquer, by tarnishing and by painting with
aluminum is shown by certain results obtained by
Heilman13b (Fig. 13). For the temperatures in
volved, it is obvious, (a) that polished copper
has very low total emissivities, (b) that tarnished
copper has much higher emittances than has
polished copper (the increase in the very bright
new copper curve in going from 300°F to 500°F
is undoubtedly due to the appearance of tarnish),
(c) that the total emissivities of polished alumi
num are greater than those for copper, (d) that
the total emittances of unpolished aluminum are greater than the corresponding emissivities,
(e) that the thin coats of lacquer were not
opaque, and (f) that the white iacquer when
opaque is nearly black.
Emissivity Results
SPECTRAL 'EMISSIVITIES
Spectral emissivities for various materials
mostly metals are shown in Table 1. Except for a
few cases where a room temperature value has
been one of a group showing E).=j(T), the room
temperature values have been omitted. A survey
of results, including much that is not in Table I,
VOLUME 11, JUNE, 1940 435
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Downloaded to ] IP: 130.64.175.185 On: Tue, 09 Dec 2014 20:57:41seem to point toward certain general tendencies
though the data are too meager really to make
sure in certain cases. As such tendencies we
Hun (I)!T WHIte JOQl1Dl
ON BRIGHT OOlT'PDl 8URP'.A.Cr
o. 9
-----... 8 ~ 1 'l'HIN COA'1' WHITE UOQUER
OR BRlOH'l' OOPPi1\ SURFACE o
7 --I I I
-2 THIN OOATS ctEA'R LACQ,UER - o.
ON TARNISHED (x)PPER SURrAdE
"-::..... I I 1
6 r-..... -'---1 !~I~~~ ~LA=:JEON _
2 THIN OUTS CLEAR LACQum
5 ON BRIGHT (l)PPDl stllIFAOE I -'1'ARHISHEl) OOPPER --r--
4
1 THIN OOAT CLEAR LACQUER -ON BRIGHT OOPPER stJ.R1'ACE
1 (X)A'l ALUU. PAINT (UNPOLISHED)
ON BRIGJ{'1' OOPFm SURFACE --:::c- , --, , 0.3
2 (l)AT. ALUU. PAINT (POLISHED ALOIl.)
ON BRIGHT COPJIm. SURFACE
I
I V --02
o
lEFty BRlGj NEW OOPPj
o 100 200 300 400 500
SURfACE TEMPERATURE Of 600
FIG. 13. Normal total emittances at low temperatures for
pieces of bright newly polished copper when uncoated and
when variously coated, as determined by R. H. Heilman,
reference 13b.
seem to have:
(1) The Drude spectral emissivity relation
E}.n=A(p/~)t (Eq. (9» where p stands for
resistivity, holds well for metals at wave-lengths
beyond a rather indefinite "Drude limit" in the
near infra-red. (See Fig. 8.)
(2) Spectral emissivities for metals on the
short wave-length side of the "Drude limit"
increase with decrease in wave-length to a maxi
mum generally in the ultraviolet. (See Fig. 8.)
(3) Spectral emissivities for metals that are
not highly outgassed seem at least in certain
regions on the short wave-length side of the
"Drude limit" to decrease with increase of
temperature. (See Table I.)
(4) Spectral emissivities of highly outgassed
metals seem not to vary with temperature in the
visible region. (See Table I.)
436 (5) Spectral emlsslvltles obtained using the
tubular filament method are generally lower than
those obtained by other methods. (See Table I.)
(6) On account of deviations from the Lambert
cosine law, hemispherical emissivities for metals
are generally greater than corresponding normal
emissivities. (See Fig. 1.)
(7) On a<;:count of deviations from the Lambert
cosine law, hemispherical spectral emissivities for
the semi-conductor carbon is less than for the
corresponding normal spectral emissivity.
Total emissivities for various materials, as re
ported by Professor Hottel of Massachusetts In
stitute of Technology, are to be found elsewhere.24
There also seem to be certain general tendencies
with respect to the total emissivities. Some of
them are:
(1) The total emissivities of metals increase
with temperature.
(2) The total emissivities of metals seem to be
less than those of nonmetals.
(3) The total emissivities of certain nonmetals
decrease with increase of temperature. (See
Fig. 14.)
(4) The total emissivities of metals are gener
ally greater than what would be expected were
they to obey the Drude law. (See Fig. 8.)
(5) The appearance of a nonmetal in visible
light is no guide as to its probable total emissivity.
(See Figs. 13 and 14.)
(6) The total hemispherical emissivities of
metals on account of deviations from Lambert's
law are greater than the total normal emis
sivities. (See Fig. 2.)
~ -:;. O.1f---+--~ """"""ol--t---t--t---t---l
~
'" 'E 0.6 f--+-+-+--"'~;:-1~-+--+--+--1
UJ
O.5f--+---+--+--+--f-~~ ,L--+---j
OAf--+--+--+--1--4--+---'i'-"
O-~Ob;O:-;;4.,!;OO---T.60b;oC--;s;;!;or;o -;;;IO:k:OO"I,;jZO"'O:-O;I40~O oiiv<-","""",,;;;;',
TemperaTure ~ F
FIG. 14. Some total emittances reported by R. H. Heilman,
reference 13a. .
JOURNAL OF ApPLIED PHYSICS
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Downloaded to ] IP: 130.64.175.185 On: Tue, 09 Dec 2014 20:57:41Bibliography
1. Aschkinass, Ann. d. Physik 17, 960 (1905). 24 .. McAdams, Heat Transmission (McGraw Hill, 1933),
2. Bauer and Moulin, J. de phys. et rad. 9,468 (1910). Chapter III.
3. Bidwell, Phys. Rev. 3, 439 (1914). 25. McCauley, Astrophys. J. 37, 164 (1913).
4. Burgess, Bull. Nat. Bur. Stand. 6, 111 (1909). 26. Mendenhall, Astrophys. J. 33, 91 (1911).
5. Burgess, Comment made at the 1919 Temperature
Symposium. 27. Mendenhall and Forsythe, Astrophys. J. 37, 38 (1915).
28. Millis, Master's Thesis, University of Pittsburgh
6. Burgess and Waltenberg, Bull. Nat. Bur. Stand. 11, (1933).
591 (1915). 28a. Ornstein, Physica 3,561 (1936).
7. Coblentz, Bull. Nat. Bur. Stand. 14,312 (1918). 29. Pirani, Physik. Zeits. 13, 753 (1912).
8. Committee on Radiation, Rev. Sci. Inst. 7, 322 (1936). 30. Pirani and Meyer, Elektr. u. Masch. 33, 397 and 414
9. Davisson and Weeks, J. Opt. Soc. Am. and Rev. Sci. (1915).
Inst. 8, 581 (1924). 31. Prescott and Hinke, Phys. Rev. 31, 130 (1928).
10. Fery and Cheneveau, Comptes rend us 148,401 (1909). 32. Prescott and Morrison, Rev. Sci. Inst. 10,36 (1939).
11. Foote, Bull. Nat. Bur. Stand. 11,607 (1915).
12. Geiss, Physica 5, 203 (1925).
13. Hamaker, Doctor's Thesis; Univ. of Utrecht, Holland
(1934). 33. Shackelford, Phys. Rev. 8, 470 (1916).
34. Spence, Astrophys. J. 37, 194 (1913).
35. Stephens, J. Opt. Soc. Am. 29, 158 (1939).
36. Stubbs, Proc. Roy. Soc. A88, 19-5 (1913).
13a. Heilman, Trans. Am. Inst. Chern. Eng. 31,165 (1934) 37. Stubbs and Prideaux, Proc. Roy. Soc. A87, 451 (1912).
plus additional materia!' 38. Utterbach and Sanderman, Phys. Rev. 39, 1008 (1932).
13b. Heilman, Heating Piping Air Condo 5,458 (1933). 39. Wahlin and Whitney, Phys. Rev. 50, 735 (1936).
14. Henning, Zeits. f. Instrumentenk. 30, 61 (1910). 40. Waidner and Burgess, Bull. Nat. Bur. Stand. 3, 163
15. Henning and Heuse, Zeits. f. Physik 16, 63 (1923). (1907).
16. Holborn and Henning, Ber!' Ber. 12, 311 (1905). 41. Weber, Ann. d. Physik 54, 165 (1918).
17. Holborn and Kurlbaum, Ann. d. Physik 10,225 (1903). 42. Weniger and Pfund, Phys. Rev. 14,427 (1919).
18. Hulburt, Astrophys. ]. 45, 149 (1917). 43. Whitney, Phys. Rev. 48, 458 (1935).
19. I. Langmuir, Phys. Rev. 6,138 (1915); 7, 302 (1916). 44. Worthing, Astrophys. J. 36, 345 (1912); J. Opt. Soc.
20. Laue and Martens, Physik. Zeits. 8, 853 (1907). Am. and Rev. Sci. Inst. 13, 635 (1926).
21. Lax and Pirani, Zeits. f. Physik 22, 273 (1924). 45. Worthing, Phys. Rev. 10, 377 (1917) and Zeits. f.
22. Lummer, E. T. Z. 34, 1428 (1913).
22a. Lummer, Verflussigung der Kohle, (1914), p. 42.
22b. Lummer and Kurlbaum, Verh. Deut. Phys. Ges. 17,
106 (1898). Physik 22, 9 (1924).
46. Worthing, Phys. Rev. 25, 846 (1925).
47. Worthing, Phys. Rev. 28, 174 (1926).
48. Worthing, J. Opt. Soc. Am. 30, 91 (1940).
23. Malter and D. Langmuir, Phys. Rev. 55, 743 (1939). 49. Zwikker, Proc. K. Akad. Amsterdam 28, 499 (1925).
VOLUME 11, JUNE, 1940 Special Issue on Temperature
A word of appreciation is due to many
who have contributed to the preparation of
this issue. The principal papers have been
taken from the Symposium on Tempera
ture, sponsored by the American Institute
of Physics in New York, November 2-4. The
success of that Symposium was due pri
marily to the work of the members of the
Program Committee, and particularly to
that of the Chairman, Dr. C. O. Fairchild.
Dr. W. E. Forsythe, our Associate Editor,
was of great assistance in choosing the
papers to appear in this issue. Finally, we
express our appreciation to a large nu.nber
of manufacturers who have contributed in
formation for the Directory of Commercial
Temperature-Measuring Equipment.
437
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1.1769772.pdf | A Silica Gauge for Measuring Thickness by Means of Interference Colors
Katharine B. Blodgett
Citation: Rev. Sci. Instrum. 12, 10 (1941); doi: 10.1063/1.1769772
View online: http://dx.doi.org/10.1063/1.1769772
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Downloaded 15 Mar 2013 to 128.143.22.132. Redistribution subject to AIP license or copyright; see http://rsi.aip.org/about/rights_and_permissions10 KATHARINE B. BLODGETT
Certain impassable limits seem indeed to have
been reached. It would be a huge surprise to hear
of a substance more conductive than silver,*
denser than osmium, or possessed of a greater
magnetic moment at saturation than the already
known alloys of iron and cobalt. Yet twenty-five
years ago it would have been a huge surprise to
hear of a substance with a magnetic permeability
hundreds of times as high (at suitable field
strengths) as the purest iron then known, and
such are now common, being obtained by the arts
of purifying, alloying and heat-treating used sep
arately or together. Many properties of metals
* Supraconductors excepted! have been developed or enhanced in these ways,
but much of the credit should probably go to
metallurgists rather than physicists. Chemistry
also may lay claim to many new substances, such
as the "plastics," now so wonderful in their vari
ety. To physics even in the narrowest sense should
go the credit for two new categories of substances:
single crystals of metals large enough for meas
uring all the qualities which hitherto have been
measured only on polycrystalline aggregates (and
in some cases large enough for practical use);
and radioactive isotopes of literally all the ele
ments of the Periodic Table, many of them suit
able for use as tracers or for therapeutic purposes.
(To be continued.)
JAKUARY. 1941 R. s. 1. VOLUME 12
A Silica Gauge for Measuring Thickness by Means of Interference Colors
KATHARINE B. BLODGETT
Research Laboratory, General Electric Company, Schenectady, New York
(Received August 20, 1940)
Details are given of the construction of a gauge for measuring the thickness of monomolecular
films by means of the interference of light. The intensity of monochromatic light reflected
from a thin film of a transparent material varies with the thickness of the film according to
a cosine curve. When light strikes a film at an angle of incidence i = 15°, the variation of
the logarithm of the intensity with thickness is greatest at thicknes~es 0.75>../4n and 1.282>../4n,
where n is the refractive index of the film. In order to bring the thickness to this
critical value a silica film was developed on lead glass by treating the glass with HNOa•
Monolayers of various substances can be deposited on top of the silica film, and the thickness
of the monolayer determined from the change in intensity of reflected light produced by the
added thickness. The change of intensity can be determined very accurately by a method of
measuring the "match angle" at which two steps of different thickness reflect light of equal
intensity. When this angle can be measured with an accuracy of ±1O' the thickness of the
added monolayer is known with an accuracy of ±0.76A. Equations are given for calculating
thickness.
SEVERAL workersl-6 have studied the inter
ference of light reflected from surfaces of
lead glass and barium glass after the glass was
treated with acid. The acid treatment dissolved
the lead or barium from the surface of the glass,
1 Harold Dennis Taylor, The Adjustment and Testing of
Telescope Objectives (T. Cook, York, England, 1896).
2 F. Kollmorgen, Trans. Soc. Ill. Eng. 11, 220 (1916).
3 F. E. Wright, Ordnance Department Document No.
2037, p. 76.
4 K. B. Blodgett, Phys. Rev. 55, 391 (1939).
5 A. Vasicek, Phys. Rev. 57, 847 (1940). leaving a residual film of silica. The depth of
the silica film depended on the concentration
and temperature of the acid, and on the type of
acid used. The refractive index of the film was
found to be approximately 1.46. Since this value
of refractive index is considerably less than that
of lead glass or of barium glass, films of this type
on the surface of lead or barium glass reflect
vivid interference colors when the films have
suitable thicknesses.
Downloaded 15 Mar 2013 to 128.143.22.132. Redistribution subject to AIP license or copyright; see http://rsi.aip.org/about/rights_and_permissionsA SILICA GAUGE FOR MEASURING THICKNESS 11
This method of making silica films can be
employed to make gauges with which to measure
the thickness of molecular films by means of
interference colors. The glass is treated so as to
produce films of two different thicknesses, 1 and
2, which are called "steps." The graph in Fig. 1
illustrates the principle which is used to deter
mine the choice of thickness of these steps. The
graph is drawn for the case of a sample of lead
glass having a refractive index n=1.757.
The reflection of light from this type of glass
was measured by Mr. Malpica, using polarized
sodium light. The polarized ray R. was used,
that is, the ray having the plane of polarization
perpendicular to the incident plane. He obtained
the values given in Table I for the intensity of
the reflected light, the intensity of the incident
light being taken as unity.
The curves in Fig. 1 show the variation in
intensity of reflected sodium light with the
thickness of the silica film. As a result of inter
ference between the light rays reflected from the
upper and lower surfaces of the film, the intensity
of the reflected light varies with the film
thickness in a series of alternating minima and
maxima of intensity. Figure 1 shows the first
minimum of the series for a family of curves
H, J, K. This minimum occurs for each of the
curves at a thickness given by the equation
(1)
where n. is the refractive index of the silica film,
and r is the angle of refraction of light in the
film. In the case of a film of an isotropic sub
stance, cos r can be calculated from i by the
equation
cosr=(1-[(sini)jnJ2)l, (2)
where i is the angle of incidence of light illumi
nating the film.
The curves in Fig. 1 were calculated for the
case of a silica film for which n. = 1.46. The
ANGLE OF INCIDENCE
i TABLE I.
REFLECTION FROM
ONE FACE OF
tJNETCHED GLASS
0.0806
.1017
.1499 REFLECTION FROM
ONE FACE OF CLASS
ETCHED TO GIVE
MINIMUM REFLECTION
0.0146
. 0218
.0371 .3
.2
I
.08
~,06
c;;.05 ,.
~.04
~ .03
.02
.01 I I
r--....
'-..." V y_ Lj45" ··+i ). K / V i= 15" ~
"" ~~ Irf I I f--Vh I
\-'" \ Ft. V! i I \ Q Q"", +-1--
1\ \ ~ li2
p
1\ ./
o 1.0 2.0
THICKNESS (IIULTIPLES OF AI" ns)
FIG. 1. Plot of intensity of R.-polarized sodium light
reflected by a silica film on lead glass as a function of the
thickness of the film, for angles of incidence, i= 15°,
30°,45°.
minima occur at thicknesses tM given in Table
II.
The calculated points were plotted on a semi
logarithmic scale, since it is the percentage
difference of reflected light which determines the
visibility of two different intensities to the eye.
The slope of curve H is greatest at the points 1
and 2, that is, at thicknesses which are 0.75Xj4n.
and 1.282Xj4n •. The points corresponding to
these thicknesses lie at equal distances on
opposite sides of the intensity minimum and
therefore these thicknesses reflect equal intensi
ties. In other words, the steps match when seen
by monochromatic light at an angle of incidence
i= 15°.
Thin films such as monolayers of fatty acids,
proteins or other substances may be deposited
on top of the silica gauge. The graph in Fig. 1
shows that if a film having a thickness 0.048Xj4n.
is added to both steps, bringing the thicknesses
of the steps to O. 798X/4n. and 1.330X/4n., these
steps will then have intensities corresponding to
the points P and PIon curve H, to Q and Q'
on curve J, and to Rand R' on curve K. It is
seen that the steps then reflect the intensities
0.0219 and 0.0292 when illuminated at i = 15°,
and therefore have a difference in intensity of
33 percent. When illuminated at i = 30° the steps
match, both steps having an intensity 0.0333.
At i=45° the intensities are 0.0589 and 0.0439 .
Figure 2 shows how the intensities of the steps
change as the angle i is varied. The contrast
Downloaded 15 Mar 2013 to 128.143.22.132. Redistribution subject to AIP license or copyright; see http://rsi.aip.org/about/rights_and_permissions12 KATHARINE B. BLODGETT
.0 8
.0 7
.0 6 R
.05 V
4 ./ ./ ...... VR'
.---W ~ !--i--
p' st~ L--
3 -m ~/
2 .0
.0
10 20 30 40
Angle of incidence i
FIG. 2. Plot of intensity of R.-polarized sodium light
reflected by silica films as a function of the an~le of
incidence. Steps 1 and 2 have thicknesses correspondmg to
points P, Q, R and pI, Q', R', respectively, in Fig. 1.
diminishes to zero as i is increased to 30°, and
then reverses and increases at higher values of i.
The increment of thickness 0.048X/4n 8 which
changed the match-angle from i=15° to i=300
was the difference between the values of tM
corresponding to i = 15° and i = 30° given in
Table II.
The following method is employed for meas
uring the thickness of a thin film such as a
deposited monolayer. The silica gauge is mounted
on a spectrometer table with the boundary
between the steps in the axis of rotation of the
table. The gauge is illuminated by polarized
sodium light, using the R8 ray. The angle io is
measured at which steps 1 and 2 match. The
gauge is then removed from the spectrometer,
and the monolayer which is to be measured is
deposited on the surface of the gauge, coating
both steps. The layer can be deposited by any
of the methods commonly employed in the
handling of monolayers, such as deposition from
a water surface or adsorption from solution.6-9
The gauge is then replaced on the spectrometer
and the angle ia measured at which the steps
match.
The thickness of the monolayer is calculated
in the following way. From Eq. (1) we have
n.i8( cos ro). = X/4, (3)
where the subscript s refers to the silica film and
6 I. Langmuir, Trans. Faraday Soc. 15, 62 (1920);
reprinted in Gen. Elec. Rev. 24, 1025 (1921).
7 K. B. Blodgett, J. Am. Chern. Soc. 57, 1007 (1935).
8 I. Langmuir and V. J. Schaefer, J. Am. Chern. Soc. 59,
1406 (1937).
• I. Langmuir, V. J. Schaefer and H. Sobotka, J. Am.
Chern. Soc. 59, 1751 (1937). (cos rO)8 is the value of cos r calculated by
means of Eq. (2) for the case i=io and n=n8•
When the silica is coated with a film of thickness
if and refractive index nj, the angle at which
the minimum occurs increases from io to ia and
Eq. (1) becomes
(4)
where (cos ra). and (cos ra)1 are the values of
cos r corresponding to the refractive indices n.
and nf respectively, calculated by means of
Eq. (2) for the case i =ia. Since in the case of a
deposited monolayer the second term on the
left side of Eq. (4) is small compared with the
first term, this equation may be written
(n8t.+nlif) (cos ra).=X/4. (5)
The error introduced into the calculations by
writing the equation in this form is usually less
than 1 percent.
It follows from Eq. (3) and Eq. (5) that
nlif= (X/4)[1/(cos ra).-l/(cos ro).]. (6)
The curve in Fig. 3 gives a plot of l/(cos ro). as
a function of i, calculated by means of Eq. (2).
Values of nltl are calculated by reading the
values of l/(cos r). corresponding to io and ia
from this curve, and substituting these values
in Eq. (6).
This method of measurement is similar to the
methods previously used for measuring mono
layers by means of step-gauges made of barium
stearate.8 The silica gauge has the great ad
vantage over the stearate gauge that a deposited
monolayer can be wiped from the silica surface
with a cloth without injuring the silica film.
Therefore the gauge can be used repeatedly for
a large number of measurements. In the case of
a stearate gauge, the monolayer cannot be
removed without injuring the stearate film, and
therefore a new gauge is usually needed for
each measurement.
The steps of the gauge were made by the
TABLE II.
CURVE ANGLE OF INCIDENCE i
H 15°
J 30°
K 45° Cos r
0.9842
. 9395
. 8749 1.016Aj4n.
1.064X/4n •
1.143 Aj4n •
Downloaded 15 Mar 2013 to 128.143.22.132. Redistribution subject to AIP license or copyright; see http://rsi.aip.org/about/rights_and_permissionsA SILICA GAUGE FOR MEASURING THICKNESS 13
following method. A plate of glass was used
which was 1 X 2 inches in size. The glass was
one-quarter inch thick and had a slight green
color. The back of the plate was painted with
black paint in order to reduce reflection from the
back and thus make the interference colors more
readily visible. The glass was polished with
yellow rouge (Goldite No. 34) on a rotating disk
covered with fine billiard cloth. One end of the
glass was then dipped to a depth of t inch in a
solution of polystyrol dissolved in toluene in a
concentration about 10 percent, and was sus
pended in an oven at 70°C for 10 minutes to
allow this coating to dry.
The glass was next immersed in 1 percent
HNOa at SO°C until the uncoated glass reflected
a blue color. The polystyrol formed an acid-proof
covering so that the coated glass was not etched.
The progressive increase of thickness of the silica
film formed by the etching action of the acid on
the untreated glass was observed by watching
the change of interference colors while the glass
was in the acid bath, the glass being illuminated
by white light. The colors progressed through
the series which is characteristic of films having
thicknesses in the neighborhood of the first order
minimum: yellow brown, red brown, purple,
deep blue, medium blue. The color reached a
medium blue in 1 minute, 30 seconds. The glass
was then taken from the acid, rinsed in a beaker
of water and plunged while wet with water into
a dish of toluene where the polystyrol was
removed with one or two strokes of a cotton
swab. It was then plunged into a dish of water
and the toluene removed with a single stroke of
a swab. If the glass was swabbed vigorously the
subsequent etching of the glass took place in a
manner which was uneven over the surface.
The glass was then immersed again in 1
percent HNOa at SO°c. At first the area which
had been brought to a medium blue color (step 2)
was seen to be dark by sodium light and the
fresh area (step 1) was bright. As the etching
progressed, step 1 became darker and soon
matched step 2 in intensity when the glass was
seen at the angle i = 0 (perpendicular light).
The etching was carried beyond this point in
order to obtain steps which would match at
angles greater than i=O. The additional etching
was also needed to allow for the shrinkage of 1.3
/
1.2 1/
-II I
II
/
I V
/
/
/
--V
0" 10" 20· 30· 40 50" 1.0
Angle of incidence L
FIG. 3. Plot of calculated values-of 1/(cos r), as a function
of angle of incidence i, for n, = 1.46.
the film which took place during subsequent
heat treatment. The extent of additional etching
which was needed was learned by experiment
and was readily reproduced by the following
method. The angle i. was determined at which
the steps matched in the acid bath when they
had been etched to the required depth. A strip
of metal was bent into a V-shape having an
angle 90°-i. at the apex. It was fastened to
the glass with one side of the V lying against
the face of the glass. The other side then served
as a sight by means of which the glass could be
viewed at the angle of incidence i •. This angle
was found to be i. = 40° for the glass used in
the present experiments. After the glass was
etched it was rinsed in distilled water and placed
in an oven at 70°C for S minutes for the water to
evaporate.
During the second etching, step 2 increased
only slightly in thickness, while step 1 was
rapidly etched. This was in accord with previous
experiments4 with lead glass in which it was
found that the rate of etching decreased greatly
as the thickness of the film increased. With the
type of lead glass used in the earlier experiments
the thickness of the film increased with the 0.37
power of the time. Barium glass was found to
differ greatly in this respect from lead glass.
Two samples of barium glass were studied, and
both gave the result that the thickness of the
film obtained by etching was proportional to
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the length of time in the bath. Measurements
were made until the film reached a thickness
}../n., and were not carried beyond this point.
The silica films which were formed on lead
glass had the striking property that they were
rendered almost completely impermeable to acid
by being heated at 70°C for 5 minutes. This
could be shown by the following experiment.
When a freshly polished piece of glass was
placed in an etching bath a thin layer of silica
was formed on the surface in a few seconds. If
the glass was then heated at 70°C for 5 minutes
and was placed again in the same etching bath,
no further etching took place. For example,
glass which had been freshly polished was etched
by acid to a depth of 1.4}../4n. in 1 min., 30 sec.;
whereas if the same type of glass was etched to
a depth of 0.9}"/4n. and was heated for 5 minutes
and then placed again in the acid for 3 minutes,
no further etching occurred. The test to find
whether any etching occurred was made by
lowering only one-half of the glass in the acid
bath. After it was removed from the acid no
difference could be detected between the areas
which had been above and beneath the acid
surface. An increase of 0.02}"/4n. could have
been readily detected, since the interference color
reflected by a film changes rapidly with increase
of thickness in the region of thickness from
0.9X/4n. to }"/4n •. An exceedingly thin film was
sufficient to form this type of protective covering.
Films which were too thin to reflect any inter
ference colors and therefore had a thickness not
greater than 0.1}"/4n. were found to be as
effective in preventing etching as the thicker
films.
The first gauges that were made were found
to be not sufficiently hard, for when the films
were rubbed very vigorously with a cloth they
became gradually thinner. They lost approxi
mately 0.002}"/4n. in thickness each time they
were rubbed for a few seconds. This fault was
remedied by heating the gauges in a furnace at 350°C for 5 minutes. The heat treatment caused
the film to become very much harder. The film
shrank a few percent in thickness while it was
being heated. The difference in hardness was
made very apparent if the gauge was polished
with rouge until the film disappeared, the film
heated to 350°C being far more resistant to the
action of rouge than the film heated to 70°C.
Measurements of the thickness of monolayers
of various substances, made with a silica gauge,
will be published in a later paper. The addition
of a monolayer of thickness t, = 25A and re
fractive index n,= 1.50 produces a change in
match angle which can be calculated by means
of the equation
[l/(cos ra).-l/(cos ro).J=0.02546 (7)
derived from Eq. (6) for sodium light X=5893A.
Calculation shows that when io=30°, the match
angle obtained with the added monolayer is
ia=35° 30'. Therefore measurements of angle
made with an accuracy of ±10' will yield an
accuracy of ±0.76A in the determinations of
film thickness.
The match angle is determined by rotating
the film to and fro through a small angle, from
an angle at which step 2 is slightly brighter than
step 1 to an angle at which the contrast is equal
and reversed. The match angle then lies halfway
between these two angles, since Fig. 2 shows that
in the neighborhood of the match angle (Q'Q)
the logarithm of the intensities of the steps
varies nearly linearly with the angle i. An
accuracy of 10' can be obtained when the match
angle is measured by the eye, but the measure
ments have to be made at the lowest limits of
contrast that are visible to the eye and are
therefore tiring to make and their accuracy can
sometimes be doubted. Apparatus is being built
in which a photoelectric cell will be used to
measure the light intensities reflected by steps 1
and 2.
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1.1750963.pdf | The Photolysis of Acetone in Presence of Mercury
Kenneth W. Saunders and H. Austin Taylor
Citation: The Journal of Chemical Physics 9, 616 (1941); doi: 10.1063/1.1750963
View online: http://dx.doi.org/10.1063/1.1750963
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/9/8?ver=pdfcov
Published by the AIP Publishing
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141.209.100.60 On: Mon, 22 Dec 2014 22:30:53AUGUST, 1941 JOURNAL OF CHE:'vlICAL PIlVSICS \" 0 L U i\l Ie <J
The Photolysis of Acetone in Presence of Mercuryl
KENNETH \V. SAUNDERS AND H .. \USTI~ TAYLOR
Department of Chemistry, New York University, New York, New York
(Re('eived May 21, 1941)
The photolysis of acetone in the region 2600-2900A has been studied at temperatures from
100-275°C, alone, in presence of liquid mercury, mercury vapor and mercury dimethyl. From
a comparison of the products formed in each case and the effect of temperature thereon a
mechanism is suggested which indicates that mercury methyl, if not mercury dimethyl, is
formed by reaction between methyl radicals and mercury atoms suggesting a greater stability
of the mercury methyl radical than hitherto believed.
DESPITE the rapidly increasing amount of
data being accumulated on the reactions
between organic radicals and metals by the
mirror method, relatively little is known con
cerning the reactions in the vapor phase. Leighton
and Mortensen2 reporting on a quantum yield for
the photolysis of lead tetramethyl of 1.11 de
creasing to unity in presence of oxygen conclude
that the observed yield may represent a balance
between a considerable chain length and a
considerable recombination. A somewhat similar
reduction of quantum yield was observed by
Linnett and Thompson3 for mercury dimethyl
photolysis in presence of nitric oxide. The in
creased rate of decomposition of mercury di
methyl in presence of hydrogen was accounted
for by Cunningham and Taylor4 on the basis of
a chain reaction involving hydrogen atoms
formed by reaction between methyl radicals and
hydrogen. TaylorS and Burton drew attention to
the neglect of a consideration of any recombina
tion between mercury and methyl radicals and
indicated on this basis a possible alternative
explanation. The observation by Heidt and
Forbes6 that the pyrolysis of azomethane was
unaffected when 100 mm mercury vapor were
intentionally introduced was not confirmed by
analysis of the reaction products.
1 Abstract from a thesis presented in partial fulfillment
of the requirements for the degree of Doctor of Philosophy
at New York University, March, 1941.
2 P. A. Leighton and R. A. Mortensen, ]. Am. Chern.
Soc. 58, 448 (1936).
3 J. W. Linnett and H. W. Thompson, Trans. Faraday
Soc. 33, 501, 874 (1937).
4 J. P. Cunningham and H. S. Taylor, J. Chern. Phys. 6,
359 (1938).
• H. A. Taylor and M. Burton, J. Chern. Phys.. 7, 675
(1939).
6 L. J. Heidt and G. S. Forbes, ]. Am. Chern. Soc. 57,
2331 (1935). Since it is generally agreed that the photolysis
of acetone proceeds through a primary step
involving the production of methyl and acetyl
radicals, if reaction can occur between methyl
radicals and mercury atoms the products of
acetone photolysis in presence and absence of
mercury would be expected to be differen t.
Furthermore, acetone photolysis in presence of
mercury dimethyl would be expected to be
similar to that of acetone and mercury. To
simplify the interpretation of the results the
radiation has been restricted to wave-lengths
2600-2900A since mercury dimethyl absorbs
below 2600A while acetone gives its maximum
radical concentration below 3000A. The tem
peratures used were restricted to the range
100-275°C since, above 100°, no diacetyI forma
tion is observed in acetone while above 275°C
mercury dimethyl pyrolysis becomes measurable.
EXPERIMENTAL
Materials
Acetone obtained from the sodium iodide
complex compound was dried over calcium
chloride and fractionally distilled. The middle
fraction boiling at 55.8-56.0°C was further
purified by distilling twice in vacuum from an
ice-water mixture to dry-ice-toluene.
Mercury dimethyl was prepared by the method
of Marvel and Gould7 from mercuric chloride
and Grignard reagent, dried over calcium chloride
and fractionally distilled. A fraction boiling at
90.5-91.0°C was further distilled in vacuum
from phosphorus pentoxide at room temperature
and collected at dry-ice-toluene temperature.
7 C. S. Marvel and V. L. Gould, J. Am. Chem. Soc. 44,
153 (1922).
616
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141.209.100.60 On: Mon, 22 Dec 2014 22:30:53PHOTOLYSIS OF ACETONE 617
When not in use acetone and mercury dimethyl
were protected from light and stored in dry ice.
Radiation
The light source was the General Electric
Type H6 lOOO-watt, water-cooled, high pressure
quartz mercury arc which emits relatively little
resonance radiation. The lamp intensity varied
considerably with use. Deposits of ferric oxide
on the water cooler and quartz filter were re
moved daily. The quartz filter made according
to the suggestion of Bowen 8 consisted of two
compartments, the first 3 em in depth contained
chlorine at 1 atmos. pressure, the second, 1 em
in depth, through which an aqueous solution
containing 45 g HgCl 2 per liter flowed con
tinuously. The whole filter was water-cooled.
Photographs of a low pressure mercury arc
showed transmission by the filter from 2652 to
2967A.
Reaction system
A quartz reaction vessel of approximately
200-cc volume was connected by a graded seal
to a Pyrex mercury manometer and to a Crist9
valve, the latter eliminating contact between
acetone and stopcock grease. In the experiments
with acetone alone the reaction system was
protected from mercury vapor by gold-leaf traps.
The absence of change in the photolysis when
these were removed eliminated the possibility of
any mercury photo-sensitization having occurred,
while at the same time showing that the low
vapor pressure of mercury gave too small a
concentration of mercury to show a measurable
reaction with acetone decomposition products.
The reaction vessel was placed in an electric
furnace carrying a two-inch aperture faced with a
thin quartz plate at each end. The temperature
was controlled manually and temperature gradi
ents were minimized by having an air stirrer in
the furnace. For the experiments with mercury
present about 0.5 cc mercury was added to the
reaction vessel. The mercury refluxed continu
ously into the vessel from the cooler connecting
tube outside the furnace during the experiments.
In the runs in presence of mercury vapor, the
8 E. J. Bowen, J. Chem. Soc. p. 76 (1935).
9 R. H. Crist and F. B. Brown, Ind. Eng. Chem., Anal.
Ed. 11, 396 (1939). manometer was removed and the Crist valve
replaced by a mercury V-tube cut-off filled from
a reservoir below. The arm of the V connected
to the reaction vessel was heated throughout its
length with resistance wire and thermally insu
lated. A thermometer in the mercury in the
V-tube indicated the temperature of the mercury
and thus the partial pressure of mercury vapor
in the reaction system. Particular care was
taken during these latter runs to see that no
liquid mercury could be present in the reaction
vessel.
Procedure
The reaction cell was evacuated overnight
before each run by a mercury vapor pump
backed by an oil pump. Just prior to the run the
cell was flushed out three times with acetone
vapor and filled to a pressure of 90 mm. The
Crist valve was then closed; the pressure on both
sides of the valve being the same any leakage
was minimized. Exposure to the arc was then
made for the required period. At the conclusion
of the run, the light was turned off, the pressure
permitted to reach a steady value and the Crist
valve was opened slightly to permit the gases
to be drawn slowly through a trap in liquid
nitrogen into a liter Toepler pump. From here
the gas was pumped into the analyzer. To
obtain complete fractionation it was sometimes
necessary to remove the liquid nitrogen allowing
the trap contents to melt and then refreeze
and pump out residual noncondensible gas.
A second fraction containing residual methane
and C2 hydrocarbons was obtained by pumping
the condensate in the trap cooled to -131°C by
melting sec-butyl chloride. As before the last
fractions of the gas were recovered following
vaporization and condensation. In a few tests a
minute quantity of gas was obtained between
-131° and -115°C and slightly above -l1Soe
acetone itself began to come through. Two frac
tions only were therefore collected and the
volume of each was measured at low pressure in
the gas analysis apparatus.
Micro gas analysis
Since, under the experimental conditions, an
exposure of 30 minutes yielded seldom more
than 0.6 cc gas for analysis a micro method
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141.209.100.60 On: Mon, 22 Dec 2014 22:30:53618 K. W. S A IT 1\ J) E R SAN n H. A. T A Y LOR
To
vacuwn
K
M A ::
FIG. 1.
was essential. A technique was developed capable
of analyzing for hydrogen, carbon monoxide,
ethylene, methane and higher saturated hydro
carbons which was much less tedious than, yet
at least as accurate as, the methods of ManninglO
and H. S. Taylor and his associates,n features
from both of which were adopted. The method
involved some modifications of that of Haden
and Luttroppl2 and used a measurement of the
pressure at constant volume, rather than the
actual volume of the gas. Fig. 1 is a plan of the
apparatus used.
A, the combustion chamber whose volume plus connect
ing capillary was 2.67 cc was equipped with a standard
ground joint (size 14/29) carrying two tungsten lead-in
wires 1 mm in diameter insulated in small glass tubing.
A small platinum coil of six to eight turns was spot-welded
to the tungsten electrodes. During operation the upper
tube was filled with water and surrounding A was a water
jacket (not shown) which prevented the trace of grease on
the upper part of the joint from flowing.
10 W. M. Manning,]. Am. Chern. Soc. 56, 2589 (1934).
11 Morikawa, Trenner and Taylor, ]. Am. Chern. Soc.
59,1103 (1937); H. S. Taylor and C. Rosenblum,]. Chern.
Phys., 6,119 (1938); H. S. Taylor and W.]. Moore, ibid.,
8, 396, 466 (1940).
12W. L. Haden ]r. and E. S. Luttropp, ]. Ind. Eng.
Chem., Anal. Ed. In press. B, this tube contained gold foil to prevent mercury vapor
passing into A.
C, is a series of tubes to hold reagents for various tests
carrying 7/15 interchangeable ground joints. The volume
of one such tube plus the capillary tube was 2.83 cc.
D, is a stopcock designed so that both A and C may be
evacuated simultaneously through M and that by proper
manipulation either A or C may be connected to R. The
volume of the capillary in D was 0.14 cc.
E, F, G, permanent markings. The volume from E to D
was 0.48 cc, that from F to D was 2.95 cc. Any small error
in these volumes is immaterial since all measurements are
differences of two readings. The volume from G to D was
549 cc.
K, R, H, is essentially a Toepler pump so designed that
when the mercury level is at F the pressure of gas in F-D
can be read from the difference in levels in K and F. The
reading is independent of atmospheric pressure. The
distance H-F should be as short as possible. In this appa
ratus it was about 45 cm.
L, is the inlet tube for the gas to be analyzed; it was 2
mm bore capillary.
S, is a two-way stopcock connected to a pump and
through a capillary leak to the atmosphere used to manipu
late the mercury levels.
Before use the system is evacuated through M
and L for about two days to remove gases from
the grease around the stopcock. Picein was
found suitable as a lubricant. The gas to be
analyzed is brought into the evacuated system
through L, the mercury level raised to F and the
pressure of the gas is determined by reading the
level in K. From the known volume of the
system and the recorded pressure and tempera
ture, the volume of the gas at S.T.P. may be
calculated. It is assumed in all cases that the
gases are ideal. The stopcock D is then opened
to the proper chamber according to the test to
be made and after due time for reaction to
occur the mercury level is lowered to G and the
stopcock closed. The pressure is again observed
after the level is raised to F. The process is
repeated until constant pressure readings are
found. The difference before and after is the
contraction when allowance is made for the
residual gas left in the reaction chamber; the
latter is easily calculable from the volume ratio
of A or C and R.
Since the conclusions drawn from the work
depend on the analyses of the products of
acetone photolysis it has been thought advisable
to outline the methods used in some detail and
indicate the precision available.
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141.209.100.60 On: Mon, 22 Dec 2014 22:30:53PHOTOLYSIS OF ACETONE 619
Analysis of hydrogen
Pure hydrogen was prepared from tank hydro
gen by passing it through a trap in liquid
nitrogen, then over a platinum Grillo catalyst at
200-300° to remove oxygen and finally through
a dry-ice trap to remove water. It was analvzed
in three ways; (1) by direct combustion ~ith
oxygen on a heated platinum filament, (2) by
combustion in oxygen on a platinum Grillo
catalyst heated to 250-300°C, and (3) by oxida
tion on copper oxide at 300°C. For the latter,
copper oxide wire as used in organic micro
combustion methods was placed in C and sepa
rated from it by glass wool was some anhydrone.
A small furnace raised the temperature of the
copper oxide to 300° where it was evacuated for
one hour. Oxidation of hydrogen at the pressures
here used (50-200 mm) then occurs readily
within two minutes. The shortness of this time
is advantageous not only as a time saver but
also in reducing the possibility of the liberation
of CO2 which was found to be adsorbed tena
ciously by copper oxide even at 300°C. A sum
mary of the results obtained is given in Table I
where for convenience volumes are expressed as
the pressures observed.
Analysis 'of carbon monoxide
Carbon monoxide was prepared from sodium
formate and concentrated sulfuric acid and dried
by passing through a trap in a dry-ice-toluene
mixture. The silver oxide method used by Blacet13
proved extremely slow, and gave inconsistent
METHOD
Combustion
Grillo catalyst
and anhydrone
CuO and
anhydrone TABLE 1.
mm HzTAKE:-;
50.6
48.2
44.6
125.1
163.0
81.8
115.1
93.1
97.5
94.2
80.4
86.7 mmH2FoUND %H,
50.7 100.1
48.5 100.6
44.9 100.5
124.8 100.2
164.0 100.5
82.8 100.2
114.3 99.4
92.9 99.8
96.9 99.1
93.8 99.6
79.9 99.5
86.4 99.6
13 F. E. Blacet and P. A. Leighton, Ind. Eng. Chem.,
Anal. Ed. 3, 225 (1931); 5, 272 (1933); 6, 334 (1934); F. E.
Blacet and D. H. Volman, ibid., 9, 44 (1937). results and its use for carbon monoxide-methane
mixtures rendered the remaining methane in
some way passive to complete oxidation by the
explosion method. Tests were therefore made
using iodine pentoxide at 175° and copper oxide
at 300°C. In each case solid potassium hydroxide
was used in front of the oxidizing agent to absorb
the carbon dioxide formed. The reproducibility
of the methods is shown in Table II depicting
analyses of a carbon monoxide-methane mixture.
TARLE II.
mmCO-CH. mmCO
METHOD TAKE:< Fomm %CO
145.9 89.0 61.0
133.3 81.3 61.0
102.2 62.1 60.7
154.2 94.1 61.0
CuO 126.9 79.7 62.8
137.0 84.8 62.0
139.9 87.7 62.8
The discrepancy between the two methods was
not investigated further since the copper oxide
was known to work well and could be used also
for hydrogen.
Analysis of ethylene
The method used by Morikawa, .Trenner and
Taylorll of hydrogenation of ethylene on a
nickel catalyst at 100°C was found adaptable.
From 8-10 milligrams of catalyst prepared
according to their specifications was used. It
was found necessary even with this small amount
of catalyst to use only a slight excess of hydrogen
owing to its adsorption. After hydrogenation
the excess hydrogen is determined over copper
oxide at 300°C. Table III lists some analyses on
two different samples of tank ethylene passed
over KOH and dried. It is seen that the per
centage ethylene based on the observed· con
traction is always high, due presumably to hydro
gen adsorption.
Analysis of methane
The usual combustion method on a hot plati
num filament was used. Anhydrone was placed
in C to absorb the water produced. This was later
replaced by KOH to absorb CO2• Preliminary
analyses always showed a greater absorption o~
KOH than expected. The answer is believed to
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141.209.100.60 On: Mon, 22 Dec 2014 22:30:53620 K. \-V. S,\UNDERS AND H. fl.. T/\.YLOR
TABLE III.
mm mm Co,,- TOTAL mm % C2H. (:,H. H, TRAC-II, BY H, C,Hn
TAKE.:\'" ADDED nON CuO USED FORMED CO:':T~. C2H"
49.2 65.9 50.7 15.4 66.1 49.0 101.8 100.4
3.l.X 53.X .H .. I 18.9 53.4 34.1 102.2 100.9
32.8 47.6 32.4 15.1 47.5 32.3 98.8 98.5
30.2 49.0 30.6 18.0 48.6 30.4 101.2 100.8
be due to ozone formation while the oxygen is
being passed over the hot platinum coil, for,
although the low pressures would favor decom
position of ozone, the surrounding walls of A are
cold and tend to stabilize it. Ozone reacts with
KOB to form potassium tetraoxide K204• In one
experiment pure oxygen passed successively over
the hot filament and then KOH several times
during four or five hours showed a total contrac
tion of 32 percent. It was also observed that KOB
can adsorb oxygen. This latter error is eliminated
by using minimal amounts of recently pulverized
KOH. The ozone error could not be eliminated
and depends on the amount of oxygen remaining
after combustion, the filament temperature and
the number of passes over the filament or time
of contact with the filament. These latter two
factors can be kept reasonably constant and an
empirical correction (0.5-1 mm) was subtracted
from the apparent CO2 contraction depending
on the amount of residual oxygen. Examples of
the effect of this correction arc shown in Table IV
on tank methane from two sources. Table V
exemplifies the effect of the correction when a
mixture consisting chiefly of methane, carbon
monoxide and hydrogen was analyzed.
Analysis of ethane
Analysis of ethane by the combustion method
was found to give contraction values in general
hig;her than carbon dioxide values. The reason
for this has not so far been traced. The observed
hydrogen values have been arbitrarily reduced
by four percent. The effect of this correction, in
addition to the correction to the observed carbon
dioxide based on the residual oxygen as' men
tioned previously in methane analysis is shown
in Table VI. It is seen to be small and would in
no way affect an interpretation of a mechanism
based on such analyses. Table VI presents the
results of several analyses of a mixture of
ethylene and ethane. Since attempts to analyze mixtures containing
hydrogen, carbon monoxide, methane, ethylene
and ethane were without success, fractionation
was employed. The first three constituents pass
through liquid nitrogen, ethylene and ethane
being retained. In some of the runs enumerated
later, hydrogen and carbon monoxide were de
termined directly and the methane by difference.
Since only rarely was ethylene found, the
fraction of gas between -194° and -131°C was
usually ethane. The formula for it was not
determined in all cases, particularly in check
runs, the volume alone being noted and recorded
as CxHy.
RESULTS
The principal products found in all the work
were methane, carbon monoxide and ethant'.
Traces of hydrogen and of ethylene were found
in acetone photolysis at 250°C. The sec-butyl
chloride fraction from acetone alone which was
principally ethane gave carbon values higher
than two. This has been interpreted as indicating
TABLE IV.
S~, CH4 BY ~:{ CH4 FROM % CH4 FROM
CO:;-.rTRACTION C020BS. C02 CORR.
95.5 96.7 95.0
95.5 96.0 95.2
95.0 96.3 95.0
99.4 101.0 100.2
99.8 102.2 100.1
99.7 99.7 98.9
TABLE V.
1 2 " VOL. GAS A~ALYZED IN CC 0.426 0.556 0.3.19
% H2 (by CuO-anhydrone) 17.6 17.4 16.5 % CO (by CuO-KOH) 49.8 49.5 49.5 % CH. from contraction 30.4 31.8(?) 30.4
% CH. from CO2 obs. 31.7 30.6 31.1 % CH. from CO2 corr. 30.3 30.2 30.4
TABLE VI.
VOL. CrHy CxHy
cc S{' C2H4 (OBS.) (CORR.)
--~~.
0.114 31.6 C1.96H6.18 C1.92 H,.88
0.116 31.0 C2.0• Husc'!) C,.OI H(?)
0.120 32.7 C1.9• H6.1• C1.91 H,.8.
0.104 30.1 C2.08 H6.2< C2.0; H,.97
0.128 31.1 CZ•OB H6.40 C,.O' Ho.o7
0.097 28.6(?) Cz.o• H6.32 C,.OI H6.oo
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141.209.100.60 On: Mon, 22 Dec 2014 22:30:53PHOTOLYSIS OF ACETONE 621
TABLE VII.
ACETONE TIME l>P VOL. IN CC
mm min. mm TOTAL LIQ. N, -131°
Temp.200aC
180 20 2.1 0.543 0.459 0.084
180 20 .517 .447 .070
90 30 2.6 .652 .514 .138
92 30 .631 .483 .148
46 30 0.9 .367 .272 .095
27 60 2.6 .513 .357 .156
180 30 1.7 Temp. 1000e
0.417 0.248 0.169
180 30 2.7 .640 .366 .274
90 30 1.6 .344 .192 .152
45 30 0.7 .245 .135 .110
25 30 0.3 .131 .073 .058
26 60 0.7 .287 .151 .136
the production of some propane by acetone
photolysis. Assuming one molecule of carbon
monoxide is formed for every molecule of acetone
decomposed, the carbon found in all the hydro
carbons produced should be twice that in the
carbon monoxide. Actually it is found to be less.
This percentage carbon deficiency was calculated
as follows:
2 (% CO) -(% CH4+x· % CxHy) -----------X100.
2 (% CO)
I ts value, which is quite specific for the particular
system studied, whether acetone alone, acetone
and mercury, or acetone and mercury dimethyl,
indicates the production of a compound or com
pounds whose carbon to carbon monoxide ratio
is greater' than two.
In Table VII are recorded data showing the
variation in the percentage composition of the
products of acetone photolysis as a function of
the pressure at two temperatures.
Since from the above table it can be seen that
there is a less rapid change in the percentage
products at pressures above 90 mm acetone all
subsequent experiments were made at this pres
sure. Tables VIII-XI, which are self-explanatory,
give the data found for the four systems ex
amined at various temperatures.
For comparative purposes the data in Tables
VIII-XI have been collected in the composite
graph shown in Fig. 2 which illustrates very
simply the similarity of behavior of the three
systems when mercury is present in one form
or other and the' difference from that of acetone C/ ,c % CARBON
CO CH, CrHy CxHy DEFICIENCY
44.2 40.3 J5.5 2.03 6.10 19
43.7 42.8 13.5 2.1.3 6.85 18
49.2 29.6 21.2 2.24 6.40 22
47.2 29.4 23.4
50.1 24.0 25.9 2.28 6.73 17
51.7 17.8 30.4 2.07 6.06 22
49.0 10.5 40.6 1.91 5.88 10
48.4 8.7 42.8 2.02 6.10 2
49.3 6.4 44.3 2.10 6.21 0
50.6 4.5 44.9 2.22 6.23 0
51.5 3.8 44.3 2.09 6.17 7
49.3 3.8 47.4 2.12 6.18 0
alone. Fig. 3 shows the variation of the carbon
deficiericy with temperature and although the
actual values cannot be too accurate the general
trend of them signifies a distinction in the be
havior of the systems studied.
DISCUSSION
For purposes of discussion of the above results
it will be convenient to set down a number of
reactions which appear to be the major ones
occurring in the various systems. The energies
of activation of several reactions have already
been estimated; the appropriate references are
given with these values.
System I. Acetone Eact. Ref.
1. CH,COCH, '!!'. CH,+CH,CO
2. CH,+CH,CO ~ CH,COCH, ~ 17
3. CH,+CH,CO ~ C,H,+CO (j
4. CH,CO +(CH,COCHa) ~ CH,+CO+(CH,COCIla) lR IS
5. CH,+CH,COCH, ~ CH. +CH2COCH, 16 17
6a. 2CH,COCH, ~ (CH2COCH,),
6b. CHaCO +CH,COCH, ~ CH,COCH2COCH,
7. CHa+CH,COCH, ~ C,H,COCH, 8 17
8. CH, +C,H,COCH, '--> CH.+C,H.COCH, <16
9. C,H,COCH, '!!'. (CO. C,H" C,H" C.HIO) 11
System II. Acetone plus mercury
10. CH,+Hg --> HgCH,
II. CH,+HgCH, --> Hg(CH,),
12. CH,+HgCH, --> CH.+HgCH, <13
13. CH,+HgCH, ~ C,H,+Hg
System III. Acetone plus mercury dimethyl
14. CH,+Hg(CH,j, ~ CH,+Hg(CHa)CH, 13-14
15. CH,+Hg(CH,j, ~ C,H6+HgCH;
together with 10, 11, 12 and 13.
If reactions 1 to 9 above represent the mecha
nism of acetone photolysis it is apparent that
for each molecule of acetone decomposing (ex
cluding the reverse reaction 2) one molecule of
carbon monoxide is formed either by reaction 3
or 4. Regardless of which reaction predominates
the VOllll1W of carbon monoxide produced should
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141.209.100.60 On: Mon, 22 Dec 2014 22:30:53622 K. \V. S.\ U N D E R SAN D H. A. T.'\ Y LOR
TABLE VIII. Variation of the composition of products with temperature from acetone.
Pressure of acetone ,....,90 mm, time of radiation ",30 min.
VOL. I:S-CC '70 CcH!/ o/c. CARBO:\'
TI;:l\IP. TOTAL LIQ. N2 -1310 CO CH. CxHII x Y DEFICIE~CY
~.--.---~~--.- -~------- ... ---
250 0.869 0.765 0.104 44.2 43.9 12.0 1.93 5.94 24
225 .998 .812 .186 46.7 34.7 18.6 2.19 6.52 17
225 .568 .487 .082 46.2 39.5 14.4
225 .913 .743 .169 46.7 34.8 18.5
200 .652 .514 .138 49.2 29.6 21.2 2.24 6.40 17
200 .631 .483 .148 47.2 29.4 23.4 14"
175 .445 .322 .123 48.9 23.6 27.6 2.33 6.45
175 .548 .384 .164 48.6 21.5 30.0
150 .575 .370 .204 51.2 13.4 35.4
150 .544 .352 .192 50.6 14.2 35.2 2.22 6.51 9
100 .344 .192 .152 49.3 6.4 44.3 2.10 5.94 0
• Calculated using x =2.2 in CrHlI•
TABLE IX. Acetone photolysis in presence of mercury. Acetone pressure ~90 mmr time of radiation ~30 mm.
VOL. IN cc S-'c, CrH. % CARBO';
TEMP. TOTAL LIQ.N, -1310 CO CH. CrH. x y DEFICIE~CY ----_.-
250 0.652 0.597 0.055 43.4 48.4 8.3 25"
225 .611 .535 .076 45.0 42.6 12.4 2.06 6.16 25
225 .520 .452 .068 45.0 42.0 13.0 24"
200 .276 .236 .040 47.5 38.1 14.5 1.88 6.03
200 .510 .405 .105 48.1 31.4 1'0.6 25"
200 .551 .433 .118 47.8 30.8 21.4 23a
175 .587 .416 .171 49.8 21.2 29.2 1.97 6.25 20
175 .527 .378 .149 48.1 23.8 28.3 17a
150 .617 .396 .221 49.6 14.6 35.8 2.02 6.10 13
100" 49.8 5.0 44.0 71~
-- .-~-----
a Calculated using x =2.0 in CxHy•
b Extrapolated from experiments not summarized here.
TABLE X. Acetone photolysis in presence of mercury vapor. Acetone pressure ",90 mm, mercury pressure ~ 30-35 mm.
TIME VOL. IN CC % CxHy % CARBO';
TEMP. min. TOTAL LIQ. N, -13\0 CO CH. CrHy x y DEFICIEXCY
275 60 0.454 0.437 0.017" 39.0 57.3 3.7 181.
250 30 .354 .328 .026" 42.1 50.8 7.3 231,
250 60 .584 .544 .040" 41.7 51.6 6.8 22"
235 45 .999 .871 .128 44.7 42.5 12.8 1.92 5.88 24
227 60 .818 .718 .100 44.7 43.1 12.3 2.08 5.92 24
225 30 .495 .428 .067 45.5 41.0 13.5 2.12 6.39 24
• Too small to analyze. b Calculated using x =2.0 in CrH •.
TABLE XI. Acetone photolysis in presence of mercury dimethyl. Acetone ",90 mm, Hg(CHa)z ~ 10 mm, radiation time ~30 min.
TEMP.
250
250
225
225
225
225
200
200
200
175
175
150 VOL. IN CC
TOTAL LIQ. N, -1310
0.790
.540
.549
.590
.648
.527
.640
.558
.690
.490
.673
.504 0.676
.480
.463
.493
.537
.445
.489
.432
.520
.351
.452
.319 0.114
.060
.086
.097
.111
.082
.151
.126
.170
.139
.221
.185
a C'akulat("d using x =2.0 in c.! H.II' CO
40.2
39.4
42.7
42.4
43.0
41.2
45.4
44.6
45.4
45.8
46.7
48.3 ()-;'
IC CH.
45.4
49.4
41.6
41.3
39.8
43.3
31.0
32.8
30.0
25.8
20.5
14.0 C;t:HlI
14.0
11.1
15.6
16.4
17.1
15.6
23.6
22.6
24.6
28.4
32.8
36.7 1.95 6.23
2.09 6.23
1.96 6.03
2.01 6.12
1.99 6.02 % CARBO"
DEFICII~~CY
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141.209.100.60 On: Mon, 22 Dec 2014 22:30:53PHOTOLYSIS OF .'\CETONE 623
27~
2,0
22,
0"
j 200
i
{!
175
1,0
12,
100 Acetone --------- Acetone and l.eereury ( vapor and ,surface )
~~~------------.-- Acetone and Mercury Vapor· ----- Acetone and Mercury Dimethyl
10 20 30 40 50 60
FIG. 2.
be constant and independent of temperature.
The variations in light intensity of the lamp
used in this work preclude a definite test of this,
though the lack of any trend in the volumes of
gas formed gives it support. On this assumption
the relative quantities of hydrocarbon formed
together with a fixed quantity of carbon mon
oxide have been calculated as a more desirable
basis for comparison. The values are shown in
Fig. 4. The CHy fraction in acetone alone has
been taken as a mixture of ethane and propane
and although it is unlikely that all of the propane
is pumped from the condensate at -131°, the
trend of the CoH8/CO ratio with temperature is
comparable with the results of Moore and
TaylorY They found a maximum percentage of
propane in the photolysis of methyl ethyl ketone
at llD-120°C. The propane shows a maximum
here around 140°C.
The primary source of ethane in acetone
photolysis has been taken to be reaction 3 rather
than a combination of two methyl radicals14 for
if the energy of activation of the latter is 8 kcal.
14 See A. Gordon and H. A. Taylor, J. Am. Chern. Soc.
In press. 275,--.-----------------,.-, \
225
OU
'00
175
150 C)Re
co
125
0.0 O,? 0.' o.~ 1.'
,: Hydrocarbon / f Carbon ::onodde
o --- Ace-ton.
• ~ - - --Acetone jl,nd Mercury
• --_ .. Acetone and Mercury Dimethyl
)0
10
100
FIG. 4.
reaction 3 would offer effective competition.
The energy of activation may be estimated by
Eyring's method15 using the C -C bond strength
in acetyl as compared with the C - H bond
strength in methane. The activation energy of
the \Valden inversion in methane was shown by
Eyring to be 37 kcal. The C - C bond in acetyl
was found by Gorin and by Herr and Noyes16 to
be about 18 kcal. and taking 95 kcal. as the
C -H bondgivesE 3=37 X 18/95 = 7 kcal. Burton,
Taylor and Davis17 have calculated Es as 5.8
1. Gorin, Kauzmann, \Valter and Eyring, J. Chern. Phys.
7, 633 (1939).
16 E. Gorin, J. Chern. Phys. 7, 256 (1939); D. S. Herr and
W. A. Noyes, J. Am. Chern. Soc. 62, 2052 (1940).
17 Burton, Taylor and Davis, J. Chern. Phys. 7, 1080
(1939).
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141.209.100.60 On: Mon, 22 Dec 2014 22:30:53624 K. W. S:\ tT ;\ j) E R S .\ ~ D H. .~. T ,\ Y LOR
kcaL as the probable chain ending-reaction ill
the decomposition of acetaldehyde indun'd hy
methyl radicals. The lower value 5.8 kcal. as
compared with the calculated 7 kcal. is probably
the better value since in Eyring's calculation
the Walden inversion involved a C -H bond.
formation in methane whereas here the weaker
bond C -C in ethane is being formed.
Methane production by reaction 5 for which
16 kcal.l8 seems to be a reasonable value would
offer little competition to ethane production at
low temperatures. It is observed that ethane
predominates over methane at lOO°e. Taking E4
as 18 kcaI. the increase in rate of reaction 4 with
increasing temperature with its consequent in
crease in methyl radical concentration can ac
count satisfactorily for the decrease in ethane
and increase in methane as the temperature rises.
The production of acetonyl acetone was demon
strated by Rice, Rodowskas and Lewis19 in the
thermal decomposition of acetone at 3S0-400°C
when one percent of mercury dimethyl was
present. I ts presence in the products of photolysis
might explain the white deposit which is always
observed in the condensation trap and which
slowly sublimes. At the same time the ratio
CH4/CO must attain a value greater than unity
at higher pressures at temperatures about 200°C
judging by the trend of the results in Table VII.
This can only occur if the acetonyl corresponding
to CH4 produced retains its CO in some such
form as in acetonyl acetone and the CO does
not appear in the gas phase.
The carbon deficiency observed is accounted
for by reaction 7 with the formation of methyl
ethyl ketone. The presence of this has recently
been reported by AIlen20 in the high temperature
photolysis of acetone. A carbon deficiency can
only occur with the formation of a compound in
which the carbon to carbon monoxide ratio is
higher than that in acetone. The presence of
propane in the products from acetone photolysis
follows from reactions 7 and 9. Moore and H. S.
Taylor have shown that propane is the pre
dominant hydrocarbon in reaction 9 below
18 a. F. O. Rice and K. Herzfeld, J. Am. Chern. Soc. 56,
284, 488 (1934). b. Haden, Meibohrn and O. K. Rice, J. Chern. Phys. 8, 998 (1940).
19 F. O. Rice, Rodowskas and Lewis, J. Am. Chern. Soc.
56, 2497 (1934).
2°A. O.Allen, ].Arn. Chern. Soc. 63, 708 (1941). 200°C. .\t the same time they point out that
methane is formed more readily (reaction 8)
from methyl ethyl ketone than from acetone
suggesting that E8 is somewhat less than 16 kcal.
Qualitatively the suggested reaction scheme 1
to 9 seems adequate to account for the observa
tions. Quantitatively it is not completely satis
factory since the complexity precludes a com
plete calculation of the stationary free radical
concentrations, and the relative importance of
the subsequent reactions is difficult to establish.
Inspection of the data in Table VII at 200°C
shows that at higher pressures the ratio of
CH4/CO varies approximately as the two-thirds
power of the acetone while the C2H6/CO ratio
varies inversely approximately as the one-third
power. This would require that the methyl
radical concentration was roughly proportional
to the two-thirds power of the acetone, a not
impossible eventuality.
Turning now to the system in which mercury
or mercury dimethyl is present, it is evident
that a greater similarity in behavior exists be
tween them than between anyone of them and
acetone alone. Particularly is this true so far as
methane formation is concerned. The increase in
the CH4/CO ratio probably indicates new meth
ane forming reactions other than 5 or 8. Since
reaction 14 is the probable cause of methane
formation from mercury dimethyl it would seem
that this reaction or its alternative, reaction 12,
must be proceeding in system II, acetone plus
mercury, necessitating reactions 10 and 11. This
is borne out by the observed greater carbon
deficiency in the acetone-mercury system wherein
methyl radicals are removed from the system
as mercury methyl and thus do not appear as
hydrocarbons. Further confirmation appears in
the lesser carbon deficiency in the system con
taining mercury dimethyl wherein methyl radi
cals have a chance to react producing hydro
carbons, greater even than in acetone alone.
The absence of propane in detectable amounts
in systems II and III shows a more efficient
methyl removal than ill system I reducing
thereby the possibility of reaction 7 to form
methyl ethyl ketone. The small differences in
the CH4/CO ratios in systems II and III can
probably be traced to differences in mercury
methyl and dimethyl concentrations.
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141.209.100.60 On: Mon, 22 Dec 2014 22:30:53PHOTOLYSIS OF ACETOKE 625
Considering the ratio C2Hu/CO, it is observed
that the value is greater in the mercury dimethyl
experiments. This is to be expected since the
mercury dimethyl concentration is relatively
large favoring reaction 15. Conversely in the
mercury experiments since methyl radicals are
removed by reactions 10 and 11, their concentra
tion is lower. There is some doubt concerning
the source of ethane in these systems. Cun
ningham and Taylor4 have suggested reaction 15,
even attributing the value 1.5 kcal. obtained
from the rate of increase of ethane production
with temperature to its energy of activation.
Simply from analogy with acetone, reaction 13
would seem to offer an even easier path. Although
a Walden inversion type calculation as made
above with acetone might not be quantitatively
reliable, qualitatively it is significant. The Hg -C
bond in mercury dimethyl is given by Terenin21
as about 40-50 kcal. The bond in mercury
methyl is probably considerably less, and thus
ethane formation might be expected to be easier
by reaction 13 than by 15. A decreasing concen
tration of HgCHa with increasing temperature
would account for the low value 1.5 kcal. found
by Cunningham and Taylor.
The crossing of the curves for the acetone and
acetone-mercury systems at higher temperatures
can be accounted for by the fact that if the
2I A. Terenin and N. Prilezhaeva, Acta Physicochim.
U.S.S.R. 1, 759 (1934). propane found in acetone photolysis arises from
methyl ethyl ketone decomposition, there would
also be produced according to "Moore and Taylor
an approximately equivalent amount of ethane
at these temperatures. If the total ethane found
in the acetone system is reduced by an amount
equal to the propane found, no crossing of curves
would occur. It then follows that ethane is
probably produced more easily by reaction 13
than by reaction 3.
From the data in Fig. 4 an approximate
value of the relative activation energies of reac
tions 5 and 14 for methane production can be
obtained. The CH4/CO ratio for the acetone
mercury dimethyl system is about 1.2 times
that for acetone alone in the temperature range
200 to 225°C. The ratio of acetone to mercury
dimethyl in the former is 9 : 1. Hence approxi
mately 1.2=1/9.exp (6.E/RT) whence 6.E=2-3
kcal. If ED is 16 kcal. then E14 is about 13-14
kcal. Since the ratio of mercury methyl to
acetone in system II must be less than 1/9 the
energy of activation of reaction 12 must be less
than 13 kcal.
In conclusion it seems certain that mercury
methyl, if not mercury dimethyl also, is formed
by reaction between methyl radicals and mer
cury. From the general agreement of the results
using liquid mercury with those where only
mercury vapor is present, the reaction must
involve mercury atoms.
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141.209.100.60 On: Mon, 22 Dec 2014 22:30:53 |
1.1750809.pdf | The Reaction of Hydrogen Atoms with Butane
E. W. R. Steacie and E. A. Brown
Citation: The Journal of Chemical Physics 8, 734 (1940); doi: 10.1063/1.1750809
View online: http://dx.doi.org/10.1063/1.1750809
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/8/9?ver=pdfcov
Published by the AIP Publishing
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IP: 132.174.255.116 On: Sat, 29 Nov 2014 08:02:37SEPTEMBER, 1940 JOURNAL OF CHEMICAL PHYSICS VOLUME 8
The Reaction of Hydrogen Atoms with Butane
E. W. R. STEACIE AND E. A. BROWN
Physical Chemistry Laboratory, McGill University, Montreal, Canada
(Received June 21, 1940)
The reaction of hydrogen atoms, produced by the Wood-Bonhoeffer method, with butane has
been investigated over the temperature range 35° to 250°C. The activation energy is 9±1.5
kcal. The products consist solely of methane at low temperatures. At high temperatures ethane
is also formed. It is concluded that the results indicate a mechanism in which a series of "atomic
cracking" reactions play the main role. The main steps in the postulated mechanism are:
Primary process
H +C,H,o-C,H e+ H2•
Secondary processes at low temperatures
H+C.H9-C sH7+CHa
-2C 2H6
H+CsH..-C2H6+CHI
H+C2H6-2CHs
H+CHs-CH,.
Additional secondary processes at higher temperatures
C,H9-C2H,+C2H6
H+C2H.-C2H6
CaH..-C2H.+CH I
H2+C2H6-C2He+H
H2+CHs-CH.+H.
INTRODUCTION "A TOMIC cracking" reactions of the type
H + C2H5--t2CHa,
first suggested by Taylor,l have assumed con
siderable importance in connection with the
mechanism of the elementary reactions of the
hydrocarbons. 2 Strong evidence for the occur
rence of reactions of this type was furnished by
the work of Steacie and Parleea,4 on the reaction
of hydrogen atoms with propane. They found
that at low temperatures the only product of the
reaction was methane, and concluded that its
exclusive formation could only be explained by
the postulation of an initial abstraction of a
hydrogen atom
H + CaHs--tCaH7+ H2,
followed by a series of atomic cracking reactions
H+CaH7--tCH3+C2H5,
H+C 2H5--t2CHa.
1 H. S. Taylor, J. Phys. Chern. 42, 763 (1938).
2 E. Gorin, W. Kauzmann, J. Walter and H. Eyring,
]. Chern. Phys. 7,633 (1939).
a E. W. R. Steacie and N. A. D. Parlee, Trans. Faraday
Soc. 35, 854 (1939).
• E. W. R. Steacie and N. A. D. Parlee, Can. J. Research
B17, 371 (1939). In view of the importance of the results wi th
propane, it was considered of interest to extend
the work to butane. The only previous work on
the reaction of hydrogen atoms with butane is
one run made by Trenner, Morikawa and Taylor5
in the course of another investigation.
EXPERIMENTAL
The reaction was investigated by the Wood
Bonhoeffer method, atomic hydrogen being pro
duced by an electrical discharge. The apparatus
was similar to that used in a number of previous
investiga tions. 3,4.6
Hydrogen was taken from a commercial
cylinder and passed through a tube containing
platinized asbestos at 500°C. The gas then
passed through a blow-off trap, a liquid-air trap
to remove water and other impurities, and
entered the discharge through a capillary flow
meter.
Butane was obtained from the Ohio Chemical
and Manufacturing Company. It contained no
impurities detectable by the analytical methods
used. Variations in the flow rate of both gases
6 N. R. Trenner, K. Morikawa and H. S. Taylor, J.
Chern. Phys. 5, 203 (1937).
• E. W. R. Steacie, Can. J. Research B15, 264 (1937).
734
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IP: 132.174.255.116 On: Sat, 29 Nov 2014 08:02:37REACTION OF HYDROGEN ATOMS WITH BUTANE 735
TABLE I. Reaction of hydrogen atoms with butane.
Pressure =0.35 mm.
BUTANE HYDROGEN PRODUCTS OF THE PER-
FLOW, lI'LQW, REACTION, CENT
TEM- ATOM MOLES MOLES MOLES PERCENT'" OF
PERA- CONCEN- PER SEC. PERBEC. C,RlO
RUN TUBE, TRATlON, ATNTP ATNTP RE-
No. ·C PERCENT Xl()& XI0' C.RlO CR. C,}{. ACTED ---- -----
1 35 5 0.332 2.03 63.8 36.2 0.0 12.2
2 35 5 0.326 2.03 65.8 34.2 0.0 11.8
3 35 5 0.332 2.03 66.2 33.8 0.0 11.3
4 100 5 0.334 2.03 73.6 19.6 6.8 10.0
5 100 5 0.306 2.03 72.4 20.2 7.4 10.4
6 100 5 0.282 2.03 72.5 20.1 7.4 10.5
7 100 5 0.277 2.03 72.0 19.2 8.8 11.5
8 100 5 0.243 2.03 70.0 23.6 6.4 11.4
9 170 3 0.325 2.03 70.2 12.9 16.9 145
10 170 3 0.300 2.03 71.5 10.7 17.8 13.8
11 170 3 0.303 2.03 68.2 12.5 19.3 15.5
12 170 3 0.300 2.03 71.8 12.6 15.6 12.8
13 250 (l)t 0.303 2.03 70.8 9.1 20.1 14.8
14 250 (l)t 0.282 2.03 70.6 9.2 20.2 15.1
15 250 (1lt 0.288 2.03 72.4 7.4 20.2 14.8
• Together with traces of unsaturates and higher hydrocarbons at higher tem
peratures. t Roughly. The accuracy of the determination of these small values is poor.
were accomplished by varying the pressure on
the supply side of the capillary flowmeter.
The hydrogen was passed through a straight
Pyrex discharge tube of 2.5 cm bore, about 30
cm long, to which were sealed side tubes con
taining cylindrical aluminum electrodes. The
electrodes were pinched on to stout platinum
wires which passed out through the glass by
means of capillary tubes and De Khotinsky
seals. The discharge was operated with an applied
voltage of 3500 across the tube and a 5000-ohm
resistance. The operating current of 200 milli
amperes was kept constant by means of a
rheostat in the primary of the transformer.
The reaction vessel was situated as close as
possible to the discharge. It consisted of a
Pyrex cylinder 7 cm in diameter and 30 cm long,
and had a volume of 1370 cc. It was surrounded
by a removable electric furnace. Two tubes
entered the reaction vessel from below, one of
which served as an inlet for propane, while the
other was a thermocouple well.
The walls of the apparatus were "poisoned" in
the usual way with phosphoric acid. At higher
temperatures, the efficiency of the poisoning fell
off owing to the dehydration of the phosphoric
acid. After a number of preliminary runs, it was
found that although the effi~iency of the poison
ing had fallen off considerably, conditions were
extremely stable. The system was therefore used
in this condition, although the atom concentra-tions were t.hus lower than those usually em
ployed (1-5 percent). The atom concentration
was measured by means of a Wrede diffusion
gauge of the usual type.
The size of the reaction vessel and the speed
of the pumps were such that the contact time
was of the order of one second. After leaving the
reaction vessel the products passed through a
liquid-air trap which removed butane and
higher hydrocarbons together with most of any
TABLE II. Average values of analyses.
PERCENT BUTANE Co>!-
VERTED TO
TEMPERA- TOTAL
TURE, PERCENT °c CH, C,H. REACTION
-
35 11.8 0.0 11.8
100 7.9 2.8 10.7
170 5.8 8.3 14.1
250 4.4 10.5 14.9
ethylene or ethane present. The remainder of
the gas passed through a fast three-stage steel
diffusion pump. After leaving this the low boiling
products were removed by a trap containing
silica gel at -180°C. The unadsorbed gas
passed out of the system through a Hyvac pump.
At the end of a run, which normally lasted
about two hours, the traps were allowed to warm
up, and the products were pumped into a port
able mercury gas holder by means of a Toepler
pUlpp. Trials showed that all the ethane and
ethylene and virtually all the methane were
trapped by the silica gel. A small amount of
hydrogen was also retained by the gel.
The products of an average experimen t
amounted to about 500 cc of gas at NTP. The
gas was analyzed in a low temperature distilla
tion apparatus of the Podbielniak type. In the
distillation methane and hydrogen were taken
off together, and this fraction was analyzed by
combustion. In addition to the distillation
analysis, occasional checks on the fractions were
made for unsaturates by conventional methods.
RESULTS
The experimental results of runs made at four
different temperatures are given in Table I.
It is noteworthy that the sole product of
reaction at room temperature is methane. There
is no doubt, as shown by blank runs, that ethane
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would have been detected if it had been present
to the extent of 0.5 percent. Ethane is formed in
considerable amount at higher temperatures, but
the absence of propane over the whole tempera
ture range is surprising. Higher hydrocarbons
were not present in detectable amount, but a
slight oiliness on the surface of the mercury in
the Toepler pump indicated that traces must be
present.
The trend of the products with temperature is
best shown by the data of Table II.
Table III gives the collision yield and the
activation energies calculated on the assumption
that the steric factor A in the equation
Collision yield =Ae-E1RT .0
.. o -20
Ie
t
f
10
is equal to 0.1. In the table ZC,HlO• H represents
the number of collisions of one butane molecule
with hydrogen atoms in the reaction time.
In making this calculation, the diameter of the
butane molecule was taken as 4.8 X 10-8 cm,7
and the diameter of a hydrogen atom as 2.14
X 10-8 cm.8 FIG. 1. Collision yields of the individual products.
Methane-full black circles, ethane-open circles, total
half-black circles.
In Fig. 1 the collision yields of the individual
products (i.e., the number of molecules of each
product produced per collision between a hydro
gen atom and a butane molecule) are plotted
against temperature. This gives the most un-ambiguous picture of the results, since the use of
collision yields automatically corrects the results
for variations in atom concentration, reaction
time, etc.
Comparison of the collision yields with those
of Steacie and Parlee for propane shows that
butane reacts with hydrogen atoms considerably
faster than propane. This agrees with previous 7 T. Titani, Bull. Inst. Phys. Chern. Research (Japan)
8,433 (1929).
8 K. F. Bonhoeffer and P. Harteck, Photochemie (Leipzig,
1933).
TABLE III. Calculation of collision yields, etc.
TOTAL FLOW.
CORRECTED
FOR PRESENCE PARTIAL
ZC,HlO.H of ATOMS. PRESSURE OF
RUN TEMPERA- MOLES PER SEC. REACTION HYDROGEN IN REACTION No. TURE.oC X 10' TIME, SEC. ATOMS. MM TIME
1 35 2.46 1.01 0.016 4.81 X 106
2 35 2.46 1.01 0.016 4.81
3 35 2.46 1.01 0.016 4.81
4 100 2.46 0.84 0.016 3.62
5 100 2.43 0.85 0.016 3.66
6 100 2.41 0.86 0.016 3.70
7 100 2.41 0.86 0.016 3.70
8 100 2.37 0.87 0.016 3.76
9 170 2.42 0.72 0.0093 1.71
10 170 2.39 0.73 0.0093 1.73
11 170 2.39 0.73 0.0093 1.73
12 170 2.39 0.73 0.0093 1.73
13 250 2.35 0.63 0.0031 4.57X 10'
14 250 2.33 0.63 0.0031 4.61
15 250 2.34 0.63 0.0031 4.59 ACTIVATION
ENERGY.
KCAL.
PERCENT COLLISION ASSUMING
REACTION YIELD A =0.1
12.2 2.45x 10-7 7.9
11.8 2.45 7.9
11.3 2.35 7.9
10.0 2.76 9.5
10.4 2.84 9.5
10.5 2.84 9.5
11.5 3.11 9.4
11.4 3.03 9.4
14.5 8.49 10.3
13.8 7.98 10.3
15.5 8.97 10.2
12.8 7.41 10.4
14.8 3.32X 10-" 10.7
15.1 3.28 10.7
14.8 3.23 10.7
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IP: 132.174.255.116 On: Sat, 29 Nov 2014 08:02:37REACTION OF HYDROGEN ATOMS WITH BUTANE 737
investigations which indicate increasing reaction
with increasing molecular weight of the hydro
carbon.5•9
The present experiments. show no formation of
propane. This is not in agreement with the results
of the run made by Trenner, Morikawa and
Taylor, who reported three percent propane in
the products at 110°C. In their experiments,
which were made with deuterium atoms, the
propane formed was not deuterized. This is
difficult to understand, since the only possible
way for propane to be formed and not deuterized
would seem to be by the reaction
D +C4H lo-+CaHs+CH 2D,
and all recent evidence seems to be against the
occurrence of hydrocarbon chain breaking re
actions of this type.
Apart from this the results are in excellent
general agreement with those of Trenner, Mori
kawa and Taylor.
DISCUSSION
The main facts to be explained are (a) the
occurrence of methane as the sole product at low
temperatures; and (b) the occurrence of ethane
at higher temperatures.
The primary step
For the primary step the possibilities are
H+C4HIO-+C4H9+H2, (1)
H+C4Hlo-+CaHs+CHa, (1a)
-+CaH7+CH4, (1b)
-+C2H6+C2H5. (lc)
If (la) or (lc) occurred, propane and ethane
should be found even at low temperatures.
Since they are not found in the products at room
temperature they may be ruled out. (lb) can be
ruled out by analogy with (la) and (lc). The
primary step must therefore be reaction (1).
Secondary reactions at low temperatures
The only way in which methane can be the
exclusive product at low temperatures would
appear to be by a set of "atomic cracking"
reactions.
H +CH9-+CaH7+CHa, (2a)
-+C2H5+C2H5, (2b)
H +CaH7-+C2H5+CHa, (3)
9 W. Frankenburger and R. ZeU, Zeits. f. physik.
Chemie B2, 395 (1929). H + C2H5-+2CHa,
H+CHa-+CH4. (4)
(5)
Reactions of hydrogen molecules with radicals
can be ruled out at low temperatures, since these
would lead to the formation of propane and
ethane. Also
(7a)
does not occur measurably below l60°C.10•1l
Radical recombination reactions can also be
ruled out since they would lead to the formation
of ethane and propane, and in any case the con
centration of atomic hydrogen is so much greater
than that of any radical that reaction (5) will
outweigh other recombination reactions.
Secondary reactions at higher temperatures
At higher temperatures two additional types
of reaction may be expected to make their
appearance:
(a) decomposition of radicals
C4H9-+CaH6+CHa,
-+C2H4 + C2H5,
CaH7-+C2H4+CHa. (6a)
(6b)
(6c)
(b) reactions of radicals with molecular hydrogen
H2+CaH7-+CaHs+H, (7a)
H2+C2H5-+C2H6+H, (7b)
H2+CHa-+CH4+H. (7c)
The increasing formation of ethane IS un
doubtedly to be ascribed to two causes. In the
first place the concentration of ethyl radicals rises
due to (6b) and to the hydrogenation of ethylene
produced by (6b) and (6c) by the reaction
(8)
This reaction is known to be very fast, since the
presence of ethylene causes a rapid removal of
hydrogen atoms. In the second place reaction
(7b) comes into play at higher temperatures.
It is further favored by the diminished hydrogen
atom concentration which results from the
occurrence of (8).
The absence of propane requires explanation,
since it would be expected that (7a) would lead
to its formation. Its absence is apparently due to
the fact that (7a) only becomes appreciable at
10 H. S. Taylor and C. Rosenblum, J. Chern. Phys. 6,
119 (1938).
11 K. Morikawa, W. S. Benedict and H. S. Taylor, J.
Chern. Phys. 5, 212 (1937).
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temperatures at which (6c) is fast enough to
destroy the propyl radicals before they can react.
Any propylene formed by (6a) will presumably
be immediately hydrogenated by the analog of (8).
CSH6+H~CsH7. '(8a)
It should be emphasized that the most im
portant feature of the mechanism is the fact that
the products of the reaction can only be ac
counted for on the assumption that "atomic
cracking" reactions play the major role. This
work, therefore, furnishes further strong evidence
for the occurrence of such reactions as
H+C2Hs~2CHs
H +CSH7-C2Hs+CHs
and adds to the list the reactions
H +C4H9-CHs+C3Hi
H+CH 9-2C 2Hs.
The activation energy of the reaction
Over the temperature range of this investiga
tion, the value of the activation energy of the
over-all reaction rises from 7.9 kcal. at 35°C to
10.7 kcal. at 250°C. Since the primary process in the above mechanism is the only butane con
suming step, and since practically no substances
other than transitory ones are consumed in
secondary processes, the above activation energy
may be assumed to be that of the primary step.
The variation in E from 7.9 to 10.7 kcal. with
rising temperature is presumably to be ascribed
to uncertainties in the concentration of atomic
hydrogen. In the first place the values of the
atom concentration at 250°C are only approxi
mate. Secondly, the measurements of atom
concentrations can only be made in blank runs
with no butane present. At the higher tempera
hIres the collision yield increases and since the
main steps in the process involve the consump
tion of hydrogen atoms, the atom concentration
must be appreciably reduced. The lower value
of the activation energy, therefore, is probably
the more reliable one. We may therefore take
the value of E as 9± 1.5 kcal. This is somewhat
lower than the value found for propane, 10±2
kcal. The difference is undoubtedly significant,
since the collision yields are definitely higher for
butane than for propane.
SEPTEMBER. 1940 JOURNAL OF CHEMICAL PHYSICS VOLUME 8
Molecular Structure of Nitrogen Dioxide and Nitric Acid by Electron Diffraction 1
LOUIS R. MAXWELL AND V. M. MOSLEY
Bureau of Agricultural Chemistry and Engineering, Washington. D. C.
(Received May 13, 1940)
New electron diffraction photographs have been taken
of N02 extending the region previously investigated to in
clude larger angles of scattering. An interference ring was
found at (II>') sin to=0.49 followed by another ring ap
pearing at 0.94 as determined by visual measurements. The
outer portion of the pattern consists of two rather broad
rings and two well-defined minima. Theoretical intensities
of scattering were computed for various nitrogen valence
angles, assuming the positions of the two oxygens to be
equivalent. The best fit, and probably the correct structure.
gives the angle O-N-0=130±r with the N-O dis
tance 1.21 ±.02A. Photographs were obtained from pure
nitric acid vapor at 70°-85°C. The interference maxima
were measured visually as far out as the eighth maximum
INTRODUCTION
PREVIOUS electron diffraction work2 on N02
showed certain nitrogen valence angles to be
1 For a preliminary report on this work, see Phys. Rev.
57, 1079A (1940).
2 Maxwell, Mosley, and Deming, J. Chern. Phys. 2, 331
(1934). at (1/>.) sin !O= 1.83; a prominent minimum was seen at
1.54. Theoretical intensities were computed for various
likely models, disregarding the scattering by the hydrogen
atom. Good agreement was obtained for a planar model
having an NOz group with the same structure found for
nitrogen dioxide. The third oxygen atom 0' is located at a
distance of 1.41 ±0.02A from the nitrogen atom and equi
distant from the other oxygen atoms. A model having the
nitrogen atom slightly out of the plane containing the
oxygen atoms also gave good agreement with the experi
mental results. This model however is considered less
probable in view of Raman spectra data which apparently
require a planar structure for 0' -N02•
inconsistent with the experimental results ob
tained; however, sufficient data were not avail
able to provide an accurate determination of the
molecular structure. Considerable workS has been
done on the interpretation of the infra-red
3 Sutherland and Penney, Proe. Roy. Soc. A156,678 (1936).
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1.1750723.pdf | Gaseous Heat Capacities. III
G. B. Kistiakowsky and W. W. Rice
Citation: The Journal of Chemical Physics 8, 618 (1940); doi: 10.1063/1.1750723
View online: http://dx.doi.org/10.1063/1.1750723
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IP: 160.36.178.25 On: Tue, 23 Dec 2014 05:05:38618 G. B. KISTIAKOWSKY AND W. W. RICE
impossible unless a complete vibrational analysis
is available and the Third Law Entropy data are
preferable for this purpose in case of more com
plex molecules since the vibrational contribution
to the entropies is relatively small. But only by
combining such entropy data with experimental
heat capacities can one be assured of a reasonably
accurate vibrational assignment and hence of a reliable as well as a precise value for the internal
potential.
It is a pleasant duty to thank Professor E. B.
Wilson, Jr., for his interest and many valuable
contributions to this work. We would further like
to express our appreciation to Mr. E. E. Roper
of this laboratory for the use of his equation of
state data before publication.
AUGUST, 1940 JOURNAL OF CHEMICAL PHYSICS VOLUME 8
Gaseous Heat Capacities. 1111,2
G. B. KISTIAKOWSKY AND W. W. RICE
Department of Chemistry, Harvard University, Cambridge, Massachusetts
(Received May 8, 1940)
The present paper presents a continuation of measurements on the gaseous heat capacities by
the adiabatic expansion method. The apparatus and the experimental procedure are exactly
the same as described in the previous papers denoted herein as Part I and Part II. The com
pounds with which the present paper deals are dimethyl ether, ethylene oxide, dimethyl acety
lene, cis-butane·2 and trans-butene-2. For the correction of the experimental data to the ideal
gas state several procedures had to be used, as discussed in Part II.
FOR dimethyl ether critical data are available3
and they were put into the Keyes equation
of state4 to obtain the second virial coefficient
(B) and its derivatives. As pointed out in Part II,
the resultant correction of the heat capacity data
to atmospheric pressure (Cp) comes out too low,
by as much as 10 to 2S percent, and therefore
we do not list this heat capacity in the following
tables. In the further correction to the ideal state
(CpO) the error is fairly welI compensated.
For ethylene oxide only the critical tempera
ture3 is known and the following somewhat
dubious, procedure was resorted to. Maass and
Boomer5 have determined the gas density of
ethylene oxide at several temperatures and
pressures. Their data are not of sufficient
accuracy to evaluate the second virial coefficient
(B) as a series expansion in temperature but a
satisfactory average value of (Va-RT/P) could
1 Part I, G. B. Kistiakowsky and W. W. Rice, J. Chern.
Phys. 7, 281 (1939).
2 Part II, G. B. Kistiakowsky and W. W. Rice, J. Chern.
Phys. 8, 610 (1940), preceding article in this issue.
S Int. Crit. Tab., Vol. 3.
4 F. G. Keyes, J. Am. Chern. Soc. 60, 1761 (1938).
• Maass and Boomer, J. Am. Chern. Soc. 44, 1726
(1922). be obtained. This, together with the critical
temperature, was substituted into the Keyes
equation2 and the correction to the ideal state
thus calculated. The critical pressure calculated
on this basis is found to be 49.1 atmos. as a
weighted average.
For dimethly acetylene also only the critical
temperature T =489°K is known.6 We have
used the plot of critical temperatures vs. critical
pressures given in Part II to estimate the latter
as 31.3 atmos.7
Accurate equations of state were available for
both butene-2 isomers8 and were used directly.
For these latter gases, therefore, the errors due
to the correction are quite small, but in the other'
cases also, the final data should be accurate to
better than 0.1 cal./mole degree, except perhaps
in the neighborhood of the boiling points.
In the following sections the gases will be
considered one by one.
6 Maass and Morehouse, Can. J. Research 11,640 (1934).
7 Osborne, Garner and Yost (J. Chern. Phys. 8, 131
(1940)), estimate this by a different procedure and find
41 atmos.
8 A. B. Lamb and E. E. Roper, J. Phys. Chern. (to
appear shortly) 1940.
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IP: 160.36.178.25 On: Tue, 23 Dec 2014 05:05:38GASEOUS HEAT CAPACITIES. III 619
The sample of dimethyl ether used in these
measurements was taken from a cylinder having
a stated purity of 99.95 percent and obtained
from the Ohio Chemical Company. It was sub
jected to repeated vacuum distillations to eli~i
nate small traces of air and moisture which
might be present.
The following Table I gives a summary of the
experimental results obtained. As emphasized in
Part II none of the completed experiments have
been di~regarded in forming the averages of this
table because of too large deviations from the
mean. The same is true of other heat capacity
tables given in this paper.
In Table I, TAv OK is the average temperature
of the gas before and after expansion for each
series of runs. The column headed (range of f1P),
gives the maximum and minimum values of the
pressure drop of the gas upon expansion. Pfinal~ v.
is the average barometric pressure for the senes
of runs. The temperature coefficient of resistance
of the Wollaston wire thermometer is given in
column five. Column six records the radiation
correction (see Part I). Column seven shows the
apparent heat capacity of the gas (C/) calcu
lated as in Part I, and finally the last column
gives the heat capacity of the gas at zero pressure
(CpO) which is to be used for comparison with
the theoretical calculations.
Crawford and J oyce9 have studied the infra
red spectrum of dimethyl ether and combining
this with the available Raman data have given a
tentative assignment of the vibrational fre
quencies: 2900(6), 1466(6), 1180(4), 1122(1),
940(1), 412(1); all but the lowest frequency
412 cm-1 were taken from the infra-red spectrum.
The numbers in the parenthesis indicate the
statistical weights attached to each frequency. Two degrees of freedom are allowed for the
rotation of the methyl groups. .,
We have calculated the theoretical heat capaci
ties on the above assignment, at the temperatures
of the experimentally determined heat capacities,
assuming the harmonic oscillator and dassical
rigid rotator as the molecular model. The results
are shown in Table II.
In Table II, the third column gives the theo
retical heat capacities calculated from Craw
ford's assignment exclusive of the internal rota
tion of the methyl groups, (Ci.r.). Column four
gives the contribution to the heat capacity due
to the internal rotation of the methyl groups,
"'r Co -(CO -Ci.rJ. The last column .., P(exp) P(calc} •
gives the contribution to the heat capacity for
two methyl groups calculated from Pitzer's
tables10 for a barrier of 2500 cal./mole. The
moments of inertia used were: Ixo=21.666,
Iyo = 82.474, J.O= 93.604 and 5.18, the latter bei~g
for the methyl group. These moments are m
units of gcm2 X 1040 and were calculated on basis
of the dimensions given by Pauling and Brock
way.ll 1.° is the moment of inertia about the axis
through center of gravity and perpendicular t.o
the carbon plane. Iy, the moment about aXIs
bisecting the C -0 -C angle in carbon plane.
Ixo=moment about axis through center of
gravity and perpendicular to Y +Z axis. The cor
relation with experimental data is seen to be
excellent if a potential of 2500 cal./mole is taken
to restrict the rotation of the methyl groups.
TABLE II. Internal rotational heat capacity of dimethyl ether.
CpO Ci.r. calc TOK (EXP.) (CpO-Ci.r)calc Ci.r. (V =2500 CAL./MOLE) ---
272.20 14.82 10.79 4.03 4.20
300.76 15.75 11.59 4.16 4.24
333.25 16.81 12.63 4.18 4.20
370.42 17.96 13.89 4.07 4.12
TABLE 1. Heat capacity of dimethyl ether. (C2H60).
No. OF RANGE OF Pfinal
RUNS TAv OK AP MM AVERAGE MM
5 272.20 37.609-33.882 757.10
6 300.76 38.385-33.611 759.73
5 333.25 38.168-32.864 760.80
5 370.42 37.163-30.563 746.60
9 B. L. Crawford, Jr., and L. Joyce, J. Chern. Phys. 7,
307 (1939). dR OHM RAD. CORR. CpO
dT DEGREE PERCENT Cp' CAL./MOLE DEG. -----
1.1182 0.107 14.52±.02 14.82
1.1108 .113 15.49±.02 15.75
1.1008 .141 16.59±.02 16.81
1.0871 .174 17.77±.02 17.96
10 K S. Pitzer . Chern. Phys. 5, 469 (1937).
11 P~uling and 1rockWay, J. Am. Chern. Soc. 57, 2684
(1935).
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IP: 160.36.178.25 On: Tue, 23 Dec 2014 05:05:38620 G. B. KISTIAKOWSKY AND W. W. RICE
TABLE III. Heat capacity of ethylene oxide (C.H.O).
No. OF RANGE OF Pfinal
RUNS TAv oK tlP MM AVERAGE MM
5 307.18 36.712-30.090 762.05
4 337.04 37.778---31.342 763.70
4 371.23 37.010-33.173 764.30
The only significant deviation of calculated from
experimental values is at the lowest temperature
(272°K). Here, however, the correction to the
ideal state is least certain and the discrepancy
may be due to this cause. It has been shownI2
that the more complete calculation involving the
consideration of the coupling of the angular
momen ta of the top and of the whole molecule
may give results differing appreciably from the
values given in Pitzer's tables for the heat
capacity contribution due to restricted rotation;
therefore the value of the restricting potential
used in Table II should be regarded as pro
visional.
ETHYLENE OXIDE (C2H40)
The sample of ethylene oxide used in these
measurements was a commercial sample ob
tained from the Matheson Chemical Company
and had a stated purity of 99.9 percent. The
sample was subjected to repeated vacuum dis
tillations and pumping to remove traces of air
and moisture. Only the middle portion of the
sample was used for actual measurements. Since
ethylene oxide boils at 10.7°C, the heat capacity
was determined at only three temperatures.
Table III gives the experimental results.
The infra-red and Raman spectra of ethylene
oxide have been investigated by LinneW3 who
has given the following tentative vibrational
assignment: 3000(2), 1494(1), 1122(1), 1270(1),
811(1),1453(1),1163(1),868(1),3062(2),1172(1),
673(1), 807(1), -(1), em-I, with the 811(1),
1172(1), and a frequency which may be corre
lated with the methylene rocking motion being
uncertain.
We have calculated the theoretical heat capaci
ties for ethylene oxide assuming, as suggested by
Linnett, a value of 1350 cm-I for the missing
methylene rocking frequency. The following
Table IV gives the results. It is seen that the
12 B. L. Crawford, ]. Chern. Phys. 8, 273 (1940).
13]. W. Linnett,]. Chern. Phys. 6, 692 (1938). dR OHM RAD. CORR. C.' dT DEGREE PERCENT C.' CAL.jMOLE DEG.
1.1090 0.157 11.57 ±.01 11.80
1.0994 .183 12.57±.01 12.79
1.0868 .219 13.76±.03 13.96
agreement between the experimental and the
theoretical values is not good. The discrepancy
cannot be attributed to an error in the correction
of the experimental heat capacities to the ideal
state, as it is around 0.4 cal./mole degree,
whereas the total gas correction as shown in
Table III is only around 0.25 cal./mole degree
and its uncertainty is at most about 0.1 cal./mole
degree.
We have changed therefore the 811 cm-I
frequency to 1100 cm-I because it is only a
matter of conjecture as to whether there are
two frequencies at 807 and 811 cm-I or only one.
The other two uncertain frequencies namely 1172
and 1350 cm-I remain unchanged. Column four
in Table IV gives the corrected calculations.
The agreement with the experimental data is
seen to be quite good but until heat capacity
data over a larger temperature range are avail
able, one cannot be sure that the new assignment
is substantially correct.
DIMETHYL ACETYLENE (C4H6)
The dimethyl acetylene used in these measure
ments was part of the same material which was
prepared and used in the heats of hydrogenation
by Kistiakowsky and co-workers.14 The material
was vacuum distilled before introducing it into
the expansion chamber. Because of the high
boiling point of dimethyl acetylene, the heat
capacity was determined at only two tempera
tures. The experimental results are given in
Table V.
TABLE IV. Statistical heat capacity of ethylene oxide.
C.' C.' C.' LINNETT'S NEW
TAvOK (EXP.) ASSIGNMENT ASSIGKMENT
307.18 11.80 12.16 11.80
337.04 12.79 13.18 12.78
371.23 13.96 14.34 13.94
14]. B. Conn, G. B. Kistiakowsky and E. A. Smith, ].
Am. Chern. Soc. 61,1868 (1939).
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TABLE V. Heat capacity of dimethyl acetylene (C4H.).
No. OF RANGE OF Pfinal
RUNS TAv oK aP MM AVERAGE MM
5 336.07 40.796-33.643 771.55
6 369.46 40.102-34.384 770.90
Crawford15 has studied the infra-red and
Raman spectra of dimethyl acetylene and has
given an assignment for the vibrational fre
quencies of this molecule: 725(1), 1380(1),
2270(1), 2916(1), 1126(1), 1380(1), 2976(1),
213(2),1050(2),1468(2),2976(2),371(2),1029(2),
1448(2),2966(2).
Crawford and Rice16 using this assignment and
the heat capacities given in Table V have calcu
lated the contribution to the heat capacity due
to the internal rotation of the methyl groups
relative to each other and find the restricting
potential to be at most 500 cal./mole. Table VI
reproduces these calculations. The experimental
results for (C.r.), the contribution from the
internal rotation, are in good agreement with
the value 0.99 cal./mole degree expected for a
completely free rotator, or a restricting potential
of zero; 500 cal./mole is undoubtedly the upper
limit.
Recently Yost et aU have published measure
ments on the third law entropy of dimethyl
acetylene, from which they also conclude that
the restricting potential in this molecule is very
low, possibly zero. Their conclusion is less de
pendent on a correct vibrational assignment than
the evidence given here and together the two
studies offer indisputable proof of a practically
complete absence of hindrance to the rotation of
the methyl groups in this molecule. It seems to
us that the theory of restricting potentials
offered some time ago by Gorin, Walter and
T ABLE VI. Internal rotational heat capacity of
dimethyl acetylene.
CLr. calc
Cp' (V=500
TAvoK (EXP.) (Cp' -CLr)calc C' CAL./MOLE) l.r.
336.07 20.21±.1 19.14 1.07 ±.1 1.16
369.46 21.43±.1 20.47 .96±.1 1.14
15 B. L. Crawford, Jr., J. Chern. Phys. 7, 555 (1939).
16 B. L. Crawford, Jr. and W. W. Rice, J. Chern. Phys.
7,437 (1939). dR OHM l:tAD. CORR. Cp' dT DEGREE PERCENT Cp' CAL.(MOLE DEG.
1.0998 0.162 19.41 ±.03 20.21
1.0874 .200 20.76±.04 21.43
Eyring17 will find it rather difficult to account
simultaneously for the existence of a rather high
potential in dimethyl ether and the absence of
same in dimethyl acetylene.
CIs-BuTENE-2 (C4H8)
The sample of cis-butene-2 was part of the
original material prepared by Kistiakowsky and
co-workerslS for the determination of the heats
of hydrogenation. The sample was vacuum dis
tilled several times before being introduced into
the expansion vessel but after the experiments
were carried out it was found that a small trace
of water vapor remained in the sample. Because
of this the heat capacity values given in Table
VII may be 0.1 to 0.2 percent too low. The
experimental results are shown in Table VII.
TRANS-BuTENE-2 (C4Hs)
The sample used was also part of the material
prepared by Kistiakowsky and co-workers.18 It
was subjected to the usual vacuum distillations
and was definitely freed of water vapor. The
experimental results are shown in Table VIII.
No vibrational analysis of the two isomeric
butenes has been suggested as yet, although
Gershinowitz and Wilsonl9 have studied the
infra-red and Raman spectra of these molecules.
The important conclusion which can be drawn
from their work is that the spectra of the two
molecules have very different appearance and
the present measurements, which show a differ
ence in vibrational plus internal rotational heat
capacities of as much as 12 percent, bring
convincing evidence that the fundamental fre
quencies of the two isomers are significantly
17 Gorin, Walter and Eyring, J. Am. Chern. Soc. 61,
1876 (1939).
18 Kistiakowsky, Ruhoff, Smith and Vaughan, J. Am.
Chern. Soc. 57, 876 (1935).
19 Gershinowitz and Wilson, J. Chern. Phys. 6, 247
(1938). .
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TABLE VII. Heat capacity oj cis-butene-2. (C.Hg).
No. OF RANGE OF Pfinal dR OHM RAD. CORR. Cp' ,
RUNS TAv OK tlP MM AVERAGE MM dT DEGREE PERCENT Cp' Cp CAL.jMOLE DEG.
5 298.58 38.424-26.831 759.20 1.1114 0.135 18.47 ±.05 20.06 19.39
5 332.85 38.088-32.972 769.00 1.1009 .164 20.37±.03 21.54 21.09
5 371.24 38.554-32.275 769.40 1.0868 .157 22.46±.05 23.30 23.01
TABLE VIII. Heat capacity oj trans-butene-Z. (C.Hg).
dR OHM No. OF RANGE OF Pfinal RAD. CORR. CpO
RUNS TAv OK tlP MM AVERAGE MM dT fiEGRiiE PERCENT Co' Cp CAL./MOLE DEG.
6 298.60 38.472-35.244 766.50 1.1114 0.13 20.04±.03 21.55 20.98
5 332.90 38.350-33.436 767.75 1.1009 .14 21.96±.03 23.06 22.69
5 371.50 38.322-36.302 765.95 1.0866 .17 23.97±.04 24.78 24.53
different. The neglect to allow for such differ
ences in the schematized frequency assignments
occasionally proposed20 leads evidently to sig
nificant errors in the comparative values of the
calculated thermodynamic functions.
A different approach to this problem of the
thermodynamic functions of the more complex
organic molecules is through a frankly empirical
set of recursion type formulas derived from ex-
20 K. S. Pitzer, ]. Chcm. Phys. 5, 473 (1937); M.
Huggins, ibid. 8, 181 (1940). perimental measurements on the gaseous heat
capacities. The data collected in the first three
articles of this series show indeed the possibility
of setting up such equations but we prefer to
await the accumulation of a little more experi
mental material on heavier hydrocarbons, the
work now in progress in this laboratory, before
claiming their general validity.
Professor E. B. Wilson, J r. has advised us on
several phases of the present work, for which
we wish to express to him our appreciation.
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1.1916093.pdf | Shock Waves in Air and Characteristics of Instruments for Their Measurement
L. Thompson
Citation: The Journal of the Acoustical Society of America 12, 198 (1940); doi: 10.1121/1.1916093
View online: https://doi.org/10.1121/1.1916093
View Table of Contents: http://asa.scitation.org/toc/jas/12/1
Published by the Acoustical Society of AmericaJULY, 1940 J. A. S. A. VOLUME 1 2
Shock Waves in Air and Characteristics of Instruments for Their Measurement*
L. THOMPSON
Naval Proving Ground, Dahlgren, Virginia
(Received May 21, 1940)
I
OUND waves of very great condensation may become shock waves, as a result of propaga-
tion phenomena, even if the disturbance does not
initially have the abrupt form characteristic of
shock. Shock is a kind of asymptotic condition
which finite condensations in air generally tend
to assume because the velocity of propagation is
greatest for the zone of greatest condensation.
So far as any distinction by direct physical test
is concerned, the wave surface of a shock of
great intensity is a surface of discontinuity of
density and acceleration. Other characteristics of
waves of finite amplitude which distinguish this
type of sound, in addition to the quality of
changing shape, are the finite velocity of air
flow set up at the instant of transit of the wave
surface and the extraordinarily short duration of
the compression cycle. If the intensity is great
the wave velocity may be many times the normal
velocity of sound, and the velocity of flow may
be almost as great at the wave surface. No
direct-measuring pressure gauge is fast enough
to follow the rise to maximum pressure. Because
of the shortness of the interval of condensation
the accumulation of energy in one or more of
the molecular degrees of freedom is probably
small and the effective specific heats are there-
fore abnormal. The cycle is not adiabatic. Dating
back to the studies of Rankine and Hugoniot it
has been known that the mechanics of the
system cannot be represented by the static-
adiabatic law used for the range of infinitesimal
sound but requires a pressure-density function
allowing for dynamic effects. The dynamic-
adiabatic law of Rankine and Hugoniot for
pressure-density variation was derived to repre-
sent the shock cycle and its use is justified at
the present time as the best basis available for
computation. However, even the definition of
pressure (as well as of temperature) is ambiguous
when applied to a surface of shock, and it appears
* Presented at the 23rd meeting of the Acoustical
Society of America, Washington, D.C., April 29, 1940. that no general equation of condition may exist
in the sense of those for systems in equilibrium.
Sufficiently qualified, there is a definite maximum
pressure associated with the wave surface and of
course a definite density on both sides. This
pressure may be many atmospheres on the con-
densed side. Referring to a scale of intensity or
of "loudness" values as used in normal acoustic
systems, the shock pulse may have ratings so
great that severe mechanical action would be
expected. Close to sources of shock waves, the
mechanical action may actually be sufficient to
deform rugged structures but in these zones the
action is usually accompanied by other agencies
of destruction still more severe, so that the net
effect of the shock is difficult to isolate. For
example, near a detonating charge of TNT the
shock pressure may be several hundred atmos-
pheres but the expanding gases produce dynamic
pressures much greater. For this reason blast
damage is not usually thought of as an acoustic
effect though, occurring alone, the acoustic effect
might be serious enough. In fact at considerable
distances from a detonating charge, beyond the
zone of impact with the gases from the charge,
the shock wave may be of intensity sufficient to
cause damage to ordinary buildings and to
personnel. This is plainly the case when very
great charges go off, as in accidental detonations
of storage units.
Mechanical action from shock in air is less
than might be expected from the order of
pressures at the wave surface because the times
of application are so short. A shock wave of
intensity 104 watts/cm 2, about 80 db above the
threshold for feeling and almost 200 db above
the threshold for hearing of sound of periodic
nature, may have less effect on the ear and body
than a sustained sound of intensity 10 - watt/
cm 2. The ear and all mechanical structures are
essentially "ballistic" as gauges responding to
shock disturbance. Near the muzzle of a large
gun, the sharp "crack" which should be present
as a result of the shock wave preceding the gas
198 SHOCK WAVES IN AIR, MEASURING INSTRUMENTS 199
jet and the projectile, is masked in its effect on
the ear by the long-period "boom," although the
maximum pressures in the shock waves are much
greater than the pressures elsewhere in the dis-
turbance at the muzzle.
II
The classical theory of finite waves proceeds
from the concept of a continuous cycle of con-
densation in which the maxima of pressure,
velocity of air particle and density are attained
in small but finite intervals of time after the
boundary of the disturbance first passes a point
in the medium. Poisson, Riemann, Rayleigh 1,
and others have developed the theory of velocity
from the standpoint of a superposed wave travel-
ing over a moving medium, with a result stated
in the form ß
v=u+(,'½))
in which ½(p) is the pressure-density function
applicable to the cycle and u the effective velocity
of the flow at the wave surface. In the work of
Riemann 3 the cycle was taken to be adiabatic
and, using Earnshaw's result that
log p
Riemann obtained the formula
v=a 1+
g--1 g-1
X normal density, 4 which can be written
v=a(1-+-k/r)«
(r being distance from source). Our experimental
results have indicated that a modification of this
formula is satisfactory for the velocity field of a
wide range of sources'
....... (.5)
v a lq (½-+-x)
Lord Rayleigh, Proc. Roy. Soc. London 484, 247
(90).
' H. Bateman, Bull., Nat. Research Council, Number 84,
Part IV.
3 B. Riemann, Abb. Konigl. Ges. der Wiss. G6ttingen 8,
43 (1860).
4 (a) L. Thompson and N. Riffolt, J. Acous. Soc. Am.
11, 233 (1939). (b) L. Thompson, J. Acous. Soc. Am. 11,
245 (1939). in which
( Va-a ) C= (+1) 3, Va boundary velocity, a
a characteristic constant,
x = gr,
K being the radius of an equivalent spherical
source (one having same boundary velocity).
The latter formula for velocity leads to the
definition of a "reduced" time of wave displace-
ment. Experimental results for reduced times and
velocity were presented in an earlier paper.
Though in the classical approach to the theory
of shock waves the condition of shock is supposed
to develop as a kind of limit condition as the
wave becomes steeper, the theory does not admit
ever reaching perfect abruptness. A permanent
regime is possible, as shown by Rayleigh, when a
certain balance is maintained by virtue of
dissipation in heat conduction and from viscous
forces. All of the steps in the classical theory
presume a continuous process of change in a
system in equilibrium. The alternative approach
by Hugoniot's results for a true discontinuity
offers certain advantages. Hugoniot initiated
such a theory by studying the rate of propagation
of a surface of discontinuity of the second order
(a discontinuity in acceleration). He found that
the equations of motion could be treated by
means of his dynamic and kinematic conditions
of compatibility, with the result that the velocity
of the disturbance is
v = (ap/ap).
A full treatment of the subject is given in
Hadamard's book, and an abridged discussion in
Webster's book. It will be noted that this
velocity refers to the rate of displacement with
respect to the air particles on one side of the
discontinuity, and that the velocity on the other
side is given by the equation of continuity of
flow. The difference in interpretation of the
velocity obtained by this analysis, comparing the
formula of Riemann, arises from the fact that
velocity of the air particle is not subject to dis-
J. Hadamard, Lecons sur la Propagation des Ondes
(A. Hermann, Paris, 1903).
A. G. Webster and S. J. Plimpton, Partial Differential
Equations of Mathematical Physics (B. G. Teubner, 1927),
p. 280. 200 L. THOMPSON
continuous change at the wave surface even
though acceleration and density experience
"jumps" at that surface. Hence the wave velocity
is taken here as referring to the undisturbed
medium.
Using the Hugoniot velocity for the shock
wave (the surface of discontinuity of accelera-
tion), in combination with the dynamic equation
of condition, the equations for pressure and
density have been given in terms of wave
velocity. 4b It is possible to make some calcula-
tions applying to sound waves of finite amplitude
without encountering directly the difficulties in
handling the differential equation when the
assumption of small condensations is not legiti-
mate. The work done in condensing the gas in
the head of the wave, per unit volume, is
(using the Hugoniot-Rankine equation of con-
dition)
= fpd w= J'pav -
= 4p0f v pdp Ep(+
-4a2 -- Lp(+l)+p0(--l)
----+log
2 2p0
and the energy in the pulse of effective thickness
X per unit area is WX. Therefore the rate of
transmitting energy through unit surface is
WX WX
t X/v
where bt is time or condensation and v is wave
velocity. The power per unit area of such a
source may be taken, however, as
P=bp.o/Ot
and bp is known from the equation for the
pressure at a surface of discontinuity, where
O/Ot is the maximum particle velocity at wave
boundary in terms of velocity' hence
O/Ot= Wv/bp, the maximum particle velocity.
If one chooses to think of the amplitude of particle displacement as the displacement ac-
quired at the condensation maximum, corre-
sponding to this point as the first fourth of a
complete oscillation, it is possible to obtain
rough values by substitution
Taking for n the value
2- 2- Oi/,rv at 4X/v mx= ß 2X
Results for max and O/Ot by these formulas are
not sufficiently reliable to justify including them
in Table I. However, it is of interest that dis-
placements / so obtained are extremely small
even for waves of great intensity. Their smallness
is the result of the excessively short times
(excessively great equivalent frequencies), being
perhaps 10 -a or 10 -4 cm for the conditions
listed below.
The table contains numerical estimates of
certain characteristics of shock waves at various
distances from sources of great intensity.
Using the Rankine-Hugoniot equation for
pressure-density, we may state the equation for
plane waves as
O po( 2 ) Otl at oo ax
p0( p0 1- (- 1)s/2 Ox
This identifies the effective velocity in terms of
the ordinary sound velocity a and the condensa-
tion s, as
l+s ) u--a
1-(- 1)s/2
+1 2-1 ) =a 1+ s+----s+ ... .
2 4
The static-adiabatic law usually given, defines
by same procedure,
+1 --1 ) v=a(1-}-s)(+l)/=a 1 + s+- s+ "' , 2 8 SHOCK WAVES IN AIR, MEASURING INSTRUMENTS 201
TABLE I. Shock pulse, typical conditions.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
DISTANCE FROM
SOURCE
HALF- COM-
DIAM. CONDEN- PRES-
OVER-ALL POWER EQ. TIME OF SATION a SION ACOUSTIC INTENSITY
WAVE OF SOURCE SOURCE CONDENSATION 8=P--P0 P--P0 POWER WAVE b SOURCE VELOCI (ORDER OF) METERS X *t P0 p0 P (P/ARm) NOTES . . .
Cal. 0.30 bullet 750 m/sec. 2 or 3 hp At 1 About 10 -o sec. 1.5 5. -- 106 to 107 Data for nose only
(in air) nose (X About 10-5 cm) watts/cm 2
i.e., rate of d. issi.pating energy m air
__ . _
Largest projectile 750 m/sec. 104 hp At I AbOut 10 -o sec. 1.5 5. 106 to 107 Comparing columns (3) (in air) nose (X About 10 -5 cm) watts/cm 2 (9), the effective areas ot
condensation at nose (ot
bullet and projectile)
< 1 mm 2,1 cm2, respectiveb
Spark 750 m/sec. -- -- -- About 10 -0 sec. 1.5 5. -- 106 to 107
(X About 10-* cm) watts/cm2 _
16" Gun fire 1500'- 107 hp Gas jet I 10 -11 sec. 2.4 20. -- About 107 Gun fire also accompanie 1800 m/sec. (for 0.05 sec.) muzzle watts/cm 2 by other sounds of finit(
amplitude which have
greater effect on ear.
16" Projectile ira- -- 108 hp -- I Comparable
pact on heavy (for 10- sec.) with explosion
armor
.
10 lb TNT 5000 m/sec. 109 hp Surface 1 10 -n to 10 -x2 sec. 2.8 50. 106 to 107 108 watts/cm 2 Boundary value of ve!ocit
1350 m/sec. (for 3X10-* sec.) 0.8 10 10-o sec. 2.0 10. hp (for of shock equals detonatin
390 m/sec. 8.1 100 10-sec. 0.4 0.7 10-1Osec.) 10a to 10 velocity of explosive fm
watts/cm -ø sources of great brisance. _
1000 lb. TNT 5000 m/sec. 10 o hp Surface 1 10 -1 to 10 -2 sec. 2.8 50. 107 to 108 10 s watts/cm2
1350 m/sec. (for 10- sec.) 3.7 10 10 -1ø sec. 2.0 10. hp (for
390 m/sec. 37 100 10- sec. 0.4 0.7 10 -o sec.) 10 a to 10
watts/cm 2
Condensation approaches maximum value depending on g (ratio specific heats). See references 4 and 8a. For example, for =5/3, s=.ap/oo--'3-3a/v (a velocity of
sound).
b Threshold for feeling at very high frequencies is about 10-a watt/em2 (of order 102 dyne/cm2). The intensity values of table are therefore'of order 100 db to 120 db
above threshold for feeling (for oseil!atory source). Yet the ear, and entire body, acting as ballistic "receivers" are not affected to a corresponding extent because of the
extremely short times of action. Disabling effects are not likely to be experienced by personnel exposed to shock from detonation beyond the x--' 100 distances noted above.
Boundary velocities for various high explosives do not differ enough to change this limit (appreciably) among the available explosives of high brisance.
while the result using Eq. (1.6) 4 is
ß
v--a 1----'S
2
--ls+ ... ). 2 (1.63)
For large values of s the above procedure based
on the wave equation is not valid.
III
Characteristics given in the table, except for
velocity sequences, are estimates of a rough
nature not well enough checked by actual
experiment. Because of greater precision, it is
often preferred to measure velocity of wave as
an index of intensity (i.e., use velocity apparatus
as a blast meter). In some cases relative pressures
by "gauge" have been measured by a piezo-
gauge and by condenser microphone, (the latter at great distances from source). In general, the
calculations depend on assumptions which are of
doubtful validity though apparently leading to
results of the right order. Experimental work is
being conducted for the purpose of measuring
simultaneously the condensation and compres-
sion ratios for typical conditions, using methods
which can properly be considered absolute or
capable of quantitative calibration. With simul-
taneous measurements of both amplitudes it is
believed possible to extract empirically from the
results, by statistical procedure, not only the
effective ratio of the specific heats for these
cycles but also that equation for pressure-density
relation which describes the conditions existing
in these transient states.
The methods available are not very different
from those sometimes employed in experiments
with infinitesimal sound, though the fact of
great intensities makes certain techniques suit-
able which are less suitable for infinitesimal 202 L. THOMPSON
waves because of their lack of sensitiveness.
This is a fortunate circumstance since other
methods, depending on the occurrence of a
steady state such as the Rayleigh disk, the
radiometer, and A. G. Webster's technique with
tuned units, cannot be used for measurements of
single-pulse amplitudes, at least not in the
customary manner.
The following outline refers to the principal
available experiments for measurements of shock
waves.
A. Condensation
Density can be measured by refractometric
methods:
(1) An optical circuit may be set up to show
the accumulated deviation of a ray of light
passing through the surface of a shock wave
nearly tangent to the wave. The best procedure
is that of Dvorak's spark photography giving
shadow records. Hilton 7 has recently published
some results and a discussion of an analytic
technique for reduction of the measurements to
values of condensation in terms of index of
refraction and the geometry of the system. These
researches were concerned with shock waves in
the field of a rotating propeller.
(2) Propagation of shock through an inter-
ferometer field. This method is probably best
for the study of intense waves. The path of the
ray which includes a section of a shock wave
system travels an equivalent distance D-t-nX
and the condensation is
Ap nk
p0 D(u- 1)
where D is the actual distance intercepted by
wave, X the wave-length, and n the number of
fringes in the observed shift at the point. Spark
photographs have been published by Cranz, 8b
showing the pressure field near projectiles in
flight, and an optical circuit well adapted for
density exploration of shock wave areas.
The procedure is an absolute one in the sense
of absence of effect of the measuring apparatus
on the wave field. It is possible to obtain quanti-
tative values of condensation in terms of the
7 W. F. Hilton, Proc. Roy. Soc. A169, 174-189 (1938).
8 (a) C. Cranz, Innere Ballistik II (J. Springer, 1926),
p. 171; (b) III (1927), p. 271. geometry of the fringe pattern of the system and
index of refraction t for light of wave-length
used; Cranz used a magnesium gap. Measurements
given by Cranz for one case contain sequences in
quite good agreement with those of Table II of
reference 4b. For example, at a point 2 cm
behind the nose of the bullet and 1.28 to 1.44 cm
normal to axis of flight Cranz gives the values
ap/p=0.24, (ap/p)(calc)=0.34.
Table II gives about
Zp/p=0.22 for zp/p=0.35.
The corresponding wave velocity (Eq. (1.71))4 is
1.05a. The equivalent x value is about 175.
(3) Measurement of the velocity of air flow set
up at the wave surface. The displacements avail-
able are so small that optical methods for ob-
taining rates of change are not very promising.
Tests of a filament microphone have been made
with the hope of obtaining velocity directly,
though the problem of setting up a sufficiently
light filament to follow the stream is a difficult
one. The ordinary velocity microphone is not
satisfactory since the basis for its application with
infinitesimal waves no longer holds with waves
of great intensity. Assuming that particle velocity
can be measured, the condensation can be
obtained from the equation for continuity of flow.
It will be noted that none of the above-
mentioned techniques is capable of measuring
pressures or displacements directly. Their use to
obtain pressure, as in the work of Cranz and of
Hilton, is through some assumed equation of
condition and accordingly the results are not
reliable for shock waves of great intensity. But
the identification of condensation, itself, is just
as important for a complete experimental solu-
tion of the problem as the measurement of
pressure, even though it does not itself provide
the complete solution offered in the case of
waves of low intensity.
B. Compression
Pressure amplitude can be obtained directly
by:
(1) Mechanical gauges operating as "ballistic"
instruments. These are satisfactory as over-all
blast gauges, in which case the effective mean
pressure is made up of two components, the SHOCK WAVES IN AIR, MEASURING INSTRUMENTS 203
L
FIG. 1.
second being the dynamic pressure from air flow.
Here, as in all cases, it is necessary to know
something about the relation between mean
pressures and maximum pressures, and to be
able to calculate separately the dynamic pres-
sure, if the results are to be used for estimates of
compression. A good form of ballistic meter is a
"swinging door" type, with the door mounted in
a baffle support.
(2) Piezoelectric gauges. These are also bal-
listic, as far as measurements of the development
of pressure in shock pulses are concerned, even
when the crystals are mounted for direct expo-
sure to the wave. The interval of compression in
the wave surface is several orders shorter in
time than the interval of propagation of the
wave through the thinnest practicable crystals.
However, the gauges made up of single crystals of
tourmaline, Rochelle salt or quartz, so mounted,
are the best available pressure gauges. Satis-
factorily calibrated, they will give maximum
pressures, although Rochelle salt is not very
suitable because of its sensitiveness to tempera-
ture changes. It will be noted that for shock
waves of considerable intensity, a crystal of any
practicable size constitutes an approximately
perfect reflector and therefore permits identifica-
tion of compression as half the observed change
of pressure after subtracting the dynamic pres-
sure. To obtain the dynamic pressure it is
necessary to have the data for condensation
(either by measurement or by calculation) and
the wave velocity. One of the most extensive
programs being developed in this country for
the measurement of pressures by piezoelectric technique is that of the Aberdeen Proving
Ground, where excellent results have been ob-
tained by Kent and Hodge in the determinations
of gun pressures. Their recording and calibration
systems have been described recently in the
Transactions of the A roerican Society of Mechani-
cal Engineers. ø Gun pressures, cycles of which
may be considered similar to those for shock-
pressures but with time range many orders
greater, are obtained by cathode-oscillograph
recording of potentials developed on stacks of
quartz crystals mounted in rugged holders. Pres-
sure is applied through a piston. A similar
gauge was also used by Kent for the measure-
ment of blast pressures from explosions. In one
case his result of 75 lb./in. 2 at a distance of 24
feet from 25 lb. of TNT corresponds to a value
of Pc calculated in reference 4b as about 55
lb./in. 2. Our work on the relative pressures in
shock waves was done initially with open crystals
of Rochelle salt (cut 3_ to electric axis, 45 ø to the
other axes). Records by cathode oscillograph
were calibrated at point of mid-range of intensity
by calculations described in reference 4b. At the
present time a method is being developed to
accomplish calibration by a dynamic experiment
described below.
(3) The Hopkinson bar. An interesting tech-
nique was invented by Hopkinson ø in which the
pressure of shock was estimated by a steel bar
suspended to swing in a vertical plane, having a
small bar of same diameter stuck on at one end
with vaseline. A source of shock near the other
end sets up a wave of compression which travels
to the opposite end and is reflected as a wave of
tension. When the tension at the junction ex-
ceeds the compression of the tail end of the wave
the "time piece" flies off with momentum equal
to the product of time for wave to travel twice
the length of rod and the mean force transmitted
by the wave. Length of time piece about 1".
Measure velocity of piece with ballistic pendulum.
Results are therefore measure of pressure de-
livered by source during first (condensation)
phase of its action.
(4) The condenser microphone. The standard
technique with the condenser microphone has
9 R. H. Kent and A. H. Hodge, Trans. A.S.M.E.,
April, 1939.
o Marshall Explosives III (Blakiston, 1932), p. 156. 204 L. THOMPSON
been used by Schneider u for measurements of
pressure in shock waves at considerable distances
from the source. The method might not be
satisfactory at points fairly close to the source,
primarily because of lack of a satisfactory
inethod of calibration. Possibly a device similar
to the one described below for piezo-gauges
could be adapted. In any case the results would
be those of a ballistic unit. Schneider measured
the pressure of the shock pulse from a detonating
charge of 1 kg TNT at 160 meters to be 2.7
g/cm . The value obtained by first computing b
v = a(1-i- C/ ( ,-i-x)2)
for x (=3200) used, as v=l.00017a and then
substituting in Eq. (2.31) is-Pc'-14p0. (0.00017)
-' 2.4 g/cm 2 (neglecting small term in V,). Use of
K=7/5 is apparently justified for waves so
weak.
Calibration of piezo-pressure gauge
The apparatus shown in Fig. 1 was designed to
provide a dynamic calibration for a crystal or
for other pressure gauges which can be mounted
in the position C.
The gauge "standard" at the other end is an
optically recording spring system of very high
natural frequency. Pressure curves are obtained
on a moving film on which are superposed
standard timing lines. The crystal records by
cathode oscillograph, using a resistance-capacity
coupled amplifier of good response to about
30,000 cycles/second. Pressure is applied by
dropping a weight of 25 to 50 lb. on the vertical
piston. The weight and guides for control of
impact on -P1 are not shown. The chamber is
filled with glycerine (which has the lowest com-
pressibility among available liquids and permits
getting high pressure cycles of very short dura-
tion). It is necessary to use care in filling to
insure satisfactory freedom from small air
bubbles; valve V is opened slightly, pouring
glycerine in a narrow stream through the piston
holders H. The procedure in calibration is to
take simultaneous records with the optical
standard and the gauge C.
1 W. Schneider, Zeits. f. das gasamte Schiess u. Spreng-
stoffwesen, December, 1939, pp. 329-31. The advantage in using the optical standard,
which is an adaptation of a gauge for gun
pressures developed in 1919 by Webster, Thomp-
son and Riffolt, s is that it provides at once both
the time interval necessary for computing the
mean pressure for calibration and the relation
between mean pressure and maximum pressure
(as well as relative pressures at any other point
in the cycle). The reflection coefficient applicable
to the gauge for specific pulse cycles can probably
be identified. Calibration tests can be carried out
with intervals possibly as short as 10 - second.
While this interval is several orders longer than
the interval of condensation in shock waves, the
characteristics shown over a wide range of
available intervals should provide a satisfactory
check of calibrations for short transients.
IV
By simultaneous use of methods A (2) or A (3)
and B(2) one may hope to obtain parallel
sequences of values of K for typical sources of
shock at several points in the field. Equations
similar to those of reference 4b, set up on any
assumed equation for pressure-density will then
lead to unique values of , the ratio of specific
heats, applicable to the cycle in question for
each of the conditions. There will be two inde-
pendent equations, each giving a value of , one
between wave velocity and p and one between
wave velocity and p.
That equation of condition (pressure in terms
of density) which leads to the same value of by
the two independent sets of data, may be taken
as the correct function in the sense of definition
by these experiments (i.e., as applicable to the
time and condensation ranges of a specific test).
The procedure is one of successive approxima-
tions, which constitutes a kind of empirical
extraction of an equation of condition without
involving any assumptions as to the actual
condition of the system.
I am indebted to Mr. Nils Riffolt for super-
vising the construction of the calibration unit
and for collaboration in its design; also to Mr.
Milton Lipnick for contributions to the develop-
ment of a filament microphone.
12 Proc. Nat. Acad. 5, 259 (1919)' J. Opt. Soc. Am. X,
June, 1925; U.S. Naval Inst. Proc. 58, March, 1932. |
1.1712911.pdf | Abstracts from the Conference on Applied Nuclear Physics, Cambridge,
Massachusetts, October 28–November 2, 1940
Citation: Journal of Applied Physics 12, 296 (1941); doi: 10.1063/1.1712911
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from the
Conference on Applied Nuclear Physics
Cambridge, Massachusetts
October 28-November 2, 1940
A GENERAL Conference on Applied Nuclear
Physics, sponsored by the American Insti
tute of Physics in cooperation with the Massa
chusetts Institute of Technology, was conducted
during the week of October 28-November 2,
1940, at the Massachusetts Institute of Tech
nology, Cambridge, Massachusetts. The rapidly
increasing number of applications of methods
and apparatus characteristic of nuclear physics
in the fields of biology, radiology, chemistry,
geology, and industrial physics has long em
phasized the usefulness of a joint conference
between physicists and their colleagues in other
fields of science.
The purposes of the Conference were to bring
together investigators who may be widely sepa
rated geographically, and to provide a forum for
assembling and correlating present knowledge
and difficulties, and for directing attention
toward fundamental lines of research which
should be the subject of future investigations.
The week's activities were divided into sepa
rate sessions on applications to biology, chem
istry, radiology, metallurgy, geology, and to general sessions relating to the production and
use of radioactive and stable isotopes, and the
protection of workers from radiation.
The individual sessions were extremely well
attended, and the total number registered ap
proximated 600 persons.
The Committee in Charge of the Program was
as follows: Robley D. Evans, Chairman, Massa
chusetts Institute of Technology; Elmer Hutchis
son, Secretary, University of Pittsburgh; Henry
A. Barton, American Institute of Physics; Edw.
U. Condon, Westinghouse Electric and Manu
facturing Company; Lee A. DuBridge, Uni
versity of Rochester; G. Failla, Memorial Hos
pi tal, New York; Clark Goodman, M assach usetts
Institute of Technology; Ernest O. Lawrence,
University of California; and Harold C. Urey,
Columbia University.
The order of the abstracts has been somewhat
changed from that in the original program;
hence the numbering of the abstracts which
follow is not consecutive. Instead, the papers
have been classified according to the fields in
which the work occurs.
Geology I
Techniques and Standards in Terrestrial Radioactivity Measurements
Chairman: DR. LYMAN J. BRIGGS, National Bureau of Standards
1. The Rate of Emission of a-Particles from Uranium
and the Relative Activity of Actinouranium. ALms F.
KOVARIK AND NORMAN I. ADAMS, JR., Sloane Physics
Laboratory, Yale University, New Haven, Connecticut.
In The Physical Review of 19321 we published determina
tion of the rate of emission of a-particles from uranium.
During similar experiments with thorium, the apparatus
was improved to give a greater resolution of close counts
of a-particles. Subsequent observations on uranium gave
slightly greater rate of emission than the original experi-
296 ments. The same two specimens used in 1932 and two new
specimens of U.O. were used in the experiments. The
weighted mean from all experiments involving about 106
counted a-particles gives 25.010 X 103 a-particles per second
per gram of uranium, i.e., for U I, U II and act.inouranium.
The 1932 value is 24.770 X 103• The uranium used was pure
UsO. prepared by the late B. B. Boltwood.
Attempts have been made to obtain relative activity of
actinouranium, in this material, by a method similar to the
"step" method used in the study of thorium and its
JOURNAL OF APPLIED PHYSICS
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cable, but with the apparatus used the results were affected
by changes of atmospheric pressure so that the desired
accuracy has not yet been obtained. However, the results
show that the ratio of the activity of actinouranium to that
of U I is of the order of 5 percent. More accurate deter
minations are in progress.
I Phs. Rev. 40, 718-726 (1932).
, Phys. Rev. 54. 413-421 (1938).
2. The Certification of Radioactive Standards. L. F.
CURTISS, Physicist, National Bureau of Standards, Wash
ington, D. C.
The National Bureau of Standards is cooperating with
a Committee of the National Research Council on stand
ards of radioactivity in a program intended to make
available standards which will be useful in determining the
radium and thorium content of minerals and ores, in the
study of radium poisoning, and in the field of artificial
radioactivity.
Types of standards which have been considered to date
are as follows: (1) Radium standards containing 10-9 and
10-11 g of radium, suitable as sources of known amounts of
radon. (2) Radium standards containing from 0.1 to 100
X 10~s g of radium, suitable as gamma-ray standards.
(3) Rock samples of known origin which have been
analyzed for radium and thorium content as well as
chemical and mineral constitution. (4) Thorium standards
containing suitable amounts of thorium as sources for
known amounts of thoron. (5) Beta-ray standards con
sisting of electrolytic deposits of Ra D on platinum.
The general procedure for preparing the radium stand
ards is well known. It consists simply in dissolving a
radium salt of known content and, by dilution, obtaining
solutions so that a given volume will contain the desired
amount of radium. Precautions must be taken to insure
that the radium stays in solution throughout the process.
This paper describes the procedure which has been fol
lowed at the National Bureau of Standards in preparing
two series of standard radium solutions, one to be used as
radon standards and the other as gamma-ray standards.
The radon standards consist of 100 ml of solution in sealed
Pyrex flasks, one group containing 10--9 g of radium and
the other 10-11 g of radium. The gamma-ray series consist
of sealed Pyrex ampoules holding 5 ml of solution with the
following radium contents; 0.1, 0.2, 0.5, I, 2, 5, 10, 20,
50 and 100 X 10-6 g. The 0.2, 2 and 20M g ampoules are
available in pairs so that complete sets of 13 ampoules are
available.
Certification of these radium standards is based upon
the work of Madame Curie and later of Honigschmid, who
prepared carefully purified and weighed samples of radium
and sealed them in glass tubes to serve as gamma-ray
standards. These are the primary standards by which the
radium content of preparations for medical purposes are
usually determined, in terms of their gamma-radiation.
For the preparation of the standard solutions radium
bromide was used. The sample available was found to
contain 16.394±0.005 mg of radium by comparisons with
the National Primary Standard. The value of this standard
VOLUME 12, APRIL, 1941 is certified by the International Radium Commission to
0.5 percent. Therefore, in preparing the solution, methods
of dilution and pipetting were adopted which would be
certain to introduce no errors greater than this percentage.
The resultant standard solutions, after suitable checks on
uniformity, may therefore be certified directly in relation
to the National Primary Standard.
The radium content of the rock samples is determiJ4ed
by the emanation method, using standard radium solutions
for comparison. The measurements for certified standard
samples are complicated by a number of factors. Therefore,
the committee has decided to submit samples of rocks to
at least two laboratories equipped to make such deter
minations and to base the values in the certificates on the
results of these measurements in addition to those made
at the National Bureau of Standards. The Massachusetts
Institute of Technology and the Geophysical Laboratory
of the Carnegie Institution are cooperating in these meas
urements.
The work on thorium standards and beta-ray standards
has not progressed to the point where methods of certifi
cation can be discussed.
3. Measurement of Terrestrial Radioactivities. ROBLEY
D. EVANS, Department of Physics, Massachusetts Institute
of Technology, Cambridge, Massachusetts.
For uranium or radium analyses, radon can be separated
from rock samples either by the carbonate fusion or the
direct fusion furnace. Ionization chamber and electrometer
techniques are satisfactory for the measurement of 10-12
curie or more of radon, while recording a-ray pulse counters
are preferable for weaker samples. The actinium series can
also be evaluated from radon measurements on rocks,
because of the constant value of the actinium and radium
series activity-ratio. For thorium analyses on rocks,
chemical separation of ThX provides a parent solution
from which the short-lived gas, thoron, can be liberated
and flowed continuously through an ionization chamber.
Recording a-ray pulse COllntels again offer the highest
sensitivity for detection. Frequent recalibration, using
accurate radioactive standards having about the same
activity as the samples being analyzed, should be made on
all detection apparatus. The National Research Council's
Committee on Standards of Radioactivity is continuing to
develop new standards of all types. Standard radium
solutions, and accurately analyzed standard samples of the
principal types of rocks are now available for distribution
by the National Bureau of Standards. Standard thorium
solutions are in preparation. Results obtained in various
laboratories on identical rock samples have now been com
pared directly by exchange of samples. This international
interchecking program has been in progress for about four
years, and has brought about substantial improvements in
analytical techniques and in the proper use of standards.
Much of the data on terrestrial radioactivity, especially in
the older literature, requires revision. Determination of
the geologic age of an igneous rock primarily involves the
measurement of the total helium content and the total
rate of production of helium (rate of emission of a-particles)
297
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U, Th, and Ac series from the radon and thoron content.
A direct physical method, independent of standards, decay
constants, and possible samarium interference, is provided
by counting the a-rays emitted from very thin layers of
rock sample. This requires a-ray pulse counting apparatus
having a very low background. The U, Ac, and Th content
of a rock sample can be computed from a comparison of the
total a-ray count and a separate radon analysis of the same
material. The marked inhomogeneities which occur in some
rocks must be evaluated by repeat analyses on the same
material. Gamma-rays can be measured by discharge
counters if rock samples of about a kilogram or more are
available. Such observations represent the combined effects
of potassium and of all members of the U, Th, and Ac
series. Gamma-ray surveys of oil well drill holes have
become a significant new geophysical tool, especially in
locating stratigraphic variations. The mean radioactivity
of the different rock types is needed for calculations on the
earth's internal heat. Mean values of radium content, in
10-12 g Ra per g rock, and the ratio of thorium to uranium
concentration, for specimens analyzed recently, are as
follows. Radium: 1.7 ±0.2 for 26 acidic rocks; 0.51 ±0.05
for 7 intermediate rocks; 0.34±0.03 for 41 basic rocks;
0.70±0.12 for 13 sedimentary rocks. Ratio of thorium to
uranium: 4.3 for 16 acidic rocks; 2.6 for 6 intermediate
rocks; 4.0 for 35 basic rocks. 4. Requirements for a Primary Thorium Standard and
Progress in Its Preparation. JOHN PUTNAM MARBLE,
Division of Geology and Geography, National Research
Council, Washington, D. C.
No primary standard for the thorium series exists, so
far as is known. Thorium preparations and radioactive
measurements in the thorium series have usually been
checked against a sample of a mineral of known thorium
content. Different workers have used different source
materials.
An adequate standard should, we find, consist of a
preparation of a thorium salt, made from a mineral whose
thorium and uranium content is known, and from which
the radium (and its congeners) have been quantitatively
separated on a known date. This will enable the correction
curve for the growth of radium from the ionium present,
and for the subsequent members of the uranium series, to
start from a definite zero point, and thus increase the
accuracy of the thorium activity measurements.
Preliminary work by Kovarik and Marble, aided by
others, has indicated the type of mineral most desirable
for lise; the practical limits of chemical analysis; the
method of preparation to be followed; the means by which
reagents of adequate radioactive purity may be prepared;
and the difficulties involved in the quantitative separation
of radium as of a given date.
Geology II
Geochemical Applications of Radioactivity
Chairman: DR. S. C. LIND, University of Minnesota
8. Radioactivity and Geochemistry. ROGER C. WELLS,
U. S. Geological Survey, Washington, D. C.
Thorium is found in monazite and thorite, which occur
in pegmatites, and in some columbo-tantalites. It has also
been found in augite syenite. Uranium is found in granitic
rocks as uraninite, and also in samarskite, and as the
phosphates autunite and torbernite and in several other
similar minerals. Carnotite occurs in sedimentary sand
stones. For a semiquantitative estimate of the abundance
in the crust of the earth of these two radioactive elements
(which seem to have a fairly definite abundance ratio to
each other) it is necessary to find some common element to
which they are related in abundance.
Such an element is potassium (which is also slightly
radioactive), and the abundance of potassium in different
kinds of rocks is definitely related to the density of the
rocks. Studies of the velocity of earthquake waves and of
isostacy enable us to arrive at provisional conclusions
concerning the density-altitude gradient in the earth and
therefore offer a means of estimating the abundance of
thorium and uranium in the outer ten-mile crust at least.
Following Williamson and Adams the writer assumes the
existence of a basaltic substratum of density 3.3 at a depth
298 of about 37 miles below sea level. Sub-oceanic rocks are
about 0.14 more dense than continental rocks on the
average. Surface continental rocks have a density of about
2.76 and therefore sub-oceanic rocks must have a corre
sponding density of 2.90. Taking account of the relative
areas of continents (including continental shelves) and
seas the average surface density is about 2.85. With these
figures as starting-points it is possible to compute three
different figures for the abundance of thorium and uranium,
assuming that: (1) the composition of rocks continues
essentially unchanged from the surface to the level of equal
pressure (about 37 miles); (2) the density gradient rises
uniformly from the surface to the depth of compensation;
and (3) as it is not thought possible for the average density
of this layer to exceed 3.1 the other possibility is the density
gradient rises rather rapidly to about 3.05 and then
continues almost unchanged to a depth of about 29 miles,
whence it rises to 3.3 at 37 miles.
With these density gradients it is possible to make an
estimate of the abundance of thorium and uranium in the
ten-mile crust. The effect of sedimentary rocks and the
ocean is only a minor correction.
JOURNAL OF APPLIED PHYSICS
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second a reasonable mean, and the third a minimum figure
for the content of radioactive elements. According to the
first method there is no change in the radioactive content
down to 10 miles below sea level. This conclusion is not
supported by the known tendency of rocks to segregate by
gravity and hence it seems more likely that density in
creases at least somewhat even in the "granitic" layer. The
second method yields a decrease of about 42 percent in the
radioactive content in a distance of ten miles. The third
method yields a rather improbable decrease of 50 percent in
the same distance.
9. Radioactivity and Oceanography. C. S. PIGGOT,
Carnegie Institution of Washington, Washington, D. C.
The radioactive relations in the ocean and its sediments
are complex in comparison with the simple relations for the
igneous and sedimentary rocks that form the continents.
This is because neither in the ocean nor in the upper layers
of the ocean bottom are elements such as uranium, ionium
and radium in radioactive equilibrium. In discussing
radioactivity and oceanography the dimension of time is
therefore of prime importance. The sediments underlying
the deeper portions of the ocean provide suitable material,
correlated with this dimension, for studying the growth and
decay of these elements. Such studies have established the
distribution of the radioelements between the ocean and its sediments, but little is known of the biological, chemical
and physical processes which may be responsible for this
complex distribution.
10. Pleochroic Haloes and Radioactive Chemistry. G.
H. HENDERSON, Dalhousie University, Halifax, Nova Scotia.
In the course of an extensive study of pleochroic haloes
six distinct types have been recognized. In the two most
familiar types the original radioactive elements or parents
are uranium I and thorium, respectively. These elements
are so long-lived that halo formation could proceed in
almost any manner consistent with geological requirements.
Four other types of haloes, tentatively designated as
A, B, C and D, have rings whose radii indicate that their
parents are probably intermediate members of the uranium
radium family. The half-lives of these parents being
exceedingly short on a geological time scale, the problem
arises as to how a quantity of one of these parents, sufficient
to form a halo, could be segregated in the mica. Radio
active evidence thus restricts the possible modes of forma
tion of these haloes and the most probable hypothesis
seems to be that they arose from diffusion through the
mica of hydrothermal solutions from which the parents
were deposited at certain points constituting the halo
nuclei. Such an hypothesis appears to satisfy the physical
requirements of these types of haloes and if supported
by geochemical evidence, throws light on problems of
mineralization.
Geology III
Radioactive Methods of Geologic Age Determination
Chairman: DR. A. C. LANE, Tufts College
15. Radioactivity and Geochronology. CLARK GOODMAN,
Department of Physics, Massachusetts Institute of Tech
nology, Cambridge, Massachusetts.
The structural and paleontological methods of corre
lating geological time are inherently unable to give more
than a qualitative indication of age. It is well recognized
that a number of important results accrue from the
establishment of a quantitative time-scale. The systematic
disintegrations of the geologically long-lived radioactive
elements provide methods of measuring broad expanses of
time, but at present there is some uncertainty in the
interpretation of the observations on lead and helium
ratios. A direct comparison of these two methods on the
same geological materials is complicated by the nature of
the disintegration products and the resulting vastly
different concentrations in which they occur. Accordingly,
no reliable direct comparison has yet been made. If there
is a clear-cut stratigraphic relationship between the
geologic occurrence of a radioactive mineral, suitable for
dating by the lead method, and a rock body, suitable for
helium age studies, an indirect but sharp comparison may
be possible. In general, however, we are dependent upon
VOLUME 12, APRIL, 1941 separate geologic dating of the radioactive minerals and the
igneous rocks. Hence, the comparison must be based upon
the interdigitation of time scales containing numerous lead
and helium ages covering a wide range of geologic time.
While the revised helium time-scale is not nearly as com
plete as the lead scale, sufficient reliable measurements have
been made to establish that helium ages, as formerly
applied to igneous rocks, are substantially lower than the
corresponding lead ages. This disagreement has stimulated
a reinvestigation of the fundamental assumptions under
lying these radioactive methods. The retentivity of rocks
for helium has been found to be extremely variable and is
the major source of uncertainty in the application of this
method. Metamorphosed rocks are definitely unsuitable for
helium age measurements. Recent researches on separate
mineral components indicate that, with only a few ex
ceptions, helium ages obtained on rocks as a whole, even
fine-grained, unaltered mafic rocks, can only represent
minimal values. Certain minerals, notably the feldspars,
appear to lose a large fraction of their radiogenic helium.
On the other hand, certain of the mafic minerals, pyroxene
and magnetite in particular, have a much higher retentivity
and show helium ages which approach the values to be
299
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made on rocks as a whole represent mean values dependent
upon the proportion and helium retentivity of the mineral
components. It is anticipated that further research on
selected rock minerals will yield helium ages suitable for the
establishment of a new helium time-scale in substantial
agreement with the present lead time-scale.
16. The Lead Time-Scale. JOHN PUTNAM MARBLE,
Division of Geology and Geography, National Research
Council.
The lead time-scale is based primarily on the value of
the ratio PbjU+k·Th, where the correct value of Uk" and
a proper choice of constants enable us to transform this
ratio into years. Since lead exists in nature (apparently) as
a stable element, as well as the end-product of radioactive
decay, suitable tests must be made to distinguish between
radiogenic and common lead in a mineral which carries U
and Th. One of these methods, mass-spectroscopy, also
gives us an apparently independent check on the "lead
ratio," as the "isotope ratio" Pb206 : Pb207 is also a function
of the age of the mineral. Furthermore, a consistent "lead
ratio," after correcting for common lead---or, to a lesser
degree, without such correction-for minerals of differing
ThjU ratio from the same geological formation, affords a
valuable second-order check.
It is most important that adequate geologic, mineralogic,
and petrographic studies accompany the chemical and
physical analyses. The identical sample should be used for
all the studies. Unfortunately, lack of material sometimes
makes this impossible, and some of the material studied
earlier is no longer available.
Where only uranium or thorium (except for very small
amounts of the other) are present in a mineral, a deter
mination of the chemical atomic weight of the lead will
also indicate the common lead impurity. It is also still
worth while to use this value as a check on the isotope ratio.
Among other suggested checks may be mentioned the
"oxygen ratio," or ratio of U02/UO. in a mineral. Theo-.
retically, under certain conditions, this should be of value,
but studies so far made do not, in general, lead to a close
agreement with the age as otherwise determined.
From the geological side, we can sometimes place an
igneous formation which bears radioactive minerals in the
relative age-scale. This is truer of formations in post-pre
Cambrian time, but not very frequently the case even here.
For the vast extent of the pre-Cambrian we have little
confirmatory evidence available, as fossils are absent, and
stratigraphic correlations are extremely difficult.
A review of the literature indicates a comparatively
small number of determinations which may be given high
ran~ing as possible fixed points in the lead time-scale. These
are discussed briefly. Assuming the validity of the present
values for the radioactive constants, and hence of the
formulae based on them, a tentatively revised lead time
scale is presented.
The complexity of the problem as a whole, and the diffi
culties involved in the various fields should be emphasized.
Analytical methods for the determination of Pb, U and
Th,as they exist in minerals, need further study. The proper
300 value to assume for the isotopic composition of common
lead, and the various forms of common lead are still under
discussion. Further work needs to be done on the relative
leaching and weathering of the three elements involved.
17. Helium Retention in Common Rock Minerals.
PATRICK M. HURLEY, Department of Geology, Massachusetts
Institute of Technology, Cambridge, Massachusetts.
In the helium method of age determination the age of
the materia! to be tested is given by the ratio of the content
of helium to the content of radioactive elements in the
material. The application of the method involves the
following basic requirements: (1) A known, systematic rate
of disintegration of the radioactive elements; (2) absence
of disintegration product as a primary constituent; (3)
accurate sampling and measurement; (4) no addition or
subtraction of the disintegration product or its source
during the history of the material. The first three condi
tions may be satisfied, it is believed, by careful selection of
material, and by cross-checking of measurements by differ ..
ent methods of analysis. A program of work was under
taken, designed to test the fourth requirement.
The radioactive elements commonly occur in the mafic
minerals of a rock in larger proportion than in the salic
minerals. In an unaltered igneous rock, where, presumably,
the minerals are of the same age, it would be expected that
the distribution of helium in the various minerals should
correspond with the distribution of the radioactive ele
ments, if the fourth basic requirement is satisfied. In each
mineral the ratio of helium to radioactivity should be the
same. This was found not to be the case. Pyroxene, feldspar
and magnetite were separated from six samples of Triassic
diabase. Age measurements on each yielded a mean "age"
of 103 million years for the pyroxene samples, 104 million
years for the magnetite, and 36 million years for the feld
spar. The "ages" were closely grouped about the mean
value in each case. Measurements on unseparated samples
of the diabase gave "ages" between the feldspar and
pyroxene in approximately the correct proportion for the
mineral composition of the rock. It appears that pyroxene
and magnetite retain most, if not all, of their helium, while
feldspar loses a part of its helium.
It is concluded that age determinations made directly on
rocks containing feldspar are likely to be in error, but that
possibly correct helium ages may be obtained by separation
and analysis of certain mineral constituents in rocks.
Pyroxene and magnetite at present appear to be satis
factory minerals. An age of slightly over 100 million years
is indicated for the Palisade diabase of New Jersey.
18. Lead Isotopes and Geologic Time. ALFRED O. NIER,
Department of Physics, University of Minnesota, Minne
apolis, Minnesota.
The computation of the age of a mineral from its lead to
uranium or lead to thorium ratio requires a knowledge of
the amount of common lead contamination. Ordinarily,
this may be readily found from a measurement of the
atomic weight of the lead. An isotopic analysis of the lead
gives this same information, and, in addition, in the case
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the age of the mineral can be checked.
A recent investigation of112 different samples of common
lead indicated that in spite of the nearly constant atomic
weight the relative abundances of the isotopes Varied from
sample to sample. This opens the question as to how to
correct for common lead in the radiogenic lead samples.
Recently 12 more samples of common lead have been analyzed and variations essentially as large as the previous
have been found.
In addition to the above results, isotopic analyses of a
number of radiogenic lead samples will be given. The
Pb207/Pb206 ratio method2 of measuring geologic age will
be fully discussed.
1 A. O. Nier, J. Am. Chern. Soc. 60, 1571 (1938).
• A. O. Nier, Phys. Rev. 55, 153 (1939).
Geology IV
Geophysical Applications of Nuclear Physics
Chairman: DR. L.' H. ADAMS, Carnegie Institution of Washington
31. Radioactivity as a Geophysical Tool. LYNN G.
HOWELL, Humble Oil and Refining Co., Houston, Texas.
Measurements of radioactivity in geophysical studies
have been made both on the surface and in the subsurface
of the earth. On the surface, German workers, in several
localities, have found high contents of radon in soil gas
samples taken over faults. On the Gulf Coast of this
country, no correlation between faults and radon content
of soil gases has been found. As to gamma-ray intensity
measurements made in situ on the surface, little if any
change in activity has been observed over faults by the
German geophysicists; significant variations over out
cropping formations have been found only when the
weathered layer is very thin or absent.
In the subsurface, in early work done on samples from
wells and ·tunnels, no great geological significance was
attached to the data. However Anbronn found interesting
changes in radioactivity in samples extracted in the neigh
borhood of oil-bearing sands in a well. In Russia, Spak and
others made point-to-point measurements of gamma-ray
intensities by using a Geiger-Mueller counter inside bore
holes.
On the Gulf Coast of this country, we made point-to
point measurements of gamma-ray intensities inside bore
holes using an ionization chamber containing nitrogen
under high pressure. Pulses proportional in size to the
ionization current were produced by periodically grounding
the grid of an electrometer tube connected with the insu
lated electrode of the chamber. At the surface, these pulses
were amplified and the throw's of an output galvanometer
were observed. The curves obtained in the producing
section of several oil wells showed correlation with the
electrical properties of the formations as found on com
mercial electrical logs made in these wells.
Following these measurements, a continuously recording
apparatus was built using a Geiger-Mueller tube, the am
plified pulses from which were fed to a thyratron-controJled
frequency meter. The output current of the frequency
meter was recorded photographically as a function of
depth. In the beginning, two Geiger-Mueller counters were
used with separate amplifiers and frequency meters,
whereby two independent curves could be recorded simul
taneously.
VOLUME 12,' APRIL, 1941 The "gamma-ray logs" disclose a striking correlation
with commercial electrical logs made in the same wells, the
latter showing the variation of potential of a moving elec
trode in the well with respect to a fixed electrode and also
the variation of formation resistivity or a similar quantity.
Through years of use, electrical logs have become a very
important tool in correlating geological formations. An
obvious advantage of the gamma-ray over the electrical
method, is that logs can be made inside wells cased with
iron pipe, which offers too much shielding action for elec
trical measurements but does not seriously absorb the
penetrating gamma-rays.
In general, sands are low in radioactivity in comparison
with shales. So far, no marked characteristics have been
found which distinguish oil-bearing from water-bearing.
sands.
A different application of this technique of measuring
radioactivity in wells has been found in the location of
cement which has been pumped behind the casing in a well.
Carnotite, a radioactive ore, was added to the cement
before it was pumped out through perforations or through
the lower end of the pipe. The presence of the carnotite was
detected by measuring the variations of gamma-ray in
tensity with depth inside the casing.
32. The Internal Heat of the Earth. L. B. SLICHTER,
Department of Geology, Massachusetts Institute of Technology,
Cambridge, Massachusetts.
The most important factors in the problem of the earth's
internal heat are taken to be the following six: (1) The gain
of heat from radioactive sources throughout the interior;
(2) The loss of heat as measured by the upward heat flux
in the earth's crust; (3) The original heat of the earth, as
represented by the initial temperautre distribution when
the crust first solidified; (4) The value of the thermal con
ductivity, and its change with depth; (5) The presence or
absence of significant heat transport by convection currents
in the interior; (6) The large heat capacity and thermal
inertia of the earth.
1. The recent measurements by Evans and his co
workers are adopted as affording the most reliable values
for the heat generated in rocks. If these results be used to
301
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proposed by Washington, it results that the total heat
being generated is about tenfold greater than that being
lost. This result is typical of others, deduced from other
proposed earth models. Several reasons are presented for
believing that the estimates of the heat-gain based upon
these models may far exceed that actually occurring in the
earth.
2. Measurements by Ingersoll, Bullard, Benfield and
others indicate that the mean value of the heat loss in
continental areas is not far from 1.2 X 10-6 cal./cm2/sec.
3. Fundamental difficulties preclude satisfactory esti
mates of the original temperatures in the earth. No satis
factory data are available from which to estimate the
change of melting point of rocks with pressure. Hence the
original temperature gradients in the solidified earth are
unknown.
4. It is possible that the thermal conductivity at depth
differs significantly from its surface values. It is well to
admit a generous range of possible values for the thermal
conductivity at depth.
5. If they exist, thermal convection currents having a
velocity as small as one kilometer per million years, would
transport about a hundred fold more heat than would the
thermal conductivity. I t is conceivable that convection may
exist and may maintain an essentially adiabatic tempera
ture distribution at depth.
6. The enormous heat capacity of the earth is significant.
Indeed, the observed rate of heat loss could be maintained
throughout the earth's lifetime with only a small percentage
decrease in internal temperatures, and without any con
tribution from radioactivity. Because of the size and heat
capacity of the earth, temperature decreases at depth must
occur exceedingly slowly. Without radioactivity, a decrease
of the order of I"C in 10 to 50 million years may be ex
pected. With radioactivity, a net increase of at least 30"
per million years is indicated, provided the minimum
values of radioactivity observed in available surface
samples are realized at depth. It is shown that heat sources
of considerable magnitude may exist at depth without
being detected by thermal observations at the surface. It is uncertain whether the earth is heating, or cooling at
depth. Geological evidence supports no distinct trend either
in one direction or the other. It is of interest" then, to
examine the middle possibility; namely, the equilibrium
temperature state. Steady-state temperature distributions
are computed for a number of different distributions of the
radioactivity and of the conductivity.
In summary, it is obvious that thermal evidence alone
does not suffice to yield definite results about thermal con
ditions in the interior. However, evidence from independent
sources is sometimes available and helpful. For example,
the large increase in electrical conductivity at depths
below 500 km deduced from studies in terrestrial mag
netism has significance. More accurate knowledge of the
variation of seismic wave velocities in the mantle may
prove helpful. The fluidity of the earth's core, as deduced
from several types of geophysical evidence, obviously has
important thermal implications. Finally, future contribu
tions from atomic theory conceming the probable mechan
ical and thermal constants of rock-materials in the' deep
interior would distinctly advance our deficient under
standing of the problem of the earth's internal heat.
33. Earth Heat and Geological Processes. DAVID
GRIGGS, Harvard University, Cambridge, Massachusetts.
The internal heat of the earth is the only known reservoir
of energy which is sufficiently large to have served as a
source for the primary processes of geology which formed
the surface features of the earth exemplified by our
mountain chains. In choosing between the various physical
hypotheses of the mountain-building mechanism, the two
most important considerations are: (1) the distribution of
temperature within the earth, and (2) the proportion of the
surface heat loss which is due to the primary heat of the
earth compared to that due to .radioactive heat. The
answer to both these questions depends on knowledge of
the distribution of radioactivity within the earth. It is the
purpose of this paper to reexamine the hypotheses of
mountain-building in the light of recent measurements of
physical constants and estimates of the radioactivity in
the earth.
Metallurgy I
Tracer Studies of Metal Diffusion
Chairman: DR. F. SEITZ, University of Pennsylvania
5. The Importance of Diffusion in Physical Metallurgy.
R. F. MEHL, Metals Research Laboratory, Carnegie Institute
of Technology, Pittsburgh, Pennsylvania.
It is the purpose of this paper to present a discussion
in an informative and descriptive rather than an analytical
manner-of the metallurgical phenomena in which diffu
sion plays an important or a dominant role. This abstract
will merely list these phenomena.
302 The freezing of alloys; segregation; solid solution and
heterogeneous segregation; annealing of ingots and forg
ings, homogenization, and diffusion; directional properties
in forgings; banding.
Treatment of alloys of the age-hardening type; the
process of age-hardening; ingot segregation; ingot break
down and homogenization anneal; solution heat-treatment;
quenching and precipitation hardening; concentration
JOURNAL OF ApPLIED PHYSICS
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nucleation; particle growth; time-temperature relations in
aging; interaction and activation energies.
Steel-treating and quench hardening; constitution of
annealed steel at room temperature and at high tempera
tures; constitution of steel on slow cooling, on quenching;
a Fe, FeaC, 'Y Fe, pearlite, austenite, martensite; rate of
solution of carbides on high temperature annealing; forma
tion of pearlite, nucleation and growth, effect of austenite
grain size and of alloy content; interlamellar spacing, rate
of formation of pearlite; rate of diffusion of carbon in
austenite; martensite and hardening; decomposition
products of austenite, diffusion and nondiffusion reactions;
tempering of martensite and spheroidization of pearlite.
Diffusion in solid-gas systems; carburizing of steels,
depth of carburizing, rates and variables; dezincing of
brass on annealing, calculation from rates of diffusion,
effect of grain size; nitriding and diffusion of nitrogen in
a iron; oxidation of metals and alloys, constitutional
relationships, nature of oxide films and scales, rates of
oxidation, mechanism of diffusion through oxide films and
scales, variation of rates with crystal orientation, temper
ature, time, and gas pressure, effect of alloy content,
scaling-resistant alloys and mechanism of oxidation
internal oxidation, embrittlement of copper.
Metallic diffusion coatings; chromizing, siliconizing,
sherardizing; structure and properties. Veneer metals and
bimetallic strip; diffusion bonding. Powder metallurgy;
preparation of alloys by annealing of mixed metal powders;
diffusion. Annealing of multiple electrodeposits; types
and thickness of phase layers and rate of formation of
layers.
Self-diffusion; processes in single metal phases analogous
to self-diffusion; recrystallization, nucleation and growth
of recrystallized grains, rates and activation energies;
creep and activation energies; crystal plasticity and
forming operations.
6. Atomic Mechanisms of Diffusion. R. P. JOHNSON,
Research Laboratory, General Electric Company, Schenectady,
New York.
The conventional diffusion coefficient D(T,c) for a
binary alloy is a measure of the rate of disappearance of
an infinitesimal chemical nonhomogeneity in the alloy.
Its value depends on the detailed mechanism of atomic
place-changes, but so many other factors enter that it is
practically impossible to use the measured diffusion
coefficient for deciding among various possible models of
the motion of atoms past one another.
On the other hand, if one marks (by means of radio
activity) some of the atoms of one element of the alloy
and studies the diffusion of these marked atoms, keeping
the chemical composition of the entire specimen at all
times homogeneous, one can calculate directly from the
measured diffusion coefficient the average number of
elementary moves made by an atom of that element
during the time of the experiment. This is a quantity
that can be predicted theoretically, once a model for the
place-change mechanism has been adopted. A comparison
VOLUME 12, APRIL, 1941 between the observed number of moves and the predicted
number will test directly whether the imagined mechanism
is satisfactory. The temperature and the composition of
the homogeneous binary alloy can be varied, and at each
temperature and composition two quantities, the average
number of moves made in unit time by each of the two
components, can be measured and compared with predicted
values. In principle it is possible by the same method to
measure the motility of any element in any homogeneous
surroundings however complicated.
This use of tracer-atom techniques yields direct informa
tion about the mechanism of atomic migration, which
can be had by no other means. It is not to be confused
with the use of radioactive atoms in diffusion experiments
of the conventional type, where they serve merely as
convenient indicators of the concentration of inert nuclei
of the same chemical kind.
7. Radioactive Methods in Diffusion. P. H. MILLER, JR.,
Randal Morgan Laboratory of Physics, University of Penn
sylvania, Philadelphia, Pennsylvania.
In the measurement of diffusion in solids using radioactive
indicators (either artificial or natural), a sample is used
which has a non-uniform distribution of some radioactive
isotope and the change of di!'tribution is determined as a
function of time. For mathematical convenience it is con
venient to have an infinitesimal and plane layer of radio
active material placed upon an inactive sample as the
initial distribution. This has been accomplished by
electroplating, evaporation and the collection of radioactive
disintegration products from a gas. These procedures have
the disadvantage that the exact conditions at the surface of
contact are unknown. Secondly, samples have been pre
pared by rolling together an inactive metal foil with an
active one of finite thickness. Finally, radioactive isotopes
have been formed in the sample itself by bombarding it
with neutrons; other nuclear particles could be used. This
method of activation has the advantage of being simple and
avoids any possibility of the existence of a boundary
disturbance between the active layer and the bulk of the
sample.
There are various methods of measuring the change in
distribution which is a result of the diffusion process. If Dt,
where D is the diffusion coefficient and t the time for which
the sample is kept at high temperature during which the
appreciable diffusion takes place, is greater than 10-5 cm2
the sample can be cut into sections (say 4 X 1O-a cm thick),
mechanically and the activity of each section measured.
This is the most direct method for the surface effects can be
eliminated and Fick's law ac/at=DCJ2c/ax2 which is 'as
sumed in all the other methods can be checked. It has the
disadvantage that each sample can be used only once. The
activity is measured with a counter or electroscope and in
the case of a-particles by counting scintilations on a zinc
sulphide screen. Since the particle radiation is strongly
absorbed the activity of a sample will fall off as the radio
active atoms diffuse into the interior, and the activity of
the inactive side of the sample which is usually made
slightly thicker than the range of the emitted particles will
303
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greater than 10-10 cms. Here the absorption coefficient and
the half-life of the radioactive isotope must be accurately
known. Since the range of the recoil atoms is extremely
short they provide an even more sensitive method and can
be used for values of Dt greater than 10-18 cm2• The recoil
atoms are collected on a charged plate and in cases where
they are radioactive their number determined from this
property. The diffusion of lead in ionic crystals under the influence
of an electric field has been investigated for certain lead
salts and has given valuable information as to which ions
are transferring the charge. The use of artificially radio
active atoms will extend this method and give much useful
information.
Measurements of diffusion in liquids have been made
using radioactive indicators but there is no practical
advantage in this method except in the case of self-diffusion.
Metallurgy II
Metallurgical Applications of Nuclear Physics
Chairman: DR. C. S. BARRETT, Carnegie Institute of Technology
11. Radiography with Gamma-Rays. JOHN T. NORTON,
Department of Metallurgy, Massachusetts Institute of
Technology, Cambridge, Massachusetts.
Gamma-rays from radioactive sources are used in in
dustry for the inspection of heavy castings and weldments.
The radiograph is in effect a shadow picture of the object,
recorded photographically, and defects which represent a
change in thickness of the object are shown as shadows on
the film. The technique is simple and straightforward.
Since radiographic inspection depends upon the absorp
tion of the radiation in the object, the wave-length distri
bution and conditions of scattering of the radiation are of
primary importance. The very short wave-length of
gamma-radiation results in a low absorption in the object
so that large thicknesses of metal can be examined. At the
same time, the low absorption permits the examination of a
considerable range of thicknesses at a single exposure. For
many classes of work this is of the greatest practical im
portance. On the other hand, the low absorption reduces the
ability to detect the smallest defects in the object and this
is a very real disadvantage. The scattering of the radiation
within the object is not particularly troublesome in the case
of gamma-radiation.
It is of interest to compare the practical application of
gamma-ray inspection with that carried out by means of
x-rays. In the case of x-rays generated at 200 to 300 kv, the
two methods really fall into separate classes. The x-ray
method is capable of greater sensitivity in detecting small
defects and requires short exposures. The gamma-ray
method will handle much greater thicknesses of metal, has
a greater latitude in recording differences in thickness of the
object, and has the advantage of excellent portability of
the radiation source. If the x-rays are generated at 1000 to
1250 kv, the physical characteristics of the radiation are
similar to gamma-radiation but the very much greater
intensity makes the exposure a matter of seconds rather
than hours. In this case, one would have to balance the
greater complexity of the radiation source against the
material saving of exposure time.
The industrial use of radiographic inspection always
involves some sort of compromise to obtain optimum
304 working conditions. This compromise can be made to the
best advantage if the fundamental factors underlying the
problem are understood.
12. Tracer Studies in Metallurgy. WILLIAM A. JOHNSON,
Westinghouse Research Laboratories, East Pittsburgh,
Pennsylvania.
Radioactive materials have not enjoyed an extensive
application in metallurgical studies, but a number of
experiments have been reported which indicate an in
creased use of them in the future. Such experiments may be
divided roughly into three groups: the measurement of
rates of self-diffusion; the determination of changes in
surface and internal structure by the Hahn emanation
method; and the detection of segregation and cracks by
contact photographs.
The first measurements of the rate of self-diffusion were
made by von Hevesy in 1920, using ThB as an indicator in
lead. Recently, other metals have been studied, using
artificially radioactive isotopes: gold by Sagrubskij and
McKay; copper by Rollin and Steigman, Shockley and
Nix; zinc by Miller and Day, and Banks and Day; and
silver by Johnson. Several experimental procedures have
been employed. The active isotope may be electrolytically
plated on the nonactive isotope; a thin foil of active ma
terial may be rolled onto the nonactive base; and an active
layer may be produced on a stable base by direct bom
bardment by particles of low penetrating power. Two
general methods have been used for determining the
diffusion coefficient after heat treatment. The earlier
method, and the one of more use when short-lived isotopes
are employed makes use of the absorption of ionizing
particles by the metal into which the active atoms diffuse;
the diffusion coefficient may then be calculated from a
knowledge of the decrease in activity of the active surface
after diffusion, and the absorption coefficient of the metal
for the particles emitted (usually i3-rays). This method
suffers from the disadvantages that there is no check on the
quality of the interface between active and inactive layers,
and that quite small errors in measuring the activity may
produce large errors in the diffusion coefficient. In the
JOURNAL OF ApPLIED PHYSICS
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layers parallel to the original interface, and the activity of
each layer is determined. The diffusion coefficient is then
easily calculated from ,standard equations. Self· diffusion
measurements have not been very satisfactory in the past,
but more careful attention to detail, and the use of the
sectioning method should yield better results in the future.
The Hahn emanation method has been applied to
metallurgical problems by Werner, Seith, and others. An
active material (usually thorium X) is introduced in very
small amounts into the metal under investigation by
melting, electrolysis, or diffusion. The noble gas thoron
produced in the disintegration of thorium X diffuses out of
the specimen and may be measured. It is found that the
activity of such specimens increases smoothly with temper
ature; if structural changes occur in the metal-recrystal
lization, polymorphic transformation, welding of pressed
powders-there is a sudden change in the emanation from
the specimen. Such changes may be detected with good
accuracy by this method, but its advantages over other
methods have not yet been clearly demonstrated.
Tammann has used thorium B to reveal segregation and
ingot structure in cast metals. A small amount of active
material (10-6 weight percent) is incorporated in a specimen
by melting and, after polishing, a photographic plate is
placed on the smooth surface. An exposure time of 24
hours is sufficient, and after development, dark areas on the
plate reveal the position of the active material in the
specimen. This procedure clearly reveals the segregation
and dendritic structure of castings and should become a
valuable tool in the future.
Kaiser has recently described a very similar method for
locating fine cracks in polished surfaces. The active
material is carried in a grease which is forced into the
invisible cracks by high pressure. After removirig all
excess active grease, a plate is exposed, which, upon
development, shows the position of cracks. This procedure
has not been sufficiently refined to compete with the
Magnaflux method for ferrous materials, but may prove
important for nonferrous materials.
13. Outlook for Use of Neutron Scattering in Studying
Ferromagnetic Substances. F. BLOCH, Department of Phys
ics, Stanford University, Stanford University, California.
The fact that neutrons, although carrying no charge,
have a magnetic moment has been experimentally verified
and the neutron moment has been measured. Being about
a thousand times smaller than ordinary atomic moments
it is, nevertheless, big enough to contribute essentially to
the scattering of slow neutrons in magnetized bodies. This
is due to the interaction of the neutron moment with the
amperian molecular currents which cause magnetism. Any
quantitative prediction of this so-called "magnetic scat
tering" of neutrons has to make rather detailed assumptions
as to the size and distribution of the amperian currents. It
is feasible, on the other hand, to use it as a tool to obtain
more detailed knowledge about those characteristic fea
tures of magnetism, particularly of ferromagnetism, which
do not show up in the magnetization curve. At the present
VOLUME 12, APRIL, 1941 moment two rather separate groups of problems seem tall
gible and of interest.
The first group centers around investigations of the
amperian currents themselves. As in the determination of
"atomic form factors" by means of the scattering of x-rays
the dependence of the magnetic scattering on the energy
and the angle of scattering of slow neutrons must yield a
characteristic "magnetic form factor." The determination
of this quantity would make it possibleto trace the amperian
currents within the elementary magnets and should clearly
exhibit the role that valency electrons may play in ferro
magnetism. This seems to be particularly interesting with
respect to those ferromagnetic alloys which consist of
nonferromagnetic elements.
The second group is suggested by the discovery that the
magnetic scattering shows a sharp increa~e and subsequent
saturation within the last few percent of the magnetic
saturation. It is most likely that this phenomenon is due to
rather macroscopic features of ferromagnetic substances.
Since the magnetization curve exhibits the result of the
"turning in" of the various Barkhausen regions the ap
proach of saturation must mean that practically all these
regions have found their proper orientation. One can
understand, however, that a very slight deviation from
. saturation will still offer enough space within the substance
practically to destroy the polarization effect of the mag
netic scattering by rapid precession of the neutron moment
around the direction of the magnetic inductance. Thus this
last lack of saturation, hardly noticeable in the mag
netization, seems to be very pronounced in the magnetic
scattering of neutrons. If so, single crystals should, in this
respect, behave very differently from polycrystalline
materials; the further investigation of this effect will
furnish more information about the relation between grain
size, mechanical treatment, etc., and the saturation of
ferromagnetic substances.
14. Neutron Studies of Ordef in Fe-Ni Alloys. F. C.
NIX, Bell Telephone Laboratories, New York, New York;
AND H. G. BEYER AND J. R. DUNNING, Columbia Univer
sity, New York, New York.
Neutron transmission measurements are used to study
order in Fe-Ni alloys. The difference in neutron trans
mission between fully annealed and quenched alloys when
plotted against the nickel content displays a broad peak
around Ni3Fe and falls to vanishingly small values near 35
atomic percent Ni and pure Ni. The higher the degree of
order the greater the neutron transmission. The substitu
tion of 2.3 atomic percent Mo or 4.1 atomic percent Cr
for Fe in the annealed 78 atomic percent Fe-Ni alloy
caused a decrease in the neutron transmission, relative to
the annealed 78 atomic percent Fe-Ni alloy, of 15.6 and
21.2 percent, respectively. The cold working of an annealed
binary 75 atomic percent Ni alloy, a treatment known to
produce disorder, gave rise to a decrease of 20.6 percent in
neutron transmission. These results demonstrate that
neutron techniques serve as a useful tool to study order in
Fe-Ni alloys, and suggest that they can be extended to
study other solid state phenomena.
305
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Tracer Techniques in General Chemistry
Chairman: DR. H. S. TAYLOR, Princeton University
19. Radioactive Methods in the Study of Co-precipitation
and Adsorption. KAsIMIR FA]ANs, Department of Chemistry.
University of Michigan, Ann Arbor, Michigan.
The paper consists of two parts. In the first part, a brief
review is given of the development of the subject since the
early days of radioactivity. In the second part, are de
scribed experiments, as yet unpublished, which, by use of
artificially produced radioactive isotopes, help to clarify
the m chan ism of the adsorption of dyestuffs.
The precipitation rule (Fajans and Beer, 1913) and the
adsorption rule (Paneth and Horovitz, 1914) emphasize
the insolubility as an important factor for the elimination
from the solution of an element present in extremely small
concentrations.
Investigations with von Beckerath (1921) and Erdey
Gruz (1931) and those of Hahn (1926) have demonstrated
that the adsorption of a radio-element increases when the
adsorbent has a charge opposite in sign to that of the.
element and is decreased, but not always excluded, by a
charge of like sign.
These results when applied with Hassel (1923) to the
adsorption of organic dyestuff anions and cations on silver
halides led to a new type of indicators for volumetric
analysis, named by Kolthoff adsorption indicators.
The dyestuffs can be measured in small concentrations
because of their intense color, which imparts to them
properties of indicators or tracers, as radioactivity does in
the case of elements. The combination of both types of
indicators has been applied, e.g., for the determination of
the area of the adsorbent surface (Paneth), investigations
of the aging of precipitates (Kolthoff), indirect estimation
of relative adsorbability of ions (with Erdey-Gruz).
Two main mechanisms of adsorption of ions were dis
cussed:
1. The attachment of the adsorbed ion to the oppositely
charged ion of the lattice surface: addition mechanism.
2. The replacement by the adsorbed ion of a lattice ion
of the same sign: exchange mechanism (applied by Kolthoff
especially in case of dyes).
The two mechanisms lead to different expectations in the
case of adsorption of dye anions in the presence of an excess
of lattice cations. Experiments with Gretchen Mueller
(1939) have shown that the saturation values for the ad
sorption, e.g., of eosin on silver bromide increase consider
ably with the silver ion concentration. This supports the
addition mechanism and cannot be reconciled with
Kolthoff's theory. Further experiments were performed
with Amos Newton, using radioactive indicators.
Eosin and erythrosin were adsorbed on silver bromide
precipitates containing radioactive bromide. In case of
eosin an excess of silver ions was used. No increase of the
activity of the solution was found, showing that no notice
able exchange of the dye anion with the bromide ions of the
306 lattice surface takes place. Thus the adsorption must be
due predominantly or wholly to the deposition of eosin ions
on the silver ions of the adsorbent.
In the case of erythrosin, which is adsorbed considerably
even in the presence of an excess of halogen ions, no excess
of either ion was used. It was found that for each adsorbed
erythrosin ion about two bromide ions are brought from
the adsorbent to the solution. This result is not a proof for
a direct exchange between the adsorbed erythrosin ion and
the bromide ion of the lattice.
In fact, the solubility of silver erythrosinate is 1 X 10-6 m,
that of silver eosinate 5 X 10-5 m. The considerable adsorp
tion of eosin on silver bromide from a solution containing
only 1 X 1O-~ m eosin and silver ions can be formally con
sidered as 3. two-dimensional precipitation of silver eosinate
below its normal solubility product. Thus in the presence
of the adsorbent the solubility product of silver eosinate is
diminished.
This mean~, when applied to silver erythrosinate, that its
"solubility" in the presence of silver bromide is diminished
below 1 X 10-6 m and thus becomes of the same order of
magnitude as that of silver bromide itself (5 X 10-7 m). In
such a case the precipitation of erythrosin from the solution
containing no excess of silver ions must be accompanied by
dissolution of silver bromide and it is this secondary phe
nomenon which causes the radioactive bromide ions of the
adsorbent to appear in the solution.
For different reasons, e.g., because of the results of light
absorption measurements with Marie Farnsworth (1937),
the addition mechanism appears to be the most probable
also for the primary adsorption of erythrosin ions.
By using radioactive sodium it was found that the ad
sorption of eosin and erythrosin on silver bromide is not
accompanied by an adsorption of the sodium ions. This
agrees with similar results of Kolthoff (1935) obtained in
other cases.
20. Measurement of Vapor Pressures and Solubilities
of Certain Thorium Compounds by Radiochemical
Methods. RALPH C. YOUNG, Department of Chemistry,
Massachusetts Institute of Technology, Cambridge, Massa
chusetts.
Radiochemical methods are being devised on an ever
increasing scale for the study of many hitherto unsolved
problems in inorganic and physical chemistry. Reference is
here made to the measurement of vapor pressure and of
solubility.
Thorium 3cetylacetonate can be sublimed readily at
1600 at a pressure of 1 film. It is similar in many respects to
the acetylacetonates of the rare earth metals. These, how
ever, decompose below a temperature at which any marked
rate of sublimation occurs and consequently this property
has not been used for their separation. At 100° the rare
JOURNAL OF A,pPLmn PHYSICS
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vapor pressures would likely be of the same order of mag
nitude as that of the thorium compound. Because it is so
low, this value could not be obtained by the usual pro
cedures, but a radiochemical method was found adaptable.
A known volume of inactive nitrogen was saturated with
thorium acetylacetonate by being passed through a long
column of the compound maintained at 100°, and was
subsequently directed into hydrochloric acid where the
vapor of the acetylacetonate was converted into thorium
chloride. The vapor pressure was calculated by use of the
perfect gas equation, P V = nRT, and the molal quantity of
the thorium compound in the gas mixture obtained by
means of its radioactivity. A comparison of the alpha-count
of a deposit from an aliquot part of the chloride solution
with that from a standard solution of thorium chloride
prepared from a known weight of the acetylacetonate pro
vided data for the necessary calculation. The alpha-counter
used was of the parallel plate condenser type with photo
graphic recording device described by Finney and Evans.
A rapid stream of nitrogen was passed through the ioniza
tion chamber in order to prevent the accumulation of
thoron. From measurements of the deposits of the standard
solution it was found that 1 X 10-6 g of thorium acetyl
acetonate gave an alpha count of 7.3±0.7 per hour 10
months after the preparation of the compound from thorium
nitrate. The value at equilibrium was calculated as 9.0±0.9.
The theoretical count based on ! of the total activity of
four alpha-emitters is 10.9. By means of the foregoing
standardization and the alpha-counts of deposits from
solutions derived from the sublimed acetylacetonate, which
gave 50 to 100 alphas per hour above a background of 20,
the vapor pressure of the thorium compound at 100' was
calculated as 3.2±0.3XI0-' mm.
Thorium pyrophosphate, a salt of two tetravalent ions,
has long been used in the analytical chemistry of thorium.
The effect of salts on the solubility of a salt of this type is of
great interest to those engaged in the study of solution
theories. Because of the great insolubility of thorium pyro
phosphate a radiochemical method has been used for this
study. Salt solutions were allowed to pass at rates which
insured saturation through a thermostated cell containing
a long column of the thorium compound. Deposits were
made from these solutions on small copper dishes which
were subsequently covered with a cellulose acetate glyptal
film, the purpose of which was to retain the thoron but
allow passage of the alpha-particles. To convert the alpha
counts of such deposits into grams of thorium pyrophos
phate, it was necessary to obtain an alpha-absorption co
efficient for each salt. This was accomplished by compari
son with the alpha-activity of deposits of a standard
thorium chloride solution with and without added salts.
The solubility of thorium pyrophosphate was found to be
6.1 X 10-6 g per liter at 25°. The added salts have a very
marked effect on the solubility. For example, in a solution
of copper chloride containing 13.5 g per liter, the pyro
phosphate was over 100 times as soluble as in pure water,
and about 170 times as soluble in a solution of copper
sulphate containing 16 g per liter. These results are in
accord with the theory of Debye.
VOLUME 12, APRIL, 1941 21. Use of Stable Oxygen Isotopes in Tracing Reaction
Kinetics. IRVING ROBERTS, Weiss and Downs, Inc., New
York, New York.
The production at Columbia University of sizable
amounts of water containing an increased concentration of
the oxygen isotope of mass 18 made possible the discovery
of a new series of reactions, namely, oxygen exchanges
between organic compounds and water. The kinetics of
such reactions are interesting because they proceed at
measurable rates with no change in medium, and because
they exhibit acid and basic catalysis. In addition, their
mechanisms are related to those of well-known organic
reactions, and may shed some light on the latter.
For example, in the exchange of oxygen between benzoic
acid and water, the reaction in dilute solution is found to
be first order in the difference of 018 content of the reactants
and independent of the concentration of benzoic acid. An
equation expressing these kinetics may be derived from a
consideration of the nature of the reactions and the sta
tistical factors involved in the system. In addition, it is
observed that the rat~ of the reaction is proportional to the
hydrogen ion concentration in the reaction mixture.
A comparison of this reaction with those of acid catalyzed
ester hydrolysis and esterification shows the following
similarities: (1) The reactants and products are structurally
similar. (2) All three reactions are catalyzed by acids.
Esterification and ester hydrolysis are known to exhibit
general acid catalysis. (3) The rates of all three reactions
are of the same order of magnitude. (4) Heavy oxygen
studies have shown that in all three reactions, the same
linkage is broken, namely, the carbon-oxygen bond of the
acid or its residue.
On the basis of the above, it is concluded that the three
reactions are similar in mechanism, and that these mecha
nisms will be symmetrical ones, i.e., that the reverse of
the mechanism for esterification will be a mechanism for
hydrolysis which is similar to it. The mechanism of the
exchange reaction will of course be symmetrical.
From the existence of the equilibrium relationship
moles ester X moles water K
moles alcohol X moles acid
it is argued that the esterification and hydrolysis are first
order in alcohol and water, respectively. While equi
librium data do not generally prove kinetic dependences,
a comparison of this particular system with the exchange
reaction indicates this conclusion to be very probable. In
addition, there are some kinetic data which show a first
order dependence of esterification rate on the alcohol
concentration.
Granting that the exchange, esterification and hydrolysis
reactions are general acid catalyzed and first order in
alcohol or water, there are three possible mechanisms which
fit these requirements. Two of these consist of a series of
bimolecular steps, and the third is termolecular in nature.
At the present time, there seems to be no method of dis
tinguishing among these possibilities.
However, it is evident that the combination of the results
of heavy oxygen studies with previous kinetic data has
307
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nisms which may be proposed, down to three which are
most probable.
22. The Thermal Exchange Reactions of Mg, Cu, Mn,
Fe, CI, Br, I and Hg Studied by Their Radioactive Isotopes.
S. RUBEN, G. T. SEABORG AND J. W. KENNEDY, Depart
ment of Chemistry, University of California, Berkeley,
California.
Radioactive Fe59 (47 days half-life) was used to study
some exchange reactions of iron. An immeasurably rapid
exchange of electrons between ferrous and ferric' ions in
6N hydrochloric acid at room. temperature was found.
No electronic exchange between aqueous ferrocyanide
and ferricyanide ions was observed even after four days
at room temperature. No exchange of iron atoms was
observed between any of the following pairs of substances:
ferric and ferricyanide ions, ferric and ferrocyanide ions,
ferrous and ferricyanide ions.
Two other instantaneous exchanges, which may also
proceed by an electron transfer mechanism, were observed
to occur in aqueous solution at room temperature. The
43-min. Hg197 was used to show that mercurous and
mercuric ions undergo rapid exchange and experiments with the 2.6-hr. Mnss have revealed a rapid exchange
between manganate and permanganate ions in alkaline
solution.
Radioactive CI'8 (37-min.), Br8' (34-hr.) and p31 (S-days)
have been used to study the measureable rates of exchange
between these halogens and their corresponding halo
genates in acid solution at room temperature.
The 10.2-min. Mg27, 47-day Fe59 and 12.S-hr. CUM have
been used to measure the exchanges at room temperature
between the corresponding metallic ions and some metal
organic compounds. There was no exchange in 40 min.
between magnesium ions and highly purified samples of
either chlorophyll a or chlorophyll b in a buffered SO
percent acetone solution. The exchange between mag
nesium ions and the magnesium compound of S-hydroxy- .
quinoline proceeds rapidly in aqueous ethyl alcohol
solution. There is no exchange between ferric ions and
ferrihemoglobin in aqueous solution or between ferric ions
and ferriheme in ethyl alcohol even in experiments lasting
several weeks. Th~ exchange between copper ions and
copper acetylacetonate in chloroform is complete within
2 min. Some of these results are rather surprising in view
of other evidence concerning the bonds in these metal
organic compounds, and hence give additional valuable
information about these bonds.
Chemistry II
Tracer Techniques in Analytical Chemistry
Chairman: DR. H. C. UREY, Columbia University
34. Use of Isotope Tracers in the Study of the Compo
sition of Proteins. DAVID RITTENBERG, College of Physi
cians and Surgeons, Columbia University, New York, New
York.
The analytical chemist is able to analyze a mixture only
when he has available a specific reagent for the substance to
be determined. This reagent must give a reaction, either a
precipitate, color, or other indication, with only one con
stituent of the mixture.
Proteins when hydrolyzed give rise to a mixture of from
15 to 20 alpha-amino acids. For some of these there are
known specific reagents which precipitate them. For others
there are known reagents which give color reactions which
can be made quantitative. For the majority no such
reagents are known.
To make a quantitative determination of the amount of
such an amino acid present in a mixture one must isolate
all of the amino acid in a pure state by some suitable
fractionation procedure. The two conditions are, in practice,
mutually contradictory. One can isolate all of an amino
acid in animpure state, or some of the amino acid in a pure
state.
The isotope dilution procedure requires the isolation of
only a pure sample of the substance to be determined, the
yield being unimportant.
308 If, to a mixture of amino adds, is added x grams of
glycine containing Co atom percent excess of N15 (or CIa),
this glycine will mix with the glycine already present and
form an inseparable mixture. If, now, glycine is isolated
and found to contain C atom percent excess of N15, then
the original amount (y) of glycine in the amino acid mixture
is given by Eq. (1),
y=[(Co/C)-I]x. (1)
As, by this method, only a small sample need be isolated,
merely enough for an isotope analysis (about 5-15 mg),
large losses may be permitted during the purification
process. By the proper choice of experimental conditions
the error of the method may be reduced to about one
percent.
All the amino adds with the exception of glycine exist in
two enantiomorphic forms. In protein, the I-configuration is
found almost exclusively. By the addition of a dol mixture
and isolation of both the I and d components or of the I and
dl components, the amino acid content of both the I and d
can be calculated. By this method the extent of racemiza
tion of glutamic acid of normal and tumor tissue has been
found to be very small.
The same method can be employed in the estimation of
fatty acids in fats.
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amino acid isolated is quite impure (contains 10 percent
impurity), the analytical result will not be in error by more
than one percent.
35. Applications of Radio-elements in Analytical Chem
istry. CHARLES ROSENBLUM, Prick Chemical Laboratory,
Princeton University, Princeton, New Jersey.
The sensitivity with which radio-elements may be
detected and quantitatively measured makes them admi
rably suited for use as isotope indicators in analytical
chemistry. In general such indicator experiments fall into
two groups, one which depends upon the chemical insepara
bility of isotopes once mixed, and a second in which a
change in ratio of active to stable isotope occurs. When the
isotopic ratio remains constant, the indicator is a true
"tracer" element; and its radiations reveal the presence and
concentration of the inactive form throughout a given
system. Most analytical applications belong to this group.
Those applications in which the isotope ratio varies are of
equal interest in that frequently they cast light upon the
mechanism of processes of fundamental importance to the
analytical chemist.
The relatively limited reproducibility of electroscope and
counter measurements when compared with that of the
usual quantitative analysis restricts the use of radio
elements to the field of microchemistry. However, here
their usefulness is amply illustrated by solubility determi
nations on certain lead-, cobalt-and phosphorus-containing
compounds, as well as by s: udies of adsorption and
coprecipitation phenomena at low concentrations. Even in
ordinary analytical chemistry, when a gravimetric separa
tion is uncertain or undeveloped, the activity of a com
ponent containing a radioactive isotope furnishes a simple
and rapid means of locating it, and permits one to work out
proper precipitation conditions. Going a step farther, it is
evidently possible to determine just how far an analysis is
in error and to make the proper correction. Furthermore, a
whole system of radiometric microanalyses, based on
precipitation reactions with thorium B, has been proposed
by Ehrenberg.
Generally speaking, the radio-elements are so sensitive
to detection that it is possible to test the limit of validity
of any analytical procedure, be it the efficacy of washing a
precipitate, the completeness of a precipitation reaction, or
the lower limits of applicability of fundamental laws. Thus
the distribution of a solute between phases, so important in
crystallization and extraction processes, has been studied,
in addition to the law of mass action and the Nernst
electromotive force law. Indeed, the latter has been shown
to hold for bismuth in concentrations as low as 10-12
normal, and has been suggested as the basis for determining
minute quantities of this element.
Aside from being useful in routine analytical procedures,
radio-elements have proven to be of service in examining
the mechanism of certain fundamental reactions as well as
in studying the nature of a number of common analytical
VOLUME 12, APRIL, 1941 precipitates. They have disclosed unsuspected changes
which take place during the aging of precipitates such as
lead sulfate and silver bromide. Such observations have
led to a better understanding of the perfection processes
which occur during this period of change and which are
often characterized by a liberation of contaminating
impurities. Not only have the external surfaces of such
solids been measured by means of radio-elements, but the
easy accessibility of ions at the interior of fresh precipitates
has been demonstrated. Judging from the above examples it
is evident that analytical chemistry offers a fertile field f~r
further indicator researches.
36. The Contribution of Artificial Radioactivity to the
Completion of the Periodic System. EMILIO ~EGRE, Radia
tion Laboratory, University of California, Berkeley, Cali
fornia.
At the time of the discovery of artificial radioactivity,
four elements with atomic number lower than 92 were still
unknown, viz., elements 43 (eka-manganese), 61, a rare
earth, 85 (eka-iodine) and 87 (eka-caesium). Element 87
has been found by Mlle. Perey1 as a rare branching product
in the natural radioactive actinium family. Perrier and
Segre2 found element 43 among the products of neutron and
deuteron bombardment of molybdenum; element 61 has
probably been produced by the bombardment of neodymium
with deuterons," but, because of the well-known difficulties
connected with the separationof the rare earths, no chemical
studies have been undertaken on 61. Corson, MacKenzie
and Segre4 have prepared element 85 by the bombardment
of bismuth with alpha-particles.
The essential contribution of artificial radioactivity to
the discovery of new elements is that these substances,
with the exception of element 87, can be artificially pre
pared by transmutation and can be easily detected through
their radioactivity. The amounts of these elements which
can be artificially produced is extremely minute (10-10 to
10-14 gram), but using the methods of radioactive chemistry
it is possible to attain a fairly complete knowledge of their
properties.
This information makes it possible to predict geochemic
ally the probable ores in which these elements could be
found, should they exist in nature, and to devise suitable
methods for their concentration. Moreover, the use of the
artificially prepared element as a tracer would make it
possible to check directly each step of the extraction. These
points are of considerable importance since it has been
found in certain instances that the chemical properties
suggested by the analogies of the periodic system are
significantly different from some of the observed properties
of these new elements. These differences between the
predicted and observed chemical properties of element 85
are sufficient to invalidate the past attempts to isolate this
element from natural sources, which were based upon a
strict analogy between iodine and 85. Should 85 be present
as a branching product in natural radioactivity, its isolation
would not offer great difficulties.
309
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Downloaded to ] IP: 130.18.123.11 On: Thu, 18 Dec 2014 17:54:59In the case of element 43, most of its characters resemble
very closely rhenium, and it seems natural to assume that
geochemically it would be associated with it and not with
manganese. The enrichment process used by Noddack for
rhenium should also have concentrated 43. A final separa
tion between these two elements can be performed by distillation in hydrogen chloride current under controlled
conditions.
1 M. Perey, Comptes Rendus 208, 97 (1939).
, C. Perrier and E. Segr~, J. Chem. Phys. 5, 712 (1937); Nature 143.
460 (1939).
• M. L. Pool and L. L. Quill. Phys. Rev. 53, 437 (1938) .
• D. R. Corson, K. R. MacKenzie, and E. Segre, Phys. Rev. 57, 459
(1940).
Chemistry III
General Chemical Problems Involving Tracers
Chairman: DR. J. B. CONANT, Harvard University
57. Synthesis in Vitro of Radioactive Organic Sub
stances. A. K. SOLOMON, Harvard University, Cambridge,
Massachusetts.
Earliest applications of artificial radioactive tracers to
biology made use of the radioactivated atoms in their
elementary state, or in the form of some inorganic com
pound easily derived from that state. Shortly, the necessity
of synthesizing more complex organic molecules from the
simple radioactive atom became apparent. As is well
known, these complex molecules can not be made radio
active by the process of simple bombardment; the recoil
of the radioactivated atom usually suffices to break the
bond which holds it to the desired molecule.
Synthesis of radioactive organic molecules has as its
aim, in common with normal syntheses, the highest
possible yield; that is the highest concentration of radio
activity in the synthesized product. The first step towards
this goal is the complete separation of the activity from
the bombarded target. If the new artificial radioactive
element is different than the bombarded element, the
problem can usually be solved by ordinary analytical
methods. If on the other hand, the new element is isotopic
with the bombarded element, these means fail. However,
the method of Szilard and Chalmersl which takes ad
vantage of the fact that radioactivation means release of
the struck atom in a highly reactive state, has been
employed with great success.
After concentration which is sometimes combined with
one of the succeeding steps, comes the problem of the
synthesis itself. For this purpose, radioactivities can be
divided into two general classes; those like phosphorus
whose long half-life (14.3 days) permits the use of ordinary
laboratory methods practicaIly unchanged, and those like
carbon whose rapid disappearance (half-life = 20.6 minutes)
requires the development of new syntheses in which speed
is the most important factor. For example, any step
which increases the over-all time of the operation by 20
minutes must justify itself by a twofold increase in yield.
To meet these conditions a synthesis' has been developed
to produce purified lactic acid from raw carbon in one
hour and three-quarters.
Other syntheses and general methods are discussed.
1 Szilard and Chalmers. Nature 134, 462 (1934).
• Cramer and Kistiakowsky, unpublished manuscript.
310 58. Synthesis in Vivo of OlganiC Molecules Containing
Radioactive ·Carbon. M. D. KAMEN AND S. RUBEN,
Radiation Laboratory and Department of Chemistry, Uni
versity of California, Berkeley, California.
Under the conditions of bombardment, radioactive
carbon is obtained as CO (ultimately CO2). Since it is
undesirable to dilute the C* excessively with inactive
carrier, the quantity of labeled carbon usually amounts to
2 cc or less (S.C.T.P.). If, in addition, the short-lived
carbon is used, the investigator is faced with the problem
of synthesizing quickly, and in good yields, various organic
molecules from avery smaIl quantity of CO2. Micro
syntheses of vital organic material from CO, in vitro is at
a definite disadvantage when compared with in vivo
methods involving the use of micro-organisms which can
be chosen and manipulated to produce quickly and in
high yield from CO2 almost any organic molecule needed
as a starting material in metabolic tracer studies. Of
course, in vivo synthesis also makes possible production
of labeled vital principles of unknown composition (i.e.,
photosynthetic intermediates), a desirable result un-
attainable by in vitro techniques. .
To iIIustrate more definitely the power of the in vivo
approach, attention may be drawn to some recent studies
on the production of acetic acid, propionic acid, succinic
acid, methane, etc., from CO2.l-a In experiments with
methane bacteria, 40 minutes of exposure to about 2 cc of
C*02 resulted in the production of a large fraction of
administered C*02 as active methane. P. pentosaceum
reduced 80 percent of a similar quantity of C*O, in the
presence of glycerol to propionic and succinic acids in
30 minutes. Clostridium acidiurici in fermenting uric acid
reduced appreciable quantities of C*02 in 15 minutes to
active acetic acid. Using hypoxanthine as substrate, 80
minutes sufficed to convert nearly all the C*O, to acetic
acid. It was found that both methyl and carboxyl groups
were labeled.
Photosynthetic organisms can be used for the production
of carbohydrates from CO2. Although hexoses or reducing
sugars cannot be synthesized from green algae,4 it is
possible to transform about 20 percent of a given quantity
of CO, to sugar if barley is used.6
The method is seen to be capable of practically unlimited
extension to the synthesis of a vast number and variety
JOURNAL OF ApPLIED PHYSICS
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how many micro-organisms with diversified metabolic
synthetic processes are available. Further studies on the
above-mentioned and other systems will be presented.
1 Carson and Ruben. Proc. Nat. Acad. Sci. 26,422 (1940).
2 Barker, Ruben and Kamen, Proc. Nat. Acad. Sci. 26, 426 (1940).
3 Barker, Ruben and Beck, Proc. Nat. Acad. Sci., August (1940).
• Ruben Kamen, Hassid and DeVault, Science 90. 570 (1939).
'Ruben: Hassid and Kamen, J. Am. Chern. Soc. 61, 661 (1939).
59. The Synthesis of Organic Compounds Containing
Stable Isotopes as Tracers. R. SCHOENHEIMER, College of
Physicians and Surgeons, Columbia University, New York,
New York.
This review will be limited to a discussion of such
methods as have proved useful in the preparation of
substances applicable to biological work.
A. Deuterium
Only compounds with deuterium bound to carbon
(methyl, methylene, and methane groups) can be employed
for tracer studies. With some exceptions (hydrogen in
compounds of low molecular weight, or hydrogen involved
in tautomeric equilibrium reactions as in enolisation),
such carbon bound hydrogen is "stable." In exceptional
cases, namely when the rate of enolisation is very slow.
even compounds with deuterium neighboring carbonyl
groups may be employed for biological tracer work.
The more commonly employed procedures are:
a. Catalytic hydrogenation with D2 of unsaturated com
pounds in nonpolar solvents or heavy water.-As the rate of
the platinum catalyzed exchange reaction between H2 and
H20 is considerably slower than that of the hydrogenation
of some organic compounds, the hydrogenation with D2
may be carried out in H20 as a medium. The resulting
compound will have a deuterium content below theoretical.
A number of isotopic fatty acids, amino acids, and steroids
have been prepared by hydrogenation.
b. Replacement of halogen atoms by deuterium.-Various
deutero methanes have been prepared from the corre
sponding halogen derivatives.
c. Catalytic labilization of carbon bound hydrogen at
elevated temperature with D~O. or active platinum in
heavy water.-According to Ingold the treatment with
concentrated D2SO. of a number of aromatic and hydro
aromatic hydrocarbons results in hydrogen exchange. The
method has been employed for the preparation of biological
fatty acids and amino acids with "stable" deuterium.
Aliphatic fatty acids and aliphatic amino acids thereby
acquire deuterium only at the alpha-carbon atom. Aro
matic amino acids (phenylalanine) also exchange the
hydrogen of the ring. Polanyi and Farkas have shown
that active platinum or paladium at elevated temperatures
may labilize hydrogen of some hydrocarbons. This reaction
has now been employed for the preparation of isotopic
fatty acids. In the presence of alkali and platinum, aliphatic
fatty acids exchange carbon bound hydrogen with that
of D20. The presence of hydroxyl and amino groups in
the compound interferes with the exchange, i.e., the
procedure does not seem applicable to alcohols or amino
acids.
VOLUME 12, APRIL, 1941 d. Various methods applicable for the preparation of
specific compounds.-(I) decarboxylation in D20; (2)
hydration of unsaturated compounds, etc.; (3) deutero
methylalcohol, prepared from CO according to Zanetti
has been employed by du Vigneaud and collaborators as
starting material for methylated compounds (methionine,
choline).
e. Biological synthesis.-Animals when given heavy
water to drink or plants grown in heavy water synthesise
compounds with stably bound deuterium. A large number
of such substances have been isolated. The method, while
theoretically unlimited is restricted in practice by the cost
of heavy water. More economical is the biological conver
sion of one deutero compound into another.
B. Isotopic. nitrogen
Most substances reported were prepared for biological
tracer work. They were synthesised with isotopic ammonia
as starting material. In view of the value of the isotope
the known procedures of amino acid synthesis had to be
modified so as to furnish good yields when calculated on
the basis of ammonia rather than the carbon chain.
The recovery of nitrogen should be quantitative.
Three methods of amino acid synthesis have been
employed so far: (a) The phthalimide procedure of
Gabriel; (b) the catalytic hydrogenation of keto acids in
the presence of ammonia; and (c) the reaction of coumaric
acid-hydroxy nicotinic acid-pyridone-piperidone as
starting material for ornithine and proline.
Isotopic guanido compounds (arginine, creatine) were
obtained with isotopic cyanamide, prepared from cyanogen
bromide. Isotopic urea may be prepared by the copper
catalysed reaction of diphenylicarbonate with ammonia.
Biological synthesis of a large number of compounds has
occurred in all experiments when isotopic ammonia or
amino acids were given to animals. The isotope content
of the newly formed substances is low.
For tracer work it is frequently necessary to employ
amino acids with 2 independant isotope markers in one
preparation, i.e., deuterium as a tracer for the carbon
chain and N16 for the amino group. Several such amino
acids have been prepared.
60. Production and Properties of Long-Lived Carbon.
S. RUBEN AND M. D. KAMEN, Department of Chemistry and
Radiation Laboratory, University of California, Berkeley,
California.
The recently~2 discovered long-lived radioactive isotope
of carbon has been identified as C!4. It has been found that
the radiations emitted are low energy negative electrons
with an upper energy limit of 145 ± 15 kv. No gamma-rays
( < 1 percent) could be detected. Two methods of produc
tion have been investigated. The first involves the bom
bardment of carbon by deuterons with high energy
deuterons accelerated in the Berkeley cyclotron. The
reaction is
.Cl3+1H~6C'4+1Hl.
The yield at 3 to 4 Mev (saturation energy for thin target
activation) is about 3 X 10-6 microcurie per microampere
311
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reaction and fitting an Oppenheimer-Phillips curve to the
yield data for the C12(d, p)C13 reaction at lower energies
(0.5 to 2 Mev), it has been possible to calculate a value for
the half-life of approximately 1000 years. This can be taken
as a lower limit. A sample of the active carbon has shown no
appreciable decay «1 percent) in eight months, placing
the half-life value at certainly no Jess'than 25 years. Since
the transition from C14 to N!4 by beta-emission appears
forbidden from these observations, it is necessary to assume
that the ground state of CI4 possesses several units of
angular momentum. This conclusion is not what might
have been expected from the analogous case of He6 decaying
to Li6• The fact that nucleus He6 exists in an S state would
lead on the most straightforward arguments based on
present picture of n-p forces to the supposition of a
ground state of little or no angular momentum for C14.
The second method of production is based on the
disintegration of nitrogen by neutrons, viz.:
1NI4+nol ..... 6CI4+IHI.
This reaction is exothermic8 by about 500 kv and so can
take place with slow as well as fast neutrons. This process
in all probability has a high cross section for slow neutrons.
A saturated solution of ammonium nitrate in ten gallons of
water when exposed for about six months to neutrons from
the 60-inch medical cyclotron at Berkeley yielded a sample
of the long-lived carbon, giving about 10· counts/min. as
measured in a screen-wall counter. The total inactive
carbon in which this activity was distributed could be kept
lower than one mg. However, ammonium nitrate is not the
best material to use from the standpoint of nitrogen and
hydrogen content, and moreover there exists the explosion
hazard. By using substances such as urea, guanidine,
cyanamide, etc., and making full use of the available space
around the cyclotron, it should be possible to increase the
present yields 100·fold. Such samples, when obtained, will
allow dilutions of 100,000·fold without falling below the
limit of detectability. The many advantages of neutron
activation (i.e., low carrier content, convenience, economy,
etc.) indicate it to be the most advantageous method for the
production of tracer carbon.
It has been found that nearly all the active carbon can be
recovered from the nitrate solution as volatile material
(C02, CO, and possibly CH4). Thus, the extraction of the
active carbon from large quantities of nitrogenous material
can be easily accomplished by pumping off the vapors and
subsequent oxidization to CO2• The nature of the recoil
carbon activity in a variety of nitrogen compounds other
than nitrate is now being studied to determine the optimum
conditions for production of C!4 by neutron bombardment.
It is certain that the shielding of neutron sources can
profitably be turned to account by use of nitrogenous
compounds which can also produce C14 as a by.product of
the operation of the apparatus. This is a consideration of
some importance in view of the rapidly increasing number
of such machines.
cn will be applicable as a tracer in biological studies as is
the heavy isotope 03 but will be especially useful in
312 researches where high dilution factors are encountered and
where it is inexpedient or impossible to use the C13. The
technique for detecting the radiations with special reference
to elimination of errors due to self-absorption is being
developed and a description of the apparatus now in use
will be given.
! Ruben and Kamen, Phys. Rev. 57, 549 (1940).
• Kamen and Ruben. Phys. Rev. 58. 194 (1940). 'T. W. Bonner and G. Brubaker. Phys. Rev. 49, 778 (1936).
61. Chemical Effects of Nuclear Transitions. R. S.
HALFORD, W. F. LIBBY AND DON DEVAULT, Department of
Chemistry, University of California, Berkeley, California.
The results of many workers taken together show that
neutron capture and conversion electron emission both
induce dissociation of the molecules in which the radioactive
atom is bound. The processes appear to be nearly 100
percent efficient in this respect under all conditions, al
though reformation reactions usually occur, causing an
apparent decrease in the efficiency of ejection. Dilution of a
substance undergoing such a process with another which
cannot react with the hot ejected fragments results in
increase in the fraction ejected to 100 percent in the limit.
For example, slow neutron irradiation of CBr, in the
following various forms gave decreasing percentages of the
total induced radioactivity which could not be removed by
aqueous extraction: solid CBr4, 60 percent; 1.2 mole
percent solution of CBr, in C2H.OH, 28 percent; 0.74 mole
percent, 13 percent, 0.45 mole percent, 2; 0.06 mole
percent,O.
The problem therefore assumes three phases. One is the
existence of thermal interchange between the original
substance and the ejected fragments. A second is the nature
of the rupture that occurs, e.g. whether ions or free radicals
are ejected and the constitution of these fragments. The
third is the reactions of these energetic fragments marked
with radioactivity with the molecular environment. A
rather extensive literature exists on thermal interchanges at
present. Results are to be presented indicating a rule that in
these violent ruptures the electrons in the bonds broken are
distributed among the fragments about as they are thought
to be distributed in the bond. For example, Cl08-is
probably reduced as a result of the ejections following
neutron absorption by the Cl, while MnO. -quite definitely
retains the +7 oxidation number for manganese when it is
exposed to slow neutrons.
The reformation reactions appear to obey reasonable
rules in view of the high energies of the reacting particles.
For example, in the case of the alkyl halides, activity is
found in more highly halogenated fractions but the main
portion of that which returns to the organic molecules is
found to be identical with the original substance, pre
sumably because of the higher probability of energy loss by
collision of the excited radioactive halogen atom with
another halogen atom of the same mass bound in the
molecule. This results in a replacement of the nonradioactive
atom by the radioactive one. This process will in general
form the new RX* molecule in a somewhat excited state
which may allow certain reactions to occur with other
JOURNAL OF APPLIED PHYSICS
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cited molecules. These reactions may result in the liberation
of the radioactive atom, so the effect is a net increase in the
extractable halogen radioactivity. Lu and Sugden have
shown that aniline accomplishes this effect for organic
halides. The generality of the principle is obvious and the
applications may prove to be of considerable practical
importance in the future. They should result in higher
yields of concentrated radioactive materials from neutron
irradiations.
Transitions of one nuclear isomer into another, usually
by the emission of an internally converted K-or L-electron, result in efficient ejections also. The mechanism apparently
involves partial utilization of the excitation energy of the
electronic shells resulting from K-or L-electron emission
and leaves the ejected ions in very reactive states. These
transitions may be of use in reaction kinetics because they
probably are capable of furnishing atoms at a known rate,
each marked radioactively. For example, a solution of
Br*03-with the bromine activity of 4.5 hr. life will. have
Br*-of 18-min. half-life furnished to it at a constant rate
and any reaction occurring in this system involving Be
should give a product containing 18 min. Br* providing
Br-and the product do not interchange rapidly thermally.
Biology I
The Study of Animal Metabolism with Radioactive Tracers
Chairman: DR. J. H. MEANS, Massachusetts General Hospital, Harvard University
26. Radioactive Iodine as an Indicator in Thyroid
Physiology: Observations on Rabbits and on Goiter
Patients. SAUL HERTZ, Massachusetts General Hospital,
Boston, Massachusetts.
This report summarizes a series of cooperative experi
ments started in the fall of 1937, on the metabolism of
iodine in relation to thyroid function. The only radioactive
isotope of iodine then available was 1128, with a half-period
of 26 minutes. The earliest experimentsl demonstrated that
the collection of iodine by the thyroid was extremely rapid,
the amount present in the gland within 10 minutes after
intravenous injection not being exceeded within 90 minutes.
Hyperplastic glands collected more iodine than did normal
glands, the injections being equal. A systematic study was
then undertaken of the relations among the dosage of
administered labeled iodine, the time of collection, previous
iodine administration, and the functional state of the
thyroid as indicated by its size. The results2 indicated that
the thyroid took up a larger proportion of a small dose of
iodine than it did of a large dose. Curves showing these
relations were established for normal animals, animals
treated with anterior pituitary thyrotropic hormone,
animals on an exclusive cabbage diet, and animals injected
with methyl cyanide. Previous iodine administration
caused a marked decrease in the collection of subsequent
doses. When strong samples of the newly discovered long
lived isotopes of iodine became available, further lines of
investigation were undertaken. These were the extension
of experiments on thyroid iodine collection to patients with
Graves' disease, the chemical investigation of the partition
of iodine among various iodine fractions in the thyroid, and
the introduction of a new technique, multiple labeling,2 for
the study of different doses of iodine at the same time. The
multiple labeling technique showed that the collection
from a second dose of iodine is almost invariably less than
VOLUME 12, APRIL, 1941 that from the first dose. This led to the suspicion that the
routine pre-operative massive iodinization in Graves'
disease might be unnecessary. It has now been shown that
the response to a single dose is clinically indistinguishable
from the response to protracted iodinization. At the same
time, a more complete correlation of iodine collection with
the known measures of thyroid function, viz. basal meta
bolic rate, thyroid size, histologic appearance, and with the
time and method of preparation of the subject was carried
out using rabbits. The experiments upon patients with
Graves' disease were at first concerned with measuring the
amount of iodine in the thyroid (as obtained at operation)
which remained from a single initial labeled dose of varying
size, administered at various times during the course of
iodinization and at varying intervals before operation. In
addition, the chemical fate of the iodine was investigated
and the urinary excretion followed. As in rabbits, maximum
collection was found within a short time after administra
tion, and collection was relatively largest from small doses
of iodine. Chemical analysis in the main confirmed previous
findings. In a recent series of experiments, an externally
placed counter was used to measure the relative activity
of labeled iodine in the thyroid as a function of time. By
means of a single absolute determination after surgery, it
was possible to calculate the absolute content at any pre
vious time. The initial thyroid collection in previously un
treated Graves' disease patients approximates 100 percent for
small doses (0.2-5.0 mg), while the initial collection of
previously iodinized patients, normal controls, and the
collection of all patients from larger doses is considerably
smaller. These results are not inconsistent with the smaller
collections obtained by Hamilton and Soley3 from larger
doses. This initially collected iodine rapidly leaves the
thyroid in the untreated patients given small doses, less
than a third remaining after a week, with a slower decline
313
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thyroids isolated and surviving in a perfusion apparatus has
been instituted, and it has been shown that the behavior of
the thyroid in collecting iodine from the perfusion fluid is
directly comparable to the results in vivo.
1 Hertz, Roberts and Evans, Proc. Soc. Exp. BioI. Med. 38, 510
(1938).
'Hertz, Roberts, Means and Evans, Am. J. Physiol. 128,568 (1940)
3 Hamilton and Soley, Am. J, Physiol. 127, 557 (1939),
27. Distribution of Radio-Iodine in Normal Rabbits.
H. C. HODGE, W. MANN AND 1. ARIEL, University of
Rochester, School of Medicine, Rochester, New York.
Following intravenous injection of radioactive iodine,
there is an immediate distribution to the various tissues
from the blood with considerable fluctuation in the relative
amounts found at the various periods observed. The
thyroid takes up a relatively large percentage of the
injected dose. The radio-iodine appears promptly in the
urine. Up to 30 percent of the dose may be excreted in nine
hours, The lung and kidney tissue contain relatively high
percentages of the radio-iodine dose; liver, spleen, heart,
bile, and submaxillary gland contain intermediate amounts;
and muscle, skin, diaphragm, and testicle have low per
centages.
28. Studies in Physiology of Normal and Diseased
Thyroids of Human Beings by the Use of Radioactive
Iodine. JOSEPH G. HAMILTON AN:D MAYOH. SOLEY, William
H. Crocker Radiation Laboratory, University of California,
Berkeley, California and the University of California Medical
School, San Francisco, California.
A radioactive isotope of iodine (PSI) has been used as
tracer to study various phases of iodine metabolism in
normal subjects and in patients with thyroid diseases, The
rapid absorption and excretion of iodine has been con
firmed, Toxic goiters in 16 patients who had received pre
viously large amounts of ordinary iodine were able to take
up considerable quantities of radio-iodine, but less than the
nontoxic goiters in 8 patients who had not received iodine
prior to these experiments. Radio-iodine was given to 2
patients with carcinoma of the thyroid and it was observed
that the cancerous tissue did not have the ability to accu
mulate more than small traces of this element.
The iodine metabolism of the thyroid glands of normal
subjects and of patients with several types of thyroid
disorders (who had received no iodine previously) was
studied in the intact individuals fonowing the oral adminis
tration of radio-iodine. A Geiger-Muller counter was placed
over the thyroid gland and the amount of accumulated
radio-iodine was determined by the measurement of the
gamma-rays emitted from the gland. This procedure re
vealed that the thyroids of 5 normal subjects, of 2 patients
with nontoxic goiters, of 10 patients with toxic goiters, and
of 4 patients with hypothyroidism but no goiters, concen
trated and released iodine in a characteristic manner for
each condition described. The thyroids of the normal
individuals stored the radio-iodine slowly, the maximum
uptake of from 1 to 5.5 percent (average of 4.5 percent) was
314 observed at the end of 48 hours, but these thyroids retained
over 80 percent of their accumulated radio-iodine at the
end of 30 days. A similar pattern was observed in the
thyroids of the patients with nontoxic goiters, but these
glands took up more than twice the amounts stored in the
thyroids of the normal subjects. The thyroids of the
patients with toxic goiters took up the radio-iodine very
rapidly so that the maximum uptake of from 7 to 30 percent
(average of 14 percent) occurred at from 1 to 4 hours after
administration. At the end of 24 hours the content of
radio-iodine in these glands diminished to the extent of
one-half to one-fifth of the maximum uptake. Thereafter
the loss of radio-iodine from the glands was much less, but
was greater than was observed in the normal subjects and
the patients with nontoxic goiters. The thyroids of the
patients with hypothyroidism had a limited capacity to
accumulate the administered radio-iodine; the uptake in
these patients at the end of 48 hours ranged from 0.02 to
0.08 percent (average of 0.05 percent),
Radio-iodine has been employed to investigate the rela
tionship between the deposition of radio-iodine in thyroid
tissue and its histological structure. Two days following the
administration of the radio-iodine the thyroids were
removed and thin sections prepared from the glands.
These sections were placed against photographic films and
after a suitable period of exposure the films were removed
and developed, and the sections were stained. The areas of
darkening on the films, which were produced by the action
of the radio-iodine beta-particles, indicated the regions of
the sections in which the largest accumulations of radio
iodine had taken place. The sections and their correspond
ing radio-autographs were compared under a microscope in
order to correlate the deposition of the radio-iodine with
the microscopic anatomy of the thyroid tissue. Thyroids
from patients with toxic goiters, nontoxic goiters and car
cinomas of the thyroid were studied by this technique. The
results of these studies indicated that the radio-iodine was
stored predominantly in those areas of the thyroid in which
the greatest degree of functional activity appeared to be.
The cancerous thyroid tissue had no demonstrable ability
to accumulate the administered radio-iodine.
A comparison of the uptake of radio-iodine and element
85 (eka-iodine) by normal and hyperplastic thyroids of
guinea pigs revealed that this newly discovered halogen is
taken up by these glands in a manner similar to iodine. The
rates of excretion of these two halogens were observed to
be almost identical. A single experiment with element 85
administered to a patient with a nontoxic goiter revealed
that approximately 10 percent was accumulated in the
gland at the end of 24 hours and the uptake curve was
similar to that of radio-iodine.
29. The Use of Radioactive Iron in the Study of Prob
lems of Iron Metabolism and Experimental Anemia. P. F,
HAHN AND G. H, WHIPPLE, University of Rochester, School
of Medicine and Dentistry, Rochester, New York.
There are many opportunities for the employment of the
artificially radioactive isotope of iron and studies have been
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in the regulation of absorption of iron with especial atten
tion to the mechanism regulating the acceptance or refusal
of iron when administered orally; (2) the amount of iron
excretion and the pathway of this process; (3) the factors
governing the rate of uptake of iron by the immature red
blood cell and the state of maturation at which the iron is
incorporated in the cell; (4) the means of transport of iron
in the body and the form in which the element occurs in
combination during transport; (5) the proof of the existence
of iron in the form of hemoglobin in the red blood cell within
a few hours following the administration of the radioactive
isotope by mouth; (6) the lack of exchange of iron in the
plasma with iron of the hemoglobin molecule as a purely
physico-chemical exchange reaction; (7) the distribution
of iron in the various tissues following its oral and parenteral
administration; (8) the origin of iron in the bile and the
factors regulating the amount of secretion by this route;
(9) the rate of turnover of irOn in the metabolism of muscle
hemoglobin iron; (10) the use of radioactive iron as a
means of tagging hemoglobin and red blood cells in the
study of the volume of red blood cells in circulation and the
total volume of red cells in the vascular system.
Other possibilities are presented such as the study of the
respiratory enzymes containing iron (e.g. cytochrome) but
the studies of these substances would be better deferred
until higher potencies of the isotope are available. The
various fields of clinical research in the anemias and nu·
merous diseases involving dyscrasias of iron metabolism
have been approached but further information awaits the
use of the isotope among a wider variety of controlled
experiments which in turn depend on the availability of
large amounts of the radioactive material.
It has been demonstrated that the anemic animal de
ficient in iron stores will absorb considerably larger amounts
of iron than the normal animal. The mechanism of this
unusual physiological reaction has been studied from a
number of angles. Among the most enlightening experi
ments was one in which a normal animal was shown to have
absorbed only 1.3 percent of the dose of 130 mg of iron
containing the radioactive isotope. When this animal was
rendered acutely anemic by the removal of about two·
thirds of its total circulating blood during the course of a
few hours, and twenty-four hours later given the same dose
of radioactive iron, the amount of absorption was about
the same as before, within experimental limits. After being
allowed to return to a near normal range of circulating
hemoglobin at the expense of the body stores of iron, and
again fed radioactive iron at about the same dosage level,
the amount of absorption was 10 percent instead of less
than 2 percent. This would suggest that the level of anemia
per se did not influence the amount of the metal absorbed
but that rather the amount of tissue iron, probably one of
the iron fractions of the mucosa, was the determining
factor.
The question as to the site of iron absorption is of con
siderable interest. It has been possible to show by means
of an anemic dog with a complete gastric fistula that con·
VOLUME 12, APRIL, 1941 siderable absorption of the iron containing the radioactive
isotope takes place i the stomach, in fact, as much was
absorbed from such a pouch during a two·hour instillation
period as one might expect from the oral administration of
the same amount of iron to a standard depleted anemic dog.
Experiments are in progress to determine whether the
amount of absorption in such an intact pouch may be
altered by the maintenance of a high level of tissue iron. It
is also being investigated whether a dog with a low level of
tissue iron but a normal blood picture in every respect
(normal saturation of hemoglobin in red cells and normal
plasma iron) will absorb iron as well as a depleted anemic
animal.
It is felt that a number of fundamental processes under
lying the metabolism of iron may be much better under
stood by the continued use of the radioactive isotope in
these and similar studies.
30. Studies with Radioactive Copper. * M. O. SCHULTZE
AND S. J. SIMMONS, Departments of Chemistry and Physics,
University of Pittsburgh, Pittsburgh, Pennsylvania.
Physiological studies with radioactive copper require
material with a very high radioactivity and a low content
of total copper because (1) radioactive copper has a short
half-life (12.8hours), (2) very small amountsof copper elicit a
physiological response, and (3) copper is toxic in large doses.
With radioactive copper prepared by bombardment of
nickel with protons these requirements can be met. Some
of the samples at our disposal yielded an activity of 2
million counts per minute per mg of total copper 48 hours
after bombardment, as measured in the form of a copper
sulfate solution by a dipping counter.
Radioactive copper was fed to anemic copper deficient
and iron deficient rats. After 24 or 48 hours the distribution
of the cOPP\tr in various tissues and organs was studied.
From 100-200 micrograms of total copper fed only 3-7
pcercent were retained in the tissues (exc,luding the gastro
intestinal tract). The tissues of anemic copper deficient
rats retained more copper than those of anemic iron defi
cient rats. The kidneys and the liver had the highest con
centrations of retained copper. A small fraction of the
copper was found in the bone marrow of the copper deficient
rats. This is of special interest in relation to blood formation
because marked changes in enzyme activity associated with
hematopoietic activity of the bone marrow have been
demonstrated as early as 24 hours after copper therapy of
deficient rats.
Copper can be extracted quantitatively from aqueous
solutions by converting it into the copper complex of
diphenylthiocarbazone (dithizone) which is soluble in car
bontetrachloride. This reaction was used for the isolation
of the copper from solutions of the bombarded nickel and
of ashed animal tissues prior to counting the activity in a
Geiger-Muller counter. It also permitted concentration of
the radioactivity in small volumes, aliquots of which were
used for counting.
* The cooperation of the Department of Physics. University of
Rochester, Rochester, New York, is gratefully acknowledged.
315
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The Study oj Animal Metabolism with Radioactive Tracers
Chairman: DR. J. C. AUB, Collis P. Huntington Memorial Hospital, Harvard University
40. The Permeability of Cells to Cations. WALDO E.
COHN, Collis P. Huntington Memorial Hospital of Harvard
University, Boston, Massachusetts.
The radioactive isotopes of sodium and potassium afford
a direct method for measuring the permeability of cells to
these ions. After intravenous injection of Na24 or K4Z, in
the form of the chloride, the radioactive isotope disappears
rapidly from the plasma, reaching a relatively constant low
level in an hour or two. This then falls but slowly. From a
study of such curves, coupled with direct analyses of
certain tissues, information can be obtained as to the
relative permeability of the tissues of various animals to
these cations.
From such a study in normal dogs, it appears that in
jected Na24 distributes itself uniformly throughout extra
cellular water within 100 minutes. No appreciable amount
enters the intracellular phase, with the exception of the
erythrocytes. These undergo a slow exchange of sodium
ions with the plasma, requiring about a half-day for 50
percent completion of the process. The rate of this exchange
seems to be proportional to the difference between the
plasma and erythrocyte Na24 concentrations.
After the intravenous injection of K4ZCI into dogs, the
plasma radioactivity falls more rapidly than is the case
with Naz" and reaches a lower plateau concentration in 60
to 100 minutes. From the value of this concentration it can
be calculated that only 4 percent to 4! percent of the
injected K4Z is then present in the extracellular phase. The
remainder (less that excreted) must be present in the intra
cellular phase at a concentration 10 to 12 times that in
the plasma. This represents about a 40 percent exchange of
intracellular K within this time. After this rapid exchange,
there seems to be a secondary slow exchange requiring two
or three days to approach completion. The erythrocyte K
is apparently exchanged in a similar manner.
Intraperitoneal or oral administration of these isotopes
to rats leads to conclusions that are qualitatively the same
but quantitatively different. The distribution of NaZ4
throughout the various tissues conforms to that expected
from the amount of extracellular water in each. There is no
storage of orally-administered Na24 by the liver, as is the
case with K4Z. The rate of entry of K42 into muscle cells and
erythrocytes is apparently much lower than that observed
in dogs, and the initial rapid entry of K4Z seems to be
lacking. At the end of four hours, the exchange of muscle K
seems to be only 4 percent completed. These relatively slow
exchanges are comparable to those observed in rabbits by
other investigators.
Experiments on human subjects lead to the tentative
conclusion that tissue cell and erythrocyte exchange of K
is here also a relatively slow process. Small exchanges
within the first few minutes are noted, and within two
316 hours the intracellular K42 concentration is 3 to 5 times that
in the extracellular phase, representing a 10 to 20 percent
exchange of K. As time goes on, this seems to rise slowly.
The erythrocytes at first behave as though the K42 is evenly
distributed throughout all the water of the blood. Although
human red blood cells contain much more K than those of
the dog, these results are quite similar to those obtained
on the latter.
These results, in conjunction with those of other in
vestigators, make it apparent that the peculiar distribution
of cations between intra-and extracellular fluids cannot be
ascribed to the classical semipermeable membrane. What
ever mechanism is postulated must permit an exchange of
cations between intra-and extracellular fluids.
41. The Distribution of Radioactive Potassium, Sodium
and Chlorine in Rats and Rabbits. WALLACE O. FENN,
University of Rochester, School of Medicine and Dentistry,
Rochester, New York.
The animals were killed at various times after injection
and the tissues were sampled. The samples were dissolved
in concentrated nitric acid. After measuring the radio
activity the same solutions were analyzed chemically for
the element concerned.
The potassium experiments were performed by Dr. T. R.
Noonan and the author with the collaboration of Miss L.
Haege. From the results calculations were made of the
tissue of plasma "activity" (percent of injected counts per
gram) and of tissue or plasma "potassium activity" (per
cent of injected counts per millimol of potassium).
The potassium activity in the plasma rises rapidly to a
maximum and then falls asymptotically to a low level
indicating complete mixing.
The tissues may be classified according to their behavior
into two groups. The first group, consisting of liver, gastro
intestinal tract, kidney and heart, shows a rise and subse
quent fall of potassium activity similar to that of plasma
but with the peak delayed to varying degrees. A result
similar to this would be expected as a result of rapid ex
change of radioactive potassium for normal potassium.
The second group consists of skin, muscle, testes, brain and
red cells. In this group the rate of exchange is so slow that
the potassium merely rises slowly to a maximum value
equal to the final low level reached in the plasma at the time
of complete mixing (4 to 10 hours). The results could also
be explained by a mass movement (without exchange) of
highly active potassium if that movement were greater
into the tissues of the first group than into those of the
second group. There is evidence of a difference of this sort
between liver and muscle. It is impossible from the present
data to distinguish between mass movement and exchange
as factors in this experiment, but both are certainly
involved.
JOURNAL OF APPLIED PHYSICS
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more rapidly than resting muscles, but this is probably due
to an increased circulation because the same acceleration is
found on merely denervating a muscle and because isolated
frog muscles stimulated in Ringer's solution do not show
this effect.
Rat red blood cells in vivo exchange 55 percent of their
K in 10 hours and 79 percent in 18 hours. Human cells
in vitro exchange 12-14 percent in 10 hours. Without
evaluating the thickness and the surface area of the mem
branes a pseudo-diffusion coefficient can be calculated.
Values in min.-' of 0.2 to 0.25 X 10-3 for human, 0.32 to
0.66 X 10-3 for rabbits and 1 X 10-3 for rats were calculated.'
Using rats and rabbits injected with radioactive Na or
CI, Dr. Jeanne Mahery with the cooperation of Dr. Bale
has compared the tissue to plasma ratio of Na and CI
determined by chemical analysis with the same ratios for
Na2' or cras determined by the radioactivity. The time
necessary for the Na2' or Cl3s ratio to reach the correspond
ing ratio for the normal isotopes is taken as a measure of
the rate of penetration. In most tissues penetration of Na24
was complete in 1 hour and nearly complete in 8-15 min.,
but was delayed in brain, testes and femur. Likewise radio
active chloride completely exchanged with normal Cl
within 8-10 min. in most tissues of both rats and rabbits.
In testes both Na2' and Cps penetrate quickly only about
20 percent of the tissue (presumably extracellular space)
while the usual Na space is 30 percent and the usual
chloride space is 45-50 percent.
1 See Dean. Noonan. Haege and Fenn. J. Gen. Physiol.. in press.
42. The Use of Radio-Sodium and Radio-Potassium in
the Study of Adrenal Physiology. EVELYN ANDERSON,
MICHAEL JOSEPH AND HERBERT M. EVANS, Institute of
Experimental Biology and the Division of Medicine, Uni
versityof California, Berkeley and San Francisco, California.
The role of sodium and potassium in the physiological
mechanisms of the adrenal cortex is still obscure, as is also
our understanding of the essential function of this endocrine
gland. Two very important facts on the relation of sodium
and potassium metaholism to adrenal cortical physiology
have been well established in the last few years, namely:
(1) that the removal of the adrenal gland causes a lowering
of the sodium and an increase of the potassium levels in
the blood serum, which is associated with a wastage of
sodium in the urine and a retention of potassium by the
kidney; and (2) that the administration of sodium chloride
to adrenalectomized animals considerably delays the onset
of adrenal insufficiency. The first of these observations has
been extended recently by Harrison and Darrow who have
shown that the selective reabsorption of sodium and po
tassium by the kidney tubule is seriously impaired in the
adrenalectomized animal.
The use of radio-sodium and radio-potassium has greatly
facilitated the investigation of the relation of these two
electrolytes to the function of the adrenal cortex. We have
been able to confirm observations (1) and (2) as stated
above and also to extend these findings. A summary of our
studies shows the following:
VOLUME 12, APRIL, 1941 1. Adrenalectomized rats fed a standard diet and given
tap water to drink show an increased rate of excretion of
administered radio-sodium and a diminished rate of excre
tion of radio-potassium. The rate of excretion of these
"tagged" electrolytes can be correlated with the excretion
of body sodium and potassium. The giving of a 1 percent
sodium chloride solution to adrenalectomized rats instead
of tap water to drink corrects the wastage of sodium and
the retention of potassium so that these animals excrete the
electrolytes in the same proportion as normal animals.
2. Removal of the posterior lobe of the pituitary in
adrenalectomized rats also prevents the wastage of sodium.
3. Rats which have been reared on a low sodium diet
excrete radio-sodium more rapidly than normal rats and
retain radio-potassium in greater amounts than normal.
In this respect they resemble untreated adrenalectomized
rats. Rats reared on a low potassium diet excrete radio
sodium at a normal rate, but retain radio-potassium.
4. In the first 24-hour period after operation, adrenalec
tomized rats show a significant increase in the rate of
excretion of an administered dose of radio-sodium and a
retention of radio-potassium. This early change in electro
lyte excretion is accompanied by changes in carbohydrate
metabolism.
5. Rats will survive and continue to grow for several
months after adrenalectomy without hormone therapy
provided an "optimum" amount of sodium chloride is
given. The animals so treated at first excrete the adminis
tered radio-sodium at the same rate as normal animals,
but later they show sodium retention which is in marked
contrast to the sodium wastage of untreated adrenalecto
mized rats. The excretion rate of radio-potassium is the
same in these animals as in the normals.
6. The administration of adrenal cortical hormone to
normal rats causes a retention of radio-sodium and an
increased excretion of radio-potassium. A given dose of
adrenal cortical hormone causes an increased excretion of
radio-potassium to a more pronounced degree in the
partially depancreatized rat than in the normal animal.
43. The Intake of Radioactive Sodium and Potassium
Chloride and the Testing of Enteric Coatings. K. LARK
HOROVITZ, Department of Physics, Purdue University,
Lafayette, Indiana.
The intake of radioactive NaCl and KCI has been
measured' using the activity measured in the hand as an
indicator. The salts have been administered orally in
aqueous solution or in a soluble capsule to study the intake
from the stomach and by using capsules with enteric
coatings for absorption through the intestines. For com
parison the salts have also been injected and the intake
from aqueous solutions applied to the skin and mucous
membranes has been studied. The absorption in the stomach
detected after two minutes in the hand shows a steady rise,
reaching a constant level in a few hours which is kept for
over thirty hours as already observed by others.
Using two counters simultaneously, one to measure the
activity in the hand as indicator for the appearance of the
salts in the body and one to follow the capsule containing
317
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decide whether the capsule dissolves in the stomach, de
velops a leak, letting the salt slowly escape, or whether it
breaks in the small intestines. In this way it is possible to
locate the capsule on its way through the intestines quite
definitely, to test the efficacy of the enteric coating, and to
observe the difference in behavior when the salt is taken up
from either the stomach or the small intestines. If taken up
from the intestines, the measurements in the hand indicate
a strong initial absorption marked by a temporary rise of
the sodium level in the blood stream which is equalized
again by back diffusion. This temporary rise is similar to
the one observed after injecting the salt, in which case the
back diffusion is indicated by a strong activity of the gastric
juice.
For a quantitative evaluation of the measurements in
the hand these have been compared with the activity of
blood samples taken at different intervals either from the
finger tips or from the vein. It has been found that the
amount of sodium, potassium, and chlorine found in the
blood increases with increasing dosage of the salt taken.
While the rate of intake obtained from the measurements of
the blood samples is similar to the one observed in the hand,
the amount of salt found in the blood indicates a different
mechanism of intake for Na and K. Assuming a total blood
volume of 4 to 5 liters, the total amount o~labeled Na and
CI found in the blood is much larger than one would expect
if all the Na and CI in blood, tissues, bones, and muscles
could be freely exchanged; the K content of the blood on
the other hand is much smaller than to be expected. In
agreement with those observations, the activity measured
in the hand after the intake of K corresponds to a larger
blood equivalent than in the case of Na and the absorption
takes place much more slowly. Most of the K activity in
the hand must be due to the uptake of labeled ions in the
tissues, bones, and skin.
To distinguish between the uptake in the serum and the
blood corpuscles, the blood samples taken from the vein
have been centrifuged and the activity of the separates
determined. The ratio of labeled ions in serum and cells
shows that while over 80 percent of the sodium content of
the red cells can be exchanged, only 10 percent of the
potassium can be replaced. These values have been reached
both for the intake of salts from the stomach and from
injections. With the activities used so far an uptake from
aqueous solutions by the skin and mucous membrane
directly has not been found.2
1 These experiments have been carried out during the last few months
with H. Leng (now A.A.V.W. Research Fellow for 1940-41 at Pnrdue
University).
2 Recent experiments by Johnson and Leng at Purdue University
have shown that a definite intake of Na takes place through .the skin
from ointments with a lanolin base.
44. Tracer Studies with Radioactive Isotopes of the
Metabolism of Calcium and Manganese in the Animal
Organism. DAVID M. GREENBERG, Division of Bio
chemistry, University of California Medical School, Berkeley,
California.
Calcium.- The preparation of labeled calcium salts will
be described. The essential procedure is to scrape off the
318 active portion of the calcium target, free it, from con
taminating radioactive scandium and then by repeated
precipitations as the oxalate and ignition obtain the calcium
as the carbonate from which it is readily converted to any
desired salt.
Measurements of the very soft ,,-radiation of calcium
have been carried out with the Libby screen wall counter
tube. This gives very accurate results, but is time con
suming.
The subject of biological study has been the absorption,
excretion, and distribution of orally administered calcium
by the normal rat. Differences in the metabolic picture
when the chloride, lactate, and gluconate of calcium are
employed will be brought out. More than 90 percent of the
retained calcium is stored in the bone and teeth. This
distribution of the labeled calcium in the different struc
tures of the bone and the teeth will be pointed out.
Manganese.-Radioactive manganese Mn64 of fairly high
specific activity was obtained from iron bombarded in the
cyclotron by separating it from radioactive iron, cobalt,
and other impurities. The radioactivity of the manganese
in the biological material can be suitably measured with a
metal wall counter tube.
The results obtained show that radioactive manganese,
MnM is suitable for "tracer" studies on the metabolism of
manganese.
On a normal diet, manganese is very poorly retained by
the rat. Over 90 percent of a one mg dose was excreted
when administered either by stomach tube or by intra
peritoneal injection. There is a preferential excretion via
the intestines, only a trace is excreted in the urine.
Liver, bone, and muscle take up appreciable quantities
of the absorbed manganese.
The results of a comparison study of the manganese
metabolism of normal chicks and chicks suffering from
perosis will be described.
45. ~iological Investigations with Radioactive Calcium
and Radioactive Strontium. Simultaneous Production of
a Radio-Strontium for Therapeutic Bone Irradiation and
a Radio-Yttrium Suitable for Metallic Radiography.
CHARLES PECHER, William H. Crocker Radiation Labora
tory, University of California, Berkeley, California.
Radioactive Ca46 and Sr8., produced by the bombard
ment of calcium and strontium with 16 million-volt deu
terons of the Berkeley 60-inch cyclotron have been used as
tracers for mineral metabolism studies. The low yield of
Ca46 and the softness of its beta-rays compells the use of
a screen-wall counter as detector. The yield of Sr8> is
high, and its beta-radiation is easily measured with an
electroscope.
When a tracer dose of radio-calcium lactate is injected
intravenously to mice, 45 to 70 percent (average: 58 percent
in 30 mice) of the dose is recovered in the skeleton after 20
hours. When the dose is given orally, 13 to 30 percent is
recovered in the bones. The activity of the soft tissues is
negligible. 33 percent (average of 35 mice) of a tracer dose
of radio-strontium lactate when administered intravenously
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orally is retained in the bones of adult mice 20 hours after
administration. The excretion of the radio-strontium during
the first day is larger than that for radio-calcium, but the
distribution of the activity among the different tissues is
almost the same for Ca* and Sr". Uptake of both radio
calcium and radio-strontium is highest in the trabecular
bone, lowest in the liver and fat. Table I compares the
TABLE 1. Percent of dose per gram wet weight.
SKIN AND
BONE MUSCLE HAIR DIG. TRACT LIVER
Ca" 22 0.33 0.20 0.36 0.12
Sr'" 12 0.17 0.15 0.23 0.07 p32 5.2 1.4 0.75 1.3 2.1
activities of some tissues 24 hours after intravenous ad
ministration of three radioactive agents.
Tracer doses of radio-calcium and radio-strontium, ad
ministered intravenously to mice, are excreted both in the
urine and feces-generally more in the feces.
Uptake in the bones of the chloride, lactate and gluconate
of strontium has been compared when the dose is injected
intravenously and when it is introduced into the stomach.
In a group of 60 mice, the uptake has been found to be
independent of the anion for both ways of administration.
Calcium metabolism during pregnancy.-In mice, a large
fraction (5 to 25 percent) of the radio-calcium (or radio
strontium) previously fixed on the mother's bone migrates
to the foetus during the last days of the pregnancy and to
the milk during the first days of the lactation period.
The specific activity of the calcium in the whole body of the newborn mice is higher (1.1 X 10-3 the specific activity
of the injected solution) than the specific activity of the
mother's bone (0.67 X 10-'), although the activity of the
newborn mice issues from the mother's bone. So it appears
that the last calcium fixed on the mother's bone is the first
to be removed.
When radio-strontium is given intravenously to mothers
during the lactation period, a large fraction of the dose
(20 percent) is recovered in the offspring after two days.
The excretion of radio-strontium in the milk of two cows
intravenously injected with radio-strontium lactate has
been studied by Dr. Erf and the writer. 7.9 and 10.0
percent of the injected dose have been recovered in the milk
during the four days following the injection.
The selective fixation of radio-strontium on the bones,
its ease of production, the suitable energy of its beta-rays
(1.5 X 10' ev), its convenient half-life (55 days), the
innocuousness of small doses of strontium, have suggested
its use as a specific method of irradiation of the skeleton.
(Applicable in multiple myelomas, giant cell tumors,
polycythemia, some metastatic bone tumors, etc.)
The first clinical experiments have been started by John
H. Lawrence and the writer.
Incidentally, there was found as a secondary product in
the preparation of radio-strontium a large amount (13
milligra s radium eq ivalent per 1000 microampere hours
deuteron bombardment) cf long life (100 days) radio
yttrium (y86). It emits a penetrating gamma-radiation
nearly identical to radium gamma-radiation and may be
used instead of radium as a gamma-ray source. It has
produced successful metallic radiography.
* Fellow of the Belgian-American Education Foundation.
Biology III
The Study of Animal Metabolism with Radioactive Tracers
Chairman: DR. J. G. HAMILTON, University of California
65. The Use of Radioactive Tracers in Biological
Investigations. GEORGE HEVESY, Copenhagen.
Read by title.
66. The Phospholipid Activity of the Liver as Measured
with Radioactive Phosphorus. I. PERLMAN AND I. L.
CHAIKOFF, Division of Physiology of the Medical School,
University of California, Berkeley, California.
The problem of fatty livers has received considerable
attention both· experimentally and clinically. Thus far,
however, little success has been attained in arriving at an
explanation for their production or cure. Attempts have
been made to obtain insight into the mechanism of fat
mobilization to and from the liver by analyzing the lipid
constituents of normal and fatty livers. The results of such
investigations have shown that the lipid composition of
VOLUME 12, APRIL, 1941 normal and fatty livers usually differs only in its levels of
triglycerides. Relevant to the present study is the fact that
the total phospholipid content remains relatively constant
when a liver goes through a cycle from the normal to fatty
and back to normal state.
Recent studies from this laboratory have shown that
under the conditions investigated the level of liver fat
depends upon the rate of phospholipid turnover. Since tae
total quantity of phospholipid remains relatively static
this could only be shown by labeliI;lg the newly-formed
phospholipid molecules, in this case, with radioactive
phosphorus. It was found in general that the ailministration
of a substance which prevents or cures fatty livers in rats
results in an accelerated phospholipid turnover. Cholesterol
feeding, on the other hand, which accentuates the produc
tion of fatty livers, depresses the phospholipid turnover
in the liver.
319
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experiments:
Choline.-Rats maintained for several days on a high
fat and low protein diet received radioactive Na2HPO. as
a labeling agent and the effect of choline administration
upon the turnover of phospholipid was determined at
several intervals. Livers removed 1 hour after choline
administration had the same labeled phospholipid content
as those from rats which received radioactive phosphorus
but no choline.' At the 3-and 6-hour intervals the phos
pholipid activity of choline-treated rats exceeds that of the
controls by 30---40 percent but by 12 hours this effect of a
single administration of choline had largely disappeared.
It was also observed that a graded increase in phospholipid
turnover results from successively increasing the amount of
choline administered.
Betaine.-Experiments of the same type were carried out
with the betaine of glycine. Qualitatively the results were
similar to those of choline but whereas 10 mg of choline
chloride produced a definite acceleration of phospholipid
turnover, over 50 mg of betaine chloride were necessary to
produce a comparable effect.2 This is in keeping with the
relative lipotropic activities of choline and betaine.
Amino acids.-In keeping with its lipotropic action,
methionine produced an elevation in phospholipid turnover
of the liver.3 Of all the other amino acids investigated only
cystine and cysteine behaved similarly. Glycine, alanine,
tyrosine, glutamic acid, asparagine, proline, serine, as well
as creatine, sarcosine, taurin and di-,B-hydroxyethyl sulfox
ide had no effect.4
eholesterol.-When a few hundred mg of cholesterol were
ingested along with butter over a 30-hour period, the level
of newly-formed phospholipid in the liver was depressed.6
This may be a factor in the production of fatty livers by
cholesterol. Choline administration to cholesterol-treated
rats resulted in a marked increase in the phospholipid
turnover.
Summary.-With the aid of radioactive phosphorus it
has been found possible to measure the phospholipid ac
tivity of the liver under a variety of experimental condi
tions. A theory is presented which indicates that one of the
factors involved in the fat balance of the liver is the
phospholipid turnover. If an increased phospholipid turn
over is induced (other factors remaining constant) the lipid
content of a fatty liver is reduced.
11. Perlman and I. L. Chaikoff. J. BioI. Chern. 127. 211 (1939).
• 1. Perlman and 1. L. Chaikoff. J. Bio\' Chern. 130. 593 (1939).
3 1. Perlman. N. Stillman and 1. L. Chaikoff. J. BioI. Chern. 133. 651
(1940).
• 1. Perlman. N. Stillman and 1. L. Chaikoff. J. Bioi. Chern. (in
press).
• I. Perlman and 1. L. Chaikoff. J. BioI. Chern. 128. 735 (1939).
67. Phospholipid Metabolism Studies Using Radioactive
Phosphorus. FRANCES L. HAVEN, Department of Bio
chemistry and Pharmacology, School of Medicine and Den
tistry, The University of Rochester, Rochester, New York; and
the National Cancer Institute of the United States Public
Health Service.
The two biological tracers which have been the most
widely used in studies of phospholipid metabolism are
elaidic acid and radioactive phosphorus. Since elaidic acid
320 is a solid unsaturated fatty acid while most solid fatty
acids are saturated, it can be traced among the fatty acids
of the phospholipids and in this way serves as a marker. By
feeding elaidin, Sinclair found that the rate of turnover
of elaidic acid was rapid in the liver phospholipids and slow
in the muscle phospholipids. Similar results on the phos
pholipids of these tissues were obtained by Chaikoff and by
Haven using radioactive phosphorus.
Phospholipids are essential constituents of tumor cells,
being more abundant in malignant than in benign tumors.
By feeding elaidin to rats bearing Carcinosarcoma 256
Haven found that the tumor phospholipids resembled
muscle rather than liver phospholipids in their rate of
turnover. However, when radioactive phosphorus was used
to study the phospholipid metabolism of this tumor, the
rate of turnover was found to resemble the rapid rate of
liver phospholipid rather than the slow rate of muscle
phospholipid. Sinclair has recently pointed out that kidney
phospholipid shows a similar difference in rate of turnover
as measured by him using elaidic acid (slow turnover), and
as measured by Artom and co-workers and by Chaikoff
and co-worke~s using radioactive phosphorus (rapid turn
over). These divergent results obtained by the use of the
two indicators seem to show that phospholipids may have
at least two different functions, one concerned with fatty
acid, the other with phosphoric acid metabolism.
Radioactive phosphorus has also been used to measure
the rate of turnover of the individual phospholipids,
lecithin and cephalin, of Carcinosarcoma 256. Rats bearing
this tumor were killed from four hours to twenty days after
receiving by stomach tube a solution of disodium hydrogen
phosphate containing radioactive phosphorus. Tumor phos
pholipids were isolated and the lecithin and cephalin frac
tions separated by means of absolute alcohol. The degree
of separation was measured by choline determinations on
the total mixed phospholipid and on the lecithin fractions.
The radioactivity of the lecithin fraction expressed as
percentage of dose per gram of phospholipid was greater
even at four hours than that of the cephalin fraction. While
the activity of each fraction increased with time, that
of the lecithin fraction did so at a faster rate than that of
the cephalin fraction until the peak in activity was reached
at 24-30 hours. After this the activity of the lecithin frac
tion decreased while that of the cephalin fraction continued
to increase, reaching its peak at 40 hours. The activity of
each fraction then decreased at approximately the same
rate. The faster rate of turnover of the lecithin fraction of
the tumor constitutes a further resemblance between the
phospholipids of this tumor and those of liver. Moreover,
it may mean that cephalin is formed from lecithin.
68. Radio-Phosphorus Studies in the Chemistry of
Anaerobic Muscular Contraction. JACOB SACKS, Laboratory
of Pharmacology, University of Michigan, Ann Arbor,
Michigan.
In contraction of striated muscle under anaerobic condi
tions, the principal chemical reaction is the formation of
lactic acid from glycogen. There is associated with this a
decrease in the amount of phosphocreatine; part of the
phosphate thus lost is found as inorganic phosphate, and
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in the quantity of adenosine triphosphate.
Studies of the enzyme systems present in cell-free muscle
extracts have resulted in an interpretation of the chemistry
of anaerobic contraction which considers that the phosphate
changes are associated with the formation of lactic acid.
According to this formulation, generally known as the
Embden-Meyerhof schema, lactic acid is formed by a
complex series of reactions which involves interchanges of
phosphate groups between all these compounds and various
others which appear as intermediates.
From studies of the reactions taking place in the con
tracting muscles themselves, a different formulation has
been developed. In this it is postulated that the formation
of lactic acid is independent of reactions involving the
phosphorus compounds. This formulation regards the
hydrolysis of phosphocreatine as serving primarily as a
source of alkali to neutralize the lactic acid formed, and
considers that the formation of hexosemonophosphate is a
supplementary reaction in contraction, rather than an
intermediate one in the formation of lactic acid.
Radio-phosphorus offers the possibility of determining
whether the formation of lactic acid does involve the
postulated interchanges. If a differential distribution of
radio-phosphorus among the four compounds of muscle can
be obtained in the animal body, the changes in this dis
tribution which accompany the formation of lactic acid in
contraction will establish whether the interchanges do take
place.
Using cats under amy tal anesthesia, it was found
that radio-phosphorus, injected as Na2HPO., underwent
such a differential distribution. The inorganic phosphate of
the resting muscle had ten times the relative radioactivity
of the phosphocreatine P. The relative radioactivities of
the adenosine triphosphate and hexosemonophosphate P
were even lower than that of the phosphocreatine P.
In companion muscles stimulated so as to produce large
amounts of lactic acid, the differential distribution of the
radio-phosphorus was retained. The observed distribution
was that which would be anticipated if the only reactions
involving phosphate compounds which took place were the
hydrolysis of some phosphocreatine and the conversion of
an additional amount to hexosemonophosphate. There
was no evidence of participation of phosphocreatine,
adenosine triphosphate or hexosemonophosphate in the
formation of lactic acid. From this it is concluded that the Embden-Meyerhof
schema does not represent the mechanism of lactic acid
formation used by the contracting muscle, and that the
mechanism of lactic acid formation used by the muscle is
radically different from that which has been described in
cell-free extracts.
The author is indebted to the Department of Physics of
the University of Michigan for the supply of radio
phosphorus used in these experiments.
69. Studies on Permeability of Tissue Cells to Phos
phorus. AUSTIN M. BRUES, ELIZABETH B. JACKSON AND
WALDO E. COHN, Collis P. Huntington Memorial Hospital
of Harvard University, Boston, Massachusetts.
A technique has been developed whereby the uptake of
radioactive substances by cultures of cells can be measured.
The cells are grown on a coverslip 0.15 mm in thickness
attached to one side of a roller bottle. By placing the bottle
in a suitable position, the radioactivity in the cells, inde
pendently of that in the perfusing medium, can be meas
ured without removing them from their environment.
With this method, it is possible to measure the permea
bility to and concentration of substances in isolated groups
of cells. The effects on permeability of altering the con
stituents of the medium and other environmental factors
can thus be demonstrated. In the course of experiments,
parallel observations are made on the morphology and
behavior of the cells by direct high-power microscope ob
servations, and on chemical changes in the media brought
about by cell metabolism.
We have studied by this technique some of the conditions
attending the uptake of inorganic and some organic radio
phosphate compounds. Certain embryonic and adult tissue
cells and tumor cells accumulate radio-phosphorus to a
higher concentration than that in the extracellular medium.
Growing cells take it up in significantly higher amounts
than those which are surviving but not growing. The rate
of uptake is most rapid in the first few hours. Cultures
allowed to remain in the same medium until cell death
occurs then release radio-phosphorus into the surrounding
fluid. In this way, the behavior of cells towards radio
phosphorus can be used as an indicator of their viability.
Various effects of altering the constituents of the media,
of growth inhibitors, and of specific enzyme poisons, on
transfer of phosphate are being studied.
Biology IV
Biochemical Studies with Stable and Radioactive Isotopes
Chairman: DR. S. L. WARREN, University of Rochester Medical School
73. Nonphotochemical Reduction of CO2 by Biological
Systems. S. RUBEN AND M. D. KAMEN, Department of
Chemistry and Radiation Laboratory, University of Cali
fornia, Berkeley, California.
Experiments with short-lived carbon (CIl) have shown
a number of heterotrophic systems assimilate small
VOLUME 12, APRIL, 1941 amounts of CO,l-4 lending support to the view that CO2
reduction is not exclusive to photosynthetic and chemo
synthetic autotrophic organisms.5 It seems reasonable to
suppose the formation of reduced radio-carbon from
labeled CO2 is not due to simple interchange but rather
that CO2 is used as a specific oxidizing agent in one or
321
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information concerning the manner in which the CO2 is
utilized, an investigation of the metabolism of varied types
of organisms using labeled carbon as a tracer has been
inaugurated.
In addition to the heterotrophic organisms in which a
net absorption or net evolution of CO2 occurs during
respiration (yeast, rat-liver, B. coli, ground plant roots,
P. pentosaceum, clostridium Acidi-Urici), some autotrophic
organisms which show a net absorption of CO2 have been
studied (M. omelianski and Methanosarcina methanica).
A dark pick-up of CO2 has also been observed with photo
synthetic organisms. 6
In studies with yeast! attempts to identify chemically
the radioactive molecules resulted negatively. Most of the
active carbon was extractable with boiling dilute acid.
No acitivity was found in pyruvate. While the active
material could be precipitated with Ba++, very little
could be decarboxylated. The chemical nature of the
active molecules in yeast is apparently quite different from
that observed in the dark pick-up by a photosynthetic
organism such as Chlorella. The reversibility of the yeast
CO2 assimilation is being investigated.
The methane bacteria2 have been found to reduce CO2
to CH. as a result of the fermentation of methanol. An
appreciable portion ("-'10 percent) of the radioactivity
appeared in nonvolatile cell ma erial. The propionic
acid bacteria2 w ich utilize CO2 during fermentation of
glycerol transformed 80 percent of the labeled carbon
assimilated to propionic and succinic acids, the propionic
acid being three times as active' as the succinic. The re
mainder ("-'20 percent) of the C*02 was incorporated in
cell material. Glycerol enormously increased the CO2 up
take as well as the ratio of C* in the two acids. A mecha
nism based on these experiments will be discussed. The
uric acid bacteria' ferment uric acid, xanthine and hy
poxanthine to acetic acid, ammonia and CO2 anaerobically.
Evidence was obtained for the production of active acetic
acid. C* was found in both the methyl and carboxyl
groups. The active volatile acid produced from uric acid
appeared to be almost entirely acetic acid. The hypothesis
of CO2 as an oxidizing agent in fermentation seems to be
born~ out in these experiments.
The researches with C*02 are being continued, and it is
expected much useful information bearing on the mecha
nism of CO2 reduction will be obtained.
1 Ruben and Kamen. Proc. Nat. Acad. Sci. 26. 418 (1940).
2 Carson and Ruben. Proc. Nat. Acad. Sci. 26. 422 (1940).
3 Barker. Ruben and Kamen. Proc. Nat. Acad. Sci. 26, 426 (1940).
• Barker, Ruben and Beck. Proc. Nat. Acad. Sci., August. 1940.
5 Van Niel. Ann. Rev. Biochem. 6. 606 (1937); Gaffron. ibid. 7. 986
(1939).
• Ruben. Hassid and Kamen. J. Am. Chern. Soc. 61. 661 (1939).
74. Biological Studies with Radioactive Carbon. A.
BAIRD HASTINGS AND G. B. KISTIAKOWSKY, Harvard
University, Cambridge, Massachusetts.
The fate of carbon compounds in the body has long
engaged the attention of biochemists. Prominent in these
numerous studies have been the attempts to elucidate the
steps involved in the metabolism of carbohydrate. Al
though many steps concerned in the breakdown of carbo-
322 hydrate are now quite well understood, the steps involved
in the synthesis of glycogen from simple 3-carbon com
pounds are still obscure.
It has been demonstrated (confirming the work of Cori
and Cori) that within 2 to 3 hours after feeding sodium
lactate to a starved rat, there is a marked increase of
liver glycogen, corresponding in amount to about 30 per
cent of the administered lactate. However, the exact origin
of the carbon of the newly formed glycogen cannot be
established by chemical means. The possible sources of the
glycogen carbon include: (a) the 3 carbons of the original
lactate molecule; (b) the 2-carbon residue left after de
carboxylation and oxidation of the lactate molecule; (e)
other glycogen precursors already present or formed in the
organism; (d) carbon dioxide produced by metabolic
activity.
With radioactive carbon (CIf), experiments have been
performed in an effort to determine from which of the above
carbon source, or sources, the liver glycogen originates.
Lactic acid containing radioactive carbon in the carboxyl
position was prepared by Dr. R. D. Cramer by a rapid
synthesis requiring only it to 2 hours (see paper by Dr.
A. K. Solomon). This lactic acid, in the form of sodium
lactate, was administered orally to rats; and, after a lapse
of 2t hours, the liver glycogen was isolated. The expired
CO2 was collected over the 2t-hour period and was found
to contain about 15 percent of the radioactive carbon
administered. The biochemical procedures were carried out
by Dr. F. W. Klemperer and Dr. B. Vennesland. The radio
activity of the glycogen represented only a small fraction
(1.6 percent) of the radioactivity administered, whereas
the amount of glycogen formed corresponded to 30 per
cent of the lactate administered. This result precludes the
possibility that the carbon of the glycogen originated
directly and solely from the 3 carbons of the administered
lactate molecules. It is also highly probable that the
glycogen was not derived from any single category of the
four carbon sources enumerated above, but rather had its
origin in more than one source.
75. The Use of Organic Compounds Containing Stable
Isotopes for the Study of Intermediary Metabolism. R.
SCHOENHEIMER, College of Physicians and Surgeons,
Columbia University, New York, New York.
Work on the biological fate of organic compounds con
taining C, H, 0 and N is restricted to the use of stable
isotopes, as with the exception of 0" no radioactive iso·
topes with a sufficiently long lifetime is available for such
experimentation at present.
The experiments are generally carried out in 4 steps:
(1) The compound to be investigated is prepared in the
laboratory in such a way that one or more (stably bound)
atoms are present in the form of the heavy isotopes. The
synthetic methods employed are presented in another
paper.
(2) A small amount of the compound is added for short
periods to the ordinary diet of normal animals. The value
of the compounds has restricted the work to small animals
such as mice or rats.
JOURNAL OF APPLIED PHYSICS
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excreta and, after killing the animals, from their tissues.
(4) The isotope concentration of the isolated samples is
determined, Nl. by mass spectrometry and D by density
or mass spectrometry. The methods will not be discussed.
If after administration of an isotopic compound A, an
isolated compound B contains the isotopic tracer, this is
an indication that A was either converted into B or A has
been in chemical interaction with B.
The isotopes have furnished, for the first time, a tool for
the investigation of occurrence and rate of chemical reac
tions going on among the tissue constituents of normal
adult animals, i.e., of living organisms that keep constant
the total amount and composition of their components.
Almost all compounds investigated so far, even the large
molecules, fats and proteins, were found to be involved in
rapid and complex chemical reactions.
By adding small amounts of various isotopic (D)
physiological fatty acids to the normal diet of animals it
was found. that there occurs a continuous interconversion
of one type of physiological fatty acids into others. Some
are dehydrogenated while unsaturated ones are hydrogen
ated; the chain of some acids is shortened by 2 or 4 carbon
atoms and the chain of others is elongated by the same
number of carbon atoms. Aliphatic alcohols (cetyl
alcohol) seem to be intermediates in these automatic
reactions. In addition to the interconversion, there was
observed a continuous synthesis from small molecular
units simultaneous with a destruction of an equivalent
amount of others. The newly formed fatty acids are intro
duced into fats; ester linkages open and close continuously.
All these rapid reactions are so balanced that they do not
lead to ultimate changes of total amount or composition
of the animal fats. The highly unsaturated fatty acids,
linoleic and linolenic acids. known to be indispensable food
constituents, are exceptions; they are not involved in these
processes.
Even more complex automatic reactions were found to
occur among the amino acids of the proteins of living
animals. The addition of small amounts of isotopic amino
acids (N16) to the normal diet, results in the presence of
various isotopic amino adds in protein linkage. The result
reveals the occurrence of continuous opening and closing of
peptide linkages, deamination at alpha-position of tem-porarily liberated amino acids and simultaneous amination
of nitrogen free substances, and the replacement of the
amidine group in the arginine of the proteins by nitrogen
from amino acids. Besides this continuous transfer of
nitrogen among the constituent of proteins. the carbon
chain of some amino acids is converted into that of others:
ornithine is continuously coriverted into arginine, into
proline. and into glutamic acid and phenyl-alanine into
tyrosine. The amino acids newly formed by the various
reactions replace the same type of amino acids in the
proteins. Almost all proteins of the animal are involved in
these extensive rearrangements; even the specific antibody
of the serum of immunized animals. Only few compounds
e.g. the amino acid lysine. do not take part in these proc
esses. All these rapid reactions like those observed with
fatty acids are so balanced that the total amount and
structure of proteins is ultimately unchanged.
The nitrogen excreted by the animals is not that of the
food. but a sample of the mixture originating from the
extensive chemical interaction of the dietary amino acid
nitrogen with the relatively large amounts of reactive
nitrogen in the organ proteins.
The application of N15 and deuterium to normal animals
in different laboratories has established the source of all
parts of the creatine molecule. The glycine part is derived
from glycine of the proteins and the amidine group is
transferred from arginine of the proteins. Du Vigneaud and
collaborators have synthesized methionine with an
isotopic (deuterium) methyl group. Its administration
resulted in the presence of isotopic creatine and isotopic
choline. The methyl groups of both compounds are thus
derived from methionine.
The experiments with the isotopic fats and proteins
seem to show that all chemical reactions that the animal
can perform are carried out continuously at a rapid rate.
The opening of peptide. ester. and other linkages of the
large molecules liberates active groupings which take part
in metabolic cycles. Additional evidence for this theory is
the finding that isotopic ammonia given to birds results
not only in the formation of isotopic uric acid, which is
excreted, but also of isotopic purines (adenine and guanine)
which are introduced into nucleo-proteins. The purines of
the nucleo-proteins thus seem to be involved in the process
of uric acid formation.
Biology V
The Study of Animal Metabolism and Radioactive Tracers
Chairman: DR. D. W. BRONK, Cornell University Medical School
82. The Use of Radioactive Sulfur, S35, for Metabolic
Studies. HAROLD TARVER AND CARL L. A. SCHMIDT.
Division of Biochemistry. University of California Medical
School, Berkeley. California.
Next to nitrogen, the element sulfur is most commonly
used as an index to protein metabolism. This is due to the
VOLUME 12, ApRIL, 1941 fact that most proteins contain one or more of the sulfur
containing amino acids: cystine. methionine. and djenkolic
acid. Many biologically important compounds contain
sulfur. The fate of these compounds in the animal body is
often determined by following the transformation and the
form in which the sulfur appears in the excretory products.
323
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particularly well adapted for studies dealing with sulfur
metaboiism. Thus, when methionine containing this isotope
was fed to rats it was possible to isolate cystine containing
S" from the hair and tissues of the experimental animals,
indicating the transformation of methionine to cystine.
While the mechanism of this reaction is still not wholly
clear, a tentative hypothesis is advanced to account for the
facts.
Experiments of the above type often necessitate a new
technique for the synthesis of a particular sulfur-containing
compound. A simplified technique for the synthesis of
methionine is presented.
The rate of the appearance of SM in the proteins of egg
white was determined by feeding methionine containing
radioactive sulfur to hens. S35 was first found in the egg
white on the second day and reached its maximum value
on the fourth day.
Preliminary experiments on the appearance of radio
active sulfur in p-bromophenylmercapturic acid, when
bromobenzene and 535 containing methionine were fed, are
also reported.
The experiments cited above serVe to indicate that
radioactive sulfur is a particularly useful tool in studies
dealing with the fate of sulfur-containing compounds in the
animal body. It will probably be especially usefui in the
determination of rates of certain reactions that occur in
living matter.
83. The Fate of Inorganic Arsenic in Certain Animals
and in Man. F. T. HUNTER, Massachusetts General Hospi
tal, AND A. F. KIP, Massachusetts Institute of Technology,
Cambridge, Massachusetts.
Subcutaneous injections of radioactive potassi um arsenite
were given to 37 albino rats, 2 guinea pigs and 2 rabbits.
The daily dose per kilo of body weight in all animals was
about the same order of magnitude (minimum 0.3; maxi
mum 1.6 mg). After a series of daily injections, usually four
in number, the animals were killed at varying time inter
vals. During life, daily blood arsenic determinations Were
done and after death the arsenic content of the liver,
kidneys, spleen, and in a few instances the brain, were
made.
Rats.-The highest concentration 'of arsenic was found
in the blood, the measurable amount being confined to the
red corpuscles. I t appeared to be attached to the hemoglobin
molecule and on fractionation the globin portion yielded
twice as much as the heme fraction. No arsenic was found in
association with the stroma of the cell. In all cases the
maximal concentration in the blood occurred 24 to 48
hours after the last injection, and at this time the total
arsenic in the blood accounted for 50 percent to 60 percent
of the total amount injected. The spleen showed the
highest, the kidney the lowest concentration. Regardless of
the daily dose, the concentration in these organs was
maximal 24 to 48 hours after the last injection. Two
animals previously given considerable amounts of ordinary
arsenic showed somewhat higher blood levels of radio
arsenic than controls. Splenectomy performed prior. to
324 injection did not appreciably alter the distribution of the
metal.
Because our animals were all infected with bartonella
muris and since this organism is localized within the red
cell and is affected by certain arsenicals, some of the
experiments were repeated on bartonella-free animals.
This group of animals showed somewhat higher concen
trations of arsenic in the liver and somewhat lower
concentrations in the spleen, but the kidney concentrations
were a great deal higher than in infected animals. The
amount of arsenic excreted daily by these animals, as
measured on mixed samples of urine and stool, showed a
constant relationship to the blood concentration while
arsenic was being given, but when arsenic was stopped, the
excretion dropped rapidly to zero.
Guinea pigs and rabbits.- Two specimens of each type
were studied. In all animals the blood arsenic was migli
gible. In contrast to rats, the liver arsenic of the guinea pigs
was considerably greater than that of the spleen. The
figures on the organs of rabbits have little significance since
the livers of both animals showed heavy infestation with
coccidia.
Studies on humans
Normal humans.- Two normal humans received 1.5 mg
per day for four days. No arsenic could be demonstrated in
the blood. Of the daily excretion via kidney and intestinal
tract, 99 percent was excreted in the urine and only 1
percent in the stools. In both cases, 24 hours after the first
dose, 50 percent of the amount injected had been excreted.
This percentage excretion of the accumulated dose re
mained approximately constant until 24 hours after the
last injection, when excretion dropped precipitously to less
than 2 percent.
Leukemic humans.-One case of untreated chronic
myeloid leukemia and one case of untreated lymphoblastic
leukemia were studied. No arsenic could be measured in the
blood. Excretion took place almost entirely via the
kidneys, but 24 hours after the first injection, only 20
percent of the injected dose was recovered in the urine. As
the experiment continued, the percentage excreted of the
accumulated dose rose gradually to about 40 percent.
Twenty-four hours after the last injection, the excretion via
the kidneys began to fall and fell gradually, over three
days, to about 2 percent of the total injected. The case of
lymphoblastic leukemia came to autopsy and complete
determinations of the arsenic content of all the organs were
made.
84. Metabolism of Arsenic Compounds. OCTAVIA DU
PONT, IRVING ARIEL AND STAFFORD L. WARREN, Strong
Memcrial Hospital, The University of Rochester, Rochester,
New York.
Small volumes of solutions containing small subtoxic
amounts of radioactive arsenic in the form of pentavalent
arsenate were injected into the rabbits' ear vein and the
animals sacrificed at various intervals from 5 minutes to
168 hours after injection. Radioactive arsenic content was
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25 rabbits by the usual Bale technique.
The expected widespread distribution and prompt
excretion in the urine occurred quickly. After the first
hour the blood concentration slowly fell to almost disappear
by the 168th hour. The concentration in the liver, lung,
muscle, bone, and tumor rose to a peak rather quickly by
the third hour and fell by the 12th hour. Almost 50 percent
of the total injected may be excreted in the urine by the
12th hour. For the liver and kidney where the concentration
rises to the highest levels per gram of tissue, the critical
period from the single dose apparently begins at the third
hour, and is much less hazardous by the 12th hour.
Storage in muscle, bone, tumor, and lung also seems to
parallel the changes in concentration although at a lower
level. There is a considerable amount of variation from
animal to animal but the relative values are comparable.
Concentrations in various glands and other organs are
low and in some cases (brain) surprisingly so. The high
values in the tumor are apparently not directly related to
its blood content.
This work is the basis for further studies with complex
arsenical compounds.
85. The Course of Vitamin BI (Thiamin) Metabolism in
Man as Indicated by the Use of Radioactive Sulfur.
HENRY BORSOOK, JOHN B. HATCHER AND DON M. YOST,
Gates and Crellin Laboratories of Chemistry, California
Institute of Technology, Pasadena, California.
Exp2rimental methods.-For the quantitative measure
ment of the low activity of samples of radio-sulfur, which
emits beta-particles with the low energy of (0.107 Mev),
the coincidence method was used. The two sulfide-coated
copper Geiger counter tubes were enclosed in a large,
partially evacuated bell jar and the samples were carried
to position in front of the slots in the counter tubes by an
externally operated chain belt arrangement. The amplifiers,
utilizing the standard Rossi coincidence circuit, had time
constants of 3 X 10-4 second and single counts of the two
counter tubes as well as the coincidence counts were
scaled by thyratron type scales-of-eight and recorded on
Cenco recorders. Many of the weaker samples were
measured over a period of days, the background and sample
measurement being alternated for short periods. The
activity of the sample and the satistical error of the
measurement were calculated from the total number of
counts; a run was discarded unless the short period counts
of sample or background agreed to within their probable
errors.
The sulfur from the original material was precipitated as
barium sulfate, converted successively to barium sulfide,
hydrogen sulfide, and finally to elementary sulfur. The final
samples for measurement being made from the elementary
sulfur made into films of known area and "infinitely thick"
to the weak radiation (greater than 15 mg/sq. em).
Depending upon the sample the over-all absolute errors of
measurement of quantity of radio-sulfur varied from 1.2 to
30 percent.
VOLUME 12, APRIL, 1941 Results.- Thiamin synthesized from radio-sulfur was
injected intramuscularly in two series of experiments, using
a human subject on a normal and on BI-free diet. Determi
nations of the free (unphosphorlyated) BI in the urine were
made by the thiochrome method, and the radioactive sulfur
of the feces and of the inorganic sulfur, ethereal sulfur, and
neutral sulfur compounds in the urine were determined.
Rapid destruction of the injected thiamin was indicated
in both experiments by the appearance of the radio-sulfur
in the inorganic fraction of the urine, in amounts increasing
to about 15 percent of that injected daily. No radio-sulfur
was found in the ethereal fraction.
In the neutral sulfur fraction of the urine the excreted
radio-sulfur during the period of injections was less than
that corresponding to the free BI found, indicating the
rapid interaction of the injected material with that already
present in the tissues, and the displacement of pre-existing
thiamin. After 36 days of the BI-free diet the injection of 8
mg of radio-BI over a period of three days resulted in the
excretion of 0.8 mg of pre-existing thiamin. On discontinuing
the injections the destruction of BI was again indicated by
the appearance of quantities of radio-sulfur greater than
that corresponding to the free BI.
On the normal diet a total of 61 percent of the injected
thiamin was recovered from the urine and 11 percent from
the feces over the period of the experiments. Of the urinary
radio-sulfur recovered, 25 percent represented destroyed
thiamin appearing as inorganic sulfate and 18 percent
destroyed thiamin appearing with the neutral sulfur
compounds.
86. The Use of Radioactive Elements in Insect Physi
ology. RODERICK CRAIG, Division of Entomology and
Parasitology, University of California, Berkeley, California.
In the study of insect physiology we are not only inter
ested in normal physiology but even more in derangements
of the normal produced by toxic materials, since man's
chief interest in the insect where toxins are used is to
destroy it. Our fear of insects is more than justified when
one considers that insects are responsible for malaria, which
causes more loss than any other disease, and several other
important human and ani~al diseases. No less important
is the agricultural damage caused not only by the feeding of
insects but by their transmission of plant virus diseases. A
knowledge of insect physiology is essential in understanding
the role of the insect as a vector of animal and plant disease
and equally essential in understanding the mode of action
of poisons used to kill the insect. The insect is so small that
in most cases the presence of a toxic material cannot be
determined by ordinary analytical methods. Since public
health hazards have necessitated the limitation of insecticide
residues on foods, new insecticides have been sought, many
of them organic compounds. The increasing importance of
organic insecticides will require more study of toxicologic
action which can often be carried out by use of tracer
elements.
Many problems in insect physiology are unsolved today
because no adequate technique has existed. Such general
problems as absorption, excretion, distribution of substances
325
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procedures delicate enough to determine fractions of a
microgram of material.
The technique used with tracer elements is the same as
that in larger animals. The radioactive element is either fed
or injected parenterally. If the distribution of the material
is the principal object, the insect is sectioned with a
freezing microtome and radio-autographs obtained. If
quantitative studies are desired, the portions of the insect
are ashed and the activity determined in the usual way
with either an electroscope or Geiger counter.
In 1935 M. A. Hamiltonl used polonium to show the
amount of material removed from a plant by a feeding
aphid and also the amount of the ingested material
returned to the plant during the next feeding period which
was of the order of 0.1 mm3• This sort of work might be
extended with profit to a study of insect vectors of human
disease. Patton2 in 1939 used radioactive sodium to show
the path of ex'Creted material in the yellow meal worm. In
this case the volume of fluid being studied is about 1 mm3•
At the present time the role of phosphorus in metabolism, the rate of circulation of the insect blood and the rate of
absorption of simple substances are being studied. Since we
know that phosphorus is present in the blood of insects in
amounts of 5 to 20 times that found in mammals and since
during the developmental period of most insects large
quantities of fat are stored, one would expect the role of
phosphorus to be very important and easily studied.
Preliminary studies by means of radio-autographs of the
tissue of insects fed on radioactive phosphorus as phosphate
have shown that the phosphorus is largely concentrated in
the actively metabolizing cells. The rate of circulation of
the blood cannot be directly studied because of the open
circulatory system, but the time required to give a uniform
distribution of a substance in the blood can be estimated.
Much work will be required to determine the normal limits
and factors affecting rates of distribution. The absorption
of phosphorus and sodium from several regions of the
alimentary tract of insects is being studied by the same
technique as used by Patton in his work on excretion.
1 M. A. Hamilton. Ann. App. Bioi. 22, 243-258 (1935).
'Patton, J. Exp. Zoo\. 81, 437-457 (1939).
Biology VI
Studies of Plant Metabolism with Radioactive Isotopes
Chairman: DR. D, R. GODDARD, University of Rochester, Rochester, New York
87. Studies in Photosynthesis with Radio-Carbon, M.
D. KAMEN AND S. RUBEN, Radiation Laboratory and
Department of Chemistry, University of California, Berkeley,
California.
The short-lived radioactive carbon, Cll (half-life=21
minutes), has been used to study the reduction of C*02
by green plants. 1-. The bulk of the work has been carried
out with the unicellular green alga, Chlorella.
Chlorella, as well as higher plants (sunflower and barley)
assimilates 2 small quantities of CO2 in the dark. The dark
pick-up exhibits the same sensitivity to various inhibitors
(HCN, phenyl-urethane, ultraviolet light) as does normal
photosynthesis and is not associated with the respiratory
processes. It is reversible and independent of chlorophyll
concentration.
Simultaneous measurements on the rate of CO2 reduction
in the light by manometric methods and the radioactive
technique give identical results within the experimental
error. Hence, exchange reactions can account for very
little of the CO2 reduced in the light,
Chemical tests on the water soluble material formed in
the light and dark indicate the presence of at least one
alcoholic hydroxyl and one radioactive carboxyl group in
the active molecules. Attempts to identify the active
compound as one of a large number of organic substances
known to exist in plants (i.e., sugars, aldehydes, ketones,
proteins, etc.) were unsuccessful. In particular, the
presence of such intermediates as formaldehyde or low
molecular weight organic acids seems to be excluded.
326 The major part, if not all, of the C*02 taken up in the
dark was found in carboxyl. A smaller but appreciable
fraction of the light reduction products was in -COOH
groups. From measurements of the diffusion constant and
sedimentation velocity, the molecular weight of both light
and dark reduction products is in the close neighborhood
of 1000.
While no radioactive reducing sugars are formed in
Chlorella even after 100 minutes of exposure to C*02, about
20 percent of the water soluble activity from the higher
plants can be recovered in this form after exposures of
an hour.
The experiments performed with radioactive carbon
suggest a tentative mechanism for photosynthesis in which
the first step in CO2 reduction is a reversible non photo
chemical process with the formation of carboxyl, viz.:
R H+C0 2pRCOOH
Here, R is a large molecule-in all probability a part of
an aggregate of very high molecular weight. Several
analogous reactions are known in organic chemistry. The
light reaction can be written:
R COOH+H20~R CH20H+0 2•
The energetics and advantages of this approach will be
discussed.
1 Ruben, HasSid and Kamen, J. Am. Chern. Soc. 61, 661 (1939).
, Ruben, Kamen, Hassid and DeVault, &ience 90, 570 (1939).
'Ruben, Kamen, Hassid, J. Am .. Chern. Soc., in press.
• Ruben, Kamen, Perry, J. Am. Chern. Soc., in press.
'Ruben and Kamen, J. Am. Chern. Soc., in press.
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gations of Mineral Movement in Plants. F. G. GUSTAFSON,
Department of Botany, University of Michigan, Ann Arbor,
Michigan.
For many years plant physiologists have been investi
gating the path of the upward movement of minerals in
plants. In most of these experiments the different tissues
have been analyzed for the particular mineral under
investigation, and this is not easily done.
With the preparation of artificial radioactive chemicals
by means of the cyclotron, a new method 6f approach to
this problem was made available. The irradiated elements
could be used as tracers, and, as small quantities can be
detected, short intervals of exposure to the chemicals could
be used. As far as is known to the writer, only three
groups of investigators have thus far made use of this
method in this country: Gustafson and Darken at Michi
gan, Bennett and Stout and Hoagland at California. The
elements potassium, phosphorus, sodium and bromine
have been used in these experiments. The first two are
found abundantly in plants and are, therefore, well suited
for such experiments.
The procedure has been to use intact plants rooted
either in solution or sand medium. The roots have been
uninjured. Gustafson and Darken applied the irradiated
phosphorus as a 0.5 percent solution of KH2PO., while
Stout and Hoagland have incorporated their active
material in carefully balanced nutrient solutions. The
activity in the plant has been determined either by an
electroscope or a Geiger counter. The length of the exposure
to the radioactive material has varied from a few hours
to three days.
The set-up has varied a little with the different investi
gators. All investigators have used experiments in which
a section of the bark was separated in the middle from
the wood and the amount of active material present in
different sections of wood and bark determined. Gustafson
and Darken also set up experiments in which a ring of
bark was removed from one plant and a section of wood
of the same length from another plant, and the amount
of active phosphorus above the cut compared with a
third plant intact, or they removed all of the wood leaving
a strip of bark to which were attached several leaves, and
determined the amount of irradiated phosphorus in the
bark or/and leaves.
In an experiment with Bryophyllum lasting 40 hours,
Gustafson and Darken found that phosphorus was present
in the bark which had leaves attached to it but was itself
attached to wood only at the base. They found active
phosphorus as far as 23 cm above attachment, and, in
experiments where leaves were tested, they also contained
active material. In other experiments where wood or bark
was removed there seemed to be no appreciable difference
in the amount of activity found some distance up the
stem either in the wood or the bark. In other experiments
where a section of bark was loosened from the wood they
found that there was active phosphorus in all parts of the
bark, which was attached to wood only at the ends.
From these and other experiments they came to the
VOLUME 12, APRIL, .1941 conclusion that minerals are conducted upwards in the
bark as well as in the wood.
With a set-up similar to the last mentioned, Stout and
Hoagland used cotton, willow and geranium plants. The
time the plants were in solution was shortened to only a
few hours, but with bright sun and wind movement the
transpiration was quite active. Their published report
shows that the middle sections of the bark, which was
separated from the wood, had the least activity and that
the two ends, which were in contact with the wood, had
the most. Therefore, their interpretation is that the activity
in the middle sections was partly due to downward
diffusion.
From their experiments they came to the conclusion
that minerals move upward only in the wood of a stem.
They explain away the difference between their findings
and those of Gustafson and Darken as being due to
difference in the length of the experiment. In experiments
lasting for a longer time they maintain there is more of
an equilibrium obtained and pure diffusion may play a
much greater part, masking the relatively rapid movement
of materials in the transpiration stream. In a more recent
paper Gustafson shows that much less material is con
ducted into the upper part when the wood is cut than
when the bark is cut, but he still believes that there may
also be some upward conduction in the bark.
In these investigations the radiated elements have
proven themselves of great value, because by their use
tedious analyses have been avoided and much shorter
periods of experimentation have been permitted.
89. Applications of Radioactive K, Rh, Na, P, and Br
to Studies of the Mineral Nutrition of Higher Plants.
P. R. STOUT, Division of Plant Nutrition, University of
California, Berkeley, California.
Radioactive indicators have been used by a number of
the staff members of the Division of Plant Nutrition at
the University of California at Berkeley in studies per
taining to plant physiology, soils, and plant and soil
interrelationships. Potassium and phosphorus are essential
elements for the nutrition of higher plants. Sodium,
although not recognized as essential, is often absorbed in
large amounts from soils containing it, and frequently
plays a predominate role in the physical condition of arid
and semi-arid soils. Normally rubidium and bromine do
not occur in plants or soils in amounts detectable by usual
analytical methods. The latter however, when made
available to plants, are readily absorbed without interfering
seriously with their metabolism. Consequently, rubidium
and bromine have been used as indicator ions in investi
gating the process of absorption, accumulation, and
translocation of mineral nutrients by plants. Since radio
active isotopes have been made available to investigators
at the University, it has been possible to run experiments
using the elements physiologically required by plants.
In addition to the obvious experimental advantages of
tagged ions involved in normal physiology of plants, the
extreme sensitivity with which the isotopes can be detected
has permitted observations to be made of small sections in
327
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gated will be reviewed and discussed under the several
categories by which radioactive isotopes take their place
as new and indispensable research tools for biological
investigations namely (1) where the nature of the experi
ment requires an indicator ion of the element in question,
and direct evidence can be obtained in no other way
(2) where the number of plants required for an appropriate
statistical treatment of "control" versus "treatment"
would be so great as to be difficult if not impossible to
achieve experimentally, and (3) where the sensitivity
permits analyses of small amounts for which suitable
chemical methods are not at present available. Of great
interest to the investigator is an unexpected revelation
that comes from new techniques. Removal of ions from
the root environment to the tops of plants eight to ten
feet high in 15 minutes, a very rapid lateral transfer of
solutes from the wood to the bark, and the outgo of
potassium from roots during the process of accumulation
are cases in point. Slides of radio-autographs showing the
distribution of phosphorus in various plant tissues will
be shown.
90. Ion Movement in Living Protoplasm. S. C. BROOKS,
University of California, Berkeley, California.
The experimentally or naturally induced changes in
the ion content of protoplasm are important in mainte
nance of its integrity within tolerable limits. Small changes
in physical aspects are probably a factor in controlling
the amount and direction of metabolism. Salt effects on
metabolism are known. Without changing the total salt
content to a cell it is possible to readjust the proportions
of ions in cells to changing salt environments, i.e., to set
up a statistical equilibrium between cells and environment
for all ions. This implies ionic exchange. Using tracer ions
it is possible to show that this equilibrium is approached
enormously faster than suggested by traditional experi
ments. Work has been done with Na+, K+ and Rb+, and
Br-and HPO.-(all radioactive); an alga (Nitella), marine
eggs, a fresh water amoeba and other forms were used.
Nitella was studied most carefully. The proportion of
protoplasm in representative samples was determined.
The sap and protoplasm were separated and, utilizing the proportion found, determinations were made of the
concentrations in each portion of the isotope in question
after various intervals of immersion in dilute solutions of
salts of radioactive isotopes. During the first few hours no
salt reached the vacuole, but within 2-5 minutes the
radioactive isotopes penetrated into the protoplasm in
concentrations greatly exceeding the external concentra
tion, e.g., O.OOSM K*CI. This ion cannot be only in the
plasma membrane; the latter can combine with only
about 1/100 or less of the observed amount of the ion.
This amount is a considerable fraction of the total com
bining capacity of the total protoplasm· for comparable
ions. It is believed that the entering (tracer) ion displaces
similar ions (e.g., Na* for Na+ and K+) and also hydrogen
or organic bases. The amounts of different ions in the
protoplasm were found to differ so that Rb>K>Na.
This can be predicted on the basis of colloid chemistry.
This ion entrance, called induced accumulation, can be
reversed by replacement of the isotope containing solution
by salt solutions (Li, Na, K, Rb or Cs chlorides, O.OlM)
but only very slowly by distilled water. Hence, ion ex
change is necessary for the movement of ions in this process.
Following induced accumulation there appears to be
loss of the isotope followed by alternating further intake
and loss phases. Losses appear to involve loss of total salt
content, i.e., simultaneous exit of cation and anion.
Changes in ion content would themselves alter the proto
plasm, possibly accounting for permeability changes and
hence losses. The later intake may lead to ion contents
still higher than the previously noted maxima. Both loss
and intake depend at least partly on metabilism, as shown
by the disappearance or reduction of these changes in
cells killed by heat or narcotics. Cyanide is ineffective.
Compatible results were obtained with other algae and
Amoeba proteus. Marine eggs show relatively slow ion
exchange, thus agreeing with findings of other workers
on erythrocytes, muscle, etc. A possible correlation is
suggested of high permeability with a normal salt-poor
environment. In Nitella, protoplasm alkali metal ions
move with rates comparable with water and small non
electrolyte molecules (10-r·G·cm-2·hc1) rather than the
traditional rates of 10-9-10-8 established by determina
tions of total salt content or made on vacuolar sap.
Radiology I
General Aspects of Cancer Therapy
Chairman: DR. G. W. HOLMES, Massachusetts General Hospital
24. PathoiQgical Analysis of the Action of X-Rays and
Radium on Tumors. FRED W. STEWART, Pathologist,
Memorial Hospital, New York, New York.
It is impossible to summarize the subject matter of this
discussion in a few words. The complexity of the field of
human tumors and the different morphologic mechanisms
328 involved in their behavior toward x-rays and radium
permit no satisfactory generalizations. The subject is still
in the stage of descriptive analysis, best discussed in terms
of examples of behavior of various individual tumors as
they occur in different individuals.
An effort is made to discuss the subject under four
JOURNAL OF APPLIED PHYSICS
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on the tumor cell or portion thereof; (2) effects on the
connective and supporting tissues and their influences on
the behavior of the tumors; (3) alterations produced in
the circulatory pattern and their effect on the cancer;
(4) undefined differences in individuals which seem to
alter the relations between tumor and host.
Various morphologic changes in tumors are individuaized
and attempts made to discuss them in terms of physical
theory and to estimate their importance in the regression
of individual tumors. The insufficiency of current physical
theory in accounting for the various processes seen to have
occurred in radiated human cancers is emphasized. By
insufficiency in theory is not meant necessarily that theory
offers an erroneous concept of how radiation affects tumor
cells,-not a denial of the fundamental ionizing effect of
x-rays and radium in cells and their surrounding media
but a lack of knowledge as to why different lesions do or
do not show morphologic changes compatible with theory.
The morphologic factors involved in radiosensitivity
are emphasized as complex phenomena requiring individual
analysis, and determination of the probable radiosensitivity
of a tumor is believed to be only possible from observations
on group behavior, individual lesions occasionally varying
widely in their response.
25. Chronological Factors in Radiation Therapy. HENRI
COUTARD, Chicago Tumor Institute, Chicago, Illinois.
The chronological factors may be defined as the time
which separates the beginning of the treatment and the
moment of its effect upon the cells. Treatment thus
dissociates and characterizes the cellular types so well that
the differences of radiosensitivity between two groups of
cells become measurable by their chronological factors.
This chronological factor may also constitute a physiologic
relationship between the conditions of a treatment of
minimum intensity and maximum effects.
\Vhen the chronological factor is of short duration, one
to six days, the action on the cells has been considered as
one of direct and individual destruction, because all
irradiation, even slight, awakens or accelerates the cellular
processes of multiplication, all the more strongly as the
cells are less differentiated. Cellular fragility is thus
increased and destruction is facilitated.
\¥hen the chronological factor is of longer duration,
more than 13 days, the action of the rays cannot be
considered as a direct and individual one. An inter
mediate factor intervenes, which is the underlying soil or
tumor bed. Under the influence of daily irradiation, when
they are reaching a certain threshold, there is produced
through the intermediary of the irradiated substrata, a
grouping and concentration of the moments of cellular
multiplication. The moments of cellular disappearance
which sooner or later follow them become simultaneous
and of short duration. They are, for example, of 2 or
3 days duration for the mucosal and skin, which have
their moments of disappearance from the 13th to the
15th day for the mucosal, from the 26th to the 28th day
VOLUME 12, ApRIL, 1941 for the skin, after an intense series of irradiation given
from the 1st to the 7th day.
The collective chronological factors, under the influence
of substrata, are substituted for the individual chrono
logical factors. An indirect effect is substituted for one
which was considered as a direct effect.
If, instead of a treatment of 12 days, one irradiates the
mucosal and the skin throughout 40 days, with small
daily doses, the moments of grouping of concentration
and of disappearance are of longer duration-5 to 6 days.
They are incomplete, a small number of cells participate
in this disappearance. But this is repeated at varying
intervals. One thus causes chronological factors to appear
which always have a collective tendency but also a periodic
character. Cellular disappearance attains its greatest
height at fixed moments, which are precise and repeated
on'the 13th, 26th, 39th and 52nd days for the mucosal,
and on the 26th and 52nd days for the skin.
This method of continuous and prolonged irradiation
when using higher daily doses has demonstrated its efficacy
on cancers moderately differentiated. If we compare
continuous treatments, which were terminated, respec
tively, on the 12th, 26th and 39th days, we see that they
have given us a proportion of five-year survivors three
times greater than when they have terminated between
the moments of the periods, on the 19th, 33rd and 46th
days, and using doses comparatively equal. The total dose
can thus be reduced when the treatment ends at the
moment of a period. At this moment cellular fragility
reaches a maximum. Larger doses, on the contrary, are
inefficacious, if the treatment ends between the moments
of the periods. The effects produced under these latter
conditions are anti physiologic, accompanied by local and
general disturbances. There is an opposition to the concen
tration of the 'time of multiplication.
To obtain satisfactory results in more differentiated
cancers, it is necessary to increase the daily dose, all the
more so as the differentiation is more marked. Continuous
treatments do not permit, without grave danger. sufficient
daily dose to allow the substrata to group and closely
concentrate. Thus we must use treatments which are not
continuous, of short duration, but intense, in series,
utilizing the times and moments so that the effects are
produced at the moments of the periods, when the cellular
fragility is maximum. For certain cancers it has been
sufficient to cause the time of irradiation to coincide with
the periods, which simplifies the problem.
The most simple and effective treatments have been
those in which the number of series and the daily doses
were increased parallel with the degrees of differentiation.
as in the three following examples: (1) Cancer slightly
differentiated-two series of 6 days separated by 14 days
without treatment. Daily doses 500 to 700 r. Doses of
the series 3000 to 3500 r. Total doses 6000 to 7000 r.
Duration 26 days. (2) Cancer moderately differentiated
three series of 3 days separated by 7 and 10 days without
treatment. Daily doses 800 r. Doses of the series 2400 r.
Total dose 7200 r. Duration 26 days. (3) Cancer very
differentiated-four series of 2 days separated by 9, 11
329
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Doses of the series 1800 to 2000 r. Total dose 7600 to
8000 r. Duration 39 days.
Thus the chronological factor has become, in the case
of skin and mucosal, and of cancers arising on these
teguments, a factor both collective and periodic whose
period corresponds to that of the larger physiologic
phenomena having to do with cellular multiplication. The
cutaneous period which reappears every 26 to 28 days
corresponds to the ovarian period. Its duration of 2 to
3 days corresponds to the duration of the elimination of utero-vaginal epithelium. The chronologic factor of the
mucosal corresponds to the half-period of the ovary. It is
remarkable that the phenomena of cellular elimination,
which appear monthly under the influence of physiologic
factors, can appear artificially with the same period, under
the influence of irradiation. If these are due in the first
case to the products of complex hormonal glandular
secretions, it is possible that they are due, in the second
case, to physiologic factors, little different from the
preceding, but localized and activated by the action of
the rays on the substrata and surrounding tissues.
Radiology II
Radium and Roentgen Therapy
Chairman: DR. G. E. PFAHLER, University of Pennsylvania
37. The Present Status of Radium Therapy. DOUGLAS
QUICK, New York, New York.
This discussion of radium therapy will be concerned
chiefly with its place in the field of cancer plus a few closely
allied or border-line conditions. Few of the malignant
neoplastic diseases are manageable to best advantage by
one agent or method alone. Radium has certain peculiar
advantages to offer in the various combinations of therapy
found best suited to the individual case, in the present
state of our knowledge of the subject. Inasmuch as it does
not afford the sole means of treatment in most of the major
groups of malignant disease, it does not seem wise simply to
enumerate its relative importance in the various groups
ordinarily discussed by clinicians. The various special
advantages will be suggested and their adaptation to
certain fields of cancer presented.
In ordinary practice, there are three general methods of
application, external or surface, intracavitary, and inter
stitial. The surface applications, usually in relatively small
amounts, are used for skin lesions, while large amounts at
substantial distance from the body surface, usually referred
to as telecurietherapy, are used for depth doses in deep
seated tumors. In this one particular, its approach to a
parallel or competitive position with x-ray therapy will be
discussed. The peculiar adaptability of radium to intra
cavitary application approaches more nearly its real place
in irradiation therapy. It affords a source of powerful
energy in small bulk which can be placed in the body
cavities for intense local irradiation. Probably the best
example of this is in treatment of the uterine cervix and
fundus. This principle of intense local irradiation at or near
the center of the malignant neoplastic area is carried one
step further in interstitial irradiation. Sources of radiant
energy are implanted in and about the tumor bearing area:
For this purpose radium salt in metal needles or radon in
small celled metal containers (seeds) is employed. The
relative values of each will be discussed and their wide
range of application, especially in conjunction with opera
tive surgery, will be pointed out.
330 It is rather generally accepted that the gamma-radiation
is the all important factor. While this is probably true in
large measure, the present trend of the day toward pro
duction, electrically, of shorter and shorter wave-lengths
may be carrying us away from an important quality of
radiation, even though its field of usefulness is limited. At
least, the question of the value of beta-rays of radium will
be raised. In its intimate application within tissues, radium
has never, in a practical way, gotten beyond the interstitial
implant. At one time it was visualized as a possible consti
tutional agent and certain clinical experimental work
carried out. Ordinary table salt was exposed to radium
emanation, dissolved in sterile water, and injected intra
venously. A pronounced effect was noted in the leukemias,
but the difficulties and hazards of the work caused it to be
abandoned without publication of a report. It is now of
interest in view of the radioactive substances made avail
able through the agency of the cyclotron.
To date, the therapeutic advances with radium have
depended largely upon adaptation of the various physical
factors to the individual problem. Dosage, for the most
part, has of necessity been the maximum that the normal
tissue structure would tolerate. There has been no secondary
or complementary agent, either biological or chemical,
which would render the tumor tissue more sensitive to
irradiation or aid in retaining more of the ionizing radiation
within the tumor bearing area. The use of colloidal lead a
few years ago was transiently regarded as a possible
"sensitizing" agent, but failed to prove ultimately of value.
Some of the more recent experimental work, particularly
that reported by Failla of injecting sterile water into the
tumor immediately following irradiation by x-rays, seems
more encouraging. It is hoped that, by setting forth the
shortcomings of radium, rather than its accomplishments,
before a mixed group of scientists, effort may be stimulated
toward solving some of the problems which would enable
radium to embrace a wider field of usefulness.
The tremendous advances made during the last few
years in the development of equipment for x-ray therapy
JOURNAL OF ApPLIED PHYSICS
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radium. Its adaptability in conjunction with x-ray therapy
should be more carefully borne in mind by all clinicians,
especially the roentgen therapists. It should also be noted
that far too many physicians having a limited knowledge,
or no knowledge, of the principles of radiation therapy, are
coming to dabble in the use of radium. Such practice not
only does irreparable harm to the patient but discredits
both radium and x-ray therapy.
38. The Present Status of Roentgen Therapy. U. V.
PORTMANN, Cleveland Clinic, Cleveland, Ohio.
The remarkable progress and extending usefulness of
roentgen therapy for many inflammatory and malignant
diseases have been the result of the collaboration of
engineers, physicists, and biologists with the physicians.
Different types of apparatus have been developed to
furnish irradiation in a wide range of quality and in
adequate quantities. Means have been provided so that
radiologists can administer treatment safely with con
siderable accuracy, and they can estimate the tissue
reactions which will be produced. Consequently, the results
of roentgen therapy are improving constantly.
However, roentgen therapy has limitations. Some of the
clinical difficulties are inter-related and include those that
are technical or attributable to the anatomical location and
extent of the diseases being treated. and also to a lack of
sufficient information about normal and pathological
cellular functions. Clinical problems which may be solved
by investigation in biophysics and biochemistry will be
presented for consideration.
39. Supervoltage Roentgen Therapy. RICHARD DRESSER.
Collis P. Huntington Memorial Hospital of Harvard Uni
versity. Boston, Massachusetts.
A discussion of supervoltage roentgen therapy naturally
resolves itself into a comparison between results obtained
with wave-lengths produced in the neighborhood of 200
kilovolts and those obtained at higher potentials. Many
radiologists have made the observation that the shorter
wave-lengths are more effective in the treatment of certain
types of malignant disease. Radium has been extensively
used for superficial application, but it is available in such
small amounts that the effective dosage at some distance
below the surface cannot be obtained. Thanks to the efforts
of physicists and engineers, x-radiation approximating in
wave-length the gamma-rays of radium is now available in
huge intensities. The output of one supervoltage x-ray
machine is equal to several times the intensity which might
be obtained from all the refined radium in the world. The
physician may now avail himself of the penetrating qualities
of these supervoltage roentgen rays and may place the
source of radiation at a distance sufficiently great from the
patient so that the effect of the inverse square law in the
dosage delivered to deep-seated malignant neoplasms
becomes negligible.
There are two important requirements of a therapeutic
x-ray machine. First. it must be mechanically reliable so
that a preconceived course of therapy can be carried out
VOLUME 12, APRIL. 1941 without interruption. Second. the output of radiation must
vary within narrow limits. The period of mechanical
instability of the electrostatic belt conveyor type of
supervoltage apparatus developed at the Massachusetts
Institute of Technology has been incredibly short. The
original unit installed at the Huntington Hospital operates
with the reliability of a commercial 200-kv machine. The
apparatus is now being run routinely at 1000 kv. 1 milli
ampre, 70 cm distance, filtration 3! mm of lead plus 8 mm
copper. The radiation thus produced has a half-value layer
of 1O! mm of copper or 4 mm of lead. The intensity is 70
roentgens per minute. This output could be nearly tripled
if the machine were operated at its full amperage capacity.
Since the unit is chiefly used in the treatment of deep
seated malignancies, it is of interest to compare depth
doses obtained at 1000 kv with those obtained at 200 kv.
This comparison is shown in the Table I.
Million-volt radiation is found to possess several
advantages: there is less scattering; the intensity below the
surface (depth dose) is greater; the depth dose is largely
independent of the size of the portal of entry. Moreover,
clinical and animal experiments have shown that the
tolerance of the skin to supervoltage x-rays is considerably
increased.
The results obtained from the medical use of superhard
radiation have been entirely in accord with what was
anticipated from physical measurements. The response of a
new growth to radiation is primarily dependent on three
factors: first, the radiosensitivity of the growth; second, the
total amount of radiation given; third, the rate at which
radiation is delivered. A neoplasm which is not affected in
any'degree by 200-kv rays does not usually respond to the
shorter wave-lengths. The lack of scattering, the greater
penetration, and the employment of small portals of entry
without appreciable effect on the depth dose result in
better tolerance of supervoltage roentgen rays on the part
of the patient. The total dosage can be increased, and the
time of administration decreased. Two hundred-kilovolt
treatment is usually limited in amount by the tolerance of
the skin. At 1000 kv the factor of skin tolerance becomes
TABLE I.
1000 KV
200 KV 70 CM
70 CM 3.5 MM PB
tMMCU 8MM Cu
PORTAL OF ENTRY % %
100 sq. em
Surface back scatter 24 6.5
Depth dose-5 em 67 77
Depth dose-l0 em 34 49
Depth dose-IS em 17 29.5
Depth dose-20 em 8 18
225 sq. em
Surface back scatter 26 9
Depth dose-5 em 71 78
Depth dose-l0 em 42 50.5
Depth dose-IS em 22 32.5
Depth dose-20 em 10.5 21
400 sq. em
Surface back scatter 33 11
Depth dose-5 em 77 79
Death dose-l0 em 45.5 5.3
Depth dose-IS em 25 36
Depth dose-20 em 12.5 23.5
331
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deeper structures. The combination of these factors has
resulted in better regression of deep seated neoplasms than
has hitherto been observed, and the results are improving
as we gain greater knowledge of depth dose technique.
The one outstanding disadvantage of superhard radiation
is in the treatment of superficially located tumors. The
production of a sufficiently intense superficial reaction may result in damage to underlying vital structures. Even this
could be technically overcome by shortening the distance
from the source of radiation to the patient, but we have
found it easier and perhaps as effective to use the longer
wave· lengths in such instances.
I am indebted to Mr. Bernard Cosman and Dr. Milford
Schulz for their collaboration in making depth dose
measurements.
Radiology III
Neutron and Artificial Radioactivity Therapy
Chairman: DR. R. H. STEVENS, Detroit, Michigan
62. Neutron Beam Therapy. ROBERT S. STONE AND
JOHN C. LARKIN, Division of Roentgenology. University of
California Medical School, San Francisco, California, and
The William H. Crocker Radiation Laboratory, University of
California, Berkeley, California.
The production of fast neutrons in sufficient quantities
for clinical use was first accomplished with the 37-inch
cyclotron in 1938. In September of that year, treatments
commenced on a series of 24 patients using neutrons pro
duced from eight million-volt deuterons striking a beryllium
target. Treatments were given once a week. Large total
doses were given in a single sitting. It was found that
approximately 200 ngiven to the face and neck produced a
well-marked erythema, whereas doses as high as 270 11: did
not cause blistering. Doses as low as 70 n on the flexor
surface of the forearm produced just visible reactions.
Tumor regressions were obtained.
In November, 1939, the new 60-inch cyclotron producing
16 million-volt deuterons became available for clinical use
three times a week. The average intensity of the beam of
neutrons has been 5 n per minute. Up to September 10,
1940, 47 patients have been subjected to fractionated
treatments. The patients were selected from that group of
cases usually too advanced for treatment with x-rays,
radium, or surgery. All the head and neck cases had
metastatic involvement of the cervical lymph nodes. The
lesions of the breast and prostate were inoperable, and some
had distant metastases. The location of the lesions were as
follows: breast (primary or recurrent) 6, prostate 5,
stomach 1, head and neck 32, brain 1, and ovary 1.
The general plan of treatment was to use 50 n per field
using 7X7 em, 10XIO cm, and 1OX15 em ports in much
the same manner as with x-rays. This was decreased when a
patient showed too severe reaction or when the apparatus
was not running at a maximum efficiency. The total doses
have averaged 425 n to two opposing fields in 45 days. The
maximum given was 775 n to one field in 40 days. The
average total elapsed time including the first and last
treatment was 45 days. The shortest treatment was 12 days
and the longest 61 days. The average number of treatment
visits for each patient was 15, the minimum being 7 and
the maximum 20 when the full courses were given. Some
332 treatments were unduly prolonged when the apparatus was
shut down for repairs. In treating the prostate cases, one
anterior and two posterior fields were used but only two
were treated in a single day.
The skin reactions produced varied from mild erythemas
to marked epidermitis. but all to date have healed satis
factorily. In general they have tended to be dry with thick,
heavy incrustations especially over the face and neck. In
several cases large numbers of subcutaneous abscesses have
formed. Subcutaneous edema and thickening of the tissues
of the neck are constant sequelae. The anterior fields of the
prostate cases showed marked reactions to 425 n in 33 days
or 525 n in 45 days, but the gluteal fields withstood 650 n in
61 days. The mucosal reactions resembled those following
x-ray, but have usually been patchy. The patients treated
about the face and neck developed dry mouths and lost
their sense of taste.
Nearly all the primary lesions have shown some re
gression, and when ulcerated have healed remarkably well.
The metastatic glands also have regressed considerably and
usually leave a smaller, hard, indurated area. Some
metastatic glands have undergone necrosis. The necrotic
material was usually thick and not watery.
Microscopic studies of some of the treated tissues show
necrosis and fibrous reactions.
In conclusion, it is obvious that malignant tissues regress
under fast neutron ray treatments. Normal tissues do not
seem to be irreparably damaged by the doses necessary to
produce tumor regression. Improvements in technique and
operating conditions will undoubtedly produce better
results. The recurrence of cancer and the rate of recovery
of tissues from neutron therapy are, of course, not known at
this early date.
63. Utilization of Slow Neutrons for Therapeutic Pur
poses. P. GERALD KRUGER, Department of Physics,
University of Illinois. Urbana, Illinois.
Studies1 of the effects of the disintegration products from
the nuclear reaction .Blo+on.' ...... sLF+ 2He4, on mammary
carcinoma, lymphoma and sarcoma, show that the ioniza
tion produced by these disintegration products is sufficient
to cause lethal effects in vitro.
JOURNAL OF ApPLIED PHYSICS
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Downloaded to ] IP: 130.18.123.11 On: Thu, 18 Dec 2014 17:54:59In the in vitro experiments small pieces of the neoplastic
tissues were immersed in a boric acid solution and then
irradiated with slow neutrons. In this way the boron nucleus
is disintegrated in the environment of the tumor cells, and
the dissipation of the energy of the disintegration products
produces an intense ionization in the cells. After implanta
tion in mice, the growth of the irradiated samples is com
pared to the growth of tumor particles immersed in boric
acid solution but not irradiated before implantation. A
comparison of these data with those from other experi
menters using fast neutrons, shows that the lethal effects
observed after the slow neutron irradiation, are produced
by the boron disintegration products.
Since all elements which appear in tissue with an ap
preciable concentration have a cross section for slow neu
tron capture which is small compared to that for boron, no
strong ionization can be produced in tissue by slow neutron
irradiation unless boron or some other nucleus having
similar characteristic is introduced into the tissue. Thus it
may be expected that results similar to those observed in
the in vitro experiments may be obtairied in vivo if sufficient
boron, in some suitable form, can be applied to tumors in
vivo. The localization of ionization by this method, when
applied to in vivo work, will remove the danger of skin
burns and similar disturbing factors which are prevalent
in x-ray, 'Y-ray and fast neutron therapy.
Before in vivo experiments of this type may be performed,
with hope of success, it will be necessary for the chemist to
supply the biologist or the physicist with suitable organo
boron compounds, i.e., they must diffuse through tissue
slowly, or be decomposed by chemical reaction in tissue in
such a way as to deposit the boron in the tissue, and they
must be nontoxic. Such a problem does not seem to be
hopeless from the chemist's standpoint.
From the data obtained in the in vitro experiments it is
possible to calculate the approximate amount of energy
which must be dissipated in a cell or in its nucleus to cause
lethal effects. The results of such a calculation indicate that
approximately 650 Mev per cell or 80 Mev per cell nucleus
are required to kill mammary carcinoma cells.
1 P. Gerald Kruger, Proc. Nat. Acad. Sci. 26, 181 (1940).
64. Intracellular Irradiation. J. H. LAWRENCE, L. A.
ERF AND L. W. TUTTLE, William H. Crocker Radiation
Laboratory, University of California, Berkeley, California.
A. Yeast cells.-When Baker's yeast cells (Sacch Cere
viseae) were suspended for one and one-half hours at 22°C
in (a) glucose-salt, (b) fluoride glucose-salt, and (c) sustain
ing salt mediae, to each of which radio-phosphorus (IOP32)
in form of phosphate had been added, radioactivity was
found only in those cells suspended in the first solution.
The uptake of the radio-phosphorus varied with the con
centration of glucose. Once the yeast cells had incorporated
P32, it was not lost by resuspending the cells in a radio
phosphorus-free media. These and other experiments
indicated that the curve representing the uptake of radio
phosphorus could be more or less superimposed upon the
curve representing the metabolic rate of yeast cells and not
upon the growth curve.
VOLUME 12, APRIL, 1941 By the use of ice-cold five percent trichloracetic acid and
hot ether-alcohol solutions, it was determined that ap
proximately 80 percent of the activity was found in the acid
soluble and 20 percent in the nucleoprotein fractions.
(Approximately 40 percent of the activity of the nucleo
protein fraction was present in the nucleic acids.) Iodoacetic
acid decreased while cyanide increased the rate of uptake of
radio-phosphorus in the nucleoprotein fraction.
B. Mouse cells.-StrongA mice which have been inbred
for nearly 80 generations and a very cellular, vascular
lymphoma with lymphemic characteristics which has been
transferred in about 80 generations, were used. The tumor
takes in 100 percent of the mice inoculated and regressions
have not been observed. After the intraperitoneal adminis
tration of radio-phosphorus to both normal and leukemic
animals, the retention of activity in the whole carcass of
the leukemic animals was greater than in those of normal
animals during a lOO-hour period. When the tissues were
assayed separately, it was noted that the muscle tissue of
the leukemic animals retained less activity than those of
normal animals, however the bone and liver slightly more,
while the lymph nodes and spleen retained much more
during a period of lOO hours. These findings were thought
to be due to the more rapid metabolism of the leukemic
cells and to their varied infiltration in organs and tissues.
The liver, spleen and lymph nodes of normal and leukemic
animals were then fractionated into three broad groups of
biologically active phosphorus compounds: phospholipids,
nucleoproteins and acid soluble fractions. Leukemic in
filtration of these organs was accompanied by an increase
of several-fold in the uptake and retention of actjvity. by
the nucleoprotein and acid soluble fractions over the
normal organs. The phospholipid metabolism of spleen and
lymph nodes was but slightly altered by leukemic infiltra
tion, while that of the liver was depressed the first day
after administration of P32.
C. Human cells.-With the realization that radio
phosphorus concentrated more rapidly in the nucleoprotein
fraction of transmitted leukemic cells than in normal mouse
cells, in addition to the marked concentration in bone and
bone marrow, it would seem to be an ideal method of giving
selective irradiation in leukemia. It has now been ad
ministered orally and intravenously to approximately 200
cases of leukemia, Hodgkins, myeloma, melanoma, osteo
genic sarcoma, polycythemia, and to four normal indi
viduals. The rates of absorption (blood and biopsies of
various tissues) and of excretion (urine and feces) have been
determined in approximately 40 cases. As was found in
the mice, the greatest concentrations of activity occurred
in the nucleoprotein fraction of leukemic cells, while lesser
concentrations occurred in normal blood cells during a
period of one week following administration: Activity
assays have been made of autopsied tissues of 30 cases. In
those patients to whom radio-phosphorus had been ad
ministered many days before death, the concentrations of
radio-phosphorus were greatest in the osseous tissue, while
in those to whom p32 had been administered just previous
to death, the concentrations were greatest in such tissues as
bone marrow, spleen and liver. This indicates that the more
rapidly metabolizing tissues quickly utilize available radio-
333
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salt in the bones.
The therapeutic results were quite encouraging. In the
group of 16 cases of various types of chronic leukemia
untreated by any other method such as x-ray or arsenic
and which have been treated with radio-phosphorus only during the past two years, only five have died, and three
of these were moribund at beginning of treatment. The
others continued to respond well to treatment. Advantages
of this form of therapy include (1) simple method of giving
localized whole body irradiation in a single cocktail or
intravenous injection; (2) absence of irradiation reactions.
Radiology IV
Dosage M easuremenis
Chairman: DR. EDITH H. QUIMBY, Memorial Hospital, New York
70. Measurement of Short Wave Radiation in Roent
gens. LAURISTON S. TAYLOR, National Bureau of Stand
ards, Washington, D. C.
A brief review will be presented covering the more im
portant attempts to measure megavolt x-rays and gamma
rays in roentgens. Particular emphasis is laid on the labora
tory standardization measurements. The measurement 9f
x-rays in roentgens up to 300 kv can be done in a straight
forward manner involving no difficult assumptions or
corrections. However, for higher excitation voltages,
measuring instruments become unwieldy, with the result
that indirect methods of measurement are employed.
Some methods, such as those employing the thick-walled
thimble chamber may involve certain assumptions as to
the counter-balancing effects of different components of
the ionizing radiations and absorption and scattering in the
chamber walls. While such chambers are to be considered
as fairly satisfactory, they cannot be considered as abso
lute in their measurements. Extension of the useful range
of free air ionization chambers through the use of high
pressures, avoids some of the assumptions involved with
thimble chambers but in turn involves corrections in the
current measurement itself through the presence of
columnar recombination effects. Simple enlargement of the
chamber dimensions may apparently avoid both of these
difficulties but the chamber itself becomes so large that the
exclusion of other secondary effects is uncertain. Conse
quently there is something to be desired in all the
methods used thus far for the absolute measurement of the
roentgen.
Practical measurement of the roentgen, as in water
phantoms, becomes more complicated in the higher
voltage and gamma-ray regions when using secondary
chambers which have been calibrated under standardized
laboratory conditions against some sort of primary stand
ard. The mode of comparison with the standard is to some
extent dictated by the purpose to which the secondary
chamber will later be applied.
71. Determination of Energy Absorbed Per Gram of
Tissue. T. N. WHITE, National Cancer Instit{lte, Bethesda,
Maryland.
There will be reviewed the conditions under which one
may ascertain the energy absorbed in tissue in terms of the
334 ionization which occurs in a gaseous cavity introduced into
the tissue. This method has been thoroughly discussed and
tested by L. H. Gray in the case of the filtered gamma
rays of radium with its decay products. Both Gray and
Zimmer have given some attention to the application of the
method with fast neutrons. In essence the method depends
upon the behavior of ionizing particles in matter, and an
attempt will be made to express the conditions which
should be fulfilled without making any direct reference
to the source or exact nature of the ionizing particles.
The purpose of this mode of presentation is to facilitate
perception of the range of applicability of the method.
The proposed conditions are summarized as follows:
(1) It must be necessary to evaluate only that energy
which is absorbed in the tissue on account of deceleration
by the tissue of the motion of ionizing particles.
(2) In any gas of low atomic number, the average number
of ion pairs formed per small decrement of energy should
be practically independent of the kinetic energy of the
ionizing particles.
(3) The rate of loss of energy in tissue by the ionizing
particles should bear to the rate of 10O's of energy in the
gas of the cavity a ratio which is practically independent
of the kinetic energy of the particles.
(4) On an average, the energy absorbed in the cavity
from any ionizing particle must be small in comparison
with the energy with which the particle traverses the
cavity.
(5) The number of primary ionizing particles of any
specified energy traveling in any specified direction should
be practically the same at all points throughout the tissue
within which the cavity is introduced.
It is considered that in any case where the above condi
tions hold the energy absorbed may, for practical purposes,
be expressed by means of Gray's formula:
E=dWJ
where E is the energy absorbed per gram of tissue adjacent
to the cavity, W is the average decrement of energy of
ionizing particle per pair of ions formed in the gas of the
cavity, J is the number of ion pairs formed per gram of
gas in the cavity, and d is the ratio stated in (3) above
(rates being expressed as energy loss per gram cm-2).
JOURNAL OF ApPLIED PHYSICS
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tions will be discussed.
Some attention will be given to the applicability of the
method in cases where tii'sue is irradiated with an externally
produced beam of ionizing particles, and where a small
amount of radioactive material is uniformly dispersed in
the tissue.
Insofar as time permits, pertinent data will be summar
ized and experimental technique will be discussed.
REFERENCES (partial list) :
G. Failla, Radiology 29,202 (1937).
G. Failla and L. D. Marinelli, Am. J. Roent. 38, 312 (1937).
L. H. Gray, Proc. Roy. Soc. London A122, 647 (1928).
L. H. Gray. Proc. Roy. Soc. London A1S6, 578 (1936).
L. H. Gray and J. Read. Nature 144. 439 (1939). c. C. Lauritsen. Brit. J. Radiol. 11. 471 (1938).
G. C. Laurence. Can. J. Research A1S. 67 (1937).
W. V. Mayneord, Brit. J. Radiol. 13,235 (1940).
K. G. Zimmer. Strahlentherapie 63.517 (1938).
72. Distribution of Ionization Produced in the Human
Body by Different Methods of Irradiation. PAUL C.
AEBERSOLD, * William C. Crocker Radiation Laboratory,
Physics Department, University of California, Berkeley,
California.
Nuclear physics has resulted in two new methods of
irradiating lesions within the human body, the use of
beams of fast neutrons and the administration of induced
radioactive substances. Comparisons of the distributions of
ionization produced in the human body by these new
methods with those achieved by x-ray and radium irradia
tion are being made in our laboratory by means of both
physical and biological tests. Comparisons have also been
made of the distributions produced by different qualities of
x-rays applied in various ways.
As yet it is not possible for all qualities and kinds of
radiation to give absolute values of the energy expended
in ionization at points in a body, i.e., absolute tissue dosage.
However, an approximation to the tissue dose can be
attained under certain conditions by measuring the ioniza
tion produced in a tiny gas cavity or chamber of special
properties introduced in the body and then applying the
Bragg-Gray relationship for the ionization in such a cavity.
The validity of this procedure for x-rays, gamma-rays and
fast neutrons will be considered. For administered radio
elements that emit only beta-rays, the absolute energy
expended per unit volume of tissue can readily be calcu-lated if the average energy of the emitted beta-particles is
known and an assay is made to determine the number of
particles emitted in the unit volume. In general there are
uncertainties in these determinations that will need to be
cleared up before absolute dosages can be stated for this
type of irradiation, but in most cases good approximations
can be made.
Assuming that a distribution of ionization can be meas
ured that will approximate tissue dosage, it is nevertheless
inadequate to compare a few such physical measurements,
e.g., percentage depth doses, in comparing the relative
efficacy of one type of irradiation over another. The density
of ionization along tracks of secondary protons resulting
from neutron irradiation is very different from that along
electron tracks resulting from x-and gamma-irradiation,
and it will vary with the energy of the neutrons. Also
radio-elements may deposit selectively in certain cells,
or even in parts of cells, and give rise to a submicroscopic
picture of ion distribution different from that occurring
under x-irradiation. The different submicroscopic distribu
tion of ionization resulting from the use of these new
irradiation methods can produce different biological effects
even when the physical measurement of volume ionization
is the same. Consequently, before the ordinary volume
ionization measurements can be used for indicating relative
biological depth doses the relation between the ionization
measurements, and the biological effects sought must be
investigated over the range of qualities acquired by the
radiation in the body. Moreover, the relative recovery
factor of different tissues, such as normal and neoplastic
tissue, may be different for neutrons than for x-rays.
Also, the relative recovery of tissues must be considered
for the slow rate of dosage that can be used with adminis
tered radio-elements.
Although no such exhaustive investigations have yet
been made, tests show that the depth doses achieved by the
fast neutron beam of the 60-inch cyclotron are as good as
those achieved by high voltage x-rays, and this is born
out by clinical observations. Also clinical results on pa
tients administered radio-elements show selective radia
tion effects found from physical and biological tests.
It appears that these new methods of irradiation may be
favorable adjuncts to present radiation therapy.
* Fellow of the Finney-Howell Research Foundation.
Radiology V
Radiobiology
Chairman: DR. CHARLES PACKARD, Columbia University
76. The Relation of Tissue Phosphatase to the Deposi
tion of Radioactive Phosphorus in Bone Tumors. HELEN
QUINCY WOODARD, Memorial Hospital, New York, New
York.
When radioactive phosphorus enters the body it is held
temporarily in high concentration in storage organs such as
the liver. After a variable period of storage it is released
for metabolism in other regions. Since all tissues contain
VOLUME 12, APRIL, 1941 phosphorus, the radioactive isotope, like the normal one.
is taken up to replace catabolized material and to build
new. The rate of uptake by different tissues depends on
their phosphorus content and rate of metabolism. The
phosphorus content of bone is high, and bone produces an
enzyme, alkaline phosphatase, which aids in making
phosphorus available for deposition as calcium phosphate.
Hence available supplies of radioactive phosphorus tend to
335
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rapidly and have the capacity to calcify contain abundant
phosphatase. In these tumors, as in normal bone, the
rate of deposition of radioactive phosphorus usually is a
function of the phosphatase activity. Many, although not
all, of the metastases from bone tumors have the same high
phosphatase activity as the primary lesions. There is a
tendency for radioactive phosphorus to localize in these
metastases. Radioactive phosphorus thus appears likely
to be a valuable therapeutic agent in the treatment of
phosphatase-producing bone tumors. It may prove to be
useful as an adjuvant to external irradiation of the primary
tumor. It may also be found to be effective as a pro
phylactic agent to inactivate metastatic deposits before
they become established. As alkaline phosphatase usually
appears in large quantities in the serum of patients with
phosphatase-producing tumors, the serum phosphatase
readings may be taken as an indication of the suitability of
a patient for radioactive phosphorus therapy.
This work was carried out in cooperation with Mr. L.
Marinelli and Dr. John Kenny of this Hospital. The
radioactive phosphorus was obtained through the courtesy
of Dr. E. O. Lawrence of the University of California.
77. Some Experiments on the Localization of Lithiated
Dyes in Tumor Tissue and Their Bearing on the Possibility
of Slow Neutron Therapy. PAUL A. ZAHL AND F. S.
COOPER, Memorial Hospital, New York, New York; The
Haskins Laboratories, New York, New York.
In a paper by Zahl, Cooper and Dunning! experiments
were described in which mouse sarcomas were injected
hypodermically with slowly diffusing suspensions of
boron or lithium salts and then subjected to slow neutron
irradiation. Resulting tumor regressions were considered
to be due to the nuclear capture reactions which occur
between lithium or boron atoms and slow neutrons with
the release of very high energetic particles. However, for
the possible utilization of this nuclear reaction in the
clinical treatment of cancer, hypodermic injection of
lithium or boron materials is not considered feasible. The
authors have therefore interested themselves in seeking
other devices for localizing slow neutron capturing ma
terials in tumor tissue.
It has been found that certain diazo dyes (most of which
are sodium salts of the disulphonic acid complex) have the
property when injected intravenously of localizing in
greater concentration in tumor tissue than in normal tissue.
Similar salt dyes were prepared in which lithium (because
of its proximity to sodium in the alkali series) replaced the
sodium. Such lithiated dyes were injected intravenously
into tumor-bearing mice, and after suitable periods
quantitative spectroscopic analyses for lithium content
were made on the tumor tissue as well as on the other
tissues of the body. Similar tests were made using simple
binary lithium salts.
It was found that considerably more lithium accumulates
in the tumor tissue than in the normal tissues. The ac
cumulation occurs rapidly, reaching a maximum at be
tween four and seven hours following injection. The maxi
mum concentration is sustained for a relatively short
336 period and is followed by slower drainage and excretion.
At between 24 to 48 hours after injection lithium is no
longer detectable in the system. Maximum concentrations
attained in tumor tissues ranged at 0.03 percent of ele
mental lithium for wet tissue. The concentration of lithium
in the tumor tissue was approximately twice that found
in the liver and kidneys, and an even higher differential
exists for the other tissues.
Results to date of this work will be presented together
with a discussion of the implications of differentiallocaliza
tion of slow neutron capturing materials considered in
relation to the problem of cancer treatment with slow
neutrons.
t Zahl, Cooper and Dunning, Proc. Nat. Acad. Sci., October, 1940, in press.
78. Relative Effect of X-Rays on Resting and Actively
Secreting Kidney Tubules. ROBERT CHAMBERS, New York
University, New York, New York.
The investigation was made on explanted fragments in
tissue culture of the chick mesonephric proximal tubules.
The cut ends of these tubular segments heal over in a few
hours and the closed segments continue to function, their
lumina becoming distended with a fluid secretion. In the
usual plasma medium of the culture the distension is
relatively slow but, when phenol red is added to the
medium, the distension is accelerated, the lumina becoming
intensely colored with phenol red. MgSO. was found to
have a similar effect of inducing distension. The difference
in the rate of distensibility of the tubules was taken as a
criterion for the active and relatively inactive state of the
secretory cells in the walls of the tubules.
Explants of the tissue c.ultures of 48 hours incubation
were exposed to x-rays of various intensities and the effect
of the irradiation noted on the ability of the closed seg
ments of the tubules to become distended with secretory
fluid.
The tubules in the explants were found to be extra
ordinarily resistant to irradiation, the tubules being able to
accumulate phenol red in the normal manner if the phenol
red is added at any time after an irradiation dosage of
25,000 roentgens. With dosages from 40,000 to 60,000
roentgens evidences of deterioration appear after about
50 to 60 hours of incubation and within 5 days the majority
of the proximal tubules have undergone necrosis, However,
the few which remain intact appear as healthy as the
controls and equally able to accumulate phenol red.
Within the 50 to 60 hours after an irradiation of as high
as 60,000 roentgens the addition of phenol red to the me
dium at varying times shows that the tubules develop
progressively increasing ability to function normally in
the accumulation of phenol red in their lumina, Thus, 3
hours after the irradiation the pick-up is much less than
that of the controls, at 20 hours it is improved and at
28 hours it is at its best. Later, the number of healthy
active tubules diminishes, until at 5 days there are very
few, but the few tubules which have survived are as good
as the controls.
There is a marked difference in the susceptibility of the
tubules to irradiation according to whether the tubules are
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inducing substances, e.g. phenol red or MgSO •. The normal
culture medium for these tubules was blood plasma which,
apparently does not contain substances to be' secreted
in sufficient quantity to induce more than a mild activity
of the tubular cells. On the other hand, when phenol red
or MgSO. is added to the medium the cells of the proximal
tubules are greatly stimulated to activity and distension
of the tubules is accelerated. Under these conditions the
toxic effect of the irradiation is more pronounced. The
tubules start to distend but in a few hours undergo progres
sive degeneration which, several days later, becomes wide
spread.
In conclusion, these experiments indicate that healthy,
"resting" proximal tubules of the chick mesonephros in
tissue culture are far less susceptible to the toxic effects of
x·rays than when the tubules are being stimulated to
accelerated secretory activity during the irradiation.
Tubules, irradiated in the "resting" condition, require
time to recover from the effects of the irradiation. If
the tubules are stimulated to secrete at or within a few
hours after being exposed to x-rays they tend to succumb.
On the other hand, the longer they are allowed to remain
in the "resting" condition after the irradiation the better
able are they to resume functional activity.
79. Some Effects of Germ Cell Injury Produced by
X-Rays. PAUL S. HENSHAW, Research Fellow, National
Cancer Institute, Bethesda, Maryland.
How radiation acts on the cells of living matter to bring
about biologic change and cell death is of importance not
only in the treatment of malignant disease and the under
standing of general biologic behavior but also in the pro
tection of the offspring of those who work with radiation.
Information bearing on these points may be obtained from
a study of the injury induced in germ cells by x-rays.
Recently it has been our privilege to observe irradiation
changes produced in a number of kinds of sperm and ova
(the gametes of the marine worm, Nereis limbata; the
marine clam, Cumingia tellinoides; the fly, Drosophila
melanogaster; the sea urchin, Arbacia punctulata; and the
common frog, Rana pipiens). In general the procedure was
to expose one or the other gamete to x-rays, after which
fertilization was allowed to occur and subsequent behavior
observed.
It was found, (1) that without exception the motility of
sperm and their ability to activate the ovum was not im
paired by doses of radiation far in excess of those which
would cause extensive abnormalities in later development;
(2) that in one case (Nereis) extensive swelling of the
fertilization membrane occurs when the ovum is exposed to
the radiation; (3) that delay in cell division and interrupted
phase relationship of cleavage mitoses occurs in sea urchin
material when either gamete is treated; (4) that in the
sea urchin material, multipolar cleavage may be induced
by the exposure of either gamete to a dose of around
20,000 r (observations (3) and (4) will be illustrated by
moving pictures); and (5) that in the case of both frog and
Drosophila material quite normal cell proliferation and
cleavage may be observed after exposure of sperm to
VOLUME 12, APRIL, 1941 radiation, whereas little or very abnormal differentiation
is found to occur.
These findings indicate (a) that injury of a variety of
types (sometimes extensive as death) may be transmitted
to offspring by changes produced in mature sperm or ova
by high energy radiation; (b) that extensive abnormalities
in development may result from irradiation changes
produced in what is essentially half a normal cell nucleus
a sperm; and (c) that since abnormal distribution of
chromatin material resulting from multipolar cleavage
usually leads to cell death, this may be pointed out as one
means by which radiation causes death in cells.
80. Effects of High and Low Temperatures During
Roentgen. Irradiation on the Susceptibility of Skin of
Young Rats. TITUS C. EVANS, Departments of Radiology
and Zoology, State University of Iowa, Iowa City, Iowa.
One-day old rats were irradiated at 0-5°C and at 30°
with dosages ranging from 300 to 3000 roentgens. In all
cases it was found that the skin of the rats irradiated at the
higher temperature was injured more than that of the rats
treated at 0-5°. The animals were kept at these tempera
tures only during the time required to give the x-ray
treatment.
The radiation (130 kv, cardboard filter only) was
delivered at an intensity of 100 r per minute. The experi
ments were begun with a treatment of three minutes and in
each following experimentthe dosage was increased by 300 r.
The young rat was taped to a sheet of lead containing a
2 X 4 mm port which was placed over the region to be
irradiated. The animals were kept near 0° during the
irradiation by packing snow or crushed ice around them.
Immediately after the treatment the animals were placed
at 30° and as soon as they regained their ability to breathe
and move, they were placed back in the cage with the
mother. In each experiment a litter-mate of the same size
and sex (only males were used) was irradiated at 30° and
moist cotton was substituted for the snow. Controls were
kept at 0-5° and at 30° during the time the experimentals
were being treated. Only periods of 30 minutes at 0° ap
peared to be near the limit of endurance, and once a rat
resumed breathing the recovery was complete.
The animals were killed and photographed when they
were two weeks of age. The injury was evident externally
by the degree of epilation produced. In all experiments the
epilation was more severe in the animal irradiated at 30°
than in the one treated while cold. A dosage of 3000 r was
required to produce an area completely devoid of hair
whereas a treatment of only 1000 r had the same effect on
exposed skin of the animal irradiated at the higher
temperature.
Histological examination revealed even more of a differ
ence in the effect produced at the two temperatures. At the
lower temperature 3000 r of radiation did not destroy
many of the deeper follicles and very little tissue reaction
was apparent. The effect of the same dosage at the higher
temperature was extreme. Not only was complete epilation
and excessive desquamation evident, but the epidermis
exhibited injury closely resembling hyperkeratosis. The
slight tissue injury of the skin irradiated at the low temper-
337
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300-600 r at 30°.
This biological material is peculiarly well fitted for a
demonstration of this kind. The metabolism of rats of this
age is inhibited quickly and perhaps completely by low
temperature. The skin is relatively undifferentiated and
growth is rapid. Thus metabolism and cell division were at
a minimum during the irradiatiOli at 0-5° and were near a
maximum during and following treatment at 30°.
81. The E1fect of X-Rays on Bacteriophage. FRANK M.
EXNER, Department of Cancer Research, AND HELEN
ZAYTZEFF-]ERN, Department of Surgery, Columbia Uni
versity. New York. New York.
The rate of inactivation of a virus by x-rays gives a basis
for calculating the size of the radiosensitive portion of the
virus corpuscle for comparison with the size given by
ultrafiltration and ultracentrifuge methods. The calculation
is based on the so-called "hit" theory. Application of this
theory to these simplest known self-reproducing entities
should help in determining the extent to which the theory
is applicable in other biological problems.
While plant viruses have been employed in x-ray
investigations for some time (Gowen). a definite action of
x-rays on bacteriophages (viruses parasitic on bacteria) has
only recently been reported.1 The work here described
represents an independent investigation of the suitability
of bacteriophages for x-ray studies.
The effect observed was the x-ray inactivation of
bacteriophage corpuscles suspended in 1 percent yeast
extract broth containing 0.5 percent NaC!, pH 7.6 to 7.8.
Concentrations of about 10' corpuscles per em' were
employed. Anticoli and antistaphylococci bacteriophages
were used with their homologous strains of bacteria.
To determine the concentration of corpuscles high
decimal dilutions of bacteriophage suspension are made and
mixed with an optimum number of the homologous strain
of bacteria. 0.01 em' pQ1"tions of these mixtures are evenly
spread on 1 percent agar plates. After incubation clear
spots (plaques) in the otherwise uniform bacterial growth represent colonies of bacteriophage derived from individual
corpuscles. which can thus be counted.
X-ray dosage measurements are based on a Victoreen
ionization chamber. Corrections including absorption and
scatter probably total under ±15 percent and are omitted.
Most of the exposures were made at the rate of about
1000 r/min. with copper half-value layer of 3.5 mm corre
sponding to about 425 kv on a tungsten target. with 0.6 mm
copper filtration.
The ratio N I No of corpuscles surviving exposure was
followed from unity to about 10-6• Over this range the
data fit well on a curve N IN 0 = e-aq where q is the dose in r.
The value of a is 2.5 X 10-6 r-I for the staphylococcus and
3.0 X 10-6 r-I for the B. coli bacteriophage.
This great range of exponential inactivation. together
with a number of special tests, points to a direct action of
the radiation on the bacteriophage as against an indirect
action through the medium.
The volume of the radiosensitive portion of the corpuscle
is obtained from the probability a that this volume will be
"hit" by an exposure of 1 roentgen. This requires a knowl
edge of the number of ion pairs per hit. From the known
gross size of bacteriophage corpuscles it is apparent that in
this case the clusters of secondary ionization along the
recoil electron tracks (3 ion pairs per average cluster) will
act as units.2 Omitting minor correction.factors which tend
to cancel, a mean diameter for the two bacteriophages
comes out 4.5 X 10-6 cm (45 mIL) in agreement with the
range of sizes (50-80 mIL) obtained with related strains of
bacteriophages by filtration and centrifuge methods.
One experiment with 200 kv x-rays showed no significant
difference from the harder radiation. This is contrary to
unpublished results with tobacco mosaic virus (J. W.
Gowen and F. M. Exner).
Irradiation of these materials with fast neutrons is
planned with the hope of helping to clarify the rale of ion
distribution in different types of biological response to
radiation.
1 E. Wollman and A. Lacassagne. Ann. de \'lnst. Pasteur 64, 5 (1940).
E. Wollmau, F. Holweck and S. Lauria, Nature 145, 935 (1940).
• D. E. Lea, J. Genetics 39. 181 (1940).
General I
Production of Radioactive and Stable Isotopes
and of Penetrating Radiations
Chairman: DR. EDW. D. CONDON, Westinghouse Research Laboratories
46A. The Production of N eutroDs and Artificial Radio
activity. M. A. TUVE, Department of Terrestrial Magnetism,
Carnegie Institution of Washington, Washington, D. C.
Information and personal opinions are being collected
on the points indicated in the following outline, with
particular reference to obtaining active discussion and
arriving at a reasonable estimate of the present situation
338 relating to the average operating performance and costs of
nuclear physics laboratories.
Outline
(A) Introduction
Spheres of usefulness of the electrostatic generator, and the cyclotron:
General <omments (ll Voltages and currents
(2 Yields of neutrons and artificial radioactivity
(3 Advantages of each for special purposes
(4) General cost comparison
(5) Radium comparisons
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(a) Nuclear reactions of most use
(b) Intensities obtained
(I) Electrostatic generators now in operation
(2) Small cyclotron
(3) Medium-size cyclotrons in operation at various in
stitutions
(4) Large cyclotron (oo-inch)
(5) Possible extensions of each technique
(c) Qualifications on these intensities
(1) The need for and disadvantages of intensity monitors
(2) Total flux of neutrons versus useful flux for various cases
(3) Fast neutrons; energy and space distributions
(4) Slow neutrons; useful flux, collimation, fast neutron
accompaniment. blur of source
(5) Homogeneity of energy
(6) Modulated neutron source for mono-energetic slow
neutrons; energy range available now; possible ex
tensions of this technique
(d) Neutron sources for biological use
(I) Victoreen units (Zimmer, Gray, Aebersold)
(2) Intensities used or needed
(3) Practical considerations; collimation, time schedules,
operating reliability
(C) Artificial radioactivity
(a) Important radioactive elements and reactions; typical uses to
date. and amounts required
(b) Electrostatic generators
(I) Yields obtained; voltages and currents used
(2) Use of weak sources for laboratory studies
(3) Indirect production using neutrons
(4) Costs
(c) Cydotrons
(1) Yields; comparison of production by direct bombard
ment and by absorption of neutrons
(2) Actual amounts produced in various laboratories;
maximum; usual; average; over-all production dur
ing one or two years past; typical sources available
(3) Costs per millicurie; direct· costs; costs allowing for
time of staff and losses of operating time; over-all
costs, including overhead and depreciation
(d) Possible extensions of these techniques
(1) Electrostatic generator; developments and expecta
tions
(2) Cyclotron; developments and expectations
(e) Chief troubles
(1) Electrostatic generators
(2) Cyclotrons
(D) Cost Data
(a) Electrostatic generator
(1) Capital investment and construction time to useful
operation
(a) Open air type generators
(b) Small pressure type generators
(c) Large pressure type generators
(d) Building space costs
(2) Maintenance and improvement costs; staff; running
costs
(3) Percentage of operating time; reliability; discounts
(4) Best present judgment for a recommendation now
(b) Cyclotron
(1) Capital investment and construction time
(a) Small
(b) Medium, 32-inch to 45-inch units
(c) Large, oo-inch and up
(d) Building space costs
(2) Maintenance and improvement costSj staff; powerj
repairs and replacements; supplies; institutional
costs
(3) Percentage of operating time; reliability; dependence
on objectives and changes
(E) Reasons given for installing nuclear physics equipment
(a) Teaching laboratories; supply and demand
(b) Research laboratories in physics; industry
(e) For fundamental research in biology and chemistry
(d) For medical studies and use
The above outline covers the topics indicated by others
as desirable for this discussion, particularly with reference
to anticipated future equipment. The topics which actually
will be covered are to be determined by the group present.
Vigorous discussion and contribution by those present is
expected.
46B. The Production of Neutrons and Artificial Radio
activity. * M. S. LIVINGSTON, Massachusetts Institute of
Technology, Cambridge, Massachusetts.
Representatives of various laboratories have contributed
data pertaining to the yield of neutrons and p82 radio-
VOLUME 12, APRIL, 1941 gm Eq.
Ra-Be
6000
o
1500
1000
500 NEUTRON YIELD/).Ia
Seq+ d1 _ s'" + n'
U. of
ROCHESTER . HARVARD
5 10 15
DEUTERON ENERGY (MEV)
FIG. 1.
P"YIELDo..ah
p'+ d' ~ P"+ p'
CARNEGIE . HARVARD . U.ofCALIF
20
U.ofCALIF.
100 I NST. U.of ROCHESTER x
0~~~~5~~~~I~O~~--~15~~--~2~O
DEl,.ITERON ENERGY (MEV)
FIG. 2.
activity from disintegration apparatus, and also installa
tion and operation costs. These data are tabulated in
Tables I and II. For comparison with neutron therapy
costs data from x-ray and radium-pack installations have
been included. The headings are as follows:
1. Instal1ation.
2. Size: pole face diameter for cyclotrons, sphere diameter and air
pressure for e1ectrostatic generators.
3. Energy (Mev): working energy for deuterons or electrons, in mi11ion
electron volts.
4. Installation cost: complete replacement cost including apparatus,
housing, shielding and salaries of technical and supervisory staff
during construction.
5. Operations crew: supervisory and technical staff required for opera-
tion and maintenance. .
6. Operating cost/yr.: salaries for operations crew, overhead and
maintenance costs, 4 percent interest on capital investment, 10
petcent building depreciation and 20 percent apparatus obso
lesCence charge per year.
7. Average operation: except where noted an average figure of 7
hr./day, 2400 hr./yr. has been used to compare relative costs, due
to present lack of performance data.
S. Operating cost/hr.
9. Deuteron beam (""): the figures in parentheses are estimates of a
proper yield for instruments not ful1y developed for quantity
production, as indicated by results in other laboratories. For the
x-ray installation electron currents in microamperes are used.
10. Operating cost/I'l' hr.
11. "" hr./mC P": reported deuteron bOmbardment in microampere
hours to produce one millicurie of P" from P (d, p) reaction.
Figures in parentheses are estimates or produced by slow
neutrons.
12. Cost/mC pat.
13. Neutron intensity: reported fast neutron intensity in the forward
direction per microampere of deuterons in terms of that from 1 g
Ra mixed with Be.
339
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LARGE MEDIUM SMALL BABY
16 MEV 8-12 MEV 3-7 MEV 1-2 MEV
1. Typical installation U. of Calif. Harvard & M.I.T. Rochester Corneil
2. Size 60 inch 42 inch 27 inch 16 inch
3. Energy (Mev) 16 11.5 4.5 1.4
4. Installation cost $182,000 $60,000 $25,000 $6000
5. Operations crew 15 6 7 2
6. Operating cost/yr. $60,500 $25,000 $20,000 S5000
7. Average operation (hr./day, hr./yr.) (7/2400) (7/2400) (7/2400) 4.5/1500 Operating cost/hr. 8. $25.20 $10.40 $8.30 $3.33
9. Deuteron beam (/La) 200 20 (100) 4 (SO) 25
10. Oper. cost/ /La hr. $.125 $.52 ($.104) $2.07 ($.166) $.133
11. /La hr./mC p32 5 10 (200) (750-n's)
12. Cost/mC p32 $.625 $5.20 ($1.04) ($207) ($16.60) $100
13. Neutron intensity (g Ra-Be Eq'//La) 6000 3000 (200) 40
14. Effective neutron int. ("n" units/min. @ 100 cm) 7.5 0.38 (1.9) (0.005) (0.0625) 0.006
IS. Cost/"n" unit of n's $.056 $.47 ($.087) ($28) ($2.20) 19.25
16. "r" units/min. (for therapy) 30 @ 100 cm 1.5 (7.5) (0.02) (0.25)
17. Therapy cost/loo "r" SI.40 Sl1.50 ($2.30) ($690) ($55)
TABLE II. Electrostatic generators.
PRESSURE LARGE AIR SMALL AIR X-RAY
3-5 MEV 2-3 MEV 1-2 MEV 1 MEV RADIUM BOMB
1. Carnegie M.LT. Carnegie Mass. Gen. Hosp. Memorial Hosp.
2. 18' @ SO lb. 15' @ atmos. 8' @ atmos. 2' @ 150 lb. 4 g radium
3. 3.5 2.5
4. $75,000 $45,000
5. 3 3
6. 120,000 $17,000
7. (7/2400) (7/2400)
8. S8.30 $7.10
9. 15 (SO) 500 elect.
10. $.55 (S.17) ($.014)
11. 1000
12. $550 ($170)
13. 100
14. 0.02 (0.07)
15. S6.90 (S2)
16. 0.08 (0.28) 250 @ 100 cm
17. $17 (S6) S.05
14. Effective neutron intensity: conversion from g Ra Be equivalent to
ionization in a Victoreen 100 r thimble chamber on the basis of
the Carnegie Institution's corrected figure of 0.005 "n"/min. at
5 cm. Neutron yields in the forward direction from cyclotrons are
reduced by a factor of 4 to give the average or effective intensities.
15. Cost/"n" unit of neutrons.
16. "r" units/min.: to compare therapy costs of neutrons, x-rays and
gamma-rays, neutron "n" units are multiplied by a factor of 4.
an average value for their relatively greater biological efficiency.
17. Therapy cost/loo "r" units.
The yields of neutrons per microampere in the Be (d, n)
reaction and of p32 radioactivity per microampere hour in
the P (d, p) reaction are plotted against deuteron energy
in Figs. 1 and 2. Although the relative accuracy of points
on the curves may be poor, these excitation functions show
a more rapid increase with energy than would be expected
on the basis of the increased penetration of deuterons into
the target. Increase in yield due to range alone would
vary with Ei. The points indicated by crosses are computed
for this variation from the value at 3.5 Mev.
* This paper was substituted for 46A. originally scheduled for this
place in the program.
47. The Separation of Stable Isotopes. HAROLD C. UREY,
Department of Chemistry, Columbia University, New York,
New York.
In the separation of the isotopes of elements other than
hydrogen which will not be discussed, all methods which
have been used have certain similarities. In one way or
another countercurrent streams of compounds containing
the element to be separated, having different isotopic
340 1.2 1.25
$7500 $20,000 $100,000
3 1 1
13800 $6500 $4000
(7/2400) 7£:2170 16/5500
$1.60 3.00 $.73
10 500 elect.
$.16 $.006
7 4
0.0008 0.00005
$33 $240
SO @ 70 cm 5 @ 10 cm
S.10 $.24
compositions, are established. The differences in composi
tion are produced by rather widely different methods.
These may be listed as follows: (1) Diffusion through
porous membranes or gaseous substances, (2) the differ
ences in composition produced by thermal diffusion, (3)
differences in composition produced by differences in
chemical and physical properties, such as exchange re
actions and distillation.
Very marked changes in the relative abundances of
isotopes were produced by the two varieties of Hertz
diffusion method. In the first of these, diffusion takes place
across a solid membrane, and in the second, through mov
ing gas streams. The speed of these methods is limited by
the speed with which diffusion through porous membranes
or gas can take place, which is relatively slow in the first
case, since the membrane must support the difference in
pressure on the two sides. This method has been used
to produce very substantial separations of the neon
isotopes, and some separation of the carbon and nitrogen
isotopes.
The thermal diffusion method introduced by C1usius
and Dickel is probably the simplest, from the standpoint of
operation, of any method that has so far been devised.
In this case use is made of the difference in composition
established between a hot and a cold wall, provided the law
of force between the molecules does not approximate
closely to the inverse fifth power law, in which case no
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placed near each other convection is set up, and a stream
having an increased concentration of the heavy isotope
moves downward while a stream having increased concen
tration of the light isotope moves upward. Large concen
tration differences can be secured in this process with
lengths of tube which are easily constructed and main
tained in scientific laboratories. The method is applicable
to a wide range of substances, depending only upon the
necessity of securing the substances in a gaseous form, the
substances being stable when heated, and not reacting with
the walls of the vessel. The theory of this method has been
given in detail by Furry, Onsager, and others. The method
has been applied to secure practically complete separation
of the chlorine isotopes and to secure substantial separation
of the carbon isotopes and, perhaps, others.
The chemical distillation methods depend upon differ
ences in composition resulting from slight differences in
the chemical and physical properties of isotopic compounds.
In these cases differences in composition between two
phases are established, and the two phases are then trans
ported relative to each other in a suitable apparatus. The
systems used so far consist of: gas-liquid systems where the
usual type of distillation column is used, the liquid-liquid
systems used in the case of concentration of lithium iso
topes by exchange between a mercury amalgam and an
alcohol solution of the lithium salt, and between solid
liquid systems using zeolites and salt solutions for partial
separation of the isotopes of lithium, potassium and
nitrogen.
There are certain important features of all of these
methods which must be considered in order to decide
which is the best for a given situation. Important factors
to consider are: (1) The change in concentration that can
be secured in a given apparatus, (2) the time that it will
require the apparatus to come to a steady state so that the
maximum concentration can be produced, and (3) the
rate of production of the isotopic concentrate.
All methods mentioned can produce desirable changes
in concentration of isotopes. Thermal diffusion or Hertz
diffusion systems can be expected to come to equilibrium
in the course of hours or, at most, a day or so. The chemical
and distillation methods require weeks to reach the final
steady state because of the larger amount of working
material' in the system.
In general, it can be said that the Hertz diffusion methods
or the thermal diffusion methods can produce in the neigh-
VOLUME 12, APRIL, 1941 borhood of 1-10 milligrams per 24 hours of such a con
stituent as CI3 in the usual sized apparatus. The chemical
methods are capable of producing about one gram of
material per 24 hours. Thus, in the region where the
chemical methods will work, and if isotopes are needed for
experiments on a rather large scale, they are the best.
This includes oxygen, nitrogen, carbon and sulfur at the
present time. However, the use of the chemical method is
strictly limited to elements of low atomic weight, and
hence the thermal diffusion method is particularly good
for elements of high atomic weight or in cases where only
small amounts of material are required for experiment.
The mass spectrograph method of separation is capable
of producing only small amounts of material, and cannot
be considered seriously as a method for securing tracer
materials. The ultracentrifuge method, on which prelimi
nary experiments have been made, is too much in the
development stage for one to be able to make any pre
dictions. It would seem doubtful that this method will be
as good as thermal diffusion because of the expensive
character of the apparatus required.
48. Production of High Voltage X-Rays. JOHN G.
TRUMP, Department of Electrical Engineering, Massachu
setts Institute of Technology, Cambridge, Massachusetts.
A brief discussion will be given of those properties of
high voltage x-rays which account for the present tendency
toward higher voltages for therapy and for industrial
radiography. Several types of x-ray installations in the
million-volt range which have appeared in recent years
will be reviewed. It appears that the compressed-gas
insulated low frequency resonance transformer and the
constant-potential Van de Graaff electrostatic generator
are the most compact and economical voltage sources for
the production of very penetrating x-rays. The operating
principles and essential features of both these voltage
sources will be discussed. Because of the low current capa
city inherent in the method, the electrostatic generator is
limited to the higher voltages but is relatively free from
an upper voltage limit. Hospital installations of both types
of x-ray generators have been made, and preliminary
evidence indicates 'effective and reliable performance
under continued use. Further gains in compactness and
simplicity, arising both from improved design and from
more effective insulation, are expected. An account will
be given of work now under way directed at greater com
pactness and portability in million-volt units, as well as
at the extension of such x-ray sources to several megavolts.
341
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Measurement of Radioactive and Stable Isotopes
and of Penetrating Radiations
Chairman: DR. K. T. BAINBRIDGE, Harvard University
49. Measurement of Relative Abundances of Stable
Isotopes. ALFRED O. NIER, Department of Physics, Uni
versity of Minnesota, Minneapolis, Minnesota.
The use of separated, stable isotopes of elements such as
carbon and nitrogen as tracers in chemical and biological
problems requires rapid and accurate measurements of
relative abundances. One of the most effective methods of
making these measurements is by means of the mass
spectrometer.
Various types of mass spectrometers can be employed
in this type of work. Large solenoids, electromagnets and
permanent magnets have been used to produce the mag
netic fields needed in these instruments. A discussion will
be given of the relative advantages and disadvantages of
the various instruments.
Special attention will be paid to the control equipment
and power supplies needed. Difficulties encountered in
operating mass spectrometers will be discussed. Slides will
be shown.
50. The Measurement of Radioactive Isotopes. ROBLEY
D. EVANS, Department of Physics, Massachusetts Institute
of Technology, Cambridge, Massachusetts.
For reasonably strong samples an electroscope is usually
the simplest and most rugged detection apparatus, al
though care must be taken to avoid the temperature
fluctuations to which electroscopes are usually sensitive.
Prompt discrimination can be made between alpha-, beta-,
and gamma-rays by means of filters. The limiting sensi
tivity of the best electroscopes usually lies near 10 beta
rays of about 1 Mev energy entering the electroscope per
second. The more complicated ionization chamber and
vacuum tube electrometer combinations offer a somewhat
higher ultimate sensitivity, and are easily adapted to
photographic registration. The use of pressure ionization
chambers and obs~rvations by the rate-of-drift method
give this combination about 5 to 10 times the sensitivity
of the best electroscopes. Maximum sensitivity, for the
detection of beta-and gamma-rays, is offered by Geiger
Muller discharge counters. These are about 20 times as
sensitive as the best electroscopes. For gamma-ray detec
tion screen-cathode counters are several times as sensitive
as solid-cathode counters. For the detection of soft beta
rays, the sample must either be placed inside the vacuum
jacket of the counter, or a very thin window must be
provided in the counter jacket. S. C. Brown has shown that
counters filled with helium, or helium and alcohol vapor,
may be operated easily at atmospheric pressure. In this
case windows may be made very thin or even eliminated
entirely. A wide variety of amplifier and recorder circuits
is available for discharge counters. Deviations from exact
342 linearity of response are most readily evaluated by observa
tions on the additive effects of a group of constant gamma
ray sources. Recording systems for low counting rates
(10 to 100 per minute) usually employ a message register.
For high counting rates a scaling circuit is used, or the
scaling circuit and message register may be replaced by a
counting rate meter whose output may be easily recorded
photographically .. Observational uncertainties due to
purely random fluctuations in the counting rate are
inherent in all measurements and cannot be reduced by
the choice of amplifier circuit. Measurement,s on weak
sources (down to 10-13 curie) emitting alpha-rays may be
made readily with either ionization chambers, or for slightly
higher sensitivities, with pulse counters employing a
vacuum tube electrometer or a linear amplifier. Detection
arrangements depend on whether the sample is gaseous,
liquid, or solid. In every case it is essential to provide a
reproducible geometry of source, windows, and detector,
so that strictly comparable observations may be obtained
on the background, the source, and the radioactive stand
ard to which the activity of the unknown source is referred.
The National Research Council's Committee on Standards
of Radioactivity is preparing standards for use in all
types of radioactivity studies. Standard radium solutions,
and absolute standards of gamma-ray intensity, varying
from 0.1 to 100 micrograms of radium gamma-ray equiva
lent, are now available through the National Bureau of
Standards. Absolute beta·ray standards are also being
prepared.
51. Measurements of Neutrons. J. R. DUNNING,
Department of Physics, Columbia University, New York,
New York.
Neutron investigations at present are principally con
cerned with the energy spectrum ranging approximately
from 0 to 20 Mev. In general, most measurements involve
a determination either of the absolute or the relative
nu~ber of neutrons per second which pass through a
given area, and which have energies within some more or
less definite band. No one technique is applicable to the
entire spectrum.
"Fast" neutrons with energy greater than 50 kev are
effectively detected through the ionization produced by
projected nuclei. Various types of ionization chambers,
when connected to linear amplifiers which in turn operate
scaling mechanical recorders or photographic oscillographs,
provide the most satisfactory methods for measuring
both neutron flux and neutron energy distributions. Pro
portional counters are useful where pulse size is not im
portant. Under proper conditions, cloud chambers and
also photographic plates possess some advantages for
determining momentum and energy of individual neutrons.
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to integrated general ionization, and also photographic
plates, are convenient for such work as neutron therapy,
hut the cqntribution of gamma-rays is difficult to deter
mine, and quantitative interpretation not always readily
possible.
Isotopes which become radioactive through n-p, n-a,
or nc2n reactions are often useful for selective detectors,
since in general each type of reaction responds only to
neutrons above some threshold energy. When more than
one reaction occurs with a given isotope, or when more
than one isc;>tope is present, the interpretation must be
made carefully.
No very satisfactory methods exist for neutron detection
in the intermediate region from 1 to 50 kev as yet, but
proportional counters, secondary emission multipliers, and
some radioactive detectors offer possibilities.
The spectral distribution of the so-called "slow" neutrons
which have diffused through hydrogenous material is
approximately that of a Maxwell distribution appropriate
to the temperature of the material, and a high energy
tail in which (above 1 ev) the number of neutrons per
unit energy interval should be proportional to 1/ E. The
neutron capture processes in Li and B obey the l/v law
and yield energetic heavy particles. When connected to
linear amplifier-recording systems, ionization chambers
lined with these elements or filled with BF 3 gas under pres
sure provide very satisfactory detectors, especially for
neutrons in the thermal region, from 0 to 0.2 ev. Propor
tional counters using BF 3 at reduced pressure posses excellent stability but are less sensitive. Neutron beams
collimated by B, Cd and paraffin may be used with
cyclotrons or other artificial sources for precision experi
ments when used with an integrating monitor system hav
ing accurately parallel characteristics. The general problem
of absolute neutron flux determinations and of precision
monitoring will be discussed.
Elements such as Rh, In, V, I, Br, and others which
become radioactive through resonance neutron capture
over a comparatively narrow energy band (or bands)
serve as excellent selective detectors and filters. Collimated
neutron beams using shielding of paraffin +B+Cd+same
element as detector, when combined with a parallel
monitor, make possible accurate studies with defined
neutron energies.
Methods for production and detection of neutron beams
with sharply defined and continuously variable energy are
essential. In the low energy region, the electrical velocity
selector of Alvarez is considerably more satisfactory than
the mechanical selector, and should be applicable from
~O to ~1O ev at least. The neutron crystal spectrometer
now further developed by Thiessen offers possibilities,
especially in the region less than 1/20 ev.
The wave-length of thermal neutrons of 1/30 ev is 1.6A,
which is comparable with atomic spacings in solids. Inter
ference phenomena thus play an important role in neutron
interaction with solids, somewhat similar to x-rays, as
shown by recent work. The need for more accurate investi
gation of neutron interaction as a function of energy is thus
emphasized, both from the standpoint of nuclear research
and for the application of neutrons to solid state studies.
General III
Protection of Workers from Injurious Effects of Radiation
Chairman: DR. G. FAILLA, Memorial Hospital, New York, New York
52. Biological Damage and Precautionary Tests. STAF
FORD L. WARREN, Department of Radiology, University of
Rochester, School of Medicine and Dentistry, Rochester,
New York.
The exposure hazards to those working with cyclotrons
are not well known, but the potential hazards are in
creasing since equipment is becoming more and more
powerful. So far very little known damage to personnel
has been observed partly because of the precautions which
were taken by the early workers and partly because of the
relative weakness of the output of the present cyclotrons.
Immediate reactions from direct, accidental exposures to
the cyclotron beam have been confined to the skin, and
to date have not been serious. They resemble a severe
reaction to ultraviolet radiation in many respects, except
for the slowly receding superficial edema and erythema,
and the minimum of exfoliation. There is no evidence yet
available as to their possible sequelae.
Exposure to gamma- and beta-radiation bears the same
VOLUME 12, APRIL, 1941 hazards as that to workers who handle radium and x-rays,
and is well known to workers in this field. Long-time
exposure of the body to relatively small amounts of
gamma-radiation has cumulative effects which are prQbably
most marked upon the blood forming elements of the
bone marrow. Neutrons and the protons arising from them
may cause damage in any portion of the body. If we
speculate that their cumulative and possibly harmful
effects will be found in those tissues of the body most
susceptible to x-rays when the whole body is exposed,
then the blood forming organs will be probably among
the first to suffer. Accidental localizations may of course
alter the situation.
Hence routine blood examinations (white blood cell
count and hemoglobin as a minmum) should be done,
certainly every m~nth on all those working with a cyclotron
to obviate .the possibility of accidental and unpredictable
exposure, even though every effort is made to design the
apparatus in such a way as to prevent this. If any fall in
343
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removed from all exposure and a thorough physical
examination and complete blood study made to determine
the cause of the leukopenia. Frequent blood examinations
should then be made and the individual should not return
to work until he is normal. Many intercurrent infections
of very mild character may produce the same result so
that considerable clinical judgment is necessary at times
in evaluating the status of the individuals. Vacations
should be adequate and should total at least one month
in the year. A senior physician should be made responsible
for the supervision of the medical status of all of the
personnel. Since most cyclotron laboratories are connected
with universities, such arrangements can often be simply
made with physicians having experience with radiation
effects in allied or university hospitals. It might not be
out of order to suggest periodic tests of the working area
with a Geiger counter-ionization chamber to detect
unsuspected gamma-radiation, and also to stipulate that
the personnel wear the common dental film, one-half
shielded on both sides by 2 mm lead.· This should be
examined every week. Enough exposure to darken the
film and show an image of the shield edge within a week
probably represents a hazardous amount of radiation
exposure. A condeJ)ser type of ionization chamber (foun
tain-pen size) should also be worn when "beam" adjust
ments are being made.
In speculating as to the probably acute and chronic
damage that may be brought about by these radiations
and particles, it is probably wise, and certainly safer, to
predict a 10-20 times greater hazard than experience has
shown to be present from equivalent quantities of other
radiations.
53. Genetic Changes. M. DEMEREc, Carnegie Institution
of Washington, Cold Spring Harbor, New York.
Genetic changes are usually taken to mean changes
which are transmitted from parents to their offspring.
In one sense this is correct, since only changes transmitted
to the offspring are able to persist through generations.
However, since as a rule every cell of an organism possesses
identical genetic material, the same genetic changes may
occur both in germ cells which transmit these changes to
the olfspring and in somatic cells which do not. Since
germ-cells and somatic cells have identical genetic consti
tution both are used in the studies of genetic changes.
In a very few branches of biologic science, the funda
mental principles are as applicable to all living organisms
as they are in genetics. It is a well established fact that
fundamental principles discovered on plants hold for
animals and vice versa. Man is no exception to that rule.
Hereditary material in the cells is present as differ
entiated regions called genes located on thread-like
structures called chromosomes. The number of genes in
every organism is large, it is estimated that the vinegar
fly, Drosophila, has between 3000 and 5000 different genes
which are present in every cell of the body. Many of them
play an exceedingly important role in life processes and if
any of these are missing, the organism, or even individual
344 cells are not able to persist. Every chromosome has a
differentiated region called centromere which is essential
in order that at the division of a cell a chromosome may
be passed to the daughter cells. If a chromosome breaks,
only the segment with the centromere will be transmitted
while the other segment is soon lost.
With this general background in mind, the effect of
radiation on heredity may now be considered. It is known
that irradiation in the regions about O.OlA to 2.4A and
about 2300A to 3000A is able to produce changes in genes
as well as breaks in chromosomes. It is well known that a
great majority of gene changes are either lethal or injurious
to the organism. Breaks in chromosomes may result in
either losses of segments, or if several breaks are induced
in the same cell, broken points may fuse and thus a
reshuffling between chromosome segments may result.
In the organisms like Drosophila losses of segments are
almost invariably lethal and reshufflings give rise to
aberrations some of which are lethal while others behave
in a manner similar to that produced by changes in genes.
As an illustration of the genetic effect of irradiation the
results of a series of experiments with Drosophila may be
used. If males are treated with 5000 roentgens, the sperm
in the testes is irradiated. Such males copulate readily and
are able to impregnate females. The sperm so transferred
is alive and functional, it fertilizes the eggs. However,
about 90 percent of individuals arising from such fertiliza
tions die before reaching adult stage, most of them in the
early embryo, but some in later stages of development. Of
the individuals which live to adult stage about 40 percent
carry chromosomal rearrangements and about 12 percent
lethal changes. I t seems very likely that an exceedingly
small number of them escape some detrimental hereditary
change.
Experimental evidence indicates that there is no thres
hold for genetic changes. They are proportional to the
dosage used. At very low dosages changes are induced
but with a very low frequency. J. G. Carlson has shown
that as Iowa dose as 7.8 roentgens produces 0.34 percent
of breaks per treated chromosomes in the neuroblast cells
Of grasshoppers.
It is a well-substantiated fact that there is no recovery
in hereditary changes, neither genic nor chromosomal.
Therefore the effect of irradiation is cumulative. This
holds true for individual cells, but not for a dividing tissue.
The rate of cell division is slowed down in affected cells
and an appreciable number of them is eliminated from the
tissue. Therefore the proportion of affected cells in dividing
tissue wi\l decrease with the length of time which elapses
after the treatment. For example, if a Drosophila male is
treated with 3000 roentgens, the sperm which was mature
at the time of treatment carries about 60 percent of
dominant lethals, while the sperm which develops later
carries only about 10 percent of dominant lethals. In this
case, the larger portion of lethal changes were eliminated
during two cell divisions which occurred between irradia
tion and the maturity of the sperm.
Geneticists are interested in the mechanism responsible
for genetic changes and have accumulated a large body of
data on the dosage frequency relationship, wave-length
JOURNAL OF ApPLIED PHYSICS
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the tolerance dose for protective purposes in addition to
these data the selective effect of cell divisions plays an im
portant role. The data on that effect are not yet available.
54. Protective Measures Against X-and ,,-Rays.
LAURISTON S. TAYLOR, National B"ureau of Standards,
Washington, D. C.
Protection against danger from x-or -y-rays may be had
for the asking, the degree of complication and expense
depending upon whether protection from direct or second
ary radiation is sought. For protection against direct
radiation it is desirable to place the barrier as close as
possible to the source, where in most cases the increase in
thickness of barrier is more than offset by its decrease in
total mass. In experimental work canalization of the direct
radiation is usually possible. Observers by remaining away
from the beam may then be very economically protected
by various means. A wide variety of protective materials
may be used, depending upon circumstances,-these
include lead, lead shot, concrete, mercury, copper-tungsten
alloys, barium compounds. Illustrations of the use of
these will be given.
55. Protection from Neutron Rays and Other Products
of Nuclear Transformation. PAUL C. AEBERSOLD, * William
H. Crocker Radiation Laboratory, Physics Department,
University of California, Berkeley, California.
So rapid has been the expansion both in the production
and in the uses of nuclear transformation products,
particularly neutrons and induced radioactive substances,
that it is tiItely and highly desirable to call attention to
the protection necessary to avoid injurious effects upon
those exposed to the radiations involved. To physicists
accustomed to very delicate methods of detecting nuclear
products the realization comes slowly that quantities of
radiations and radioactive substances are produced by
present bombarding apparatus that necessitate serious
consideration of the problem of protection. Inasmuch as
the nature and penetration of some of the radiations are
different from those dealt with previously, it is necessary
to proceed with caution in arriving at rules of safe practice.
Therefore, without claim to specifying a set of protection
rules, as are now possible for x-ray apparatus and radium,
this paper proposes to give only some of the considerations
used in arriving at protective measures for the Berkeley
cyclotrons.
The average daily tolerance limit of exposure adopted
for the gamma-rays encountered from cyclotron bombard
ments and radio-elements is the same as that adopted by
radiologists for x-rays and radium, namely 0.1 r/day.
Should another value seem desirable the following values
would be changed accordingly. For fast neutrons a toler
ance dose is assumed that is biologically equivalent to
0.1 r of x-rays. This equivalence was originally determined
by experiments on animals and other organisms. Because
of the application of neutrons in cancer therapy, equiva
lence can now be based on reactions of human tissues
to neutrons.
VOLUME 12, APRIL, 1941 An arbitrary unit, called the "n," has been found useful
and expedient in measuring neutron dosage. It is the
exposure of neutrons that will cause in the Victoreen
x-ray r-meter chamber (100 r, 0.5 cc size) the same reading
as an exposure of 1 r of x-rays. A marked human skin
reaction corresponding roughly to that caused by 1000 r
of x-rays is produced by 200 n of neutrons. Taking, as for
x-rays, the daily tolerance to be 10-4 of the single dose
for epithelial reactions (such reactions being used by
radiologists as guides in avoiding permanent tissue
damage) the value for neutrons would be 0.02 n/day.
Since on some organisms 1 n was found as effective as
10 r, the tolerance we have adopted is 0.01 n/day. This
allows for the possibility that the sensitivity of some
tissue in the body with respect to that of skin may be
twice as great for neutrons as for x-rays. Although there
is a possibility that the recovery of normal human tissues
from repeated minute doses of neutrons is much less than
that for x-rays, experience with neutron therapy indicates
no large factor need be considered on this score. In actual
practice, the average daily exposure of workers in the
laboratory falls below the above limit.
Table I gives approximations' of the intensities involved
and the distances or water shielding necessary for protec
tion. The n intensity per curie source strength is an upper
limit based both on calculations and available data.
Measurements show that the 37-inch and 60-inch cyclo
trons operate at curie strengths of more than 106 and 106,
respectively. The safe working distances are merely
calculated by inverse square decrease and take no account
of absorption, scattering, and secondary radiation. Rigor
ous calculations of the penetration of neutrons through
water shields are complicated, but a sufficient approxi
mation can be made assuming exponential absorption.
Values are given which assume that an appreciable fraction
of the neutrons have mean free paths as large as 15 and
20 cm. Using neutron indicators in water shields around
the 60-inch cyclotron, X= 12 cm was found applicable for
neutrons from 16-Mev deuterons on beryllium. However,
the thicker shields calculated on the basis of X= 15 cm
are advisable because of secondary radiation created at
depths in the shields.
The following things are recommended for shielding a
60-inch cyclotron: (1) the emergent ion beam directed
CURIE STRENGTH
OF SOURCE
1
10
10'
10'
10'
1()'
(37 -inch cyclotron)
10'
(60-inch cyclotron)
10'
10' TABLE I
TOLERANCE
WORKING
N PER 8-HR DISTANCE
DAY AT 10 IN METERS
METERS NO SHIELDING
10-' 1
10-' 3.2
10--' 10
10-1 32
1 10'
10 320
10' 10'
10' 3200
10' 10' THICKNESS OF
WATER TANKS IN
CENTIMETERS FOR
TOLERANCE AT 10
METERS
e-r/11i e-f,/20
0 0
0 0
0 0
34.5 46
69 92
103.5 138
138 184
172.5 230
207 276
345
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walls of water at least five feet thick, (3) a roof and -floor
equivalent to at least three feet of water, (4) a minimum
of openings through the shielding, (5) additional shielding
provided wherever possible between the magnet coils
directly around the target and vacuum chamber, and
(6) a concrete-walled control room over ten meters away.
* Fellow of the Finney~Howel1 Research Foundation.
56. Protective Requirements for Shipping Radioactive
Substances. L. F. CURTISS, Physicist, National Bureau
of Standards, Washington, D. C.
During the last five years the shipment of radioactive
substances has been given considerable attention. This
was brought about by the discovery by the Post Office
Department that photographic films were fogged in
transit by radium preparations shipped in close proximity.
An order excluding radium and similar radioactive sub
stances from the mails followed.
The express companies were willing to continue to
handle shipments of radium if methods could be worked
out which would preclude damage to films. Conditions
under which these companies handle shipments are more
flexible than those under which the mails are handled and
regulations have been drawn up by the express companies
which are the result of tests at a number of lab'oratories
and conferences between the manufacturers of photo
graphic films and the principal shippers of radium.
The factors entering into the fogging of films are: (1) the strength of the radioactive preparation; (2) the
time that the film is exposed to the preparation; (3) the
distance between the radioactive sample and the film;
(4) the thickness of lead screening on the radium; (5) the
sensitivity of the film.
In the practical solution of the problem, the distances
are determined from the conditions existing in the average
express car. The maximum separation of packages con
taining films and radium in such cars is approximately
20 feet. Therefore, the table used is based on x-ray films,
which are most sensitive to radium, placed at 20 feet from
all packages of radium. This table shows the relation
between the amount of radium, the thickness of lead and
the permissible number of hours in transit. This is shown
in Table I. * In order to make this arrangement workable
it is necessary that all packages of photographic films and
of radium be clearly marked as to contents. In addition,
a label stating the amount of radium contained in a
package and the thickness of lead surrounding it is required
by the express companies.
Although this table includes shipments up to 600 mg
of radium, the express companies accept shipments only
up to 100 mg without previous consultation with the local
agent. This is to permit special arrangements to be made
in handling the larger shipments so that they may be
carried in cars not containing photographic films.
The lead screening required by these regulations is much
greater than was required formerly. Some examples of the
way in which this problem has been solved by individual
shippers will be discussed.
Allowable Time of Tran.it for Radium (Table 1 uf Abstract Nu. 56)
QUANTITY OF RADIUM: THICKNESS OF LEAD-INCHES
Milligrams 1 1! 2 2t 3 31 4
Allowable hours in transit
Under 15 mg. 40 60 110
15 mg and under 25 20 30 55 110
25 mg and under 35 14 20 36 73 146
35 mg and under 45 10 15 28 55 110
45 mg and under 55 12 22 44 88 170
55 mg and under 65 10 18 36 73 142
65 mg and under 75 16 31 63 122
75 mg and under 85 14 27 55 106
85 mg and under 95 12 24 48 95
95 mg and under 100 indo 11 22 44 85 170
200 mg 11 22 43 86 172
300 mg 14 28 56 112
400 mg 11 22 44 88 172
500 mg 8 17 34 68 136
600 mg 14 28 56 112
Minimum weights of lead.
pounds 3i 9: 9! 36 58!
346 JOURNAL OF ApPLIED PHYSICS
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Contributed Papers*
Chairman: DR. ROBERT ]. VAN DE GRAAFF, Massachusetts Institute of Technology
91. The Significance of the Hit Theory of Radiobiological
Actions. UNO FANO, Carnegie Institution of Washington,
Cold Spring Harbor, New York.
Numerous experimental radiobiologists are still in doubt
as to whether their results agree with the so-called "hit
theory" and especially whether they yield any definite
evidence supporting it. An attempt has been carried out to
examine critically the logical structure of the hit theory and
its bearing on the known experimental facts.
Simple, quantitative-perhaps unduly schematized
biological reactions have been taken as indicators of the
radiation effects under physically controlled conditions;
dose-action curves and their dependence upon the charac
teristics of the irradiation have thus been studied. The hit
theory offers a simple interpretation of various results of
these experiments. It seems, however, that such results do
not necessarily require the hypothesis of the theory itself
(the evidence is more convincing in the "single hit" case
than in other cases). It is difficult to obtain any better
evidence through further experiments of the same type.
For instance the behavior of dose-action curves is critically
affected by the theoretical assumptions only in the hardly
accessible ranges corresponding to exceedingly low or
exceedingly high dose.
Further evidence should be obtained through experi
ments involving more detailed observations of the bio
logical reactions. Results available at present show that
the complication of some phenomena considerably exceeds
that of their previous interpretations on the basis of the
hit theory.
Some theoretical considerations, which might stimulate
further experiments, can be put in a general form so that
they are still valid even if the usual restrictive assumptions
of the hit theory are rejected.
92. The Effect of Fast Neutrons on the Chromosomes of
Tradescantia. NORMAN GILES, Biological Laboratories,
Harvard University, Cambridge, Massachusetts.
Fast neutrons were produced by bombarding a beryllium
target with ll-Mev deuterons in the Harvard cyclotron and
their effects on the chromosomes of Tradescantia during
microspore development have been investigated and com
pared with the effect of x-rays. Qualitatively the results are
the same as those produ·ced by x-ray treatment, and consist
of chromosome breakage and the refusion of broken ends.
Quantitatively, however, neutrons appear to differ con
siderably from x-rays in their effect on chromosomes. For
equal total doses in terms of ionization as measured with a
Bakelite Victorcen ionization chamber neutrons are from
16 to 17 times as effective as x-rays in producing chromatid
dicentrics-an aberration type known to result from a
* Proofs of the abstracts printed in this section were not read by the
authors.
VOLUME 12, APRIL, 1941 single x-ray hit. Also, exchange break aberrations, pro
ducing chromatid and chromosome rings and dicentrics,
are found to show an approximately linear relationship to
dosage instead of the exponential relation found with
x-rays. An attempt is made to explain these differences
between neutrons and x-rays in terms of the great difference
in the types of ionization paths which these two radiations
produce in tissue.
93. Magnetic and Metallurgical Studies with the Aid of
Neutron Phenomena. OTTO HALPERN, Department of
Physics, New York University, University Heights, New
York.
The magnetic moment of the neutron gives rise to a
large number of additional scattering phenomena occurring
during its passage through magnetic material. Theories
have been developed which permit to obtain information
from neutron experiments, on the magnetic, crystalline
and elastic structure of the materials used. This new
evidence refers among other things to the domain structure
of ferromagnets, to the dependence of the domains on the
crystalline state of the material and the external or in
ternal stresses, and to the influence of external magnetic
fields on the size of the domains. For paramagnetic ma
terials information concerning the inter-atomic magnetic
coupling can also be gained. Even for nonmagnetic ma
terials, experiments with neutrons sometimes lead to
results, concerning the crystalline arrangement of alloys,
which cannot be gained from x-ray studies. Examples are
discussed.
94. Preparation of Radio-Arsenic for· Biological and
Chemical Experiments. JOHN W. IRVINE, JR., Department
of Physics, Massachusetts Institute of Technology, Cam
bridge, Massachusetts.
Radio-arsenic, 33As74 with a 17-day half-life can be
produced by a d-n reaction on ger!Jlanium.1 The arsenic so
formed is in a mixture of germanium, copper, tin, lead, and
minor impurities. To free it from these impurities and
reduce the element to a form in which it can be used, the
following procedure is used. The target is dissolved in
aqua regia, some carrier arsenic added, and the solution
evaporated to dryness. This removes the excess HNOa and
most of the germanium. Concentrated HCl and a small
amount (5 ccl concentrated HBr are added and distilled
into a chilled receiver. The HBr reduces the AsH to As+3
which passes over with the HCI and Br2 as AsCIa. This
distillation is repeated after the addition of more acid to
the residue. To the combined distillates an excess of
NH4H2P02 is added, and the solution warmed to 900e for
five minutes. Metallic arsenic precipitates, and is filtered
out through a porcelain micro-filter crucible. From this
point the arsenic can be converted to any form suitable
347
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in KHC03 to make Fowler's solution. Yields of 65-75
percent are obtained by this method when 1 to 10 mg of
carrier are used. By carrying out the distillation in a stream
of hydrogen chloride, the yield can be raised to 95-100
percent.
• Sagane. Kojima and Ikawa. Phys. Rev. 54. 149 (1938).
95 .. Effects of Inhaled Radon on Mice. MEL YIN L. J ACK
SON, Massachusetts Institute of Technology, Cambridge,
Massachusetts.
A system consisting of an animal house with provision
for a continuous supply of radon-laden air has been used
in subjecting 60 male mice to an atmosphere of ca. 2 X 10-6
Curie per liter since July 2,1940. The continuous exposure
is interrupted only for removing dead animals or at ap
proximately weekly intervals when 12 blood specimens are
taken, weights recorded, and food and water replenished.
The average blood counts with their probable errors are
shown in the table. Erythrocytes are given in 10G/mm',
total leukocytes in lO'/mm'. See Table I.
TABLE 1.
Days 6 12 18 25 33 41 52 62 71
Erythrocyres 9.4 9.4 9.7 9.6 10.4 11.1 10.9 11.1 11.7 10.4
Probable Error ±0.2 ±0.2 ±0.3 ±1.0 ±0.2 ±1.1 ±0.2 ±0.2 ±0.2 ±0.2
Leukocyres 10.1 12.8 12.3 9.1 9.7 9.2 8.5 7.6 14.8 9.6
Probable Error ±0.8 ±1.1 ±1.1 ±0.8 ±1.0 ±0.8 ±1.0 ±0.7 ±1.0 ±1.1
All of the mice were between two and four months old
at the beginning of the experiment. At the end of 6 weeks,
of 8 deaths none could be attributed to the effects of radon
inhalation, although pathological changes similar to those
due to x-rays were noted. Two pregnant mice gave birth
to 11 offspring 12 hours after being placed in the animal
house. These mice are being raised in the radon atmosphere.
These inhalation experiments, conducted by a group in
cluding Professor R. D. Evans of Massachusetts Institute
of Technology and Dr. J. C. Aub and Dr. Eugene Wiege of
the Collis P. Huntington Memorial Hospital, are still in
progress.
96. The Effect of 200-kv X-Radiation on the Extraneous
Coats of Arbacia Eggs. M. J. KOPAC, New York University
and the Marine Biological Laboratory, Woods Hole, Massa
chusetts.
Mature sea-urchin eggs possess several extraneous coats,
including an outer jelly layer and a vitelline membrane
which covers the protoplasmic surface layer. On sperm or
chemical activation, the vitelline membrane separates
from the surface layer, elevates, stiffens, and becomes the
fertilization membrane. A few minutes later, a hyaline
layer is secreted by the egg and this coating lies on the
protoplasmic surface layer. The latter coating is of interest
since it eventually becomes an intercellular cement which
binds together the blastomeres of the developing larva.
Evans' has shown that high voltage x-radiation greatly
accelerates the dispersal of the jelly layer. The vitelline
membrane is also affected by similar radiation. The action
of x-radiation on the vitelline membrane can be traced by
measuring the coalescency of the eggs with oil drops.2
348 This method permits the evaluation of the tangential
rigidity of the protoplasmic surface layer as well as
extraneous coats.
Coalescency determinations on eggs were made at
various times after irradiation. Dosages of 1000r produced
no change during the first hour, but at 6 hours the tan
gential rigidity dropped to 0.7, and to 0.17,24 hours later.
Dosages of 1O,000r caused a decrease in tangential rigidity
to 0.25 of the control value during the first hour, to 0.14
at 6 and 24 hours. These two dosages did not produce any
appreciable stickiness of the vitelline membranes. Dosages
of 50,000r caused a drop in tangential rigidity to 0.67
during the first hour in about SO percent of the eggs, with
no significant change at 6 hours and a drop of 0.1 after 24
hours. These eggs showed no visible membranes but all
exhibited a pronounced stickiness to glass and to oil drops.
Oil drops pulled away from the egg's surface, usually
carried with them a small pinched-off portion of the egg,
resembling in this respect the behavior of unfertilized eggs
immersed in 0.34M CaCl, solution. About SO percent of
the eggs irradiated with 50,000r developed tight-fitting
fertilization membranes and a fully formed hyaline layer.
The perivitelline space was essentially non-existent. In all
cases, including nonradiated controls, the vitelline mem
brane is slowly dissipated and this shown by the low
tangential rigidities as measured 24 hours after irradiation.
• Evans. BiD!. Bull .• in press.
, Kopac. Cold Spring Harbor Symposia. 1940. in press.
97. Radioactive Comparison of Meteoritic and Ter
restrial Potassium. WILLIAM M. LEADERS, Department of
Chemistry, Massachusetts Institute of Technology, Cam
bridge, Massachusetts.
The relative abundance of the beta-active isotope K40
has been determined by radioactive measurements in
potassium chloride obtained from the Pultusk meteorite
and the earth. The results indicate no difference within
the limits of the statistical error.
Thus, according to the basic assumption for age deter
mination; namely, all elements have the same isotopic
abundance ratios at the time of formation, there is no
difference in age between the Pultusk meteorite and the
earth within the limits of statistical error.
The potassium recovered from the meteorite corresponds
to 0.28 percent K20. The purity of the potassium chloride,
obtained with the aid of the perchloric acid alcohol method
is not less than 99.25 percent with the major impurity
being calcium and not more than 0.15 percent rubidium
present. These percentages are based on spectroscopic
analyses. The terrestrial potassium chloride was not less
than 99.94 percent pure and contained no detectable
rubidium.
The samples of potassium chloride were mounted as a
fine powder. This technique greatly facilitates the deter
mination and makes it possible to obtain around eight
weight versus activity measurements per day. This method
could advantageously be employed, therefore, for rapidly
determining the activity of weakly active substances
obtainable in weighable quantities.
JOURNAL OF APPLmn PHYSICS
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samples of potassium were obtained by extrapolating the
experimentally obtained specific activity versus weight
curves to the point of zero sample weight.
98. The Interchange of Uncombined Oxalate Ions with
the Oxalate of Several Complex Oxalate Ions. F. A. LONG,
Department of Chemistry, Cornell University, Ithaca, New
York.
Radioactive potassium oxalate has been synthesized
from radio-carbon (20 min. half-life). This radioactive
oxalate has been used to study the interchange of uncom
bined oxalate ions with the oxalate present in complex
ions of the type M(C,O')3=' The interchange has been
studied for ferri-trioxalato, aluminum-trioxalato and co
balti-trioxalato ions. The cobalt complex shows no inter
change and thus is similar to the previously studied
chromium complex ion. The other two complex ions,
however, show complete and rapid interchange of their
oxalates.
These experimental results can be correlated with the
expected bond types for the four complex ions. The results
have direct bearing on the problem of the reported optical
activity of salts of these complex ions. The conclusion is
that the rapid interchange makes optical activity very
unlikely for the ferric and aluminum compounds although
it does not suffice to exclude entirely such optical activity.
99. The Use of Radioactive Isotopes in Studies of the
Permeability of the Human Erythrocyte. ALEXANDER W.
WINKLER, ANNA J. EISENMAN AND PAUL K. SMITH,
Department of Internal Medicine and the Laboratory of
Pharmacology, Yale University School of Medicine, New
Haven, Connecticut.
Studies recently completed in these laboratories have
made use of the radioactive salts of sodium, potassium and
phosphorus to determine whether these elements as they
exist in the human red cell are in equilibrium with the same
elements in the serum. It has been shown that no equilibrium develops in vitro
between the intracellular and extracellular potassium either
at body temperature or at 7°. Some transfer of sodium did
occur, but the degree of radio-sodium penetration was so
small that it could not be shown whether an equilibrium
existed. Phosphate entered rapidly at body temperature
but not at 7°. At 38° there was active synthesis and break
down of organic phosphorus compounds. This was inter
preted as evidence that the penetration of phosphates into
the red cell depends upon an enzymatic process.
To determine whether the chloride in the cells is in
equilibrium with the chloride of the serum, lithium chloride
was used. Human blood was defibrinated and centrifuged,
the dried salt dissolved in the supernatant serum and the
cells recombined with the serum. The samples were placed
for definite periods of time in large tonometers and rotated
slowly in a water bath at 38°. Hematocrits were determined
with Daland tubes. Part of each specimen was set aside
for whole blood analyses, the rest being centrifuged to
obtain the serum for analysis.
Radioactivity was determined by the use of a Geiger
Muller counter tube that dipped into the solution to be
analyzed. The whole blood was hemolyzed with saponin
before counting. The exact time of each count was noted to
permit correction for the rapid decay of Cps. Chloride in
the whole blood and serum was determined chemically.
The concentrations of chloride and radio-chloride in the
cells were calculated from the hematocrits and the whole
blood and serum determinations. Under these circum
stances equilibrium between chloride' in and out of the
cells exists if the ratio of radioactivity to chloride in the
cells is equal to the ratio of radioactivity to chloride in
the serum.
Our experiments indicate that when radio-chloride is
added to human blood in vitro at 38° an equilibrium is
quickly established between the chloride of cells and of
serum. Equilibrium was usually complete in one hour and
in some cases in fifteen minutes. All radioactive samples
were prepared by Dr. Ernest Pollard of the Sloane Physics
Laboratory, Yale University.
AUTHOR INDEX TO PAPERS
Adams, Norman I., Jr.-see Kovarik, Alois F ....... 296 Chaikoff, I. L.-see Perlman, I. ................... 319
Aebersold, Paul C.-Nos. 55, 72 .............. 335, 345 Chambers, Robert-No. 78. . . . . . . . . . . . . . . . . . . . . .. 336
Anderson, Evelyn, Michael Joseph and Herbert M. Cohn, Waldo E.-No. 40 ......................... 316
Evans-No. 42 ................................ 317 --see Brues, Austin M ......................... 321
Ariel, I.-see Hodge, H. C ........................ 314 Cooper, F. S.-see Zahl, Paul A ................... 336 --see du Pont, Octavia. . . . . . . . . . . . . . . . . . . . . . .. 324 Coutard, Henri-No. 25 .......................... 329
Craig, Roderick-No. 86 ......................... 325
Beyer, H. G.~see Nix, F. c. ..................... 305 Curtiss, L. F.-Nos. 2, 56 .................... 297, 346
Bloch, F.-No. 13 ............................... 305
Borsook, Henry, John B.Hatcher and Don M. Yost- Demerec, M.-No. 53 ........................... 344
No. 85 ....................................... 325 DeVault, Don-see Halford, R. S .................. 312
Brooks, S. C.-No. 90 ........................... 328 Dresser, Richard-No. 39 ........................ 331
Brues, Austin M., Elizabeth B. Jackson and Waldo E. Dunning, J. R.-No. 51. ......................... 342
Cohn-No. 69 ................................. 321 --see Nix, F. C ............................... 305
VOLUME 12, APRIL, 1941 349
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-No. 84 ..................................... 324
Eisenman, Anna J.-see Winkler, Alexander W ...... 349
Ed, L. A.-see Lawrence, J. H.. . . . . . . . . . . . . . . . 333
Evans, H. M.-see Anderson, E.. . . . . . . . . . . . . . . .. 317
Evans, Robley D.-Nos. 3, 50 ................ 297, 342
Evans, Titus C.-No. 80 ......................... 337
Emer, Frank M. and Helen Zaytzeff-Jern-No. 81 .. 338
Fajans, Kasimir-No. 19 ......................... 306
Fano, Uno-No. 91 .............................. 347
Fenn, Wallace O.-No. 41... . . . . . . . . . . . . . . . . . . . 316
Giles, Norman-No. 92 .......................... 347
Goodman, Clark-No. 15 ......................... 299
Greenberg, David.M.-No. 44 .................... 318
Griggs, David-No. 33 ........................... 3)2
Gustafson, F. G.-No. 88. . . . . . . . . . . 327
Hahn, P. F. and G. H. Whipple-No. 29 ........... 314
Halford,R. S., W.F. Libby and Don De Vault-No. 61 312
Halpern, Otto-No. 93 ........................... 347
Hamilton, Joseph G. and Mayo H. Soley-No. 28 ... 314
Hastings, A. Baird and G. B. Kistiakowsky-No. 74. 322
Hatcher, John B.-see Borsook, Henry ............. 325
Haven, Frances L.-No. 67.. . . . . . . . . . . . . . . 320
Henderson, G. H.-No. 10 ....................... 299
Henshaw, Paul S.-No. 79 ....................... 337
Hertz, Saul-No. 26 ............................. 313
Hevesy, George-No. 65 ......................... 319
Hodge, H. C., W. Mann and I. Ariel-No. 27 ....... 314
Howell, Lynn G.-No. 31 ........................ 301
Hunter, F. T. and A. F. Kip-No. 83 ............... 324
Hurley, Patrick M.-No. 17 ...................... 300
Irvine, John W., Jr.-No. 94 ..................... 347
Jackson, Elizabeth B.-see Brucs, Austin M ........ 321
Jackson, Melvin L.-No. 95 ...................... 348
Johnson, R. P.-No. 6 ........................... 303
Johnson, William A.-No. 12. . . . . . . . . . . . . . 304
Joseph, M.-see Anderson, E ..................... 317
Kamen, M. D.-see Ruben,S ................. 311, 321 --and S. Ruben-Nos. 58, 87 .............. 310, 326
Kennedy, J. W.-see Ruben, 5 .................... 308
Kip, A. F.-see Hunter, F. T ...................... 324
Kistiakowsky, G. B.-see Hastings, A. Baird ........ 322
Kopac, M. J.-No. 96 ............................ 348
Kovarik, Alois F. and Norman I. Adams, Jr.-No.1. 296
Kruger, P. Gerald-No. 63 ....................... 332
Lark-Horovitz, K.-No. 43 ....................... 317
Larkin, John C.-see Stone, Robert S. . . . . . . . . . . . .. 332
Lawrence, J. H., L. A. Ed and L. W. "Tuttle-No. 64. 333
Leaders, William M.-No. 97 ..................... 348
Libby, W. F.-see Halford, R. S ................... 312
Livingston, M. S.-No. 46B ...................... 339
Long, F. A.-No. 98. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 349
350 Mann, W.-see Hodge, H. c. ..................... 314
Marble, John Putnam-Nos. 4,16 ............ 298, 300
Mehl, R. F.-No.5 .............................. 302
Miller, P. H., Jr.-No.7 ......................... 303
Nier, Alfred O.-Nos. 18,49 ................. 300, 342
Nix, F. C., H. G. Beyer and J. R. Dunning-No. 14. 305
Norton, John T.-No. 11.. . . . . . . . . . . . . . . . . 304
Pecher, Charles-No. 45......... 319
Perlman, I. and I. L. Chaikoff-No. 66 ............. 319
Piggot, C. S.-No. 9. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 299
Portmann, U. V.-No. 38 ......................... 331
Quick, Douglas-No. 37. . . . . . . . . . . . . . . . . . 330
Rittenberg, David-No. 34. . . . . . . . . . . . . 308
Roberts, Irving-No. 21.. . . . . . . . . . 307
Rosenblum, Charles-No. 35. . . . . . . . . . . . 309
Ruben, S.-see Kamen, M. D ................ 310, 326 --and M. D. Kamen-Nos. 60,73 .......... 311, 321
--, G. T. Seaborg and J. W. Kennedy-No. 22 .... 308
Sacks, Jacob-No. 68 ............................ 320
Schmidt, Carl L. A.-see Tarver, Harold. . . . . . . . . .. 323
Schoenheimer, R.-Nos. 59,75 ............... 311, 322
Schultze, M. O. and S. J. Simmons-No. 30 ........ 315
Seaborg, G. T.-see Ruben, S ..................... 308
Segre, Emilio-No. 36. . . . . . . . . . . . . . . . . . . . . . . . . .. 309
Simmons, S. J.-see Schultze, M. O ............... 315
Slichter, L. B.-No. 32........ ...... .... ... 301
Smith, Paul K.-see Winkler, Alexander W ......... 349
Soley, Mayo H.-see Hamilton, Joseph G ........... 314
Solomon, A. K.-No. 57 .......................... 310
Stewart, Fred W.-No. 24 ........................ 328
Stone, Robert S. and John C. Larkin-No. 62 ....... 332
Stout, P. R.-No. 89... . . . . . . . . . . . . . . . . . . . . . . 327
Tarver, Harold and Carl L. A. Schmidt-No. 82 ..... 323
Taylor, Lauriston S.-Nos. 54, 70 ............. 334, 34S
Trump, John G.-No. 48 ......................... 341
Tuttle, L. W.-see Lawrencp, J. H. . . ........ 333
Tuve, M. A.-No. 46A ........................... 338
Urey, Harold C.-No. 47 ......................... 340
Warren, Stafford L.-No. 52. . . . . . . . . . . . . . . . . . . . .. 343 --see du Pont, Octavia. . . . . . . . . . . . . . . . . . . . . . .. 324
Wells, Roger C.-No.8 .......................... 298
Whipple, G. H.-see Hahn, P. F ................... 314
White, T. N.-No. 71 ............................ 334
Winkler, Alexander W., Anna J. Eisenman and Paul
K. Smith-No. 99 ............................. 349
Woodard, Helen Quincy-No. 76 .................. 335
Yost, Don M.-see Borsook, Henry. . . . . . . . . . . . . . .. 325
Young, Ralph C.-No. 20 ......................... 306
Zahl, Paul A. and F. S. Cooper-No. 77 ............ 336
Zaytzeff- Jern, Helen-see Exner, Frank M. . . . . . 338
JOURNAL OF ApPLIED PHYSICS
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1.1712937.pdf | The Theory of the Plastic Properties of Solids. IV
Frederick Seitz and T. A. Read
Citation: Journal of Applied Physics 12, 538 (1941); doi: 10.1063/1.1712937
View online: http://dx.doi.org/10.1063/1.1712937
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/12/7?ver=pdfcov
Published by the AIP Publishing
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Downloaded to ] IP: 193.0.65.67 On: Tue, 09 Dec 2014 09:41:10The Theory of the Plastic Properties of Solids. * IV
By FREDERICK SEITZ
Randal Morgan Laboratory, University of Pennsylvania, Philadelphia, Pennsylvania
AND
T. A. READ
Westinghouse Research Laboratories, East Pittsburgh, Pennsylvania
Part B~ Polycrystals1
INTRODUCTORY DISCUSSION
THE properties of polycrystals are influenced
by two separate factors-first by the
intrinsic properties of the single crystal con
stituents or grains, and second by the restrictions
neighboring grains exert on one another. If it
were not for the second influence, all properties
of polycrystals could be derived by taking some
simple average of the properties of corresponding
single crystals for various orientations. This
simple procedure is possible in a few simple
cases, of course. For example, the elastic moduli
and electrical resistivity of pure polycrystals
may be approximated closely2 by taking the
appropriate averages f~r single crystals. On the
other hand, many properties of polycrystals,
such as shear strength and internal friction, are
affected by the discontinuities in structure that
occur in a way that cannot be explained simply
by treating the system as a set of disoriented
isolated single crystals. We shall refer to the
additional factor as grain boundary influence and
shall attempt to unify present knowledge of this
factor in the next section. It should be borne in
mind that by grain boundary influence we mean
not only the effect arising from the atoms in the
transition region between two grains, but also
the effect that neighboring grains exert on one
another.
On the whole, the amount of purely scientific
curiosity that has gone into the experimental
* The previous installments of this series appeared in
the February, March, and June, 1941, issues of this journal.
1 The analytical conditions used in mathematical treat
ments of practical problems in plasticity will not be sur
veyed here. They are discussed in the book by A. Nadai,
Plasticity (McGraw-Hili Book Company, New York, 1931),
and that by M. Gensamer, Strength of Metals Under Com
bined Stresses (American Society for Metals, Cleveland,
1941).
2 See, for example, E. Schmid and W. Boas, Kristall
plastizitiit (Springer, Berlin, 1936), Section 81.
538 study of polycrystals is far less than that
expended in the investigation of single crystals.
This fact will be evident at many points in the
following pages, for only in a few cases is it
possible to draw conclusions from available
experimental work comparable with those that
may be drawn from the basic experiments on
single crystals.
7. GRAIN BOUNDARY INFLUENCE
a. The grain hound aries as harriers for
therlllal and electrical flow
Since different grains presumably grow from
different nuclei, it follows that grain boundaries
will naturally be the regions where insoluble
impurities will tend to aggregate. For this
reason, the grain boundaries may act as barriers
for thermal and electrical conductivity, particu
larly in more impure materials. We shall see
later that this fact has an influence on the
internal friction of polycrystals.
h. The nature of the transition layer he
tween grains
Even if the material of which polycrystals are
made is very pure, or if all impurities are highly
soluble, we may expect an abnormal arrangement
of atoms in the immediate vicinity of the
boundary between grains. That is, we may
expect a transition layer of atoms which occupy
positions resulting from a compromise between
the forces of the atoms in both grains. These
atoms will not be so tightly bound as the atoms
in the interior of the grains and, as a result,
may be expected to be more mobile at a given
temperature than interior atoms. This does not
necessarily mean that slip will occur more easily
along grain boundaries than within grains for,
as we have seen in the previous sections, slip is
ordinarily determined by the ease of formation
JOURNAL OF APPLIED PHYSICS
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ease with which individual atoms may move.
At most we may conclude that the diffusion of a
given atom would take place more easily3 at
the grain boundaries than inside of grains. In
fact, it is possible that, as a result of irregularities
occurring in the intergranular regions, it would
be difficult for dislocations to move through
them.
The width of the transition region between
grains in very pure crystals is not known from
experimental work. We know from other sources,
however, that the forces between atoms in solids
are of short range, extending with appreciable
intensity only over a few atom distances. For
this reason, it seems safe to conclude that the
width of the intergranular region is of the order
of five interatomic distances at most. This
conclusion is not valid, of course, in materials
containing a high percentage of insoluble im
purities, for in such cases a large fraction of this
material may be localized at the grain boundaries.
POLYCRYSTAL ~6 o
FIG. 51. Slip in a single crystal of zinc bounded by a
polycrystal. (After Miller.) The heavy contour is the
shape of the specimen after slip, the dotted line the shape
before. The line AD marks the boundary between the single
crystal and polycrystal. Slip has not occurr!!d in the region
OAD neighboring this boundary. The light lines in this
region designate the position of the latent slip planes, and
show the orientation of the basal plane in the entire single
crystal before slip. Simple slip has occurred in the regions
OBA and in the part of the specimen lying to the left of
BD, but the latter region has been bent relative to the
plane BD. The light lines show the slip bands in this
region. It may be noted that slip occurs by bending in the
region OeD, which contains planes previously intersecting
AD.
From a study of the behavior of very pure
tin at temperatures near its melting point,
Chalmers 4 has concluded that the grain boundary
material has a slightly lower melting point than
the bulk material. This conclusion was drawn
3 It does not necessarily follow that bulk diffusion occurs
more rapidly along grain boundaries, for the total amount
of intergranular material is probably very small in a pure
polycrystal.
4 B. Chalmers, Proc. Roy. Soc. A175, 100 (1940).
VOLUME 12, JULY, 1941 from the fact that grains separate along their
boundaries at temperatures somewhat below the
melting point. The difference between the
separation temperature and the true melting
temperature for any pair of grains turns out to
be independent of the relative orientation of the
two crystals and of the amount of impurity,
providing it does not exceed 0.02 percent. For
high purity tin the measured temperature
difference was 0.14°C. These results are appar
ently in good accord with the conclusion drawn
previously that the transition layer of atoms is
thermodynamically less stable than interior
atoms.
There is considerable evidence that the bond
at grain boundaries is very strong at tempera
tures not too near the melting point, in spite of
this lower thermodynamic stability. For example,
fracture occurs most commonly5 through grains
rather than at their boundaries in rupture tests
well below the melting point. On the other hand,
intercrystalline fracture is common near the
melting point. At first sight, observations of
this kind seem to support the view that the
iritergranular material actually is stronger than
the bulk material at low temperatures and
weaker at high temperatures. However, an
alternative explanation of these facts is as
follows. At low temperatures the grain boundary
material is somewhat weaker than the grains
and rupture starts at grain boundaries. The
difference in strength is not so great, however,
that a crack will automatically follow grain
boundary surfaces regardless of their inclination
relative to the plane of greatest tensile stress.
In fact, once started, a cliack will occur in the
plane of greatest tensile stress even if this plane
cuts through grains. At high temperatures it is
possible that the greater relative instability of
grain boundaries increases and a crack will
follow such boundaries. Indeed, Chalmer's
experiments indicate that the grain boundaries
are extremely weak just below the melting point
of the bulk material.
The observation that low temperature fracture
is principally transcrystalline rather than inter-
5 See, for example, the discussion in the book by Z.
Jefferies and R. S. Archer, The Science of Metals (McGraw
Hill Book Co., Inc., New York, 1924), p. 67.
539
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assumption that each grain in a polycrystal is
surrounded by a thick coating of brittle amor
phous material having much greater strength
than the interior of the grains at temperatures
not too near the melting point. Apparently this
notion must be almost completely discarded, for
investigation 7 of the electrical behavior of
evaporated films of many common metals indi
cates that crystallization can occur at tempera
tures near lOOoK. Thus amorphous coatings
many atom layers thick would be highly unstable
under ordinary conditions.
More direct evidence against a thick transition
layer hypothesis has been given by Chalmers6
from a study of the critical shearing stresses in
bicrystals of tin. He investigated cases in which
the axis of tension was symmetrically disposed
relative to the two grains in the specimen, so
that the stresses were the same in corresponding
crystallographic planes in each grain. Results
showed that the critical shearing stress increased
continuously as the relative orientations were
changed, starting from the case in which they
were the same (i.e., a single crystal). Thus he
concluded that there is no essential discontinuity
in the nature of the grain boundary in passing
from a single crystal to a polycrystal, as would
follow if the thick transition layer theories were
correct. The origin of the increase in shearing
stress with increasing disorientation will be
discussed below.
c. Grain boundaries as the seal of stress
magnification and dislocations
If block boundaries in single crystals can
contain weak spots for stress magnification, as
experiments on slip and rupture indicate, we
may expect grain boundaries to have similar
properties. Thus we may expect grain boundaries
to be the source of dislocations. Excellent
evidence for this may be derived from experi
ments on internal friction of the type discussed
in Section 2 Part d. If single crystals and course
grained polycrystals of very pure copper are
6 A survey of the theories of intercrystalline bonding is
given by E. H. Bucknall, Metals Industry 311, 369, 396
(1929). See also B. Chalmers, Proc. Roy. Soc. A162, 120
(1937).
7 R. Suhrmann and G. Barth, Physik. Zeits. 36, 841
(1935); Zeits. f. Physik 103, 133 (1936); R. Suhrmann and
W. Berndt, Zeits. f. Physik 115, 17 (1940).
540 carefully annealed, both have very low decre
ments, of the order of J.0-5.
Now we saw in Section 2 that, in the case. of
single crystals, this type of internal friction is
very sensitive to mechanical treatment, presum
ably because the number of dissipating centers
(dislocations) is increased as a result. It is found
that the coarse-grained polycrystals are much
more sensitive. For example, the internal friction
of an ordinary sized single crystal of copper is
scarcely affected when the specimen is dropped
on a wooden surface from a height of one inch,
whereas the internal friction of an otherwise
identical polycrystal is raised by a factor of
about ten. This result indicates that grain
boundaries are a ready source of dislocations
and implies, in turn, that slip nuclei are easily
formed there. Whether this is due to the fact
that there are larger numbers of weak spots at
grain boundaries or to other causes cannot be
said at present.
d. Slip interference at grain boundaries
Neighboring grains exert a strong restricting
influence on the amount and kind of slip that
16
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III
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Iii 00 r---ALNEA~ED ~LYCR~STALLNE INC I
CRYSTAL
80 160 240 320 400
EXTENSION PERCENT
FIG. 52. Comparison of the stress-strain curves for
single crystal and polycrystalline specimens of zinc. (After
Elam.)
may occur within the grains. A significant
experimental investigation of this effect has been
carried out by MillerS on specimens of zinc
consisting of a large single crystal bounded by a
poly crystal (Fig. 51). Measurements were made
on specimens extended at 180°C since slip occurs
smoothly at this temperature. Miller found
that those slip planes of the single crystal that
intersect the polycrystalline region cannot oper
ate as freely as those which do not intersect.
Thus iIi: the typical case illustrated by the figure,
8 R. F. Miller, Trans. A. I. M. E. 111, 135 (1934).
JOURNAL OF ,ApPLIED PHYSICS
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regions of the crystal were not sufficient to cause
slip in the region OAD immediately bordering
the polycrystal. Although slip occurred in the
region OBA which does not border the poly
crystal, the deformation was highly restricted
by the presence of the unstrained region in that
rotation of the slip planes was not permitted.
Similarly, slip occurred in the region OeD but
was limited to the amount allowed by bending
on the plane BD. Miller states that the total
slip in this region is somewhat less than that
occurring in the unrestricted part of the single
crystal.
The fact that slip can occur in region oeD
makes it seem surprising, at first sight, that slip
is absent in OAD, for if the shearing stress there
had the same value as in the rest of the specimen,
we might expect some bending, as in OeD. A
reasonable explanation of this fact is as follows.
Initially, the shearing stress is uniform through
out all slip pla,nes (exclusive of microscopic
fluctuations), but after an undetectab.ly small
strain has occurred in OAD, the stress becomes
redistributed in such a way that the shearing
stress is lower in this region. This evidently
requires that the polycrystalline region exert a
transverse tensile stress on the material to the
left of the boundary AD, thereby reducing the
shear in the slip planes. A condition sufficient
for this is that slip does not occur in the inter
granular surfaces along AD. Naturally, the
transverse tension across AD will diminish if
the polycrystalline material becomes deformed,
but it is clear in any case that the slip occurring
in OAD and in the polycrystalline region must
be closely correlated.
Now if a single crystal grain is favorably
oriented for slip and is entirely surrounded by
less favorably oriented grains, as occurs in the
interior of a polycrystalline specimen, stresses
similar to those occurring in Miller's cases will
be exerted across the boundaries of this grain
and slip will be permissible only when the stress
is sufficient to allow all grains to deform. Natu
rally, the more numerous and more randomly
oriented the planes of easy slip are, the more
probable it will be that one of the easy slip
planes of an arbitrarily chosen grain is favorably
oriented for deformation. Thus the stresses
VOLUME 12, JULY, 1941 12
r·, . 1/ .
\
10 I
9
/ V-'\
{./ .""."..---1--
,-;'
'POL YCRYSTAL
V 8
7
/ r---\/ V" -, ' ..
I
~ k---.. .
I • , I h l • . • 1 If .
I • . 4
3 I
2
I
o 20 40 60
ELONGATION
FIG. 53. Same as Fig. 52 for aluminum. In this case the
po)ycrystaIIine curve is intermediate between extremes of
the curves for variously oriented single crystals. (After
Schmid and Boas.)
541
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be smaller for cubic crystals, which have many
easy slip planes, than for hexagonal crystals,
such as zinc, which have only one. Figures 52
and 53 bear out this conclusion by showing that
the difference between the stress-strain curves
for single and polycrystalline specimens is much
greater in zinc9 than in aluminum,lo which is a
face-centered cubic crystal possessing four equiv
alent planes of easy slip.
It is natural to ask at this point whether or not
the actual stress-strain curVes for polycrystals
can be explained quantitatively by regarding
them as a cluster of single crystals subject to a
simple constraint, such as that there shall be no
relative motion at grain boundaries. This prob
lem has not yet been subject to careful analysis
so that it is not possible at present to say that
the constraining condition is a simple one. We
shall return to this topic briefly in the next
section.
One of the facts indicating that the strength
of polycrystalline specimens cannot be derived
with the use of a simple constraining condition
is that the Brinell hardness,l1 the form of the
stress-strain curves, and the breaking strengths
of poly crystals seem to vary with grain size12
in a range in which the grain size is much smaller
than the dimensions of the specimen and of the
ball used in the test. For example, Fig. 54 shows
the variation of the hardness of brass with grain
size. Results of this kind are very surprising if
taken at their face value, for if the width of the
grain boundary region is as small as we have
supposed, we should expect the mechanical
properties of polycrystals to be independent of
grain size as long as the size is small compared
with the dimensions of the specimen and of the
device used in measuring the hardness. A possible
explanation of this discrepancy lies in the fact
9 Taken from C. F. Elam's book, The Distortion of Metal
Crystals (Oxford University Press, 1935), p. 53.
10 R. Karnop and G. Sachs, Zeits. f. Physik 41, 116
(1927).
11 The Brinell hardness is determined by measuring the
size of the indentation produced when a 1-mm ball is
pressed into the specimen with a specified load. (See A. S.
M. Handbook (1939), p. 112 et seq.)
1. Investigations bearing on this point have been carried
out by the following; G. Masing and M. Polanyi, Zeits. f.
Physik 28, 169 (1924); W. H. Basset and C. H. Davis,
Trans. A. I. M. E. 60, 428 (1919); Wood, Phil. Mag. 10,
1073 (1930). See reference 9, p. 52.
542 that specimens must be treated in different
manners in order to obtain different grain sizes
and it is possible that this treatment has a
profound effect upon the mechanical properties,
particularly if the materials are not perfectly
pure. Good evidence for this viewpoint has been
. given by Corson13 from a study of very pure
copper. He found that the tensile strength and
hardness of coarse-grained ingots of very pure
copper are practically the same as the corre
sponding properties of fine-grained specimens
and concluded that the weakness ordinarily
observed in large-grained materials is to be
attributed to the influence of gaseous impurities.
His results suggest that the gaseous impurities
congregate at the grain boundaries and, for
reasons not yet completely understood, weaken
the bond between grains. In coarse-grained
specimens the total amount of grain boundary
area is small compared with that in fine-grained
materials so that the impurity is more concen
trated and has a larger effect.
It should be noted at this point that the con
straints provided by the intergranular material
possibly are not the only factors contributing to
variations of stress within polycrystalline ma
terials on a scale of dimensions of the order of
grain size. In this connection, Barrett and
Levenson14 have shown that the deformation
within individual grains in compressed poly
crystalline aluminum and iron is not uniform.
In particular, the relative orientation of different
parts of the grains changes progressively as
compression proceeds. For example, in the case
of aluminum the spread of orientation ranged
from 7° to 10° for 10 percent compression, from
15° to 25° for 30 percent compression and from
35° to 45° for 60 percent compression. This
variation in orientation was accompanied by
the appearance of narrow bands on either side
of which the orientation was different. These
deformation bands were also observed when single
crystals of aluminum were compressed by 50
percent between carefully lubricated plates. In
these cases the difference in orientation on either
side of the band was of the order of 3 0. The
origin of the bands has not yet been given a
13 M. G. Corson, Trans. A. I. M. E. 128,398 (1938).
14 C. S. Barrett and L. H. Levenson, Trans. A. I. M. E.
137, 112 (1940).
JOURNAL OF APPLIED PHYSICS
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ever, that they are regions such as the line BD
ill' Fig. 51 at which bending takes place. If so,
their appearance indicates that the stresses are
not uniform throughout individual grains. This
would not be surprising if the bands were ob
served only in the polycrystalline specimens for
the non-uniformity could then be interpreted as
being related to the influence of different faces
of the grain. However, the observation of bands
in single crystals indicates that the grains them
selves are inhomogeneous on a scale of distance
much larger than that of the spacing between
slip bands.
8. SLIP IN POL YCRYSTALS
It is a natural scientific desire to hope to base
a general discussion of the behavior of poly
crystalline solids in various deforming processes,
such as tension, compression, rolling and torsion
on a few primary empirical laws. Present knowl
edge of the basic principles of slip in grains was
outlined in the early sections of this series of
articles. Although this knowledge cannot be said
to be complete, inasmuch as the role of such
factors as deformation bands is not yet under
stood, we at least have a qualitative formulation
of the laws of plastic flow in single crystals.
Unfortunately, as we saw in the preceding
section, present knowledge of grain-boundary
influence is not sufficient to complement the
work on single crystals and provide· us with a
good foundation for treating polycrystals. In
spite of this, we shall outline briefly the principal
experimental facts concerning slip in polycrystals.
a. Crystalline orientationl5
When polycrystalline specimens in which the
grains are randomly oriented are subject to
uniform but directional deformation several im
portant and probably closely related changes
occur. In the first place, the orientations of the
grains become altered. This reorientation fre
quently occurs in such a way that the resultant
distribution of grains is no longer random, but
exhibits preferred arrangements. The degree of
preferred orientation is never nearly as sharp as
in a single crystal and usually depends both
upon the material of which the specimen is made
15 This topic is discussed in reference 9, Chapter V.
VOLUME 12, JULY, 1941 14 00
1200
1000
00
00
v-
200
x 0 L--I
". r/
x V
I/It-
~ •
45 47
HARDNESS rl
J il .
f
" fl.
/ V
49 51
FIG. 54. Variation of Brinell hardness of brass with grain
. size. (After Elam.)
and upon the method used to produce the
deformation. For example, when face-centered
cubic metals are placed in tension, there is a
tendency for both the (111) and (100) directions
to become oriented parallel to the direction of
tension. In aluminum the existing evidence indi
cates that most of the grains become oriented so
that the (111) direction is along the axis of
tension, but both orientations occur in other
metals having the same structure. Similarly, in
compression the (110) direction of face-centered
cubic crystals tends to become aligned normal to
the plane of compression. In some cases the final
orientations of the grains in polycrystals appear
to be similar to those occurring in single crystals
that have been subject to the same deformation,
but more often they are not. This fact indicates
once again the importance of the grain boundary
influence in determining the actual stresses
within the grains. For example, in tension tests
with single crystals of aluminum, the (110) direc
tion tends to become parallel to the axis of
tension, whereas the (111) direction tends to
become aligned in this direction in polycrystals.
The reorientations occurring during rolling are
of particular practical importance since much
543
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The stresses occurring in this process are more
complicated than in simple tension or com
pression tests, because the surface of the rolled
specimen is subject to normal stresses, and to
shearing stresses both in the direction of rolling
and at right angles to this direction. Although
strong preferred orientations ordinarily are pro-
STRAIN (POLYCRYSTAL) -
o 01 02 03 04 05
6 I.e-' V :
.....- x ! f----i--. VI( i )/ I
t7 I 7
f :
~
! -----9-
---I
I ~ P i
V i i , 3
~ o
.... 2
V ~l
o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
STRAIN (SINGLE CRYSTAL)
FIG. 55. The upper continuous curve is the computed
stress-strain relation found by Taylor for aluminum using
single crystal data. The crosses and plus signs represent
experimental values. The lower curve is a representative
stress-strain curve of a single crystal of the same material.
duced by rolling, the results are greatly de
pendent upon the conditions of rolling and
cannot be summarized in terms of a few concise
laws which could be conveniently discussed here.
Apparently rolled orientations can sometimes be
duplicated in compression tests in which the
specimen is constrained so as to spread in only
one direction in the plane of compression.
One of the interesting effects of extensive
deformation on polycrystalline materials is the
development of fiber structure. This structure
results from the elongation of individual grains
in the direction of the deformation, which gives
them the appearance of fibers of woven fabrics.
During the elongation neighboring grains appear
to maintain close adhesion at their boundaries,
for the rupture strength of the materials is not
reduced except in extreme cases of working.
This fact indicates once again the great strength
of the intergranular bond. Moreover, it shows
that such elongation takes place under great
544 restrictions. It can be shown that the develop
ment of fiber structure would not be possible in
hexagonal crystals if slip in the basal plane were
the only possible means of producing deforma
tion. Actually twinning seems to provide the
additional degree of freedom in such crystals.
It is also possible that inner-crystalline deforma
tion of the type observed by Barrett and
Levenson is an important means of deformation
in many materials.
h. Work hardening
Polycrystals harden with cold work, as may
be seen from the stress-strain curves shown in
Figs. 52 and 53. Undoubtedly work hardening of
the type observed in single crystals is a very
significant factor in polycrystals for the latter,
like the former, may be softened by heating.
It is possible, however, that additional factors
related to the' presence of grain boundaries
enter into the hardening of polycrystals. For
example, there are indications16 that complete
recovery in polycrystals requires recrystallization
of the specimen. In contrast with this, we have
1.2
t
1
I. I
-'" V ....
[7
10 I l--
V V""
V -----
I
I
20 30 t -40 MIN. 50
FIG. 56. Creep curve for polycrystalline cadmium. (After
Andrade and Chalmers.)
seen in Section 2 Part g that single crystals can
recover completely far below their recrystalliza
tion temperature. It is not unlikely, of course,
that the temperature accompanying recrystal
lization and not the change in structure is the
important factor in determining softening. Since
polycrystals recrystallize at far lower tempera
tures than single crystals, it is plausible to expect
that polycrystals happen to recrystallize in the
temperature range effective for softening, which
is the same for single crystals and polycrystals.
A highly interesting treatment of the stress
strain curve for polycrystalline aluminum has
16 See reference 9, p. 161.
JOURNAL OF APPLIED PHYSICS
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stress-strain curve on the basis of the following
assumptions:
(a) The strain is uniform in all grains of the
material. This evidently contains implicitly the
assumption that no slip occurs at grain bound
aries, but it is obviously far more stringent.
(b) The deformation takes place in each grain
by slip on the octahedral planes, as he and Elam
had found for single crystals, and in such a way
that the energy required is a minimum. The
second part of this assumption is essentially a
statement of the principle of least work.
On the basis of these assumptions, Taylor was
able to compute the stress-strain curve for a
polycrystal of randomly oriented grains with the
use of curves for single crystals. The upper con
tinuous curve of Fig. SS is the theoretically
derived one and is accompanied by experimental
points. It may be seen that the computed curve
agrees substantially with these points.
Unfortunately, the study carried on by Barrett
and Levenson14 on the orientation of grains
in "homogeneously" compressed polycrystalline
specimens of aluminum indicates that assump
tion (a) is not correct and thus detracts from the
significance of the agreement found by Taylor.
Moreover, Barrett and Levenson found that the
average change in orientation of the grains
during compression was frequently different from
that predicted on the basis of Taylor's treatment
and thus opens assumption (b) to question. The
constructive implications of Barrett and Leven
son's work have not yet been determined, but it
seems definite that Taylor's theory must be
modified in some essential respects, at least in
the case of compression.
c. Impurity hardening
The hardening influence' of soluble impurities
in polycrystals seems to be qualitatively the
same as in single crystals and indicates that the
hardening is basically intragranular.
9. TWINNING
Although twinning has been extensively in
vestigated in polycrystals, none of this work
seems to have been carried out with the view of
17 G. 1. Taylor, J. lnst. Metals 62, 307 (1938).
VOLUME 12, JULY, 1941 8 Xl
I
~ 6
~
~
~
~
III 6 -.....
Q. 4
l&J
l&J
It:: (.)
~ 0
l&J x ....
~ 2
l
X c/
x---x-----x------------~ o 200 400
STRESS (GISQ MM)
FIG. 57. Dependence of the creep rate upon stress for a
bicrystal of tin. (After Chalmers.)
finding differences between the behavior of poly
crystals and single crystals.
10. CREEp18
Just as in the case of single crystals, the
elongation versus time curves for polycrystals
may be divided into a transient and a steady
state part. Such a curve is shown in Fig. S6 for
polycrystalline cadmium19 and the possibility of
a division of this type is clearly indicated. The
dependence of the steady-state creep rate upon
both temperature and stress has been investi
gated by a number of workers20 and seems to be
18 For helpful discussions of this subject we are indebted
to Drs. W. Kauzmann of the Westinghouse Research
Laboratories and A. Lawson of the University of Penn
sylvania.
19 E. N. da C. Andrade and B. Chalmers, Proc. Roy.
Soc. AU8, 348 (1932).
20 An analysis of available experimental data is given by
W. Kauzmann, Trans. A. 1. M. E. (February meeting
1941), Tech. Pub. No. 1301.
S4S
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R=A exp (-(e'-blT)jkT), (1)
where A and e' are constants, IT is the applied
stress and b is dependent upon temperature, but
not upon stress. It is to be emphasized that this
law is derived from a study of results corre
sponding to the practical range of stress, which
is of the order of magnitude of 1 kgjmm2. This
is from ten to a hundred times larger than the
range of stress employed in the creep experiments
on single crystals of tin described in Section 3.
Figure 57 shows the creep rate as a function
of stress for a bicrystal of tin, as determined by
Chalmers.21 This result indicates that Eq. (1)
fails in this case for stresses of the order of 100
gjmm2. Figure 57 should be compared with
Fig. 44 for single crystals, for it indicates that
there is a distinct difference in the creep behavior
of single crystals and polycrystals at low stresses.
In particular, there seems to be a limiting stress
for creep in the case of the bicrystal whereas
there is none in the case of single crystals.
Extension versus time curves for polycrystalline
specimens of tin stressed in the range of Fig. 57
are shown22 in Fig. 58. It may be seen that the
steady-state rate is practically zero for stresses
below 200 g/mm2 and becomes finite in the range
from 200 to 300 g/mm2. A similar effect has been
observed by Chalmers23 in polycrystalline lead
but it has not been studied in other metals.
Values of the constants appearing in Eq. (1)
as determined by curve fitting of experimental
results are given in Table IX. The values of b
are found to vary with temperature in the
manner B exp (aT) in which B and a are con
stants; the range of b shown in the table gives the
variations over a several hundred degree tem
perature range.
On general grounds we might expect two
sources of creep in polycrystalline materials:
First, a creep analogous to that occurring in
single crystals and arising from relative motion
within grains and second, creep at grain bound
aries. Slip corresponding to the second type of
motion does not seem to be observed near room
temperature in any of the metals that have been
21 B. Chalmers, Proc. Roy. Soc. A1S6, 427 (1936).
22 B. Chalmers, ]. Inst. Metals 61, 103 (1937).
23 B. Chalmers, Proc. Phys. Soc. 47, 352 (1935).
546 studied up to the present time. However, if it
did exist we should expect to observe it just in
the range in which creep ordinarily is measured.
If this type of creep did occur, it presumably
could be separated from inner-granular creep by
investigating the dependence of creep upon
grain size, for we should expect it to play a
larger role in fine-grained specimens having a
comparatively large amount of grain-boundary
surface than in coarse-grained specimens. Ac
tually there does not seem to be any conclusive
evidence indicating that there are two contribu
tions to creep. It will be seen in Section 12 that
there is indirect evidence that intergranular flow
occurs in zinc in the range from room tempera
ture to 100°C; however, in lieu of more definite
evidence, we shall discuss creep on the basis of
dislocation theory.
We saw in Section 3 that two simple mecha
nisms of creep may be considered in discussing
creep on the basis of dislocations. First, we may
4r-----------------------~------__,
FIG. 58. Upper two curves: extension versus time curves
for specimens of tin stressed at 300 g/mm2 and 200 g/mm2.
The lower two curves give the subsequent contraction
when the stress is released. (See Section 13.) (After
Chalmers.)
consider creep as caused by the relatively slow
migration of dislocations, in which case
dSjdt=v)..N, (2)
where N is the density of moving dislocation
lines, v is their average velocity of motion and )..
is the slip distance associated with the passage
JOURNAL OF ApPLIED PHYSICS
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Downloaded to ] IP: 193.0.65.67 On: Tue, 09 Dec 2014 09:41:10of one dislocation. In the steady state, N is a
temperature-dependent constant so that the tem
perature dependence of creep rate is determined
by the dependence of both v and N.
It was also pointed out in Section 3 that there
is evidence that the activation energy for motion
of dislocations is small in a well-annealed speci
men, for which N is small. The same conclusion
cannot be expected to hold during a practical
creep test, since N may then be much larger.
Thus it is difficult to analyze the constants
appearing in Eq. (1) in terms of the quantities
appearing in (2). However, we shall attempt such
an analysis in the following way.
We shall assume that the rate at which dis
locations are generated is given by an equation
TABLE IX. Empirically determined creep data for metals.
(After Kauzmann.) (The values of " are given in ev, those of
A in units of sec.-1 for specimens of unit length. b is given in
units of Aa.
Pb{0.17
0.1-0.35
Su 0.23
Brass (60 Cu 40 Zn) 0.6
Steel (0.4%C) 1.2
of the form LOGIOA
-8 -7 to -5 -4 -4 -3 b
-5X10'
103-10'
5.103_5X10·
1Q2-5 X 10'
103-104
where No is the number of generating centers,
and that the rate of annihilation is
where N is the number of dislocations present.
Then in the equilibrium state
where
(6)
In addition, we shall assume that
d v =-e-'d/ kTeadu/ kT, (7)
Td
where d is the distance between neighboring
equilibrium positions for the dislocation, Td is
the relaxation time for passage of a dislocation
from one equilibrium position to another, and
VOLUME 12, JULY, 1941 TABLE X. Tensile strengths of annealed pure polycrystals.
(The values are given in units of kg/mm2.)
TENSILE TENSILE
STRENGTH STRENGTH
METAL OBS. CALC. METAL OBS. CALC.
Al 9.2 372 Pb 1.1 261
Au 12.0 782 Pd 14.
Ca 6.4 Pt 12. 125
Cu 22.6 885 Sn 1.4 357
Mg 9.2 Zn 13. 580
Ni 32.
the exponential coefficients give, respectively,
the influence of temperature and stress on the
probability that the dislocation will jump. For
small stresses, the second function presumably
should be a hyperbolic sine of the same argument,
but we shall consider the practical range of
stresses. Substituting (5) and (7) into (2), we
obtain
dS Xd Ta -=-N o-exp (-(E' -bu)/kT), (8)
dt Td Tg
where
Now Ta and To presumably are of the same
order of magnitude, since they are associated
with inverse processes. Moreover, >.d is of the
order of magnitude 10-15 cm2, so that we obtain
by comparison of (1) and (8)
(No/Td)10-15=A. (10)
We are at loss for a precise estimate of No, but
it seems reasonable to assume that this quantity
is of the same order of magnitude as the number
of blocks per unit cross section, namely 108•
The values of Td required to account for the
observed values of A vary between 10 and 10-4
sec. for all of the cases listed in Table IX. The
larger of these values of Td agrees in order of
magnitude with that obtained in Section 3 from
a similar analysis of the rate of creep of single
crystals of tin on the basis of Eq. (2). We note
again that if Eq. (2) is correct, it seems to imply
that the natural relaxation time for motion of
dislocations is very long compared with an atomic
oscillational period.
A second possible simple mechanism for creep
is based on the notion that dislocations move
very rapidly a distance L from the point at
547
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Downloaded to ] IP: 193.0.65.67 On: Tue, 09 Dec 2014 09:41:10which they are generated and then become stuck.
The corresponding equation was discussed in
Section 3 and is
dSjdt=XLdN jdt. (11)
As we have seen in Section 3, the purely transient
creep observed in single crystals of tin, zinc and
cadmium at low stresses can be explained more
suitably on the basis of Eq. (2) than on the
basis of (11), but it is possible that Eq. (11) is
valid in the practical range of creep.
Substituting into (10) from Eq. (3), we obtain
dS No -=XL- exp (-(Eg-agu)jkT). (12)
dt Tg
Thus in the present case
A = 10-8LNgj Tg•
If L is of the order of magnitude 10-4 cm, as is
assumed III Taylor's theory of hardening, we
obtain
A = 10-12NojTo•
In the cases listed in Table IX, N oj T 0 varies
between 109 and 104• If our previous estimate of
Ny, namely 108, is valid, we obtain the result
that To varies between 10-1 and 104 sec., which
seems to be much too large to be reasonable.
In other words, the parameter values derived
from the use of Eq. (2) seem to be more reason
able than those derived from (11). It must be
admitted, however, that the evidence in favor of
Eq. (2) is far from satisfying. At most, we may
say that the theory of dislocations seems to
provide a rough semi-quantitative means of
correlating creep data.
Comparing Eqs. (1) and (6), we see that the
quantity b in (1) is composite if Eq. (2) is
correct. It is interesting to note that the experi
mental values of b are so large that bu is of the
order of 1 ev for stresses near 1 kgjmm2• This
implies that either ao or ad in Eq. (9) may be
large. In the first case, it would be concluded
that there is very large stress magnification near
the slip nuclei and in the second that dislocations
have lengths of the order of 10-6 cm. It is not
easy, however, to understand the strong de
pendence of the experimental values of b upon
temperature. Kauzmann20 has suggested that
548 this dependence is related to an increase with
temperature of the lengths of either slip nuclei
or dislocations. Additional evidence for such a
variation possibly is furnished by the difference
between the values of r we have obtained above
from comparisons of Eqs. (2) and (11) with Eq.
(1) and the value we might expect to obtain,
namely 10-13 sec. According to Kauzmann's sug
gestion the increase in the length of dislocations
with temperature gives rise to an increase of the
activation energy with temperature. If the creep
data were analyzed on the basis of Eq. (1),
taking into account a temperature dependence
of e', a value of A larger by a factor of 1010 could
be obtained. In this case T would come out to be
of the order of magnitude of 10-10 sec.
11. RUPTURE IN POLYCRYSTALS
It was pointed out in Section 7 that rupture
is transcrystalline except at temperatures just
beI'ow the meiting point. This indicates that
grain boundaries are not sources of great weak
ness at sufficiently low temperatures and we
might expect to correlate the breaking strengths
of polycrystals with those of single crystals.
Such a correlation is made difficult for several
reasons. In the first place, stresses within grains
are not the same as the applied stress because of
grain boundary influence. In the second place,
specimens of the same material prepared in
different ways will extend differently during a
rupture test and hente will usually have different
orientations when fracture occurs. Fortunately,
the second factor may be eliminated to an
appreciable extent by comparing specimens which
already possess the maximum degree of preferred
orientation of the type that would be produced
during the rupture test.
Now we saw in Section 5 that each crystallo
graphic plane of a single crystal appears to
possess a characteristic tension stress at which it
will rupture. Moreover, evidence was cited which
indicates that this stress is independent of
previous deformation. Reasoning from this we
should expect the rupture stress of a polycrystal
line metal to be independent of deformation as
long as the deformation does not produce widely
different orientations. This expectation seems to
be borne out in the case of copper. Figure 59
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copper wire prepared from the same material.
Prior to the test the wires were drawn to different
diameters, during which process comparable
degrees of preferred orientation presumably were
attained. The specimens were then subjected to
tension stress and the strain was measured in
terms of the contraction in cross section. The
specimens began to neck at the stress corre
sponding to point 2, and fracture occurred at
the points 3. It may be seen that the breaking
~ w
0: l(/)
00 20 40 60 80 100
CONTRACTION IN AREA 0/0
FIG. 59. Stress-strain curves for variously worked speci
mens of polycrystalline copper. It may be seen that the
rupture stresses are closely the same in each of the cases.
The strain is measured in terms of the contraction in cross
sectional area.
stresses are nearly the same in all four cases,
which indicates that the previous strain had
little effect on the breaking stress ..
24 J. v. Mollendorf and J. Czochralski, Zeits. Verein.
deuts. lng. 54, 931 (1913).
VOLUME 12, JULY, 1941 Just as in the case of slip, there seems to be
evidence that the grain size has an important
influence on the breaking strength even when the
crystal size is small compared with the dimen
sions of the specimen. As was pointed out in
Section 7, this result is inexplicable unless it is
assumed that the different treatment required
to produce various grain sizes results in different
distribution of impurities at grain boundaries.
This interpretation of the effect is supported by
the experiments of Corson, discussed in Section 7.
A comparison of experimental breaking
strengths and those computed from Polanyi's
equation with the use of experimental values of
the surface tension is given in Table X. It may
be seen that the experimental values are smaller
than the theoretical ones by a factor of the order
of a hundred or more, just as in the case of
single crystals. There is a slight indication that
polycrystals are somewhat stronger than single
crystals, but this effect may be related to the
redistribution of stresses resulting from the in
fluence of grain boundary restrictions.
12. INTERNAL FRICTION
The principal source of internal friction in non
ferromagnetic single crystals seems to be inti
mately associated with plasticity, as we have
seen on Part d of Section 2. The same source is
sometimes important in polycrystals, but, as
was first pointed out by Zener,25 is often com
pletely masked by another. The second source
has been extensively studied by Zener and his
co-workers and arises from the thermoelastic
effect in the following way ..
When a crystal is stressed suddenly its tem
perature changes, heat being generated or ab
sorbed, depending on the sign of the dilatation.
The change in temperature is proportional to the
stress and reverses its sign if the sign of the
stress is reversed. Since the stresses in a poly
crystal are not uniform but vary from grain to
grain, it follows that the temperature resulting
from the thermoelastic effect will vary from
point to point. Now if the stresses vary slowly
compared with the time required for heat to flow
2. C. Zener, Phys. Rev. 52, 230 (1937); 53, 90 (1938);
W. Otis and R. ~uckolls, Phys. Rev. 53, 100 (1938); R. H.
Randall, F. C. Rose and C. Zener, Phys. Rev. 56, 343
(1939); C. Zener, Proc. Phys. Soc. 52, 152 (1940).
549
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temperature will remain constant and the trans
fer of mechanical energy into heat, and vice
versa, takes place reversibly. In this case the net
amount of heat generated during a complete
cycle is zero and there is no contribution to the
internal friction. Similarly, if the variations in
stress take place so rapidly that no heat flows
during a stress cycle, the process is said to occur
adiabatically since each region of the material
behaves as if it were thermally isolated. It
follows that the net conversion of elastic energy
into heat during a complete cycle also is zero in
this case. However, if the frequency or the
thermal conductivity are such that the process is
neither isothermal nor adiabatic, the conversion
will not be reversible and there will be a finite
contribution to the internal friction from the
thermoelastic effect.
Zener has pointed out that if the average
applied stress is uniform throughout the speci
men, the critical distances for thermal diffusion
in a polycrystal should be the dimensions of the
grain, for stresses should vary relatively abruptly
from one grain to another. Reasoning from this
on the basis of dimensional analysis, he suggested
that the internal friction should depend on the
dimensionless quantity IId2jD. Here d is the
grain diameter, II is the frequency and D is the
thermal diffusion constant defined by the equa
tion
thermal conductivity D=--------
(specific heat) (density)
In other words, for a given material the rela
tive value of the internal friction, should be a
universal function g(IId2jD). Figure 60 shows
schematically the manner in which this function
should depend on its argument. It has a peak
near the value unity and decreases to zero on
either side. This type of dependence of internal
friction has been verified in brass.
If the average stress is not uniform throughout
a specimen, as during the transverse vibration of
a reed, there will be an additional contribution
to the thermoelastic internal friction resulting
from the variations in temperature across the
specimen. This contribution is determined by a
function similar to that shown in Fig. 60, the
argument being IIVjD in this case, where L is
550 the distance between the points of maximum
temperature difference, which is the thickness of
the specimen in the case of the vibrating reed.
The thermoelastic internal friction was first
discovered and studied systematically in in homo
geneously stressed systems of this type.
The factors contributing to the absolute value
of the thermoelastic internal friction have been
investigated by Zener, but will not be discussed
here since they would lead us too far afield.
This work shows that in general we should expect
the internal friction arising from stress variations
between grains to be smaller the more nearly
elastically isotropic the material is.
We might expect to find peaks of the type
shown in Fig. 60 in single crystals as a result of
stress variations either from domain to domain
or between larger regions. The first of these
cases corresponds to an effective grain size of
10-4 cm and would produce a peak in the mega
cycle range of frequency. This type of internal
friction actually seems to be negligible in Read's
experiments.
It should be mentioned that the value of D
will be dependent on the ease with which heat
1
t VIBRATION ~ d NEARLy I
~ lScrMRMAL ~ VIBRATION I\£ITHER NEARLY ISOTHERMAL
NOR NEARLY ADIABATIC VIBRATION
"'-EARLY
ADIABATIC
FIG. 60. Relative value of the internal friction as a
function of the dimensionless variable pdt/D. (After Zener.)
The function has its peak in the region where the argument
is unity and decreases on either side.
flows across grain boundaries and is not neces
sarily an average of the values for single crystals.
Actually, the influence of grain boundaries has
not been studied.
The separation of the internal friction of
plastic origin from the thermoelastic contribution
can be carried out in several ways. For example,
if measurements are carried out for frequencies
extending in to the adiabatic or isothermal regions,
the residual value of plastic origin will appear as
JOURNAL OF APPLIED PHYSICS
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of Fig. 60. The range of frequency needed for
this evidently will depend upon d and D. Thus
in the case of three specimens of brass of different
grain size,26 a residual decrement of 0.15.10-6
was determined by extrapolating to the region
of low frequencies.
Barnes and Zener27 carried out a similar
separation at fixed frequency in zinc (impurities
0.5 percent). Measurements were made on speci
mens of four grain sizes for various temperatures
in the range from O°C to 100°C. The values of
/ld2/D at the frequency used were O.OOB, O.OOB,
0.02 and O.B for the four specimens. In the first
three cases the internal friction varied with
temperature in the manner A exp (-E/kT), the
constant E being the same in all cases and the
constant A varying inversely as the square of
the grain size. In the fourth case, in which the
thermoelastic internal friction should be near its
maximum value, the internal friction was ex
pressible in the form
(1)
in which C was independent of temperature and
equal to 44.10-6, E was the same as in the other
three cases, and the ratio of A4 to the values of A
occurring in the other cases varied inversely as
the grain sizes. The investigators conclude that
the temperature-dependent term had its origin
in the plasticity, whereas the constant in (1)
corresponds to the thermoelastic dissipation.
They also conclude from the dependence of the
coefficient of the Boltzmann factor upon grain
size that the source of the temperature-dependent
internal friction lies on the grain boundaries,
rather than in the interior of the grains.
13. SECONDARY PLASTIC EFFECTS
In addition to the primary plastic effects, slip,
creep, twinning and rupture, there are a number
of interesting secondary effects which, like
fatigue, undoubtedly find their origin in the
primary effects. Some of these are observed only
in polycrystals; others are observed in single
crystals as well. We shall discuss both here.
26 C. Zener and H. Randall, Trans. A. I. M. E. 137,41
(1940).
27 A. H. Barnes and C. H. Zener, Phys. Rev. 58, 87
(1940).
VOLUME 12, JULY, 1941 a. Creep recovery
If a specimen of polycrystalline material is
extended by creep, it is found to contract slowly
with continually decreasing rate when the applied
stresses are removed. The lower two curves in
Fig. SB show this effect for two specimens of
polycrystalline tin. In these cases the ordinate
gives the decrease in length as a function of
time after the specimens which yielded the upper
two curves were unloaded. The rate of contrac
tion is rapid at first and then decreases to zero.
This effect did not occur in the single crystals
studied by Chalmers, which indicates that it is
primarily a polycrystalline one. The effect is also
observed after practical creep tests.
This type of creep recovery apparently can be
given a satisfactory explanation on the basis of
a principle first proposed by Masing.28 He pointed
out that the type of extension occurring in
different grains of a polycrystal during any
deformation will be different because of differ
ences in orientation. Some grains will deform
almost entirely as a result of slip whereas others
will deform elastically. For small deformations,
such as those dealt with in Chalmers' experi
ments, we may expect a continuous range
between grains which are deformed almost en
tirely elastically and those which have deformed
almost entirely as a result of plastic flow. Con
sequently the actual stress in the interior of the
metal will vary from a maximum value in those
grains which have undergone the least plastic
deformation to a minimum value in those which
have undergone the most. Thus when the ex
ternally applied load is removed and the average
stress reduced to zero, some of the grains will be
stressed in tension and some in compression, the
latter being those which had previously flowed.
If the temperature is sufficiently high, these
stresses will cause creep and the specimen will
be observed to contract in the manner of Fig. 5B.
h. The Bauschinger effect
If the previous interpretation of creep recovery
is correct, we might expect that just after a
polycrystalline specimen has been unloaded,
following an elongation or compression, there are
forces present in some of the grains which would
28G. Masing, Wiss. Siemens Konzern 3,231 (1924); 4,
74, 244 (1925); 5, 135, 142 (1926).
551
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18
16
2 ANNEALED
50(/'2 HR
I
----t
I
I
I
I
I
I i
I
I
i
i~
'v ! I I ,
I i
I I I I I
I i
I I
I I I
I I
i i
i
!
! I I I PREVIOUSLY
EXTENDED
I i-f-----
,
Ii " ,
Ii
It
If
I; , , : , ,
I
I , PREVIOUSLY
COMPRESSED
I
I
/
/
/
/
/ /
/ £
I
I
I ANNEALED AFTER
EXTENSION
I i I
I ~
V I i I
I I ,
I
I
I
!
I FIG. 61. Illustration of the
Bauschinger effect in fine-grained
polycrystalline brass. (a) shows the
extension versus stress curve for the
virgin material. (b) is the stress
extension diagram obtained after
previous extension. (c) is the same
curve obtained after previous com
pression. It may be seen that the
elastic range is very small, illustrat
ing the Bauschinger effect. (d) is
the stress-strain curve similar to (c)
obtained when the specimen is an
nealed at relatively low tempera
tures after compression. The hard
ness remains but the Bauschinger
effect is gone.
I
~ o D.2 a 0 0,2 0.4 0 D.2 0.4 D.6 a8 0 Q2 a4 . D.6 D.6 1.0
EXTENSION IN PEI!CENT
aid in producing a deformation of opposite sign.
Thus we might expect the critical stress required
to produce plastic compression following a small
elongation to be lower than the critical com
pression stress in the virgin state. An effect of
this kind was first discovered in polycrystals by
Bauschinger29 and was explained qualitatively in
the basis of :vIasing's principle, discussed in
part a of this section. Figure 61 shows30 the
Bauschinger effect in fine-grained brass. Figure
61 (a) is the stress-strain curve obtained during
an extension of a virgin specimen of the material
by a few percent. The critical shearing stress is
about 10 kg/mm2. Essentially the same value
would have been obtained if the virgin specimen
were compressed rather than extended. Figure
61 (b) shows the stress-strain curve for com
pression following the extension. It may be seen
that the critical shearing stress for this deforma
tion is very small for the range of compression
corresponding to the original extension. Figure
61 (c) shows the type of stress-strain curve ob
tained if the specimen is further extended (with
out compression) after the original extension,
and exhibits the usual effects of work hardening.
The last figure shows the stress-strain curve
obtained in compression after annealing the
originally extended specimen at 1500 for several
hours. The Bauschinger effect has disappeared, but the hardness remains, showing that the
factors contributing to the Bauschinger effect are
not immediately connected with the hardening.
A quantitative development of Masing's theory
of the Bauschinger effect was carried out by
Heyn,31 who showed that curves of the type of
Fig. 61 (b) could be obtained for polycrystals in
a reasonable manner on the basis of the theory.
It is unfortunate for the simple theory that a
well-defined Bauschinger effect has been ob
served by Sachs and Shoji30 in single crystals of
brass. A typical example of their results is shown
in Fig. 62. In this the ordinate is stress and the
abscissa is strain, the positive and negative
directions corresponding, respectively, to tension
and compression. The curve obtained in a stress
strain cycle starting with a virgin specimen is
somewhat reminiscent of a magnetic hysteresis
curve. The segment Dl of the entire curve
represents the stress-strain curve obtained in the
first extension and rises sharply in the elastic
region, as in Fig. 61(a). When the tensile stress
was relieved, the elastic contraction to the
point A occurred. Following this, the specimen
was compressed and the curve D2 was obtained.
It is evident that the decrease from the point A
is much more gradual than the original rise from
the origin, showing the Bauschinger effect. If this
part of the curve were inverted about the point
2.]. Bauschinger, Ziviling. 27,289 (1881). 31 E. Heyn, Festband Kaiser-Wilhelm Gesellschaft
30 G. Sachs and H. Shoji, Zeits. f. Physik 45,776 (1927). (1921), 131.
552 JOURNAL OF APPLIED PHYSICS
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Fig. 61(b) bears to Fig. 61(a). The main differ
ence between the polycrystalline and single
crystal specimens appears to lie in the fact that
the latter are somewhat softer, as may be seen
by comparing the ordinates in Figs. 61 and 62.
The curve Da represents another stress-strain
curve for extension following the compression D2•
A summary of the experimental facts obtained
from this type of investigation on single crystals
of brass is as follows:
1. The primary stress-strain curves obtained
in tension or compression for virgin materials are
nearly identical.
2. The Bauschinger effect is observed in the
opposite deformation following the primary one,
regardless of the sign of the primary one. We
shall call the deformation following the primary
the secondary one. The secondary curves are
very nearly identical if the primary extensions or
compressions are identical.
3. Secondary curves, and curves such as Da
obtained by later deformation, are very nearly
alike as long as the over-all extension and com
pression remains fixed in each cycle. The prin
cipal difference lies in the fact that a gradual
work hardening takes place; that is, the curves
rise to larger absolute values of the abscissa.
4. If at any period in a sequence of cycles, a
deformation larger than the preceding is carried
out, the Bauschinger effect will be more clearly
marked in the deformation immediately fol
lowing.
5. Annealing for two hours in the range from
250°C to 400°C removes the Bauschinger effect
for the next deformation, but does not appre
ciably affect the work hardening.
6. When correction is made for the slightly
greater hardness of polycrystals, the Bauschinger
effect in single crystals of brass may be said to be
fully as well defined as in polycrystals.
At first sight, the existence of a well-developed
Bauschinger effect in single crystals seems to be
in contradiction with Masing's theory. Actually,
there are two ways of interpreting the results:
(a) In the first place it is possible that the
single crystals of brass on which the measure
ments were made actually are far less homo
geneous than the best single crystals of mon
atomic substances. Thus it is possible that the
VOLUME 12, JULY, 1941 ~--r---l-,
I +4~'.:=- ,
I ~L 1i I
I I ;r J/D1 I!
I II ' +2(---1!~
II +1 I
I
I
f---_j fA
0.3 -.2 -0.1 0 +0.1 +0.2 +q3 /,
I I II Ii --r -I
I / I l
I -2 / I
I
I
I -3 r V D,
J
I
J -=::
L- --
DEFORMATION IN PERCENT
FIG. 62. Stress-strain diagram for single crystal of brass
obtained during a cyclical deformation process. Negative
strains correspond to compressions, positive to elongations.
D, corresponds to the virgin material.
deformations are not homogeneous and that
parts of the crystal undergo almost purely elastic
deformations. This possibility could be tested by
more extensive investigations of single crystals
of other materials. Apparently, pure monatomic
crystals are not well suited for tests of this
type because of their great softness. It should be
added that Sachs and Shoji made measurements
on single crystals of aluminum-copper alloys, but'
found the effect smaller than in brass and did
not extend the investigation. At the present
time, this interpretation seems to be the most
plausible one.
(b) In the second place, it is possible that
there are two contributing causes for the Bausch
inger effect in polycrystalline materials-one
being the effect suggested by Masing, and the
other an effect that occurs even in single crystals.
Since Heyn' s work indica tes that Masing's theory
is sufficient to explain at least the magnitude of
the effect in polycrystals, we must conclude that
if two co-existing effects occur they are of com
parable importance.
553
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~ z t--j---+----i-,..L=+--+-+------cU---f---~
~
!
~ I
~ 'r-74--+-+-+-+-l-/--t--" ~ . J_L
...... ~02 ~O~ Q,Oof O.OS 0.08 OD7 0.04 0.011
COMPRESSION IN PERCENT
FIG. 63. The elastic after effect in a compressed single
crystal of brass.
It has recently been suggested by Masing
that the theory of dislocations may contain
features usable for an explanation of the Bausch
inger effect in single crystals. In particular, he
has proposed the possibility that dislocations
which have moved into the crystal as a result
of the action of a given stress move backward
under a lower reverse stress than is needed to
make them move forward. According to Masing,
this unidirectional hardening is a consequence of
the fact that the newly formed dislocations will
encounter dislocations of opposite sign, generated
on the opposite sides of the particular block in
which they are moving, if they continue to pro
ceed in the direction in which they were started.
They will not encounter these dislocations if their
direction of motion is reversed.
This picture seems difficult to justify on the
basis of the theory of dislocations developed here
for we should either expect the positive and
negative dislocations in the same block to attract
and lower the shearing stress for motion in the
same direction, or we should expect them to
become in termixed in the manner suggested by
Taylor and form a lattice that possesses equal
rigidity in either direction. The following, how
ever, is an alternate possibility. In discussing
resoftening of work-hardened crystals, it was
pointed out that newly formed dislocations near
surfaces are subject to a strong attractive
"image" force which drops off as the first power
of the distance from the surface. It is readily
seen that this force operates in just such a
direction as to contribute to the Bauschinger
effect. Evidently a quantitative estimate of the
magnitude of this contribution is necessary be-
554 fore we can draw a definite conclusion as to
whether the mechanism is a likely one.
The fact that the Bauschinger effect can be
completely removed by an annealing process
that does not produce complete resoftening seems
to indicate strongly that dislocations are not
primarily responsible for the effect.
c. The elastic after effect
Another interesting secondary effect observed
commonly in poly crystals and in some single
crystals, such as the brass specimens used by
Sachs and Shoji, is the elastic after effect illus
trated in Fig. 63. It is found that the stress
strain curve obtained when a specimen is un
loaded and then reloaded, following an extension,
is not a single-valued function but has the form
shown in the figure.
This effect may readily be explained in a
qualitative manner on the basis of Masing's
principle of inhomogenous strain. We may postu
late that when the specimen is first unloaded the
contraction is entirely elastic. As soon as the
elastic forces in the regions that have undergone
the most extensive plastic deformation are re
leased, the remaining regions will exert on them
stresses of such sign as to reverse the original
deformation. These stresses increase as the un
loading proceeds and cause a small amount of
irreversible plastic flow, analogous to the flow
occurring during creep recovery (Fig. 58). In fact,
it seems likely that such creep recovery actually
would have been observed on the single crystal
specimens of brass used in obtaining Fig. 63.
Evidently, the questions that arise concerning
Masing's theory and the existence of the elastic
after effect in single crystals of brass are basically
similar to those discussed in connection with the
Bauschinger effect in single crystals.
If we grant that all three of the secondary
plastic effects presented in this section have
similar origin, we may conclude from the fact
that single crystals of tin do not show appreciable
creep recovery that they would not show a
Bauschinger effect or elastic after effect com
parable with that observed in brass. From this
viewpoint, then, it follows that the brass crystals
on which Sachs and Shoji made their observa
tions were not as homogeneous as the single
crystals of tin studied by Chalmers.
JOURNAL OF ApPLIED PHYSICS
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1.1712880.pdf | Theory of the Plastic Properties of Solids. I
Frederick Seitz and T. A. Read
Citation: Journal of Applied Physics 12, 100 (1941); doi: 10.1063/1.1712880
View online: http://dx.doi.org/10.1063/1.1712880
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/12/2?ver=pdfcov
Published by the AIP Publishing
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Solids. 1*
By FREDERICK SEITZ,
Randal Morgan Laboratory, University of Pennsylvania, Philadelphia, Pennsylvania
AND
T. A. READ, **
Westinghouse Research Laboratories, East Pittsburgh, Pennsylvania
In troduction
FROM the standpoint of direct experimental
observation,l the plastic properties of solids
may be classified into five categories, namely:
(a) slip, (b) creep, (c) twinning, (d) rupture, and
(e) fatigue.
Slip is one of the fundamental ways in which
crystals may deform inelastically. It consists, at
least from the gross experimental standpoint, of
the displacement of one part of a given crystal
relative to another along a definite crystallo
graphic plane (Fig. 1). What actually is observed
in a practical experiment with a single crystal is
as follows. Let us suppose that the specimen is
placed under stress in a tension machine and that
its elongation is measured, the machine being
able to detect Cl. certain minimum rate of elonga
tion of the order of 10-5 em/sec. Starting with
very small stresses, it is found that the elongation
initially occurs practically instantaneously, is
proportional to the stress, and is exactly reversed
when the load is removed. This is the region of
stress in which Hooke's law is valid. When the
stress reaches a critical value,' about which more
* The writers wish to express their deep indebtedness to
Dr. C. S. Barrett of the Carnegie Institute of Technology
and to Drs. A. Nadai and S. Siegel of the Westinghouse
Research Laboratories for many informative discussions
on this topic.
** Westinghouse Research Fellow.
1 Extensive accounts of experimental work in this field
may be found in the following books and periodicals:
C. F. Elam, The Distortion of Metal Crystals (Oxford
University Press, 1936).
E. Schmid and W. Boas, Kristallplastizitat (Springer,
Berlin, 1936).
A. Nadai, Plasticity (McGraw-Hili Book Company, New
York, 1931).
Reports of the International Conference in Physics 1934
(Cambridge University Press, 1935), Vol. II.
"Report of a conference on internal strains in solids,"
Proc. Phys. Soc. 52, 1 (1940).
S. L. Hoyt, Metals Progress, 38, 659 (1940).
100 will be said later, the elongation continues
relatively slowly after the first instantaneous rise.
If the stress is released after such a deformation,
only a part of the elongation is reversed and the
specimen has received a permanent increase in
length. Within limits (Section 2), this increase in
length is greater the longer the load is applied and
the further the stress lies above the critical value
for which it began. An examination of a single
crystal specimen which has undergone an elonga
tion of a percent or so shows that parts of the
crystal have been displaced relative to one
another along particular crystallographic planes
(Fig. 2). These planes may be detected by the
presence of step-wise discontinuities on the sur
face of the specimen which are called slip-bands.
In many instances these bands run continuously
around the crystal, their spacing and orientation
depending greatly upon the conditions surround
ing the experiment. In the simplest cases they are
parallel to one another and are spaced by
distances of the order of a micron. We shall defer
additional discussion of the details of the slip
process until Section 2.
Creep is a temperature dependent type of
plastic flow that occurs when the solid is stressed
below the critical stress mentioned in the pre
ceding paragraph. Its detection generally re
quires a more sensitive type of instrument than
that used in detection of slip. A separate desig
nation for this more gradual type of flow was
introduced originally because of the fact that its
measurement required a particularly designed
apparatus. Actually, it appears that the funda
mental atomic motions occurring during slip and
creep are identical in single crystals of many
substances. As we shall see in Section 3, the
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established fairly definitely in zinc, cadmium and
tin.
Twinning resembles slip in that it is another of
the fundamental ways in which plastic deforma
tion can occur. As in the case of slip, the end
result of twinning is the relative displacement of
neighboring planes of atoms. However, the im
portant difference is that in twinning millions of
successive, neighboring planes may be displaced
relative to another by a fixed distance that is not
an integer multiple of a lattice spacing, whereas
in slip parts of the original crystal appear to
move relative to one another with a transition
region whose width is less than the resolving
power of optical microscopes (about a micron).
Thus the end result of twinning in a single crystal
is the production of a region, namely that in
which the relative motion has occurred, in which
the atoms hav~ perfect crystalline arrangement,
but in which the crystalline orientation is usually
very different from that of the parent crystal.
The end result of slip in an ideal case is the
A --:--:-~-:-~-:-:-:-:-~-:--:-~-- 8
• .. • • • • * • • • • • •
A -:-~-.-:-. -.-:-:-~-.--:-:--.------ B
b
FIG. 1. Schematic representation of the atomic displace
ments resulting from slip. The lines of atoms shown in
(a) are displaced in the manner shown in (b) as a result
of slip in the plane A-B.
production of a poly crystal consisting of a num
ber of identically oriented single crystals that are
separated by the slip bands.
Rupture is the process by which solids break
when placed under static stress, whereas fatigue
is the breaking induced by periodic stress. This
division of the topic of breaking is important
because solids will break under periodic stressing
for smaller maximum load than in static stressing.
VOLUME 12, FEBRUARY, 1941 FIG. 2. A photograph of a zinc single crystal which
shows slip bands. The slip bands are ellipses formed hy the
intersections of the slip planes, which are perpendicular
to the hexagonal axis of the crystal, and the cylindrical
surface of the crystal.
In treating each of these topics, we may
recognize four types of crystalline textures,
namely pure single crystals, single crystals of
alloys, pure polycrystalline materials, and poly
crystals of impure materials and alloys. The last
two types of texture have the greatest practical
interest and naturally have been used most ex
tensively in experimental testing. Cnfortunately
only a very minor part of the results of this work
seems to have value for understanding the funda
mental mechanisms involved in the plastic prop
erties of solids. In fact this fraction of the work
dealing with polycrystals is relatively small com
pared with the work on single crystals in which
we shall be interested. For this reason the largest
part of this article will deal with the properties of
single crystals.
\Ve shall proceed with a concise discussion of
the experimental material relating to the plastic
properties of solids and accompany this with a
presentation of the theory suggested by this
experimental work. This procedure will be fol-
101
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polycrystalline materials. It should be borne in
mind that in its present state of development,
this theory is far less complete than the theories
of many other properties of solids. For this reason
the present series of articles should be viewed
entirely as an attempt to plot an orderly course
in a field in which extensive changes in View
point will undoubtedly prove necessary.
Part A. Single Crystals
1. THE ELASTIC RANGE*
Before proceeding with the plastic behavior of
solids, itis appropriate to survey the relationships
in the range of stress and strain in which Hooke's
law is valid. Careful experimental work seems to
indicate that a certain amount of plastic flow
occurs at all stresses. However, it is unquestion
ably true that for sufficiently small stresses and
sufficiently low temperatures the stress-strain
relation is practically linear and reversible. Since
such topics as internal friction and plasticity may
be introduced by discussing deviations from this
idealized linear relation, it may be said to be the
foundation of all discussions of stresses and
strains in solids.
Let us consider a homogeneous medium that is
under stress. In order to describe its state of
stress completely, we should know the stresses
acting on each infinitesimal component. To do
this conveniently, we may refer the medium to a
Cartesian reference system and subdivide it into
rectangular parallelepipeds whose faces are de
fined by the coordinate planes of the Cartesian
system. The state of stress at a given point is
then completely described by giving the forces
tha t act across each of the faces of the infinitesimal
rectangular cell surrounding this point and having
edge-lengths dx, dy and dz parallel to each of the
coordinate axes (Fig.. 3). Since the cell is infini
tesimally small, by assumption, the forces on
opposite faces will be equal to within infini
tesimals if the stress variation is continuous.
Hence there are no more than nine independent
components of force; these correspond to the
forces acting on three mutually perpendicular
faces of the cell. We shall designate the three
~ This section should merely be skimmed for its quali
tative content by a reader not interested in the details of
elasticity theory.
102 components of the force per unit area acting on
the cell across the x face by 0"11, 0"12, 0"13 in an
obvious notation in which the subscript 1 refers
to the x component, 2 to the y component and 3
to the z component. Similarly the components of
the force per unit area acting on the cell across
the other two faces will be designated by 0"21, 0"22,
0"23 and 0"31, 0"32, 0"33, respectively. These nine
quantities constitute the stress tensor, the indi
vidual components being the stress components.
It is clear from Fig. 3 that 0"11,0"22,0"33 correspond
to forces normal to each of the three faces of the
cell and hence are compression or tension stresses,
whereas the other six stress components corre
spond to forces lying in the plan faces and hence
are shearing stresses.
Now it is easy to show2 that in ordinary static
stress distributions the shear components satisfy
the following relations, which imply that the
stress tensor is symmetric,
Thus there are only six independent stress com
ponents. For simplicity these are usually desig
y
1 0"22
'. _at -_~-:-: --1---;:;:----",.,
-t-rt-==--~: ....,......:::::.==...£!.,-
I : 023
~ lL~1
'"IJ ~3:
I I
I I
I _-.-1.--------- ---------x
~L --Z ---I I r--- dx -----,
FIG. 3. The infinitesimal paral\elepiped in terms of which
the stress components are defined.
nated by a one-subscript symbol O",(i= 1,2, ... , 6)
in accordance with the following relations
0"1 = 0"11, 0"2 = 0"22, 0"3 = 0"33,
0" 4 = 0"12, 0"6 = 0"23, 0"6 = 0"13· (2)
The strains in a medium may be described in a
manner analogous to that used for stresses. Let
us suppose that in the strain-free state the points
of the medium are designated by coordinates
2 See, for example, A. E. H. Love, The Mathematical
Theory of Elasticity (Cambridge University Press, 1927).
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and that after straining has occurred the point
previously at x, y, z has been displaced to the
point x', y', z'. We may assume for simplicity
that the point at the origin of coordinates has not
been displaced for we could always translate the
origin of coordinates to the new position if it had.
Since Hooke's law is valid for small deformations,
we may consider this special case and write the
relation between x, y, and z and x', y', and z' in
the form
X' -x = S11X+S12y+S13Z,
y' -y=S21X+S22y+S23 Z,
Z' -Z=S31X+S32y+S33Z.
In general the Sif, which are known as the com
ponents of the strain tensor, are functions of
position; however, the homogeneous case, in
which they are constant, is an important one.
As in the case of the stress tensor, the practically
interesting situations correspond to symmetric
strain tensors, that is to tensors in which the
shearing strains are related by the equations
S12 = S21, S23=S32, S31=SI3. (3)
Thus there usually are only six independent
components of the strain tensor. It is frequently
convenient to designate these by the six one
subscript symbols Si(i = 1, 2, "', 6) in accord
ance with the relations
SI=S11, S2=S22, S3=S33
S4=S12=S21, S.=S23=S32, S6=S31=S13. (4)
In this case the components S11, S22, S33 give the
fractions by which the medium is extended or
compressed along the three coordinate directions,
respectively, whereas the other six components
give a corresponding measure of the relati-:e
amounts by which coordinate planes are dis
placed parallel to themselves along the coordinate
axes (i.e., sheared).
In the region in which Hooke's law is valid, the
stress and strain components are proportional to
one another, that is the following relations are
satisfied
6
(fi= L CijSj
i~l TABLE 1. The elastic constants of crystals. (The values are
given in units of 10-12 cm2/dyne.)
METAL Cll C ..
Face-centered cubic
Al
Au
Ag
Cu
Pb 1.59
2.33 2.32
1.49
9.30 -0.58
-1.07
-0.993
-0.625
-4.26
Body-centered cubic
Fe 0.757 -0.282
Na 48.3 -20.9
K 83.3 -37.0
W 0.257 -0.073
HEXAGONAL
Cll Cn C13 C"
Mg 2.23 -0.77 -0.45 1.98
Zn 0.84 +0.11 -0.78 2.87
Cd 1.23 -0.15 -0.93 3.55
LoWER SYMMETRY
Cll C" C .. C .. C" ------------
Sb 1.77 3.38 4.10 -0.38 -0.85
Bi 2.69 2.87 10.48 -1.4 -0.62
Sn 1.85 1.18 5.70 -0.99 -0.25
ALLOYS
ALLOY Cll C12
100 Ag-O Au 2.32 -0.993
75 Ag-25 Au 2.07 -0.891
50 Ag-50 Au 1.97 -0.852
25 Ag-75 Au 2.05 -0.909 o Ag-IOO Au 2.29 -1.04
CU3Au 1.34 -0.565
72 Cu-28 Zn 1.94 -0.84
50 Cu 50 Zn 3.88
95 AI5 Cu 1.5 -0.69
IONIC CRYSTALS
SALT Cll C,.
NaCI 2.27 -.476
KBr 3.17 -.462 C ..
3.52
2.38
2.29
1.33
6.94
0.862
16.85
38.0
0.660
C ..
5.95
2.64
5.40
C14
-0.80
+1.6
C66=13.5
C ..
2.29
2.05
1.97
2.06
2.34
1.508
1.39
3.7
C ..
7.89
16.1
The Cii and eli are not independent, of course, for
the two sets of Eqs. (5) are simply algebraic
inverses. We need not be concerned with the
detailed relations here. Since there are six 11'/ and
six S;, it follows that at most thirty-six constants
6
Si= L eijCTi
i~l (i = 1, 2, "', 6). (5) enter into either of the sets of equations. Not all
of these elastic constants are independent however,
for it may be proved by means of the first law of
VOLUME 12, FEBRUARY, 1941 103
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exist
Cij= Cii,
Gij= Gii•
Thus only twenty-one elastic constants are
independent at most.
Further relationships occur in crystals having
particular symmetry. For example, there are only
three independent constants in the case of cubic
crystals such as copper, iron, rocksalt, etc., and
v
o
FIG. 4. Schematic form of the potential energy of an
atom in a lattice. The abscissae represent the positional
coordinates of the atom. This potential is essentially
parabolic in the vicinity of the minimum 0, which is the
normal equilibrium position of the atom.
there are only five in hexagonal crystals such as
zinc, cadmium, wurtzite, etc. Experimental values
of some of the measured C;i are given in Table I
for several well-known crystals. We shall find
these constants useful in the following sections
for making estimates of stresses for which plastic
flow should begin in solids. I t should be added
that they are independent of the previous history
of a specimen to within a factor of about one
percent.
It is interesting at this point to consider the
facts concerning the interatomic forces that give
rise to Hooke's law. Any atom in a solid is under
forces exerted on it by its neighbors, and in an
ideally perfect crystal, translation ally equivalent
atoms are under identical forces. The form of the
potential well in which an atom moves is shown
schematically in Fig. 4, the minimum point being
the equilibrium position at absolute zero of
temperature when the crystal is not under
external stress. At temperatures above absolute
zero, the atom will oscillate about this equilib
rium point with varying amplitude in accordance
with the laws of statistical mechanics. Since the
potential energy is a quadratic function of
displacement relative to the position of minimum
104 energy, in first approximation, the forces restoring
the atom to its equilibrium position will be
proportional to the displacement for small dis
placements. Thus if the ideal crystal is placed
under stress, we may expect the atoms to be
displaced relative to one another by an amount
proportional to the stress as long as the displace
ment is small compared with interatomic dis
tances; that is, we should expect Hooke's law to
be obeyed. Elastic constants computed on the
basis of this atomic mechanism3 with the use
of quantum mechanics and the assumption of
ideal lattices are in excellent agreement with
experimental values in a number of cases.
Now these computations, and similar ones
involving molecules rather than solids, show that
the quadratic approximation is usually accurate
for displacements of the order of ten percent of
the interatomic distance, so that we should ex
pect Hooke's law to be valid in an ideal crystal
for stresses in which the strain is less than one
tenth. Thus, using values of the elastic constants
given in Table I, we should expect the law to be
valid in the materials listed for stresses at least as
high as 1010 dynes/cm 2 (or 100 kg/mm2). As we
shall see below, large deviations from Hooke's
law actually occur for stresses a thousand times
smaller than this in carefully grown, weIl
annealed single crystals of practically all pure
metals and many salts, even at temperatures in
the vicinity of absolute zero. Thus, although the
elastic constants are determined by the bulk
properties of the ideal solid, we must conclude
that deviations from the ideal state occur and are
in some way responsible for deviations from
Hooke's law.
2. THE THEORIES OF SLIP
a. Basic concepts
The most easily detected phenomenon associ
ated with breakdown of Hooke's law is the
process of slip. As was mentioned previously,
this is characterized by the irreversible motion of
one part of a crystal relative to another along a
definite plane (Fig. 1). The motion is usually
made evident by the appearance of bands on the
3 See, for example, the survey of this topic in F. Seitz,
The Modern Theory of Solids (McGraw-Hili Book Com
pany, New York, 1940).
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intersection of the slip planes with the boundary
surface. An actual representation of the slip
bands in a single crystal in which slip has
occurred along a number of parallel planes is
given in Fig. 2. This situation is typical of
both zinc and cadmium in which slip occurs most
prominently in planes normal to the hexagonal
axis (basal planes). The slip system is usually not
as simple in cubic crystals since symmetrically
equivalent planes are not necessarily parallel.
Before interpreting slip in the light of the remarks
made at the end of the preceding section, we shall
summarize several of the laws obtained as a result
of the rather extensive experimental work on slip.
(1) The rate at which slip occurs in a given
plane in a given specimen is determined primarily
by the component of shearing stress in the plane.
In general, the slip rate is very slow for a range of
shearing stress extending from zero to a more or
less definite value (for the particular specimen
and plane) at which it becomes measurable in
somewhat standardized laboratory equipment. A
readily measurable rate of shearing strain is
10-6 seC.-I. In practical work, this stress at which
the rate of slip becomes readily measurable with
comparatively crude equipment is called the
critical shearing stress.
We shall find it very convenient to follow the
practical procedure in the present section and
reserve the word "slip" for the plastic flow
occurring for stresses at least as large as the
critical shearing stress. The less rapid flow for
smaller stresses will be treated in the next section
under the heading "creep." As was mentioned in
the introduction, the two types of flow are
intimately connected so that this division of the
topic is mainly one of convenience.
(2) The critical shearing stress is different for
different types of crystallographic planes. In
some cases, such as zinc and cadmium, cited
above, the critical value is so much lower for one
set than for all others that slip is observed almost
exclusively in that system of planes. It seems to
be a general rule in the case of metals that the
planes of easiest slip are the most nearly c1ose
packed ones. Thus the basal planes are the easiest
in close-packed hexagonal crystals, whereas the
four types of (111) planes (octahedral planes) are
easiest in face-centered cubic lattices, such as
VOLUME 12, FEBRUARY, 1941 copper and aluminum. Moreover, when slip is
observed in other planes, such as in the (100)
planes of aluminum, these are also planes of
relatively high atomic density. There are several
planes of nearly equal atomic density both in the
body-centered cubic lattice and in white tin.
Andrade' and his co-workers have found slip in
the (112), (110) and (123) planes in several body
centered cubic crystals, whereas Obinata and
Schmid5 have found slip in the (100), (110), (101),
and (121) planes of tin for nearly equal shearing
stresses.
In addition to this rule that the planes of
easiest slip are the most highly packed planes in
simple substances, it is found that the direction
of slip is usually in the direction of lines of
greatest atomic density. Thus slip occurs in the
(101) direction in the (111) planes of face
centered metals and in the (1120) direction in
zinc and cadmium. Andrade' has suggested that
this rule is even of more fundamental importance
than the rule concerning the density of atoms in
the slip plane, for whereas there are several slip
planes in body-centered cubic lattices, the slip
direction is along the body diagonal in all cases.
A list of easy planes and directions in metals is
given6 in Table II, along with measured shearing
stresses.
Among the salts, slip has been investigated
most fully in those having the sodium chloride
structure and it is found that in all of these cases
the slip planes are the six systems equivalent to
(110) and the slip direction is (110). A few other
salts whose properties have been investigated
less thoroughly, are not listed in the table.
Although the (110) planes in the sodium chloride
lattice are not the most close-packed planes, the
slip direction is that of greatest atomic density.
It is clear from the values of the critical
shearing stress given in the table that slip usually
occurs in pure metals and salts for stresses not
appreciably larger than 107 dynes/cm2, which is
smaller than the value to be expected for ideal
lattices by a factor of about a thousand. As we
4 E. N. daC. Andrade, Proc. Phys. Soc. 52 (1940);-and
Y. S. Chow, Proc. Roy. Soc. 175, 290 (1940);-and L.
C. Tsien, Proc. Roy. Soc. 163, 1 (1937).
6 I. Obinata and E. Schmid, Zeits. f. Physik 82, 224
(1933).
6 These data are taken principally from the references
of footnote 1. A careful treatment of the geometry of slip
is given by M. J. Buerger, Am. Minerologist IS (1930).
105
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must conclude that actual solids do not possess
ideal structures and that the imperfections are in
some way responsible for this type of weakness.
Before continuing the discussion of slip, we shall
survey the present evidence for lattice imper
fections.
h. Types of lattice illlperfections
There is considerable evidence for the following
types of lattice imperfections in siqgle crystals.
(1) Thermal oscillations. The fact that the
atoms in crystals oscillate about their equilibrium
positions at temperatures above absolute zero is
indicated by so many sources of evidence that we
need not discuss them in detail. In addition,
atoms undergo the quantum-mechanical "zero
point" oscillations even at the absolute zero
of temperature. However, these quantum-me
chanical fluctuations are so very small for the
heavier atoms, with which we shall be almost
exclusively concerned, that we need not be con
cerned with them here.
(2) Defects extending over regions of the order
of atomic dimensions. There is abundant evi
dence7 from investigations of diffusion and ionic
conduction in solids that all crystals have many
small-scale imperfections. In the simplest cases
these consist of interstitial atoms not present in a
perfect crystal and vacant lattice sites (Fig. 5).
It is believed that these defects are generated as
a consequence of the thermal fluctuations and
play an essential role in many types of transport
phenomena in solids. We shall have occasion to
consider special types of defects of this kind in
part c of the present section.
It should be mentioned at this point that small
scale defects of this type do not give rise to
observable x-ray diffraction patterns because of
their small size. Or expressed in another way,
their patterns are so diffuse because of their small
size, that they appear in the general background
of the Laue or Hull-Debye-Scherrer x-ray pat
terns of crystals and are not measureable. They
do scatter x-rays, however, and in consequence
should detract from the intensity of the ordinary
diffraction lines. We shall be concerned with this
effect in another part of the present section.
7 See, for example the book referred to in footnote 3,
and the book by N. F. Mott and G. W. Gurney The Theory
of Ionic Crystals (Oxford University Press, 1940).
106 (3) The mosaic structure.8 The widths of the
x-ray lines scattered from small regions of crystals
TABLE II. Data concerning slip in solids.
PURE METALS
(KG/MM')
IMPURITY I SUP CRITICAL
METAL CONTENT PLANE DIRECTION STRESS
CU 0.001 (111) (101) 0.10
Ag 0.0001 (111) (101) 0.060
Au 0.0001 (111) (101) 0.092
Ni 0.002 (111) (101) 0.58
Mg 0.0005 (0001) (1120) 0.083
Zn 0.0004 (0001) (1120) 0.094
Cd { 0.00004 (0001) (1120) 0.058
(1100) >0.03
{ (110)
Na (112) (111)
(123)
Mo { (112) (111)
(110)
K (123) (111)
W (112) (111)
K (123) (111)
{ (110)
Fe (112)
(123)
{ 00001 (100) (001) 0.19
fJ-Sn (110) (001) 0.13
(101) (101) 0.16
(121) (101) 0.17
Bi ",0.001 (111) (101) 0.221
Hg ",10- 8 Complex 0.007
ALLOYS
CRITICAL
SLIP SLIP STRESS
COMPOSITION PLANE DIRECTION (KG/MM')
99.4 Zn 0.006 Cd (0001) (1120) 2.7
6.8 Al 93.2 Mg (0001) (1120) 1.4
85 AilS Zn (111) (101) 8
72 Cu 28 Zn (111) (101) 1.5
AuCus (ordered) 2.2
AuCus (disordered) 4.4
IONIC CRYSTALS
NaCl (110) (110) ",0.2
AgCI (110) (110) • rvO.l
KCI 1 KBr (110) (110)
KI f RbCI
8 Evidence for the mosaic structure is surveyed in the
Report of the International Conference on Physics, 1934
(University of Cambridge Press, 1935), Vol. II. Additional
evidence has been given by A. B. Focke, Phys. Rev. 46,
623 (1934), who showed that polonium precipitates from
bismuth on planes separated by about 1/01.
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actual lattices are of the order of 10-4 cm.
Similarly, microscopic examinations of the etch
patterns of crystal surfaces indicate that most
crystals consist of a mosaic of blocks of the order
of one micron in size. Beyond these facts, there
is very little experimental information concerning
the nature and origin of the mosaic structure.
The most reasonable interpretation9 is that of
Smekal and of Buergers, namely that the blocks
arise as a result of accidents of growth during the
formation of the single crystals, the block
boundaries being either places where some of the
impurities present in the melt congregated during
solidification or boundaries between regions that
started from different points on the growing
crystal surface and have become slightly out of
line by accident. In agreement with this picture
is the fact that some natural crystals that
undoubtedly required geological times for growth
show practically no evidence of mosaic structure.10
The factors leading to imperfections should be a
minimum in such cases because there is ample
time for the forming crystal to be at complete
equilibrium with its melt at all stages of growth.
(4) Slight variations in lattice spacing either
from domain to domain or over regions com
parable with the domain size. The contribution
to line widths arising from this type of variation
in lattice spacing can be separated from that
arising from the actual existence of domains by
studying the change in width from one order of
the x-ray diffraction pattern to another.ll The
magni tude of these variations is greatly dependen t
upon the amount of mechanical working the
specimen has received, as we shall see below.
(5) A coarser texture extending over regions of
a millimeter or more. Simple observations8 of the
optical reflection of fresh cleavage faces of most
single crystals show that such faces are rarely
perfectly flat and that variations take place over
regions of the area of one square millimeter. X-ray
examination shows that this is not a superficial
effect, but the crystallographic axes are rotated
in passing from one of these regions to another,
9 See footnote 8; also M. J. Buerger, Zeits. f. Krist. 89,
195 (1934).
10 R. M. Bozorth and. F. E. Haworth, Phys. Rev. 45,
821 (1934).
11 This topic is surveyed by U. Dehlinger and A. Kochen
dorfer, Zeits. f. Metallkunde 31, 231 (1939).
VOLUME 12, FEBRUARY, 1941 the angle of rotation commonly being as much as
several minutes. The amount of distortion of this
type does not seem to be directly related to the
existence of mosaic blocks, for it may appear
strongly even in cases in which the domain
broadening is almost absent. Thus even though
the distortion may arise in a manner closely
resembling the origin of the mosaic structure, the
• • • • • •
• INTERSTITIAL
• • • • • • ATOMS .... ..---- ---~'7
• • • • • ./ ./
• • • • • •
(0.)
• • • • 0 •
,~ VACANT
--~
• • • • • • SITES //
----------
• • 0--;--• •
• • • • • •
(b)
FIG. 5. Types of lattice imperfections that play an
important role in atomic transport phenomena in solids
such as diffusion and ionic conductivity. (a) Interstitial
atoms; (b) vacant lattice sites.
determining factors are probably different in the
two cases. For example, the coarser structure may
be related to impurity or concentration gradients
in the melt whereas the mosaic structure may be
related to temperature gradients.
c. Three hypothetical IllechanisIlls of slip
Three outstanding mechanisms for the slip
process have been suggested in the course of
development of the theory of this topic. We shall
discuss each of these and attempt to evaluate
them critically.
1. Becker's theory.-Since atoms in crystals are
continually oscillating at temperatures above
absolute zero, it is natural to consider the
possibility that these oscillations influence the
shearing strength. A theory of this type was first
given by Becker.12 He pointed out that the stress
at any point in the crystal will not be constant at
12 R. Becker, Physik. Zeits. 26, 919 (1925).
107
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of thermal oscillations. Occasionally the local
fluctuations should become sufficiently large to
cause groups of atoms to slip past one another
and produce a small amount of slip locally. Thus
the observed slip could be explained as the end
result of many such local slips.
A criticism of this theory requires that we look
into its quantitative aspects. The elastic energy
per unit volume in a region where the shearing
stress is u is equal to
(6)
where C. is the shear modulus. Thus in the
absence of an externally applied stress, the rela
tive probability that a given small volume Vof
the crystal will be under the stress u as a result
of thermal fluctuations is,13 according to Boltz
mann's theorem,
exp (-Vu2/2C.kT). (7)
If the atomic planes can slip past one another in
time T when the stress reaches a critical value uo,
the rate r at which slip will occur in the volume V
is approximately
1 r=-exp (-Vu02/2C.kT). (8)
T
For an otherwise perfect lattice, we should expect
Uo to be of the order of 1010 dynes/cm2• We need
not be concerned with the numerical value of T in
the following, although we might expect it to be
of the order of an atomic oscillation period, that
is, about 10-13 sec.
Now let us consider the case in which the
average applied stress is u'. For slip to occur in
the direction of the applied stress, it is only
necessary that fluctuations add a stress of amoun t
(uo-u'), if it is assumed that the external stress
acts constantly on all atoms. Hence (8) is
changed to
1
r(u') =-exp (-V(uo-u')2/2C.kT). (9)
T
This equation was derived by Becker in a manner
essentially equivalent to that employed here.
13 This equation is only approximate, for its use involves
the implicit assumption that the entropy of the crystal in
the stressed state is the same as in the normal state.
108 In spite of its exponential character, Eq. (9)
predicts that the critical shearing stress should
vary relatively slowly with temperature, for in
ordinary static slip tests, slip is said to occur
when r reaches a more or less constant observable
value (see part a of this section). The condition
for this is
(uo-u')/Tt=a,
where a is a constant. Thus the critical shearing
stress Uc should vary with temperature in ac
cordance with the equation
(10)
As we might have expected, Uo should be the
value of the critical shearing stress at the
absolute zero of temperature. The temperature
dependence predicted by (10) is in qualitative
agreement with the observed dependence in zinc
and cadmium, as may be seen from Fig. 6.
Unfortunately, the value of Uo obtained by
extrapolating the observed points to absolute
zero is of the same order of magnitude as the
values of Uc at room temperature, namely 107
dynes/cm2• As a result, we may conclude that the
imperfections introduced by thermal fluctuations
are not sufficient to account for the low values of
the shearing strength.
Q~----'-----r----'----~----.---~
N
~ 0.1Dt-----t-"'--,.;:----+=c--+-----+------+-----l
0-" z -0.05
b
400
TEMPERATURE -0" _ 500
FIG. 6. Temperature dependence of the critical shearing
stress for slip in zinc and cadmium (after Schmid and
Boas). The relatively slow dependence is in qualitative
agreement with equation (5). The ordinates are given in
units of kg/mm2•
2. Smekal's theory.-SmekaP4 has suggested
that the weakness of actual crystals is intimately
related to the existence of the mosaic structure.
14 This work is reviewed by Smekal in the reference of
footnote 8. See also Handbuch der Physik, vol. XXIV 2.
JOURNAL OF APPLIED:PHYSICS
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are essentially weaker than the interior of the
blocks and this weakness is the source of the low
plastic strength of solids. In general this weakness
has two mutually assisting effects: (a) The blocks
may move relative to one another more easily
than parts of the material within the blocks and
(b) the variations in structure allow for variations
in stress from one region to another when the
crystal is placed under stress, so that the values
at some regions may be considerably higher than
the average value. The second point may be fully
appreciated by considering a simple example first
considered by Griffith.15 If a bar containing,a
long cylindrical crack with an elliptical cross
section is placed under tension so that the direc
tion of the applied force is normal to the cylinder
axis and the major axis of the ellipse (Fig. 7), the
stress at the edge of the major axis is larger than
the average value by the factor 2a/b, where a is
the major diameter and b the minor diameter of
the ellipse. Thus the stress magnification at the
edge of a long thin crack may be very large.
Even if the correctness of Smekal's viewpoint
were to be granted, it would seem very difficult to
develop these ideas into a systematic theory of
plasticity, for our reliable knowledge concerning
the mosaic structure is extremely small. In its
most elementary form, a theory of this type
would presumably go as follows: Slip takes place
along the block boundaries which have an
inherent shearing strength about a thousand
times lower than that of perfect crystals; this
type of slip may be aided by temperature
fluctuations in a manner similar to that postu
lated in Becker's theory, so that an equation
similar to (10) is valid. Although the evidence
against a simple picture of this kind is by no
means overwhelming, it does face several diffi
culties, which may be summarized:
(a) It is difficult to understand why the slip
bands can extend as uniformly through single
crystal specimens as they appear to do. This
difficulty may be associated with our ignorance
of the nature of the mosaic pattern, of course, for
it is possible that it is very regular.
(b) It is difficult to interpret the fact that
crystals soften with annealing, for we should
1. A. A. Griffith, Trans. Roy. Soc. 221, 163 (1921).
VOLUME 12, FEBRUARY, 1941 expect the weak regions to become more nearly
perfect as a result of heating and the crystal to be
strengthened thereby.
(c) Crystals may be hardened by the addition
of soluble impurities, whereas insoluble ones have
b 1
FIG. 7. The concentration of stress at the edges of an
elliptical crack in a solid. In avoiding the crack, the lines
of stress concentrate at the edges, the stress magnification
factor being 2a/b.
a much smaller effect [see a later part of this
section (next installment) for additional details].
Since the soluble impurities enter the interior of
the blocks, whereas insoluble ones presumably
should tend to congregate near the block bound
aries, one would expect the latter to have a
greater influence if the simple picture given above
is valid.
(d) As we shall see in a later section, the
boundaries between crystal grains in poly crystals
appear to furnish resistance to shear rather than
to aid it. Unless the block boundaries have
entirely different nature from intercrystalline
boundaries, it is difficult to reconcile this fact
with the foregoing picture.
For these reasons, or at least until our knowl
edge of the mosaic structure is more complete,
it seems most fruitful to assume that the role
109
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if not actually minor.
Masing 16 has pointed out that one of the major
objections to Becker's theory, namely the fact
that it does not explain the weakness at absolute
A
FIG. 8. A schematic picture of a dislocation of the type
considered in the theory of slip (after O~owan). Within
the circular region there is one more atom in the line of
atomic cells above A-B than in the Itne below. In the
text it is assumed that the region of dislocation extends
indefinitely in a direction normal to the plane of the paper,
so that this figure represents a normal cross section of a
line dislocation.
zero of temperature, is removed if we postulate
that the block boundaries operate to furnish a
stress magnification factor of about a thousand
at some point of the solid, for then Becker's
slip processes could start at these regions for
values of the mean applied stress much lower
than 0'0. In the formal equations derived above,
this would mean that, in all of the equations in
which it appears, the applied stress 0" is to be
multiplied by a factor q equal to about a thou
sand. Equation (10) would then become
1
O'c=-[O'o-a(T)iJ.
q (11)
Although this result of the juxtaposition of the
Smekal and Becker concepts has fewer objections
than either scheme alone, it leaves unexplained
the mechanism by which slip travels from the
regions of high stress magnification to those of
low magnification and why soluble impurities
play an important role.
(3) The theory of dislocations.-A theory of
slip that appears to meet many of the strongest
objections of the preceding theories has been
developed as a result of independent contribu
tions of a number of workers. We shall present
the essential points of this theory from a unified
16 G. Masing, Zeits. f. Metallkunde 31, 235 (1939).
110 viewpoint and then scrutinize it from several
different angles.
Let us postulate the existence of a type of
lattice imperfection having the following three
properties:
(a) The region of imperfection may move
through a large part of the lattice without a
given atom shifting by more than a single lattice
distance. (b) The end result of the motion of the
imperfection across a crystal is to translate the
part of the crystal on one side of a plane by a
unit lattice distance relative to the other part.
(c) In an otherwise perfect crystal, the shearing
stress required to make the region of imperfection
move is about a thousand times lower than the
stress required to cause slip in an ideal lattice.
If such imperfections can occur, it is clear
that any amount of slip can be produced as a
result of the motion of a sufficiently large
number of them.
A type of imperfection that possesses the
properties (a) and (b) was apparently first
considered by PrandiJ17 in connection with a
theory of internal friction in solids and later by
Dehlinger18 in a theory of recrystallization. The
o 0 0 0 0
o 0 0 0 0
o 0 000
o 0 0 0 0
o 0 0 0 0
a
POSITIVE DISLOCATION
o 0 0 0 0
o 0 000
o 0 0 0 0
o 0 0 0 0
o 0 0 0 0
e
NEGATIVE DISLOCATION
FIG. 9. Generation of dislocations at crystalline bound
aries (after Taylor). In cases (a), (b) and (c) a positive
dislocation is generated at the left-hand side of the crystal
and moves to the right, whereas in cases (d), (e), and (£)
a negative dislocation moves to the left. The end result
is identical in the two cases.
credit for its use for the theory of slip belongs to
Orowan,19 Polanyi,2° and Taylor.21 Let us con-
17 L. PrandtI, Zeits. f. angew. Math. Mech. 8, 85 (1928).
18 U. Dehlinger, Ann. d. Physik 2, 749 (1929).
19 E. Orowan, Zeits. f. Physik 89, 634 (1934).
20 M. Polanyi, Zeits. f. Physik 89,660 (1934).
21 G. I. Taylor, Proc. Roy. Soc. 145, 362 (1934).
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Fig. 8. In this case, the part of the lattice above
the line A -B contains one more atomic cell
within the region indicated by the circle than
the part below the line. We shall call this type
of imperfection a dislocation. Taylor has pointed
out that dislocations of this type may be gener
ated at the surface of a lattice in the manner
shown in Fig. 9. In the upper set of figures, the
dislocation starts at the left-hand side of the
lattice with the compressed region above and
the extended region below and moves to the
right, whereas the converse occurs in the lower
set of figures. It is clear that the end result of
the motion of the first of these types of disloca
tion from left to right and of the second from
right to left is slip by a unit distance along the
plane containing the dislocation. The direction
of slip would be reversed if the dislocation moved
in the opposite directions in the two cases.
Following Taylor, we shall call a dislocation of
the first kind positive and one of the second kind
negative.
In addition, Orowan has pointed out that dis
locations of the same type may be generated
pairwise in the interior of a crystal in the manner
A B
FIG. 10. If dislocations are generated in the interior of
crystals, it is necessary that pairs of this type be generated
simultaneously. If the members of this pair move out of
the lattice in opposite directions, the end result is the
same as that shown in Fig. 9.
shown in Fig. 10. If the members of a pair of
this type move to the surface in opposite direc
tions, it is clear that the lattice will undergo a
unit of slip. Since this type of generation of dis
locations requires the production of pairs simul
taneously, whereas generation at surfaces re
quires only single production, it seems almost
beyond question that surface production requires
least energy.
It should be clearly understood that in the
VOLUME 12, FEBRUAR~ 1~1 A
ATOMIC COORDINATES
(0.)
A
ATOMIC CooRDINATES
(b)
B' MAXIMUM SI.OPE //
B'
ATOMIC COORDINATES -B
FIG. 11. Curves showing the change in energy of a
lattice (a) during shear in an ideal lattice; (b) during
formation of a dislocation; (c) during the motion of a
dislocation. The abscissae represent schematically tbte
atomic coordinates that are changed during these processes.
In case (a) two parts of an ideal crystal move past one
another along a slip plane. The point A represents one
equilibrium position, the point B another in which one
unit of slip has occurred. The critical shearing stress (at
absolute zero) is determined by the maximum slope, that
is, the slope at C. Figure (b) represents the change in
energy during the formation of a dislocation. A corre
sponds to the perfect crystal, whereas B' is the equilibrium
state in which a dislocation is present. The maximum
energy change El in going from A to B' is the activation
energy for formation of the dislocation. This is dependent
on where the dislocation is formed. Figure (c) shows the
periodic changes in energy during the motion of a disloca
tion through the lattice. The shearing stress required to
move the dislocation (at absolute zero of temperature) is
determined by the slope at C', which should be much
smaller than the slope at C in (a), if dislocation theory is
valid. The energy E2 is the activation energy for motion
of a dislocation.
111
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it is implied that the dislocation extends in
definitely in a direction normal to the plane of
the paper and that this entire line of dislocation
moves as a unit. We shall refer to these as line
dislocations. More will be said concerning the
actual length of dislocations in a later paragraph.
The change in energy induced in a crystal by
the presence of dislocations is illustrated sche
matically by means of Fig. 11 in which the
energy of a portion of the crystal is shown as a
function of the atomic coordinates. Naturally a
many-dimensional diagram would be required to
represent the effect of moving all atoms in the
crystal, so, for convenience, the atomic coordi
nates are represented by a single variable. In an
ideal crystal, these coordinates possess values
corresponding to an absolute minimum of energy
such as the point A. If the atoms are displaced
relative to one another from these values, the
energy rises, the change in energy varying
quadratically with change in relative spacing for
small displacements. If two parts of the ideal
crystal are sheared past one another along a slip
plane by an amount equal to a lattice spacing,
the energy will rise to a maximum and then fall
to another absolute minimum B as the atoms
again come into perfect lattice positions. The
critical shearing stress (J'i required to bring about
this change is measured by the maximum slope
of the curve leading from A to B, that is, the
slope at the point C. The energy of the crystal is
raised in the manner shown in Fig. l1(b) when a
dislocation is formed, for the atomic configura
tion is no longer that of an ideal crystal. The
system is still relatively stable, however, since
the energy has the relative minimum value B'.
We shall call the energy El required to form a
dislocation the activation energy for the disloca
tion. This energy will depend, of course, on
whether the dislocation is formed near a surface
or in the interior of the crystal. As the dislocation
moves through the crystal from one equilibrium
position to another, its energy will pass through
successive maxima (Fig. U(c)). The critical
shearing stress (J'd required to induce this motion
is again measured by the maximum slope. The
success of dislocation theory requires that CTd be
many powers of ten lower than CTi.
112 The question of the ease with which disloca
tions of the type considered above can move
through the lattice has not yet been investigated
with a degree of thoroughness worthy of the
problem; however, there is little question that
they can move far more easily than atomic
planes in a perfect crystal. A qualitative way of
seeing this fact is given in Fig. 12. We consider a
schematized lattice consisting of two lines of
atoms in which there is the dislocation shown.
For simplicity, we shall assume that the forces
exerted on the lower row of atoms by the upper
row may be represented in terms of the sinusoidal
energy curve. In an ideal lattice the atoms in the
lower row would be opposite the minima of this
curve; in the dislocation they are not. However,
they are still at equilibrium under the combined
action of the forces exerted by the atoms in the
upper row and the forces they exert on one
another. It may be seen from the figure that the
forces exerted on atoms 2 and 8 by the upper
row of atoms are in opposite directions, as are
those on atoms 3 and 7, and on 4 and 6. Hence
these forces tend to compensate one another
when the dislocation moves from one equilibrium
position to another. The situation obviously
would be very different in a perfect lattice, for
then the forces exerted on all of the atoms in
the lower line would be identical and there would
be no compensation during slip.
It should be emphasized at this point that
different amounts of energy generally will be
t
E
•
• . . •
2 3 4 5 6 7 8 9
FIG. 12. Illustration of the fact that the critical shearing
stress for motion of a dislocation is less than that for an
ideal lattice (see text). The upper curve represents the
interaction energy of the lower row of atoms in the field
due to the upper row.
required to produce dislocations that move in
different planes, and that the shearing stress
required to make dislocatiqns move in different
planes should be different. The easy plane of slip
presumably is that for which this shearing stress
is lowest.
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the size and critical shearing stress for a disloca
tion using a simplified model in which the
forces between atoms on a given side of the slip
plane were treated by regarding the material as
continuous and isotropic, and the interaction
forces between the two sides were approximated
by a sinusoidal function, the amplitude of this
function being determined approximately from
the shear modulus. The results of this work
indicate that the dislocated region extends over
only a few atomic distances in the direction
normal to the line of the dislocation. In addition,
it was found that the ratio R of the shearing
stress required to move the dislocation to the
stress required to cause slip in a perfect lattice
is given by the equation
41r R=-[5.8-log (1-p)J exp (-41r/(1- p», I-p
where p is Poisson's ratio for the material. This
leads to values of R of the order of 10-6 or
smaller for values of p applicable to continuous
media.
t: •
A
ATOMIC COORDINATES-
FIG. 13. Schematic illustration of the effect of an applied
stress on the activation barrier for production of a disloca
tion. The upper curve represents the energy in the absence
of a stress; the lower curve represents the energy in the
presence of one. It may be seen that both activation
energie~ are lowered from values El and <2 to El' and <2',
respectively.
More accurate computations of this type based
on more rigorous principles of atomic mechanics
are well within the range of feasibility at the
present time. It is to be hoped that such com
putations will be carried out in the near future.
Although the energy required to form a dis
location has not been computed even for a simple
hypothetical lattice, we may expect values of the
22 R. Peierls, Proc. Phys. Soc. 52, 34 (1940).
VOLUME 12, FEBRUARY. 1941 BLOCK
3 ~
A
FIG. 14. Schematic representation of the "nucleation"
and growth of a dislocation. The dislocation starts as a
small slip at A, and grows by elongation in successive
stages to a full length dislocation 3. At stages 1 and 2,
work must be done at regions such as B, where the dis
location meets the surface in order to elongate the dis
location line.
order of one electron volt23 per atomic plane
along the length of the dislocation since the
energies associated with interstitial atoms and
vacancies (Fig. 5) are of this order of magnitude.
An important obstacle to dislocation theory
seems to arise at this point. If the previous
expectation concerning the formation energy per
plane in a line dislocation is correct, the total
energy in a dislocation that runs through a
block about 10-4 em long is about 104 ev. This
energy is so enormous when compared with the
activation energy for ordinary atomic processes
that it is out of the range of possibility to expect
such line dislocations to be generated spon
taneously by temperature fluctuations. There are
two factors that could operate to remove this
difficulty:
(a) The activation energy for formation of a
dislocation could be much smaller in the presence
of an ,applied stress than in. the unstressed
crystal.
(b) It is easily conceivable that dislocations
start over very small regions near the surface of
crystals and become elongated as they proceed
through the crystal. In this event,. the activation
energy required to produce th~ initial dislocation
23 One electron volt is equal to 1.60,10-12 erg,
113
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dislocation.
The principles behind the first of these possi
bilities are illustrated in Fig. 13. The upper curve
of the pair shown illustrates schematically the
variations in the energy of the crystal during
the formation and migration of a dislocation in
an unstressed crystal, and is a combination of
Fig. l1(b) and (c). Now since the external forces
do work on the crystal as a result of the strain
occurring during the formation and migration of
a dislocation, it follows that the energy curve
for the system is altered when stress is applied.
This effect may be taken into account by super
imposing on the upper curve of Fig. 13 a curve
giving the variation of energy with strain due
to the external forces. If the stress acts in such a
direction as to cause the system to move from
left to right in the sense of the diagram, the
added function decreases uniformly from left to
right and leads to the second curve shown. Thus
both the activation energy for the production of
dislocations and that for their motion are
lowered. The second effect was postulated pre
viously, of course, when we assumed that a
dislocation could be made to move even at the
absolute zero of temperature for stresses of the
order of magnitude of 107 dynes/cm2, for this
effect corresponds to lowering the activation
energy to zero.
Now it is only reasonable to suppose that the
stress required to produce a change in the
activation energy El (Fig. 11) for the production
of dislocations that is comparable with El should
be of the same order as the stress required to
produce slip in a perfect lattice. This follows from
the fact that the strain involved in producing a
dislocation is closely like that occurring during
this kind of slip, as may be seen from Fig. 9.
Since the applied stresses required to move dis
locations are only of the order of 107 dynes/cm2,
we must conclude that they are not sufficient to
affect the barrier El appreciably unless large
stress magnifications occur at some regions of
the crystal.
The possibility that the original dislocated
area covers only a few atomic dimensions seems
to be well within the range of reasonableness,
particularly if dislocations start at block bound-
114 aries where the surfaces of the blocks may be
somewhat irregular (Fig. 14). Once the disloca
tion has started, it will prefer to move in the
direction determined by the applied stress since
the system gains energy when it does so. There
will then be two retarding factors: (a) The
activation energy required for motion of the
dislocation without extension of its length; (b)
the activation energy required for extension of
length. According to the previous discussion,
the first of these is very small. There is no reason
for supposing that the second is nearly as large
for an extension by an atomic length as the
activation energy for production of the first
small dislocation area. Nevertheless, there is no
reason for expecting it to be as small as (a).
Moreover, there is no reason for expecting a
particularly large stress concentration at the end
of the dislocation, at least for the model of a
dislocation we are using. Hence it appears to be
necessary to postulate that thermal fluctuations
supply the activation energy required to extend
the length of a dislocation. Thus the process of
forming a full-length dislocation would appear
to be analogous to the process of forming a
crystal of a new phase during the transformation
of a metal from one phase to another. That is,
the process of forming the first small dislocated
area is analogous to the formation of the nucleus
of the crystal, whereas the process of extension
of the length of this region is analogous to the
growth of the crystal from the nucleus. In the
present case the driving force for the "reaction"
is the applied stress, whereas it is the difference
in free energy of the new and old phase in the
case of the phase change.
Thus we see that even if stress magnification
of the type postulated by Smekal were to playa
role in the formation of the first dislocated region
(our knowledge of mosaic structure seems to be
too fragmentary to argue this point one way or
another at present), there is no reason for sup
posing that such stress magnification could play
an equally important role during the elongation
of the dislocation. We seem to be forced to the
conclusion that dislocations probably cannot be
formed at absolute zero of temperature and that
any slip that occurs at extremely low tempera
tures must involve the use of dislocations formed
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picture, the formation of a full length dislocation
also requires the presence of an applied stress to
direct the process of elongation and supply the
free energy for the reaction.
We now pause to summarize the foregoing
discussion by giving the following outline:
(a) It seems most probable that slip takes
place through the volume of blocks rather than
simply at their surface.
(b) The properties of line dislocations seem to
be sufficient to provide us with a mechanism for
the slip process, provided their existence can be
made plausible.
(c) It seems most probable that dislocations
are nucleated in small regions near the crystal
surface or at block boundaries by the production
of small regions of slip, and that line dislocations
grow from these by extension. I t is perhaps worth
adding at this point that there are reasons for
supposing that dislocations would be most effi
ciently produced in pairs at block boundaries.
These reasons will be discussed in part (e) of
this section.
(d) The initial slip-nuclei may be produced
almost entirely as a result of thermal fluctua
tions; stress can play a primary role in this
process only if stress magnification factors of the
order of loa are possible.
(e) Even if stress plays a primary role in the
formation of slip nuclei, it seems most probable
that an appreciable activation energy is required
for extension of these nuclei and that this energy
is provided by thermal fluctuations. The applied
stress plays a guiding role during extension by
providing a preferential direction in which the
extension-process should take place24 and furnish
ing the free energy required for the process.
One of the fundamental problems concerning
slip that does not receive an obvious or satis
factory answer in the foregoing picture of the
slip mechanism is the fact that the slip bands
are separated by distances equal to many lattice
spacings. Andrade4 has pointed out, for example,
that the slip bands of many metals are separated
24 The electrostatic field plays a similar role in the case
of ionic conductivity in solids. The conducting particles
are made mobile as a result of thermal fluctuations, and
the field simply provides a preferential direction for their
motion.
VOLUME 12, FEBRUARY, 1941 by distances of the order of 5 microns. A possible
explanation of this fact is that each of the
observed slip planes is formed by dislocations
generated from a single weak spot. However, if
this were true, and if the weak spots were more
or less randomly distributed, we should expect
the slip bands to be closer in large crystals than
in small ones because of the greater number of
~ IT I I L I
COPPER SINGLE CRYSTAL
4
I !
r\T L>£ALEO_ 0 I /'
L V
I •
I~ /
1
..00-y--
--j---- I-~--
4
ANNEjAL~
00 .. L I. <.'
STRAt'II AMPLITUDe: oX 10&
FIG. 15. The decrement as a function of amplitude of
oscillation in a single crystal of copper before and after
annealing. These curves are reversible functions of strain
at room temperature.
weak spots. There seems to be no evidence
bearing on this poin t. We shall return to this
question later on.
d. Internal friction
If any solid is set into oscillation, it will
eventually dissipate its vibrational energy even
if it is so completely isolated from its surround
ings that sound loss and similar effects are
negligible. Since the elastic energy reappears as
heat in' the crystal, this dissipative effect is
called internal friction. It is very convenient to
express the magnitude of the internal friction in
terms of the decrement .6., defined by the relation
where .6. W is the energy dissipated per cycle and
W is the total vibrational energy.
As we shall see in a later section, one of the
largest sources of internal friction in polycrystals
is the intercrystalline thermal currents arising
from temperature differences between crystals
which, as the work of Zener shows, originate as a
115
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internal friction is apparently not observed in
well-made single crystals at frequencies in the
kilocycle range for which measurements are
ordinarily made. Instead it is found that a
type of internal friction having very different
characteristics occurs. In brief, the decrement
resulting from the observed internal friction of a
specimen is dependent upon amplitude instead
of being constant as is the decrement arising
6XO··
4
40 80
TIME IN HOURS 120 B,
160 200
FIG. 16. The variation of the decrement with time for
a single crystal of zinc. Curve A: before annealing;
Curve B: after annealing.
from thermal currents. In addition the decrement
decreases with frequency in a manner unlike that
of the friction related to the thermoelastic effect.
From the nature of its behavior, which will be
described presently, Read26 has concluded that
the internal friction of single crystals is closely
related to slip and has its origin in plastic flow
within the crystaf as a result of the stresses
present during vibration. If this interpretation
is correct, we should expect to explain some of
the properties of the decrement with the aid of
the theory of dislocations developed above.
Let us begin by considering the internal
friction in a single crystal of copper. The varia
tion with strain amplitude of the decrement
before and after annealing is shown27 in Fig. 15.
The first striking fact is that the internal friction
decreases very much as a result of anneal. In
addition, the decrement increases with increasing
25 C. Zener, Phys. Rev. 52, 230 (1937), et seq.; Proc.
Phys. Soc. 52, 152 (1940). The thermoelastic effect, as its
name implies, is the phenomenon in which the temperature
of solids is changed as a result of the application of stress.
26 T. A. Read, Phys. Rev. 58, 371 (1940).
27 Based on unpublished work by T. A. Read.
116 strain amplitude. This change with amplitude is
completely reversible in the range of strain
shown, although it would not be if the strain
were larger by a factor of a hundred or so.
These results may be simply explained in a
qualitative manner with the following assump
tions:
(a) The internal friction arises from the mo
tion of dislocations already present in the crystal
under the action of the stresses that occur
during oscillation. It is clear that the stresses do
irreversible work on the dislocations when the
dislocations move, for the elastic energy of the
solid is decreased without a corresponding rise in
the mutual potential energy of the atoms. It is
also clear that the decrement should increase
with increasing number of dislocations if we
assume that the stress required to make them
move does not increase proportionally with their
number, for then there are more dissipating
centers.
(b) The number of dislocations in the un
annealed specimen is higher than in the annealed
one because some of the dislocations diffuse out
of the crystal during the heat treatment. With
this, we must assume, of course, that the dis
locations present before anneal were introduced
as a result of handling. If this concept is true, we
should expect the decrement of the annealed
specimen to rise when strained sufficiently, as is
the case.
(c) Not all dislocations move with the same
ease in the range of stress employed in these
experiments. If we grant this, the increase in
o
30 ,
FIG. 17. The increase of the decrement with time for
an annealed single crystal of zinc during oscillation at
constant strain amplitude (about 10-6). This indicates
that dislocations are produced in zinc at room temperature
by very small stresses.
decrement with increasing amplitude is easy to
understand since dislocations will move as the
amplitude of oscillation increases. This postulate
is entirely reasonable, for as we shall see below,
dislocations may impede one another So that the
JOURNAL OF APPLmD PHYSICS
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in regions of differing dislocation density. In
addition, the stress for which dislocations that
are in the process of formation move should be
higher than that for fully formed ones (see the
preceding part of this section).
The fact that the decrement of single crystals
can be raised by stressing them sufficiently at
room temperature implies, according to our
picture of internal friction, that dislocations can
be generated in copper at room temperature.
Now we saw in the previous part of this section
that there is good reason for believing that
dislocations can form completely only if assisted
by temperature fluctuations. Thus a good test
both of this picture of internal friction and of
the picture of dislocation formation would be
obtained by studying the effect of stresses on the
decrement at very low temperatures where
thermal processes in metals and ionic solids are
practically halted. Evidence from the study of
work h~rdening of metals, to be discussed later,
indicates that dislocations are not formed under
these conditions, but measurements of internal
friction should provide a much more sensitive
test.28
On the other hand, the fact that the internal
friction of copper does not vary with time at
room temperature when the crystals are not
stressed implies that the dislocations in this
. metal are not sufficiently mobile at this tem
perature to migrate completely out of the crystals
of their own accord.
The situation that occurs in zinc at room
temperature seems to be very different from that
in copper. In the first place if the decrement of a
previously annealed single crystal of zinc is
measured as a function of time for relatively
small but constant vibrational amplitude (say,
a strain amplitude of 10-7), and if the measure
ments are started soon after the crystal has
received the strain incident to ordinary handling
and cutting, it is found that the decrement con
tinuously decreases. This effect is shown by
curve A in Fig. 16. It may be seen that the
decrement asymptotically approaches a very
small value, the initial rate of decrease being
28 In such an experim~nt it would b~ necessar y to cool
the specimen sufficiently slowly to avoid the high stresses
that accompany thermal gradients.
VOLUME 12, FEBRUARY, 1941 rapid compared with that attained at the end
of several hours. If the specimen is removed
before it has reached a steady state and is
annealed, the decrement then rapidly drops to a
very small value, as is shown by curve B in
Fig. 16. It is not possible to say whether the
asymptote of curve A is the same as that of
curve B. The fact that the decrement at the start
of run B was nearly as high as at the completion
2 4 X 10-7
STRAIN AMPLITUDE
FIG. 18. The variation of the decrement of a single
crystal of zinc with amplitude. The lower curve represents
measurements made at successively increased strain
amplitudes. The upper curve was obtained by making the
measurements in the reverse order.
of run A is related to handling received during;
mounting prior to taking measurements.
We may interpret the facts contained in Fig. 16
very easily by assuming that the dislocations
present when the measurements were started
gradually diffuse out of the crystal. The fraction
that are in process of formation would naturally
diffuse out more rapidly since they are nearest
the surface, and would thereby account for the
initial rapid decrease in decrement. This exodus
of dislocations is greatly speeded by annealing
although a comparatively small number of dis
locations are produced when the specimen is
mounted. These are near the surfaces, however,
and disappear very rapidly.
That there should be a large difference in the
room temperature internal friction of zinc and
copper is not at all surprising for many changes
take place in zinc at room temperature that
normally occur in copper only at temperatures
of the order of 200°C. For example the effects of
work hardening disappear in zinc at normal
temperatures whereas a high temperature anneal
is required for copper.
An extension of these experiments on zinc
shows that the internal friction of a well
annealed specimen increases with time when the
117
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This implies that very small stresses are required
to promote the growth of dislocations at room
temperature. In accordance with this, it is found
that the increase of decrement with amplitude,
such as is illustrated in Fig. 15 for copper, is not
reversible in the case of zinc if measurements
are made in a time comparable with that re
quired to induce the change shown in Fig. 17.
Decrement versus amplitude curves obtained
during increase and subsequent decrease of
amplitude are shown in Fig. 18.
It should be mentioned in passing that experi
ments with variously oriented zinc crystals show that for given amplitude of oscillation, the
larger the decrement the larger the shearing
stress in the slip plane. This fact illustrates
further the close correlation between the type of
internal friction considered here and the slip
properties.
Thus we may summarize this discussion by
saying that experiments on the internal friction
of single crystals may be satisfactorily correlated
in a qualitative way on the basis of dislocations
of the type postulated in the previous section.
We shall continue with a discussion of the
theory of dislocations and its applications in the
next installment of this series of articles.
Calendar of Meetings
February
21-22 American Physical Society, Cambridge, Mas
sachusetts
21-22 Optical Society of America, Cambridge, Massa
chusetts
March
3-7 American Society for Testing Materials, Washing
ton, D. C.
4-5 Inter-Society Color Council, Washington, D. C.
30-Apri15 American Ceramic Society, Baltimore, Mary
land
April
1-3 American Society of Mechanical Engineers, At
lanta, Georgia
4-5 Southeastern Section of American Physical Society,
Vanderbilt University, Nashville, Tennessee
7-11 American Chemical Society, St. Louis, Missouri
16-19 Electrochemical Society, Inc., Cleveland, Ohio
23-25 American Society of Civil Engineers, Baltimore,
Maryland
28-30 National Academy of Sciences, Washington, D. C.
30-May 3 American Geophysical Union, Washington, D. C.
118 May
1-3 American Physical Society, Washington, D. C.
5-7 Acoustical Society of America, Rochester, New
York
5-7 Society of Motion Picture Engineers, Rochester,
New York
12-15 American Foundrymen's Association, New York,
New York
12-21 American Institute of Chemical Engineers, Chi
cago, Illinois
19-23 American Society for Metals, Los Angeles, Cali
fornia
27-29 American Society for Refrigerating Engineers, Cin
cinnati, Ohio
June
20-21 American Physical Society, Providence, Rhode
Island
23-27 American Association for the Advancement of
Science, Durham, New Hampshire
JOURNAL OF APPLIED PHYSICS
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1.1750702.pdf | An Experimental Study of the Near Ultraviolet Absorption Spectrum of
Benzene
W. F. Radle and C. A. Beck
Citation: The Journal of Chemical Physics 8, 507 (1940); doi: 10.1063/1.1750702
View online: http://dx.doi.org/10.1063/1.1750702
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Published by the AIP Publishing
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IP: 150.135.239.97 On: Thu, 18 Dec 2014 22:58:47THE JOURNAL
OF
CHEMICAL PHYSICS
VOLUME 8 JULY, 1940 NUMBER 7
An Experimental Study of the Near Ultraviolet Absorption
Spectrum of Benzene*
W. F. RADLE AND C. A. BECK
Department of Physics, The Catholic Univenity of America, Washington, D. C.
(Received April 23, 1940)
The wave numbers and relative intensities of 500 of the absorption bands of benzene vapor
in the 2600A region have been determined. A detailed study has been made of the variation of
intensity with temperature of the main band of the A, B, and D progressions. These three bands
have been assigned to the ground state, the 606-cm-1 and 2 X 606-cm-1 vibrational states,
respectively, by Sponer and collaborators. The experimental data are in good agreement with
a statistical calculation of the population factors for these states.
INTRODUCTION
THE known electronic spectrum of benzene
lies in two regions of the ultraviolet, one at
2600A and the other at 2000A. The latter is the
stronger and has been investigated in absorption
by Henril and Carr and Stiicklen2 and more
recently by Price and Tutte.3 The last two
investigations show that the 2000A region, in
reality, consists of two regions, one at 2040A and
a very strong one at 1850A.
The 2600A region has been studied in emission,4
fluorescence,5 and absorption,!·6 the latter in
* A dissertation submitted in partial fulfillment of the
requirements for the Degree of Doctor of Philosophy (1940)
at the Catholic University of America and reproduced here
in a partly revised and extended form by the permission of
the university authorities.
1 V. Henri, J. de phys. et rad. (6) 3, 181 (1922) and
Structure des Molecules (Hermann, Paris, 1925), p. 108.
2 E. P. Carr and H. Stucklen, J. Chern. Phys. 6, 55 (1938).
3 W. C. Price and W. T. Tutte, Proc. Roy. Soc. 174, 207
(1940).
• J. B. Austin and I. A. Black, Phys. Rev. 35, 452 (1930).
6 G. B. Kistiakowsky and A. Nelles, Phys. Rev. 41, 595
(1932); G. R. Cuthbertson and G. B. Kistiakowsky, J.
Chern. Phys. 4, 9 (1936); C. K. Ingold and co-workers, J.
Chern. Soc. p. 912 (1936).
6 R. Witte, Zeits. f. Wiss. Photo 14, 347 (1915); K.
Schulz, Zeits. f. Wiss. Photo 20, 1 (1920); G. B. Kistia
kowsky and A. K. Solomon, J. Chern. Phys. 5,609 (1937);
A. Ionescu, Comptes rendus Acad. Roum. 2, 39 (1937). both the liquid and vapor state. This band
system in absorption is a relatively weak one. In
contrast to the diffuse character of the absorption
bands in the vapor at 2000A, those in the 2600A
region exhibit considerable structure. Henril has
published the wave-lengths of about 75 of the
stronger bands. Almasy and Shapiro7 list about
110 bands between 35,346 cm-l and 38,121 cm-l
obtained at higher vapor concentrations. Kronen
berger8 has extended the investigation of benzene
absorption to the solid phase at -2~9°C and has
measured the wave-lengths of about 250 of the
bands.
A theoretical study of the electronic levels of
benzene has been made by Hiickel,9 Pauling and
Sherman,lo Sklar ,11 and Goeppert-Mayer and
Sklar.t2 They have investigated the nature and
7 F. Almasy and C. V. Shapiro, Zeits. f. physik. Chemie
B25,391 (1934).
8 P. Pringsheim and A. Kronenberger, Zeits. f. Physik
40,75 (1926); A. Kronenberger, ibid. 63, 494 (1930).
9 E. Huckel, Zeits. f. Physik 70, 204 (1931); Zeits. f.
Elektrochem. 43, 752 (1937).
10 L. Pauling and A. Sherman, J. Chern. Phys. 1,606,679
(1933).
11 A. L. Sklar, J. Chern. Phys. 5, 669 (1937).
12 M. Goeppert-Mayer and A. L. Sklar, J. Chern. Phys.
6,645 (1938).
507
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IP: 150.135.239.97 On: Thu, 18 Dec 2014 22:58:47508 W. F. RADLE AND C. A. BECK
TABLE I.
---
WAVE WAVE WAVE WAVE
NUMBERS INTEN- ASSIGN- NUMBERS INTEN- ASSIGN- NUM:BERS INTEN- ASSIGN- NUMBERS I:S-TEN- ASSIGN-
(VAC.) SITY MENT (VAC.) SITY MENT (VAC.) SITY MENT (VAC.) SlTY ME~T
36,158 1 (a) 37,568.9 4 38,580 55 (b) 39,230.8 55
36,174 1 (a) 37,611.7 10 38,607.5 620 } ___ Aoo 39,236.0 150 } . D," 36,233 1 (b) 37,616.8 85 ....... A_," 38,612.2 7500 39,239.4 40 ...
36,254 1 (a) 37,626.2 4 38,640.2 9 39,248 25 (b)
36,317.2 2} F"B I 37,632 4 (a) 38,649.0 25 39,255.1 170
36,334.6 1 .... ", -, 37,640 4 (a) 38,655.0 25 39,265.5 170
36,342 1 (a) 37,651.4 10 38,673.0 10 39,272.1 140 } 36,351 1 (a) 37,656.5 4 38,691.5 15 39,281.4 170 .... C,I
36,387.8 2 37,663 4 (a) 38,694 25 Ca) 39,287.7 130
36,413.7 2 37,678 5 (a) 38,699.5 12 39,330.6 350 ...... B,"
36,478.0 3 } F o. B 0 37,714.1 12 38,713 7 (b) 39,371.2 750} A I 36,496.2 4 .... 0, -1 37,766.8 25 38,718.7 12 39,376.1 510 .... ,
36,510 1 Cb) 37,795.4 12 38,728 7 (b) 39,393 55 (a)
36,526 1 (b) 37,814.0 7 38,738.1 12 39,398.9 130
36,538 1 (a) 37,822.8 9 38,746.2 15 39,408.6 55 ....... Eol
36,624.7 3 ........ A_,o 37,836.9 12 38,753.1 9 39,423.1 160
36,657 1 (a) 37,878.5 9 38,758.3 15 39,440.1 160 I
36,668 1 (a) 37,915.6 6 38,766.9 21 39,445.3
~~n' .. C,o
36,699 1 (al 37,926.8 35. ..... .Hoo 38,773.1 7 39,451.0
36,750 1 (a) 37,944.8 7 38,777.7 7 39,468 55 (b)
36,772 1 (a) 37,956.5 18 38,783.1 7 39,473 55 (b)
36,823.7 2 37,962.6 12 38,790 9 (a) 39,487.1 55
36,834 2 (a) 37,967.8 25 38,796.8 9 39,529.6 1200 } .A,o 36,841 2 (a) ..... Bo' 37,976 7 (a) 38,801.4 9 39,534.2 7000 ..
36,857 1 Ca) 37,981 7 Ca) 38,811 7 (b) 39,541.2 35
36,866 1 Ca) 37,990.8 18 38,828.1 9 39,552.2 55
36,886 1 (a) 38,000 5 (a) 38,839.7 35 39,560.8 335
36,899 2 (a) 38,009 4 (a) 38,851.5 35 39,565.3 35 } 36,905.9 2 38,021.4 9 38,867.8 25 39,568.7 250 ., .. Eoo
36,925 1 (b) 38,029.3 9 38,870.8 12 39,571.9 12
36,990.7 8 38,043.8 30 38,875.8 18 39,577.5 25
37,000.9 8 ........ B03 38,053 5 (a) 38,880.1 21 39,604 25 (a)
37,016.1 4 38,064 5 Ca) 38,883.6 15 39,614.4 25
37,048.1 5 38,084.1 55} ..... B,' 38,891.3 25 39,622.2 25
37,057.3 5 38,089.4 12 .. (origin) 38,914 12 (a) 39,627.6 15
37,064 5 (b) 38,112.9 30 38,919.9 55 39,632.1 15
37,068 5 (b) 38,118.0 25 38,927.0 55 } ... Gol 39,638.2 335
37,071.4 4 38,121.8 iq ..... A03 38,929.5 35 .. 39,648.0 12
37,076 4 Ca) 38,125.4 38,943.7 18 39,651.2 12
37,081 4 (a) 38,133.2 35 38,952.8 18 39,656.4 25
37,156.8 ~n ... .. Eo' 38,141.3 30 38,967.0 30 39,669 12 (a)
37,160.4 38,154.0 30 ..... .. D,I 38,985 12 (a) 39,678 12 (a)
37,216.7 18 38,171.1 21 38,995 12 Ca) 39,685.9 12
37,230.2 ~1 } .... .Dol 38,182.5 25 38,999.5 25 39,689.6 12
37,234.1 38,190.5 35 39,010 25 Ca) .' .B,' 39,697.2 25
37,237.9 6 38,204.3 55 39,038.6 170 39,706.4 25
37,289.9 9 38,210.0 55 39,047.0 25 } 39,715.1 25
37,296 5 (b) 38,245.4 160 } E I 39,056 25 (a) .. A 13 39,765.4 190
37,303 7 (a) 38,253 21 Ca) .. I 39,063 25 (a) 39,774.3 25
37,316 9 (a) } 38,281.1 230 } 39,073.1 30 39,783.2 250 .
37,321.1 140 ., .Bol 38,285.2 210 .... A o· 39,082.0 250 } 39,793 15 (a)
37,326.8 12 38,292.3 170 39,086.8 250 .... Goo 39,806 12 Ca)
37,330.0 4 38,316.6 130 ...... D,o 39,092.3 25 39,814 15 Ca)
37,335 4 Ca) 38,335 35 (b) 39,100.2 25 39,836 15 (a)
37,350 4 (a) 38,343.3 190 39,104.5 25 39,841.5 55
37,366 4 (a) 38,350.0 140 } 39,114.9 35 39,847.3 45
37,387.8
~5 } ..... Doo 38,359.7 250 .... Col 39,122 25 (b) 39,850.7 70
37,392.9 38,365.2 160 39,124 25 (b) .. .. CI' 39,868 21 (a)
37,402.4 38,377 25 (b) 39,134.2 130 39,889.0 15 ....... E'ol
37,452.5 25 38,401.8 55 l B 0 39,138.8 12 39,894.1 55
37,457.3 12 38,407.0 550} .... I 39,147.2 21 39,906.3 21
37,476.1 25 } 38,448.4 950 A I 39,159 12 (b) 39,916.1 15
37,481.9 420 ... .Boo 38,452.4 950 .... 0 39,163.1
21 1 39,921.3 15
37,489.7 30 38,478 25 (al 39,168.5 130 .... E,I 39,927.6 12
37,498 4 (a) 38,491.2 70 39,173.7 25 39,962.1 120
37,524 7 (al 38,517.5 210 } 39,204.5 280 39,971.9 70
37,527.4 4 38,523.0 620 .... Coo 39,209.3 230 .... AI' 39,981.0 40
37,532.6 4 38,529.3 210 39,215.6 140 39,997 55 (al
37,544 7 (a) 38,562.4 140
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IP: 150.135.239.97 On: Thu, 18 Dec 2014 22:58:47NEAR ULTRAVIOLET OF BENZENE 509
TABLE I.-Continued.
WAVE WAVE
NUMBERS I~TE~- ASSIGN- NUMBERS IKTEN- ASSIGN-
(VAC.) SITY l\IE~T (VAC.) SITY MENT
40,004.8 140 } 40,604.0 25
40,010.2 160 . ... Glo 40,616.8 25
40,015.4 25 40,627 12 (a)
40,023.6 40 40,636.8 25
40,039 40 (a) 40,648.8 18
40,050.2 190 ...... B'oo 40,686.5 170
40,056.2 55 40,696.8 35
40,069.6 25 40,704.8 335
40,079 25 (b) 40,724.5 25
40,084.8 ~n·····Bal 40,735.9 25
40,090.8 40,762 25 (a)
40,109.1 85 40,770.6 25
40,131.5 230 } .... A22 40,786.4 25
40,137.3 55 40,800.9 25
40,154.4 55 40,812.2 55 ..... .. B'II
40,159.9 210 40,835.4 18
40,177.7 230 40,840.1 25
40,186.8 140 40,862.2 12
40,193.5 65 } 40,883.3 30
40,202.5 140 .... C21 40,894.5 30
40,208.4 55 40,903.5 55
40,224.5 25 40,915 25 (a)
40,248.3 160 } .Bao 40,920 25 (a)
40,252.5 160 ... 40,927.3 55
40,261 55 (b) 40,930.4 55
40,273 55 (b) 40,968.5 230 .... .. B'lo
40,286 55 (b) 40,978.0 35
40,292.8 510} A 1 41,002.3 190
40,297.7 350 .... 2 41,014 25 (a) .... A'OI
40,313.1 55 41,028.5 55
40,319.8 130 41,053.9 55 ..... .. Aa2
40,327 25 (b) 41,075.9 120
40,328.7 35 41,081.7 120
40,333.2 55 41,099.7 140
40,344.7 160 41,107 18 (a)
40,361.4 35 } 41,114.7 35
40,366.4 420 .... C20 41,121.5 35
40,372.0 230 41,128.3 35
40,383.4 55 41,160 25 (b)
40,387.0 55 41,165.3 450
40,426 55 (b) 41,168.4 30
40,445.6 950 } 41,173.5 55 ... .... A '00
40,450.1 550 ... A2° 41,218.4 350 .. .... Aal
40,456.0 6500 41,239.9 75
40,473 140 (a) 41,253.9 25
40,482.7 335 } 41,266.6 140
40,489.4 325 '" .Elo 41,276.3 35
40,492.6 30 41,280.4 35 } 40,509 25 (a) 41,285.7 210 .... Cao
40,525.5 55 41,291.1 65
40,535.0 25 41,303.9 55
40,543 35 (b) 41,366.0 375 } 40,550.6 25 41,370.8 375 ... Aao
40,558.9 250 41,377.9 3500
40,576.8 35 41,399.2 170 } 40,590 25 (a) 41,402.3 170 .... E2°
40,598.1 15 41,409.9 190
value of the electronic terms and Sklar has
predicted that the transition responsible for the
2600A region is a forbidden one but, in accord
ance with the selection rules of Herzberg and
Teller, becomes weakly allowed due to the
interaction of non totally symmetrical vibrations WAVE WAVE
NUMBERS INTEN- ASSIGN- NUMBERS INTEN- ASSIGN-
(VAC.) SITV MENT (VAC.) SITY ME~T
41,446.5 85 42,658.2 140
41,473 30 (a) 42,683.1 21
41,478.6 350 42,704 12 (a)
41,497.2 25 42,800.9 130 ...... B'ao
41,508 12 (a) 42,845.0 130
41,524.1 25 42,872 25 (a)
41,536.4 25 42,892.1 40
41,572.3 15 42,919.0 30
41,576.8 15 42,940 21 (a)
41,606.6 140 42,954.3 25
41,624.3 325 43,009.3 325 ...... A'20
41,634 12 (a) 43,032.0 85
41,648 12 (a) 43,056.0 25
41,682 25 (a) 43,114.8 12
41,700.1 55 43,122.2 12
41,718 12 (a) 43,199.2
~~ L ... A.o 41,731 25 (a) 43,204.2
41,741.0 140 43,215.8 300 J
41,760.9 70 43,235.5 40
41,824.1 25 43,245.9 30
41,837 12 (a) 43,284 18 (a)
41,851 12 (a) 43,314 15 (a)
41,873 12 (a) 43,409 21 (a)
41,884.5 160 ...... B'2° 43,461.2 21
41,923.9 160 43,475.8 12
41,947.0 30 43,540.9 25
41,952.2 30 43,573.7 170
41,974.1 140 43,600.9 9
41,997.0 35 43,623.5 9
42,002.3 25 43,716.6 35
42,018.9 55 43,765.6 25
42,035.3 35 43,781 12 (b)
42,088.0 100 ...... A'!o 43,791 12 (b)
42,111.8 70 43,808.9 25
42,129 30 (a) 43,836.4 18
42,137.6 85 ...... . A,l 43,929.1 160 ...... A'ao
42,157 25 (a) 43,952.9 40
42,187 18 (a) 44,032.6 12
42,194.6 30 44,133.0 35 ....... A.o
42,204.1 55 44,301.8 5
42,211.8 18 44,319 7 (a)
42,221.6 25 44,459 6 (b)
42,286.6 25°1 A" 44,488.8 30
42,297.7 950 .... , 44,683.0 9
42,318.3 160 EO 44,724.9 8
42,328.2 40 .... a 44,753 6 (a)
42,365.4 35 44,847.9 35 ....... A',o
42,396.9 55 44,869.8 25
42,415.8 18 45,050.4 18 ....... A7°
42,443 17 (a) 45,083.2 7
42,456 17 (a) 45,221.6 4
42,488.2 18 45,402.9 13
42,494.4 18 45,766.1 12
42,525.1 25 45,786.5 9
42,544.2 110
42,565.4 18
42,621.1 55
of the proper symmetry. This was confirmed in
the most recent analysis of the spectrum by
Sponer, Nordheim, Sklar, and Teller.13 They have
identified most of the important bands in the
13 H. Sponer, G. Nordheim, A. L. Sklar, and E. Teller,
J. Chem. Phys. 7, 207 (1939).
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system with transitions between vibrational
levels whose frequencies are known from the
analysis of infra-red, and Raman spectra. The
appearance of the bands as a whole is due to two
main progressions, a strong one A and a weak
one B situated 1126 cm-1 from A toward longer
wave-lengths. The members of each progression
are spaced 923 cm-1 apart and extend toward
shorter wave-lengths. The origin of the B pro
gression has been disputed. Kistiakowsky and
Solomon14 have determined in absorption the
intensities of the first member of each progression
at various temperatures. With the exception of
the value of the intensity of Boo at -15°C which
was rejected because of an assumed lack of
temperature equilibrium between the absorption
cell and the benzene reservoir, the data show that
the intensity of both bands continually decreases
with increasing temperature. They interpret this
as evidence that the population of the level from
which each of these bands starts must be con
tinually decreasing and attributed the behavior,
in this case, to the vibrationless ground state and
consequently assigned the origin of both bands to
this state. This assignment of the BoO band to the
vibration less ground state is in disagreement with
the results of Sponer and collaborators, who
assign it to a transition from the excited 606
cm-1 vibrational level in the ground state.
Theoretically, it is evident that the intensity of a
band originating in the vibrationless ground
state decreases in intensity with an. increase of
temperature while the intensity of a band
starting from an excited vibrational level at first
increases with temperature up to a certain point
(which might be called an inverting temperature)
and then decreases. This is so because the more
the temperature is increased. the more molecules
leave the ground state, but for the first vibrational
state, for example, molecules are at first entering
it but later as many leave it for upper states as
reach it from the ground state. At even higher
temperatures the loss of molecules to higher
states is greater than the gain from lower ones.
This is especially marked at ordinary tempera
tures, if there are many close-lying levels lying
above due to vibrations and combinations of
vibrations and not so many levels below the one
14 G. B. Kistiakowsky and A. K. Solomon, J. Chem.
Phys. 5, 609 (1937). in question. This is especially true in the case of
benzene.*
Because of the inherent difficulty in the experi
ment of Kistiakowsky and Solomon, it was
decided to repeat the investigation as a second
part of this work. The purpose of the first part is
to provide a more complete table of wave
lengths of the absorption bands of benzene in the
2600A region.
GENERAL ApPARATUS
All spectrograms were taken with a 5-meter
concave aluminized grating spectrograph in the
first order, with a dispersion of about 3.4A per
mm. The source was an all-quartz hydrogen
tube operating from an a c. transformer at
approximately 0.9 ampere. Ballast and control
resistances were introduced into the high voltage
leads to give greater stability. Under these
conditions the tube current did not fluctuate
more than one to two percent during an exposure
of about six minutes. The absorption cell was 50
cm long and 25 cm in diameter and of fused
quartz throughout with the exception of the
benzene reservoir which was of Pyrex and con
nected to the cell by means of a graded seal.
The authors are indebted to Dr. W. T. Ziegler
for a very pure sample of benzene having a
boiling point range of only 001 DC.
PART I
Determination of wave numbers and the estima
tion of relative intensities in the wave
number tables
Due to the fact that the absorption bands
differ greatly in intensity it was necessary to
take exposures at different concentrations of
benzene vapor in order to obtain spectrograms
suitable for more complete wave-length measure
ments. The amount of vapor in the absorption
cell was controlled by varying the temperature of
the side-arm containing a small amount of liquid
or solid benzene. An exposure was taken at every
10° C interval as the temperature of the side-arm
was varied from -70°C to 50°C while the temper
ature of the absorption cell was kept constant.
Adjacen t to each exposure was the iron spectrum
* Cf. Sponer, etc., reference 13, p. 213.
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IP: 150.135.239.97 On: Thu, 18 Dec 2014 22:58:47NEAR ULTRAVIOLET OF BENZENE 511
obtained from an arc operating at 4 amperes on
220 volts d.c.
The plates were measured on a comparator
reading to 0.001 mm and fitted with a telescope
equipped with interchangeable objectives. The
method adopted was to set the comparator single
hair parallel to the short wave-length edge of the
absorption band such that a little light above the
general background illumination was visible be
tween the short wave-length edge of the absorp
tion band and the single hair of the comparator.
The accuracy with which the single hair could
be set on a band depended on the appearance of
the bands. Some were about as sharp as lines,
others were broad with a sharp short wave-length
edge while a few, designated by (a) in Table I
exhibited a diffuse character. Some of the latter
appeared to be two or more close-lying bands,
while others seemed to be broad and washed out
and quite different in appearance from the other
measured bands. At the concentrations used in
these measurements, some of the bands were
scarcely visible and are indicated by (b). The
error for the (a) and (b) bands is about ±2 cm-I,
while bands with a well-defined edge have a
probable error of 1 cm-I, these being given to
tenths which may be justified especially for close
differences.
In the same table are given the relative in
tensities estimated from a plate on which many
exposures were taken at different concentrations
at room temperature. The band that was just
visible at the highest concentration was assumed
to be of unit intensity. Then for any other band
one determined at what concentration it was just
visible. From the concentration factor the rela
tive in tensi ty of the band was determined as
suming that Beer's law holds and the bands have
the same shape.
The assignments of SNST are given to the
stronger bands. The relative intensities of the
satellites accompanying many of the bands vary
in a somewhat erratic manner as one goes through
a progression. It is, accordingly, not possible at
present to distinguish in an unambiguous manner
between the origin of a band and its branches.
Hence, in some cases, we have grouped two or
three bands together, one of which is almost
certainly the origin. For a group of three, a strong
central one is presumably the origin. PART II
The influence of temperature on band intensity
Apparatus.-This investigation required a
method of varying the temperature of the ab
sorption cell and maintaining it reasonably con
stant during an exposure. This was accomplished
by surrounding the cell with a jacket consisting
of an electrical heating unit and a cooling unit
made from i-inch copper tubing through which
alcohol cooled by solid carbon dioxide could be
rapidly circulated. The entire assembly was
designed to keep the temperature of the absorp
tion cell as uniform as possible at any tempera
ture from -50°C to several hundred degrees
centigrade.
Intensity marks were recorded on the plate by
means of a rotating sector disk with six equally
spaced slots subtending an angle of 40° each.
The disk was driven at a speed of 1200 r.p.m. by
means of a synchronous motor connected to a
reduction gear. The pha.se of the disk was
adjusted with the help of a stroboscope so that a
slot appeared in front of the slit of the spectro
graph when the hydrogen tube was luminous
during each half-cycle. The six intensity marks
were obtained by blocking out the slots in suc
cession. Thus the highest intensity mark corre
sponded to six open slots, the next to five open
slots, etc., and to one open slot for the weakest
intensity mark.
PROCEDURE
Since the two bands of interest (AoO and BoO)
differ widely in intensity a different vapor con
centration was required for each to give a
satisfactory microphotometer trace. For the
stronger of the two bands (A 0°) a side-arm con
taining solid benzene was kept at -50°C for
about thirty minutes and then sealed off from the
absorption cell. The first exposure was taken
with the absorption cell at -35°C and then at
convenient intervals up to and including 2S0°e.
While it was possible to take exposures at higher
temperatures, these were avoided because of
evidence of photochemical decomposition. In
some preliminary work an exposure was taken at
300°e. After several hours a film formed on that
part of the window of the absorption cell where
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IP: 150.135.239.97 On: Thu, 18 Dec 2014 22:58:47512 W. F. RADLE AND C. A. BECK
the light from the hydrogen discharge entered.
The absorption band of the film extended over
the entire region of investigation. For this reason
the exposure time was kept as short as possible
and the observations were restricted to 2500e
and below. As a check, observations were made
from low to high temperatures and then re
peated, on the same plate, from high to
low temperatures. There was no evidence of
photodecomposi tion.
The above procedure was repeated at a higher
concentration of benzene vapor, which was neces
sary for the study of the Boo band. In this case
the side-arm was maintained at a temperature of
-200e for some time before it was sealed off
from the absorption cell. In this part the temper
ature of the absorption cell was not allowed to go
below -15°C.
Microphotometer traces* were obtained for the
Aoo, Boa, and Doo bands. A calibration curve for
each absorption band was obtained by plotting
the effective absorption coefficient a, obtained
from the readings for the six intensity marks,
against galvanometer deflections. The effective
absorption coefficient a is equal to log (lIT),
where T is defined as the ratio of the transmitted
to the in.cident light. The value of the coefficient
a at several points on the microphotometer trace
was plotted against v, the frequency. The area
under this curve is proportional to the intensity
of the absorption band. This area was obtained
by means of graphical integration.** Unfortu
nately, it represents only approximately the in
tensity of an absorption band because of the
overlapping of neighboring bands especially at
TABLE II. Absorption intensity of the Boo band.
Toe ~4i Ap i!. (M.LT.)
-15 9.5 9.2 5.9
32 12.4 11.0 8.5
100 14.1 12.9 9.0
150 10.0 10.0 6.0
200 8.1 5.9 4.8
250 5.0 3.8
* The authors wish to express their thanks to Dr. Hibben
of the Geophysical Laboratory and to Dr. Johnson and
Dr. McAllister of the Smithsonian Institution for their
kind assistance and permission to use their Moll recording
microphotometers.
** For BoO this included the two longer wave-length
members of the group, while for Aoo ano Do" all given
memhers were taken. TABLE III. Experimental and calculated intensities.
606 (BoO) 2 X606 (DOD) GROU"D (00) Exp.
TOC CAL. (AVER.) CAL. Exp. CAL. Exp. ----------------
-35 100 100
-15 75 68 23 9
32 97 89 51 44 69 89
100 100 100 88 68 42 49
150 85 71 100 100 27 39
200 66 52 97 96 17 23
250 48 32 83 58 10 10
the higher temperatures. If, on the other hand,
one limits the integration to a fixed frequency
interval, there will be some error due to neglect
of part of the band. In both cases, the ratios are
more reliable than the individual readings.
RESULTS AND THEIR INTERPRETATION
The resul ts of the in tensi ty measure men ts on
the BoO band are given in Table II in arbitrary
units. The first column A i gives the total area
under the a VS. II curve while in the Ap columns
the integration has been limited to a fixed fre
quency interval of about 80 em-I. In the last
column, the data were obtained from measure
ments on the micro photometer traces oc'another
plate with a different microphotometer.t The
data clearly show that the intensity of the BoO
band has a maximum.
The variation of the intensity of a band with
temperature can be calculated from statistical
mechanics. Except for oyerlapping bands, the
area of an individual band' at different tempera
tures is proportional to a factor dependent on the
Boltzmann distribution at each temperature.
Hence we can write for each band area A i an
expression of the form,
piNgie-(hv,lkT)
where Pi is a proportionality factor which in
cludes the transition probability, gi the de
generacy of the absorbing state, Vi its frequency,
and N the total number of molecules, the Lk to
be taken over all vibrations and combinations of
vibrations in the ground state. This expression
t The traces were recorded on 35-mm film by the record
ing wave-length microphotometer at the Massachusetts
Institute of Technology.
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IP: 150.135.239.97 On: Thu, 18 Dec 2014 22:58:47ABSORPTION OF PHENYL MUSTARD OIL S13
for A i can ue showll to be equal to
provided the vibrations are simple harmonic as
seems to be approximately the case in benzene.
The 20 known fundamental frequencies of ben
zene in the ground electronic state were substi
tuted in the IIj• The above expression was
evaluated for the vibrationless ground state, the
606-cm-1 and 2 X 606 cm-1 vibrational states,
which are, respectively, the low levels of the
A, B, and D progressions.
The results of the calculation for the 606-cm-1
vibrational level are compared with the intensity
of the Boo band in columns 2 and 3 of Table III
(the figures· are relative to the value at the
temperature in the table for which the intensity is
a maximum). In each case the maximum intensity.
is taken to be one hundred. It is clearly seen that
the results are in qualitative agreement with the
assignment of the Boo band to the 606-cm-1 level by Sponer and collaborators. In columlls 4 and 5
the calculated intensities of the 2X606-cm-1
level are correlated with the experimental in
tensity data for the Doo band. The agreement is
sufficiently good to verify their assignment of
this band to a transition from the 2 X 606-cm-1
vibrational level. The theoretical intensity of
ground state transitions at different tempera
tures are given in column 6. The measurements
of the intensity of the ADo band are recorded in
column 7. The agreement is an additional con
firmation that the Aoo band is due to a transition
from the vibrationless ground state. *
The authors wish to express their appreciation
to Professor H. Sponer and Dr. A. L. Sklar for
suggesting the problem and to Professor K. F.
Herzfeld for his constant interest and advice.
* The results for the Aoo and Boo bands agree fairly well
with the trend of those of Kistiakowsky and Solomon.
Their discarded point at -15°C is relatively lower than
that of the authors.
JULY. 1940 JOURKAL OF CHEMICAL PHYSICS VOLUME 8
The Absorption of Phenyl Mustard Oil in the 4.8y. Region
DUDLEY WILLIAMS
University of Florida, Gainesville, Florida
(Received March 16, 1940)
An intensive study of the 4.81-' band of phenyl mustard oil has shown this band to have three
components. Although these components have not been completely resolved, the present work
indicates the frequencies involved to be 2130, 2080, and 1950 em-I. The two highest frequencies
have counterparts in the Raman spectrum, but the frequency 1950 cm-1 has not been observed
by Raman methods. Fermi resonance is discussed as a possible explanation of the observed
spectrum. Re-investigation of the spectra of the methyl, ethyl, and phenyl nitriles and isonitriles
failed to reveal complexities in the region of 2100 em-I.
RAMAN studies! of isothiocyanates have re
vealed the presence of two lines of approxi
mately equal intensity in the frequency range in
which N == C frequencies are active. Badger2 has
sought to explain this so-called "splitting of the
N == C frequency" in terms of a Fermi resonance
between the N == C vibration and some other
normal vibration of the molecule which is a sub
multiple of the N ==C frequency. In the spectra
1 Complete bibliography: J. H. Hibben, The Raman
Effect and its Chemical Applications (Reinhold, 1939).
2 R. M. Badger, J. Chem. Phys. 5,178 (1937). of ethyl and isobutyl mustard oils appears a
Raman line of frequency of 1070 cm-t, approxi
mately half the 2100-cm-1 N ==C frequency.
Badger has suggested that further infra-red study
of the mustard oils* might be desirable.
* Note: The formula for phenyl mustard oil or phenyl
isothiocyanate generally accepted by the organic chemist
is q,-N = C =S. However, two alternative structures
q,-S-N=:C and q,-N+""C-S- seem to be more in accord
with the spectroscopic evidence. The first of these is similar
to the fulminic acid structure suggested by Langmuir. In
the present paper the symbol C "" N is used to refer to the
bond in the normal thiocyanates and the symbol N ""C to
refer to the modification of the bond in the mustard oils.
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1.1750735.pdf | Studies of Equilibrium Solid Solutions in Ionic Lattices Systems:
KMnO4–KClO4–H2O and NH4Cl–MnCl2–H2O
Alexander L. Greenberg and George H. Walden Jr.
Citation: The Journal of Chemical Physics 8, 645 (1940); doi: 10.1063/1.1750735
View online: http://dx.doi.org/10.1063/1.1750735
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IP: 129.127.200.132 On: Wed, 10 Dec 2014 14:51:18THE JOURNAL
OF
CHEMICAL PHYSICS
VOLUME 8 SEPTEMBER, 1940 NUMBER 9
Studies of Equilibrium Solid Solutions in Ionic Lattices1
Systems: KMn04-KCI0 4-H20 and NH4CI-MnCb-H 20
ALEXANDER L. GREENBERG AND GEORGE H. WALDEN, JR.
Columbia University, New York, New York
(Received June 20, 1940)
1. The systems, potassium permanganate-potassium
perchlorate-water and ammonium chloride-manganous
chloride-water, have been studied at equilibrium conditions
by phase rule and x-ray diffraction methods. 2. The
system potassium permanganate-potassium ~rchlorate
water yields a continuous series of solid solutions having
orthorhombic crystal symmetry. For these, the components
of which are of similar crystal and chemical structure and
of identical valence type, Vegard's additivity law is
followed by the ao and Co lattice constants, but the bo con
stant shows a definite deviation. 3. A method is described
of obtaining homogeneous crystals with a particle size
which gives excellent powder diffraction photograms in
cases where heat annealing is not feasible. 4. A method of
analyzing for ClO.-is given. 5. The danger of making
serious errors is pointed out in the use of rapid precipitation
by chemical reaction or from supersaturated solutions as
a method of preparing solid solutions for the study of the
relationship between their lattice constants and composi
tion. 6. The system ammonium chloride-manganous
chloride-water shows three solid solution series; the crystals
INTRODUCTION
EXPERIMENTAL demonstration of the ex
istence of solid solutions rests mainly upon
two differen t kinds of evidence: (1) phase rule
investigations, and (2) the determination of the
variation of the lattice dimensions of crystalline
solid phases with change in composition by x-ray
1 Dissertation submitted by Alexander L. Greenberg in
partial fulfillment of the requirements for the degree of
Doctor of Philosophy in the Faculty of Pure Science,
Columbia University. Publication assisted by the Ernest
Kempton Adams Fund for Physical Research of Columbia
University. obtained in the first series have cubic symmetry, while in
the others the symmetry is tetragonal. 7. The mechanism
of the formation of the "anomalous" solid solutions be
tween ammonium chloride and manganous chloride is
given. Experimental and other considerations verify it.
8. It is shown that Vegard's law is not followed by the
first solid solution series in which the components are of
dissimilar chemical and crystal structure and dissimilar
valence types. The curve for the relationship between the
lattice constants and composition rises to a maximum and
then falls off. Reasons to explain why this law does not
apply to these solid solutions are given. 9. The existence of
a new "compound," 6NH.Cl· MnCl,· 2H,O, is demon
strated. This and the known compound, 2NH.Cl· MnCl,·-
2H,O, are considered to be examples of "compounds of
variable composition." They are tetragonal with ao= 15.256
±0.004A, CO = 16.008±0.007 A and ao = 7.5139 ±0.0005A.
co=8.245±0.003A, respectively. The structure of the
latter is that of 2NH4Cl· CuCl,· 2H,O which belongs to
space group D4J4h or P4mnm.
diffraction methods. Numerous experimental
investigations have been made by both methods.
One result of the x-ray investigations is
Vegard's additivity law,2a which states that the
unit cell dimensions in a continuous solid solution
series vary linearly with the mole fraction of
solute present. The validity of this rule rests upon
measurements made by Vegard2a.c and others,3
'(a) L. Vegard, Zeits. f. Physik 5, 17 (1921); (b) L.
Vegard, Zeits. f. Physik 43, 299 (1927); (c) L. Vegard and
H. Dale, Zeits. f. Krist. 67, 148 (1928).
3 R. J. Havighurst, E. Mack and F. C. Blake, J. Am.
Chern. Soc. 47, 29 (1925).
645
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IP: 129.127.200.132 On: Wed, 10 Dec 2014 14:51:18646 A. L. GREENBERG A~D G. H. WALDEN, JR.
almost exclusively on crystals of cubic symmetry.
Many deviations from this law have been ob
served in alloys.4 The only deviations, in the
literature, among ionic lattice crystals are those
observed by Walden and Cohen, 5a and by Walden
and Avere1l5b in precipitates of barium sulphate
with barium nitrate and with permanganic acid.
Since the proof that these precipitates were
contaminated through solid solution formation
rests upon the observed change in the unit cell
dimensions which did not follow Vegard's law,6
we have investigated by the x-ray method some
systems of both isomorphic and nonisomorphic
mixing where the solid solution nature of the
solid phases could be demonstrated by simul
taneously carried out phase rule studies to obtain
further data on Vegard's law in ionic lattice
crystals.
Precision x-ray data on solid solutions formed
in equilibrium with their aqueous solutions has
been lacking up to the present time. The work
done in recent years by Vegard and his co
workers,2 Grimm and his associates7 and others
too numerous to mention, in which the solid
solutions were formed from water solution either
(1) by precipitation of insoluble substances by
chemical reaction or (2) by crystallization from
supersaturated solutions with little or no attempt
at equilibrating the solid phase thus obtained,
can safely be called nonequilibrium studies.
Coupling this with the statement by Vegard2b
that "the additivity law is the limiting case of
slowly precipitated solid solutions," showed the
necessity for studies of solid solutions formed in
equilibrium systems so that the experimental
conditions would be reproducible. We have
attempted to choose systems for investigation
resembling as closely as possible the barium
sulphate precipitates referred to above. The
nearest approach would be a system with com-
'E. R. Jette, Trans. Am. Inst. Mining Met. Eng. III
75 (1934). '
6 (a) G. H. Walden, Jr. and M. U. Cohen, J. Am. Chem.
Soc. 57, 259 (1935); (b) G. H. Walden, Jr. and P. R.
Averell, J. Am. Chem. Soc. 59, 906 (1937).
6 F. Schneider and W. Rieman, J. Am. Chem. Soc. 59
354 (1937). '
7 (a~ H. G. Grimm and G. Wagner, Zeits. f. physik.
Chemle 132, 131 (1928); (b) G. Wagner, Zeits. f. physik.
Chemie 2B, 27 (1929); (c) H. G. Grimm and G. Wagner,
Ze~ts. f. anorg. allgem. Chemie 220, 31 (1934); (d) H. G.
Gnmm, C. Peters and H. Wolff, Zeits. f. anorg. allgem.
Chemie 236, 57 (1938). ponents of identical space group symmetry as
barium sulphate, limited range of solid miscibility,
and with a sufficiently high solubility in water to
permit accurate phase rule study. We have not
been able to find such a system. Therefore
two systems were investigated one of which
KCl0 4-KMn04-H 20, will serve to show how
isomorphic crystals behave in forming a com
plete series of solid solutions, and the other
NH4Cl-MnCb-H 20 will demonstrate the be
havior of two nonisomorphic solids in a limited
series of solid solutions.
This work will concern itself, then, with one of
each of the main types of solid solution possible
(1) complete miscibility (2) incomplete misci
bility. Under (1) the system has components in
the solid solutions of similar crystal and chemical
structure, of identical valence type and not too
different lattice constants. Under (2) the system
studied has components of dissimilar valence
type, chemical structure, and crystal system; of
the type whose solid solutions have been termed
"anomalous."
The KMn04-KCI0 4-H20 system, for (1),
had been described by Muthman and Kuntze8
and Barker9 as a system which yields a complete
series of solid solutions. Muthman and Kuntze
worked out the isotherm at 7° while Barker
showed by crystallographic methods that as the
weight percent of potassium permanganate in the
solid phase increased, the interfacial angles for
the crystals increased in a fairly linear fashion.
The two salts are orthorhombic and belong to the
same space group V16h.
Except for qualitative studies by Vegard2a on
one sample of potassium sulphate-ammonium
sulphate orthorhombic solid solutions, the low
precision x-ray studies of Wagner7b on the non
equilibrium barium sulphate-potassium per
manganate complete series of solid solutions and
the precision studies on limited, nonequilibrium
solid solutions of barium sulphate-barium nitrate
and barium sulphate-permanganic acid men
tioned above no other x-ray data are available for
solid solutions one or more of whose components
is orthorhombic.
For (2) the classic system of NH4CI-MnCl 2
-H20 was selected. This system has been the
8 Muthman and KUntze, Zeits. f. Kri"t. 23, 375 (1894).
• T. V. Barker, Zeits. f. Krist. 43, 529 (1907).
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subject of much controversy. The formation
of "anomalous" solid solutions between the
cubic ammonium chloride and the monoclinic
MnCb· 4H20 has interested investigators for the
last sixty odd years. Lehman10 first showed the
solid solution character of the solid phase sepa
rating from the mother liquor in the ammonium
chloride region of the system. Foote and Saxton,ll
by means of phase rule studies of the 25 ° isotherm
and calorimetric data on the solid solutions
formed, check this. Clendinnen and Rivett12
extending this work at 60°C and repeating the
25° isotherm, agreed as to the solid solutions
formed.
Benrath and Shackman13 state that no solid
solutions are obtained when ammonium chloride
solid is shaken together with a saturated solution
of ammonium chloride and manganous chloride;
that furthermore if the solid phase is formed by
precipitation from the supersaturated solution
the percentage of manganous chloride in the solid
will decrease to zero if the solid is shaken with the
mother liquor for a sufficient length of time.
Kuznecov14 concludes from x-ray data that a
contraction in the unit cell size of ammonium
chloride takes place when this and manganous
chloride form a solid solution.
EXPER~MENTAL: KCl04-KMn04-H 20
The x-ray apparatus was essentially the same
as described by Walden and Cohen,5a the pre
cision focusing cameras were the same as de
scribed by them. The method of computing the
lattice constants from the films is that described
by Cohen.15
Chromium radiation was used in taking the
x-ray photograms. The values of the wave
lengths16 of the Kal and Ka2 used in the compu
tations are KaJ = 2.285,03A, Ka2= 2.288,91.
Each of materials used in the preparation of
the solid solutions was recrystallized twice. This
10 O. Lehman, Zeits. f. Krist. 8, 438 (1883).
11 H. W. Foote and B. Saxton, J. Am. Chern. Soc. 36,1695
(1914).
12 F. W. J. Clendinnen and A. C. D. Rivett, J. Chern.
Soc. 119, 1329 (1921).
la A. Benrath and H. Schachman, Zeits. f. anorg. allgem.
Chemie 221, 418 (1935).
14 V. G. Kuznecov, Comptes rendus Acad. Sci. U. R. S. S.
15,469 (1937).
16 M. U. Cohen, Rev. Sci. Inst. 6, 68 (1935); M. U.
Cohen, Zeits. f. Krist. A94, 288 (1936).
16 Int. Tab. Kryst. Best. Vol. 11. p. 586. precaution was taken because of the large amount
of manganese dioxide in the reagent grade
potassium permanganate and the presence of
chloride ion in the potassium perchlorate. After
this treatment the permanganate when dissolved
and filtered through a sintered glass funnel
showed no sign of manganese dioxide, while the
perchlorate showed no trace of chloride Ion
(against silver nitrate in nitric acid).
The thermostat used in equilibrating the
samples was held at 25.0000±.055°. The ther
mometer used was checked against a plati
num resistance thermometer calibrated by the
National Bureau of Standards.
The samples were prepared by making solu
tions at an elevated temperature of such concen
tration as to be supersaturated at 25°C. These
solutions were placed in glass stoppered bottles,
allowed to cool to room temperature, sealed with
paraffin, and brought to equilibrium at 25°C in a
thermostat while being continuously tumbled end
over end. The approach to equilibrium was
followed by determining the Mn04-content of
the liquid phase at intervals. The process required
about It months and produced a solid phase
which was coarsely crystalline and did not give
sharp x-ray diffraction patterns. Grinding the
solid made matters much worse in this latter
respect. Annealing at temperatures sufficiently
low to avoid decomposition was found to be
without effect. The following procedure was
found to produce solid phases which gave satis
factory x-ray patterns, and at the same time to
accelerate greatly the approach to equilibrium.
By this procedure samples were prepared as
above and allowed to equilibrate for a few days,
after which time the solid phases were filtered off
on sintered glass filters, dried by drawing air
through them, crushed in an agate mortar to
below 100 mesh and returned to the mother
liquor. The bottles were then replaced in the
equilibrating machine. Equilibrium was found to
be established within two weeks.
Sampling of the liquid and solid phase
For removing samples of the liquid phase for
analysis, a modified form of the weight-pipette
described by Kiehl and Manfriedol7 was used.
17 S. J. Kiehl and E. J. Manfriedo, J. Am. Chem. Soc.
59, 2118 (1937).
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This permits the taking of a sample of the
solution without removing the bottle from the
thermostat; to prevent the solid phase from
being drawn into the pipette, a sintered-glass
filter plug was sealed on to the tube used for
sucking up the sample.
Schreinemakers' wet residue method18 was
used in the analysis of the solid phase which was
separated from the mother liquor by filtration
through a sintered glass funnel but not dried. A
portion of the wet solid was transferred to a
weighing tube and delivered from there to flasks
by means of a platinum spatula. The remaining
solid was dried on the funnel by sllcking air over
it for x-ray analysis.
Methods of analysis
The determination of the Mn04-was carried
out by adding 0.1M ferrous sulphate solution to a
slight excess and back-titrating with standard
0.1M ceric ammonium sulfate solution to the
o-phenanthroline ferrous complex end point.
After trial of many of the methods given in the
literature, a modification of the method proposed
by Rosenberg19 was evolved for the determi
nation of Cl04-. The Cl04-was reduced by
passing sulphur dioxide over the surface of a
solution of the sample in 25 ml of water con
taining 2-3 ml of 1M sulphuric acid. The excess
sulphur dioxide was boiled off by evaporating to a
small volume, the sample was then diluted to
a volume of 25 ml and 50 ml of concentration.
Sulphuric acid was added and the air displaced
with carbon dioxide. Blank runs were made at
the same time as the sample runs (with 25 ml of
distilled water and 50 ml concentrated sulphuric
acid). After the air was removed, approximately
25 ml of titanous chloride solution (approxi
mately 0.25M, made up in 1M sulphuric acid)
was added to the sample and 15 ml to the blank
(approximately the amount to be determined in
the sample flasks after the reduction of the
Cl04-). The flask was heated for two hours so
that there was gentle refluxing, during which
time carbon dioxide was continuously passed
through at a slow rate. After this time, the flask
18 F. A. H. Schreinemakers, Zeits. f. physik. Chemit' 11,
81 (1893).
" A. Rosenberg, Zeits. f. anal. Chemie 90, 103 (1932). TABLE 1.
\VEIGHT 0/0 \VEIGHT ~{; \VEIGHT '/0 Kl\1nO. KCIO. KMnO,IX
SOLID PHASE
(EXTRAP. ON
SAMPLE LIQUID SOLID LIQUID SOLID TERNARY
No. PHASE PHASE PHASE PHASE DIAGRAM) ---------
I 0.4712 1.032 1.868 76.21 1.2
2 2.065 7.075 1.381 82.15 7.7
3 2.651 10.59 1.230 77.64 11.8
4 2.628 10.71 1.245 75.77 12.0
5 4.009 22.28 0.9777 58.49 26.8
6 4.573 32.76 0.8434 52.07 38.2
7 4.864 38.12 0.7816 46.83 44.4
8 5.698 60.29 0.5872 28.21 68.0
9 5.i32 62.70 0.5548 26.48 70.2
10 6.333 76.94 0.3582 13.96 84.5
was allowed to cool to room temperature with a
stream of carbon dioxide going through.
The sample was then diluted with 25 ml of air
free distilled water and standard 0.1M ceric
ammonium sulphate solution was added to a
slight excess, while a current of carbon dioxide
was passed over the surface of the solution in the
flask. The excess was back-titrated with 0.lA1
ferrous sulphate solution, by using o-phenanthro
line ferrous complex indicator. The end point is
extremely sharp at the concentration of sulphuric
acid present in the solution (approximately 9M).
The reason for. making up the titanous chloride
solution in sulphuric acid rather than in hydro
chloric acid is to avoid the large amount of HCl
which boils off from the solutions during the
heating and which, when used, gave us erratic
results.
All volumetric apparatus and weights used in
the analytical work was calibrated. The ceric
ammonium sulfate solution was standardized
against National Bureau of Standards sodium
oxalate according to the method described by
Walden, Hammett and Chapman.20
Results of analysis
The results of the analysis are given in Table 1.
Each value is the mean of two analyses on each
sample of the liquid and of the wet residues for
both Mn04-and Cl04-. The precision measures
for the deviation from the mean of the liquid
phase determinations were 2 parts per 1000 for
Mn04-and Cl04-, for the solid phase 5 parts
per 1000.
20 G. H. Walden, L. P. Hammett and R. P. Chapman,
J. Am. Chern. Soc. 55, 2649 (1933).
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FIG. 1. The values for the solubility at 25°C of pure
potassium perchlorate and potassium permanganate, which
are plotted are given by H. H. Willard and G. F. Smith 0. Am. Chern. Soc. 45, 286 (1923)) and H. M. Trimble 0. Am. Chern. Soc. 44,451 (1922)), respectively.
These results are plotted on the triangular
diagram Fig. 1, weight percentage is used in
order to show the tie-lines to better advantage;
and by weight percen t of potassium permanganate
in the liquid phase against weight percent of
potassium permanganate in the solid phase
(obtained by extrapolation on the ternary dia
gram) in Fig. 2. X-ray results
Every measurable line on the x-ray photograms
was used in the computation of the lattice
constants of the solid solutions, but no fewer than
ten and as many as twenty-six pairs of lines were
used in anyone case. The range of the probable
errors on the individual films was:
ao= ±O.004-0.03%, bo= ±O.OOS-O.04%,
Co= ±O.003-0.02%.
However, since the values of the lattice con
stants obtained from different films for a single
substance did not always check within these
probable errors, the values given in Table II are
mean values of all films taken on each sample and
the a. d. given is the average deviation from the
mean of the lattice constants obtained from the
different films.
These results are plotted against weight percen t
of potassium permanganate in the solid phase
(extrapola ted from the ternary diagram) in Fig. 3.
Discussion of results
From the ternary plot Fig. 1, is seen that a
complete series of solid solutions of potassium
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TABLE II. Lattice constants (A). Mean values 23-29°C.
SAMPLE MEAN
No. OF ao bo Co
KClO. 3 films 8.837±.003 5.6521 ±.0004 7.240±.002
1 5 films 8.843±.003 5.6531 ±.0007 7.243±.001
2 2 films 8.859±.007 5.6574±.0008 7.255±.001
3 2 films 8.866±.003 5.6590±.0005 7.260±.001
4 2 films 8.865±.000 5.6596±.0006 7.265±.002
5 I film 8.902 5.6690 7.294
6 1 film 8.931 5.6777 7.311
7 I film 8.955 5.6803 7.320
8 2 films 9.007 ±.001 5.6940±.0016 7.360±.000
9 2 film'i 9.015±.001 5.6958±.0013 7.363±.001
10 3 films 9.054±.001 5.7030±.0008 7.389±.001
KMnO. 3 films 9.099±.002 5.7076±.0003 7.411 ±.OOI
permanganate and potassium perchlorate are
formed. This is also shown by plotting the results
differently, as in Fig. 2. Also, from Fig. 2 we see
that the liquid phase always contains a larger
percentage by weight of potassium permanganate
than the solid which, according to Roozeboom's21
classification of solid solutions, places the system
under Type I.
Our work at 25°C does not show the presence
of either a congruent point or of a definite
crystallization end point as shown in the paper
by Muthman and Kunzte8 at 90 mole percent
potassium permanganate on their 7° isotherm for
the system, but since this region was not
investigated thoroughly our evidence does not
eliminate the possibility of its existence.
Figure 3 demonstrates conclusively that the
solid solutions formed in this equilibrium system
follow Vegard's additivity law quite exactly in
the case of the ao and Co constants but for the bo
constants a small deviation is observed, the
curve being slightly convex.
It may be pointed out that there is great
danger of making serious errors in studying solid
solutions prepared by rapid precipitation through
chemical reaction or from supersaturated solu
tions to determine the relationship between the
lattice constants and composition. In such solid
solutions, homogeneous distribution of the com
ponents is not to be expected, as shown by Hahn's
discussion22 of the results obtained by his co
workers. In our work it was shown that the
21 H. W. B. Roozeboom, Zeits. f. physik. Chemie 8, 521
(1891). '
... (a) O. Hahn, Applied Radio Activity (Cornell Uni
versity Press, Ithaca, N. Y., 1936), p. 70 on, for complete
discussion and bibliography. crystals, which were first formed on cooling the
supersaturated solution while this was being
tumbled in the thermostat, gave very poor x-ray
diffraction patterns, the lines being broad and
diffuse. But after being crushed and returned to
the mother liquor for equilibration over a period
of two weeks or more, the crystals obtained gave
sharp x-ray diffraction lines. This is in complete
accord with the results given in the papers by
Mumbrauer et al.,22 which describe the conditions
for obtaining homogeneous solid solutions.
In rapidly formed solid solutions which are not
further treated to homogenize the components,
then, the best that can be expected is to get
experimental indications that the lattice is ex
panded in a more or less regular fashion by the
en trance of con taminen t. Inhomogeneous crystals
will, of course, never give a true relationship
between the weight percentage composition (as
determined by analysis of the entire crystal) and
the lattice constant (determined by x-ray re
flection from the first few hundred surface
layers). This seems to be indicated by the work
0/)
I-
Z « I-
0/)
Z b.
0
U
'" 0
l-
I-«
~
a. 5.710
UIIO
5.670
'.ISO
'.030
""0
"UO~o----=~~--7.~.---·.~o--~.~o~~~
WEIGHT PERCENT KMnO~
DASH(O LINE t~ THEORETICAL fOR '1[GARO" lA.W
FIG. 3. KMnO,-KCIO,-H.O.
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TABLE III.
%) MnCb % Cl- % NH.Cl (CALC.)
TIME IN
SAMPLE THERMO· LIQ- LIQ- LIQ-
No. STAT UID SOLID UID SOLID UID SOLIn ---- -~ --------
2 3 weeks 19.28 53.02 2().22 78.31 3.3()5 1.968
4 4 20.12 43.74 23.53 61.49 8.026 5.292
5 5 .. 20.67 46.71 22.04 63.43 10.76 8.267
6 2 .. 2\.35 43.22 20.89 56.58 13.32 10.14
7* 8 .. 21.43 50.74 20.27 65.54 14.19 12.94
7-3 3 .. 21.51 4\.40 20.25 45.60 14.36 19.82
7-2 3 .. 21.30 39.89 19.81 43.26 14.50 19.90
7-1 3 .. 21.34 38.88 19.72 41.30 14.66 20.41
7-A 3 .. 2\.33 43.98 19.51 47.52 14.91 22.15
8 5 months 2\.32 44.55 19.07 48.13 15.40 22.44
10 4 21.42 47.42 18.09 50.64 16.73 24.58
12 3! .. 21.60 42.70 17.10 44.03 18.21 23.98
14 3t .. 21.78 42.08 16.31 41.13 19.46 26.28
16 3! .. 22.18 38.19 15.94 34.70 20.62 26.94
18 3t .. 22.32 44.59 15.04 38.93 21.91 33.33
22 3t .. 22.41 48.35 13.90 39.30 23.42 39.57
26 2 weeks 22.52 42.06 10.22 29.30 27.95 40.16
29 2 23.44 45.43 5.8QO 30.62 34.70 44.61
31 2 .. 24.81 I 46.72 3.977 31.05 39.34 46.38
33 2 .. 26.29 33.66 2.978 1.387 43.16 58.11
* Sample No. 7 was shown to consist of ~wo solid phases •. one iso
tropic and the other birefringent. when. examIned under the '.mcroscope
between crossed Nicols. The second sohd phase was present In so sma.ll
an amount that no new lines were observed on x-:ay photo~rams of thls
sample, only lines corresponding ~o th~ amm~mum chlo~lde. structure
were found. This sample fixes the lnvanant pmnt on the hquldus curve
(marked b. Fig. 4) for the condensed system at ronstant temperature.
of Walden and Avere1l5b where rapid precipi
tation was the method used for the preparation
of the solid solutions. Furthermore, in Vegard's
paper2(b) on the mercuric bromide-mercuric chlo
ride solid solution series is presented evidence for
this hypothesis, in that the crystals formed by
rapid precipitation gave lattice constants which
scattered badly when plotted against the weight
percentage composition, while crystals prepared
by slow precipitation gave consistent values for
the lattice constants which corresponded almost
exactly with those predicted by the additivity
law. Vegard explained the discrepancy of the
results for the rapidly precipitated crystals, on
the basis of "uncompensated" surface atoms in
the much finer solids obtained in this way. He
attributed the increase in line width on the x-ray
diffraction patterns given by these crystals to
smaller particle size. From consideration of the
above, we are inclined to explain the deviation
from the additivity law and the line broadening
on the x-ray films for these crystals to inhomo
geneity of the solid solutions.
EXPERIMENTAL: NH4CI-MnCl 2-H20
U sing the triangular phase diagram bf the 25 °
isotherm of the NH4Cl-MnCl 2-H20 system as
given by Clendinnen and Rivett,12 supersatu-rated solutions of ammonium chloride and man
ganese chloride in water were prepared to give
approximately 8 g of solid phase to 400 ml of
liquid phase when cooled to 25°C. The points
chosen were well spaced to cover the entire range
of the first two solid solution regions as shown by
their diagram. Analytical reagent grade am
monium chloride and MnCh·4H 20 were of suffi
cient purity for the work without recrystalliza
tion.
FIG. 4.
The same procedure, used for the KMn04
-KCI04 -H20 system, was followed in regard to
thermostating the samples, crushing the solid
phases to below 100 mesh and then replacing in
the mother liquor, determination of achievement
of equilibrium, methods of sampling and so forth.
Only one change in the procedure under
sampling was adopted; after removing sufficient
moist solid phase for analysis by the Schreine
makers method, the remaining solid was washed
with alcohol and then with ether (which had no
effect on the x-ray photograms obtained as shown
by films taken on air-dried samples and the same
samples dried by alcohol and ether) and then
quickly dried by sucking air through the filter.
For studies of the compounds and the low angle
reflections of the first solid solution series in this
system, a vacuum type Debye-Scherrer camera
was used.
Methods of analysis
Manganese was determined by the bismuthate
method of Park.23 The permanganate was titrated
to a slight excess of O.lM ferrous sulphate solu-
23 B. Park, J. Ind. Eng. Cht'l11. 18, 597 (1926).
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tion and this in turn back-titrated with standard
O.1M ceric ammonium sulphate solution using
o-phenanthroline ferrous complex indicator. Am
monia was determined by distillation from strong
alkali solution into standard O.lM hydrochloric
acid solution. The total amount of chloride was
determined by the Volhard method as modified
by Caldwell and Moyer.24 The determinations
were always run in duplicate for Mn++ and NH4+
while triplicate samples were used in the CI
determina tion.
Results of analysis
It was found that the analysis of the samples
for all three ions; CI-, NH4+, and Mn++, was
unnecessary since the checks were good, so the
analysis for Mn++ was not continued and only
NH4+ and CI-were determined except in the case
of the compounds formed where complete analysis
was desired. Table III gives the results obtained
for the analysis of liquid and moist solid phases.
Figure 4 shows these results plotted on a
triangular diagram. In Fig. 5 is plotted weight
24 J. R. Caldwell and H. V. Moyer, Ind. and Eng. Chem.
Anal. Ed. 7. 38 (1935).
z.
2~
24
IIJ
of) «22
:J:
Q..
020
5 3"
Z -16 U • :r 14 z ....
Z 12
W I,)
15 10
Q..
~a ..,
jjj
~~
4 F E
2
o 10 %0 percent ammonium chloride in the solid phase
(obtained by extrapolation to the MnCI 2·2H20
base line on the ternary plot) against weight
percent ammonium chloride in the liquid phase
(from analysis).
To establish the state of hydration of the
compounds shown on the phase diagram, Fig. 5,
namely D, E and F, complete analyses were
run in duplicate on the solid phases of samples
7A, 26 and 33, respectively (dried by washing
with alcohol and ether and then sucking air over
them). Table IV gives the results of these analy
ses in weight percent.
The results shown in Tables III and IV and
plotted in Figs. 4 and 5 demonstrate the following
features of the system:
1. Starting with pure ammonium chloride
(point A) there is a solid solution range which
terminates at point B. At point B a second solid
phase appears and initiates a new short solid
solution range at point C which terminates at
point D. This series belongs to Type IV, Rooze
boom's classification,21 BC (Fig. 5) being the
boundary between the two conjugate solid
solutions.
c o
100
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TABLE IV. Complete analysis of the substances at D, E and F.*
POINT SAMPLE TOTAL WT. % H,O BY THEORETICAL FOR THE
ON PLOT No. WT. % CI-WT. % NH.+ WT. % Mn++ % FOUND DIFFERENCE COMPOUND
D 7A 58.60±.14 22.21 ±.03 11.43 ±.001 92.24 7.76 6NH.Cl· MnCI 2• 2H20 = 7.46
E 26 52.99±.06 13.74±.01 19.89±.01 86.62 13.38 2NH.CI· MnCb· 2H2O = 13.40
F 33 37.51 ±.01 28.31 ±.04 65.82 34.18 MnCl 2·4H2O=36.42
I
* The analytical data of Foote and Saxton, reference 11, have been accepted as fully proving that whenever a mole of manganous ion enters the
solid solutions (A-B, Fig. 5), 2 moles of water go in also. This situation holds across the 25° diagram from point A to point E, as shown by the
analysis of the solid phases at D and E, given in the table above.
2. The solid phase at point D is a double salt
having the formula 6NH4CI,MnCI 2· 2H20. This
compound exhibits incongruent solubility.
3. Between points D and E is a third solid
solution range. This series belongs to Type II,
Roozeboom's c1assification.21
4. The solid phase at E is a second double salt
having the composition 2NH4CI, MnCI2· 2H20,
This compound also exhibits incongruent solu
bility.
5. At point F the solid phase is the hydrate
MnCI2·4H20.
Our phase diagram while bearing great simi
larity to Foote and Saxton's,l! and CIendinnen
and Rivett's12 exhibits certain marked differences.
Our boundary (B-C) between the first two series
of solid solutions is shifted towards the am
monium chloride end. Then there is the recog
nition of a short series of solid solutions (C-D)
and the hitherto unobserved compound at
D, 6NH4CI· MnCI2· 2H20 which the previous
workers missed. The solid solution series, D-E, is a
complete one between the 6NH4CI· MnCI2· 2H20
and the 2NH4CI· MnCI2· 2H20. The remainder of
the diagram checks very closely with that of
Clendinnen and Rivett12 at 25°C. The solubilities
of ammonium chloride and MnCI2·4H20 as
determined by them are used on our plots and, as
can be seen, fit in extremely well on the liquidus
curve, Fig. 4.
All the solid phases prepared in the phase rule
investigation were studied by means of x-ray
powder diffraction methods described above.
This investigation disclosed the following facts:
1. The solid phases in the solid solution range
AB have an ammonium chloride lattice, no other
lines appearing on any of the films. The lattice
constants as computed from precision camera films are shown in Table V and are plotted in
Fig. 6 against the weight percent of MnCI2· 2H20
(obtained by extrapolation on the ternary plot).
This shows that the change in the lattice con
stants does not follow Vegard's law but increases
with addition of MnCI2· 2H20 to a maximum and
then decreases slightly. The variation of lattice
constant with composition is small, O.OB percent
maximum at a concentration of 13 weight
percent MnCI2· 2H20.
The range of the probable errors on the indi
vidual films is ao= ±0.0015 percent to ±O.OOB
percent. As in the case of the KMn04 -KCI04
solid solutions, the values for the lattice constants
obtained from all the films on anyone sample
were averaged and the mean values are those
given in Table V. The average deviation given is
the a.d. of the mean lattice constant and not the
probable error. The radii of the circles on Fig. 6
gives the a.d. of the mean.
2. The solid phase appearing at C has a lattice
of lower than cubic symmetry. Visual exami
nation of the films shows no differences between
any of the solid phases from C to D.
3. The compound D is tetragonal, ao= 15.256
±0.004, Co= 16.00B±0.007, co/ao= 1.05 from a
Debye-Scherrer film taken with calcium radia
tion. Further elucidation of the structure must
TABLE V. Mean values of the lattice constants of .first solid
solution series. Temp. 25°-29°.
\ WT.%
ao MnCI,'2H,O
SAMPLE No. (MEAN VALUE) MEAN OF (PLOT)
NH.CI 3.8680±.0003 6 films
No.2 3.8687 ±.0003 5 films 1.9
No.4 3.8691 ±.0003 15 films 3.7
No.5 3.8699±.OO05 2 films 8.5
No.6 3.8714±.0001 2 films 9.1
No.7 3.8708±.0007 4 films 16.0
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z
o
00
~"TO~----~Z~-----4+-------.~----~a~----~IO~----~IZ~-----1~4------~1~6---
WEIGHT PERCENT MnC/z.2HzO IN CRYSTALS
OBTAINED l!IY EXTRAPOLATION ON TERNARY PLOT
FIG. 6. Lattice constants of solid solutions A-B against weight percent MnC1 2·2H20.
await the preparation of single crystal diffraction
films. We were unable to prepare these since we
could never obtain single crystals. All attempts to
grow single crystals resulted in samples which,
while they resembled crystals macroscopically,
were found to be complicated structures resulting
from multiple twinning when examined under
the microscope between crossed Nichols.
4. Samples in the solid solution range between
D and E gave rather unsatisfactory films with
weak and diffuse lines. They appear to exhibit a
gradual transition from the diffraction pattern of
the compound 6NH 4Cl·MnCI 2·2H20 to that of
the compound 2NH 4Cl· MnCl 2• 2H20.
S. The compound 2NH4Cl·MnCI 2·2H20 is
tetragonal, ao= 7 .S139±0.000S, co= 8.245±0.003,
col ao = 1.09 from a precision camera film taken
with chromium radiation. The compound is
isomorphic with and has the same structure as
the compound 2NH 4Cl· CuCh· 2H20 as is shown
by the comparison data in Table VI, obtained
from Debye-Scherrer films taken with calcium
radiation.
Interpretation of results
A very revealing light is shed upon the complex
ities of this system by consideration of the struc
ture of the compound 2NH4Cl· MnCb· 2H20. As
noted above the structure is undoubtedly that of
the corresponding cupric compound which was
determined by Hendricks and Dickinson,26 and
is shown in Fig. 7. It will be seen that this
26 S. B. Hendricks and R. G. Dickinson, J. Am. Chern.
Soc. 49, 2149 (1927). structure is obtained from that of ammonium
chloride in the following manner: Consider two
ammonium chloride unit cubes having a common
face and with chloride ions at the corners. A
manganous ion is placed in the common face in
the center of the four chloride ions. Water
molecules are substituted for the ammonium
ions in the body centers. This arrangement is
shown in Fig. 8. The structure in Fig. 7 will be
seen to be an alternation of this arrangement
with the unmodified ammonium chloride arrange
ment. In such a unit the Mn++ would have a
coordination number of six.
TABLE VI.
CALCIUM RADIA nON
2NH.C1 'CuC!' '2H,O
ao =7.S83±O.OO2
co =7.9S0±O.OO2* 2NH.C1 ·MnCI, '2H,O
ao=7.S14±O.OOl
Co =8.247 ±O.002
(SAMPLE No. 26)
PLANE REL. PLANE REL.
LINE AND Exp. INTEN- LINE A~D Exp. INTEN·
SlN28 SITY No. SOURCE SIN' 9 SITY No. SOURCE
1 lOla 0.09272 9 3 lOla 0.09105 8
2 110a .09722 6 4 110a .09881 4
3 002a .1772 5 5 002a .1654 6
5 112a .2755 6 6 112a .2643 4
6 121a .2888 6 7 121a .2907 4 7t 202/3-202a .3732 4 8 202/3-202a .3640 5
8 220/3-220a .3902 5 9 220/3-220a .3990 6
9 202a .3731 10 10 202a .3642 10
10 220", .3914 10 11 220", .3980 10
13 222a .5697 8 15 222", .5638 9
14 123", .6453 6 16 123", .6197 5
15 231", .6810 8 19 231a .6885 8
17 400", .7827 10 21 400a .7958 10
* Our values for the lattice constants of this substance obtained
from this film agree with those given by Hendricks and Dickinson as
ao=7.S8 and co=7.96. t In all such tables in this paper the Kfj reflections have been con
verted to the equivalent Ka, by multiplying sin' 9 by (XKajXKfj)'.
which for caldllm rrJc1iation is 1.18 157.
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The structure of this compound points clearly
to the mechanism by means of which increasing
amounts of MnCh· 2H20 are taken up by
ammonium chloride. In the solid solution series
A -B, the interstitial inclusion of Mn++ in the
ammonium chloride lattice and the simultaneous
substitution of H20 for NH4+ occurs at random.
After the phase boundary Be is crossed the solid
phase gives a new diffraction pattern corre
sponding to tetragonal symmetry and greatly
increased cell size. It should be noted, however,
that the axial ratio is very close to unity and
that the length of the cell edge is very closely four
times that of ammonium chloride. While we are
not able to give a definite structure for this solid
phase, the change in symmetry must be due to
the appearance of an ordered arrangement of the
altered ammonium chloride cubes.
The continuous solid solution series between D
and E is very interesting because of the very large
foo"~----a.·7.514 -----J.,
. FIG. 7. Small open circle, Mn++;. triangle, NH.+; solid
circle, oxygen (water); large open circle, Cl-. Hidden and
interior atoms are designated by dashed lines.
changes in the diffraction pattern due to the fact
that the edges of the unit cell at D have twice the
lengths of the corresponding edges at E. We can
see no explanation for what happens except the
assumption that, as more and more manganous
chloride is included, an ordered arrangement of
the altered ammonium chloride cubes having
tetragonal symmetry is maintained and this
basic pattern contracts as the proportion of
ammonium chloride decreases. - - -- -
/ / / / / / - -
NH." NH •• H,O ~,; H,O
/-1/ / / /-}' -
FIG. 8.
That the process described above would be
expected to cause little change in the chloride ion
lattice is apparent from the following con
siderations:
(a) The value for the radius of Cl-, 1.86A, in
ammonium chloride· where each Cl-is coordi
nated with 8 NH4+, is obtained by increasing the
value, 1.81A, for the radius of Cl-with a
coordination number of six26 by a factor27 of 3
percent. Figure 9, showing the Cl-positions on
the unit cell side of pure ammonium chloride is
drawn to scale using ao=3.868A obtained above,
and this radius for Cl-. The space available at the
face center between the chloride ions would
accommodate an ion having a radius of approxi
mately 0.87 A. The value26 for the radius of Mn++
with a coordination number of six is 0.80A and is
drawn on Fig. 9 in a dashed line circle. No great
change in the chloride ion lattice is to be expected
from this source.
(b) The radius of NH4+ with a coordination
number of 8 is 1.52A, calculated, as above, from
the 6 coordination numbered radius given26 as
1.48A. In ice, the positions assigned to each
oxygen atom, from crystal structure work28 is
such that each oxygen atom is tetrahedrally
surrounded by four other oxygen atoms at a
distance of 2.76A. This holds for water of
crystallization as shown by the work of Beevers
and Lipson29 on BeS04·4H20, the work of
Keggin30 and of Bradley and Illingworth31 on
H3PW 12040, 5H20, H3PW 12040, 29H20 and re
lated substances. The radius of a water molecule
is, therefore, 1.38A at a coordination number of 4.
26 Linus Pauling, Nature of the Chemical Bond (Cornell
University Press, 1939), pp. 326 and 330. .
27 L. Pauling, reference 26, p. 334. Also sec V. M. Gold
schmidt Geochemische Verteilungsgesetze der Etemente.
28 L. Pauling, reference 26, p. 281: see also J. O. Bernal
and R. H. Fowler, ]. Chern. Phys. I, 515 (1933).
29 C. A. Beevers and H. Lipson, Zeits. f. Krist 82 297
(1932). '
30]. F. Keggin, Proc. Roy. Soc. London A144, 75 (1934).
31 A. ]. Bradley and ]. W. Illingworth, Proc. Rov. Soc.
London A157, 113 (1936). -
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386S
FIG. 9. NH,Cl.
Increasing this by a factor of 5.8 percent, and
then by 3 percent (Goldschmidt27) there is ob
tained 1.50A, the value for the radius of water
having a coordination number of 8. The radius of
the NH4+ and of water are then practically the
same and substitution of NH4+ by water in the
unit above should give only very small changes in
the chloride ion lattice.
These considerations of ionic size alone should
not be taken as exact as is shown by the fact that
the body diagonal distance between NH4+ and
CI-in NH4CI calculated from the x-ray data
from the relationship Cv3/2)ao gives 3.35A while
the sum of the ionic radii gives 3.38A. Con
sideration of the changes in the electrostatic
fields of force when NH4+ is replaced by a water
molecule and the polarization effects when Mn++
is inserted between the chloride ions would be
necessary for a complete picture of all that
happens. Such an analysis will not be attempted
here.
Densities of the solid solutions, A -B, and the
compounds at A, D, and E
To provide further evidence for this mecha
nism, density determinations on the solid phases
in the series A-B and of the substances at A, D
and E were made. The method used was that of
Jette and Foote.32 Duplicate determinations were
performed in three instances to determine the
precision of the results. This is indicated in
Table VII and Table VIII where the data ob
tained are summarized. The densities for the solid
solutions were calculated from the x-ray data
given in Table V for the cases of substitutional
solid solution of MnCI 2• 2H20 in the lattice of
NH4CI, of interstitial solid solutions and for the
case where the water molecules substitute for the
32 E. R. Jett and F. Foote, J. Chern. Phys. 1, 29 (1933). ammonium ions, while the manganous ion is
inserted interstitially. These values are shown in
Table VII under the heading Density calc. I, II
and III, respectively.
The calculated densities of the compounds at
D and E given in Table VIII were computed for
the unit cell size given above with 8 molecules to
the unit cell of the 6NH4CI· MnCh· 2H20 com
pound and with 2 molecules to the unit cell of the
2NH4C1· MnCI 2• 2H20 compound.
The mechanism of solid solution postulated
above, where a substitution of water molecules
takes place for NH4+ while Mn++ is interstitially
inserted, is borne out by the experimental deter
mination of the densities of the solid solutions
in the range A-B, see Table VII. For when these
values are compared with the densities calculated
from the x-ray data for this mechanism they are
found to be in good agreement (Table VII,
column III) while the densities calculated on
other postulates (columns I and II) are not.
The densities for the compounds found experi
mentally are checked by the values calculated
from the x-ray and analytical results obtained
above as shown in Table VIII.
Discussion of results
The results· given by our investigation show
that solid solutions are formed in the NH4C1
region of this system, see Fig. 4 and 5, points A to
TABLE VII. Solid solutions A-B.
DENSITY
(CALCULATED FROM X-RAY
DATA)
DENSITya
(EXPERI-
SAMPLE MENTAL) I II III
NH,Clb 1.S19±.001 1.525 1.525 1.525
No.2 1.508±.004 1.546 1.557 1.535
No.4 1.528 1.563 1.583 1.543
No.5 1.557 1.616 1.667 1.569
No.6 1.586±.007 1.621 1.676 1.571
No.7 1.610 1.706 1.814 1.610
a The density determinations were made at temperatures between
25.0° and 28.0° while the x-ray films were exposed at temperatures
between 25° and 29°.
b Tbe I. C. T. give the density of NH,CI calculated from x-ray studies
as 1.528 and from experiment as d,"'=1.536, =1.526 (Vol. I, p. 108;
Vol. III, p. 43). Our results check these values.
TABLE VIII. Compounds at D and E.
SAMPLE
No.8 (6NH 4CJ·MnCl,·2H,O)
No. 31 (2NH 4CJ·MnCI,·2H,O) DENSITY
DD1SITY (CALC. FROM
(Exp.) X-RAY DATA)
1.701
1.913 1.711
1.906
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TABLE IX. Relative intensities of lines on Debye-Scherrer
films for solid solution series No.1.
LINE No.1 2 3 4 .5 ij 7 8 9
SAMPLE PLANE 100a 110/1 110a 111a 200/1 200a 210/1 210a 211/1 --------------
NH.Cl 4 6 10 3 3 9 2 9 9
4 3 .j 10 3 2 8 2 9 9
5 3 5 10 2 1 8 1 8 8
ij 3 5 10 3 2 9 0 7 7
7 2 5 10 3 1 9 1 7 7
B, which is in complete agreement with the work of
Foote and Saxton,ll and Clendinnen and Rivett.12
The solid phases obtained were homogenous, as
shown by x-ray diffraction studies, after being
rotated for a minimum of two weeks and as long
as 8 weeks (see Table III for time in thermostat)
in contact with the liquid phase till equilibrium
was established. The results do not, therefore,
bear out the contention of Benrath and Schack
manl3 that these solid solutions eventually rid
themselves of all the MnCb· 2H20 if shaken for a
sufficient length of time.
As can be seen from Fig. 6, the lattice of
ammonium chloride is expanded very slightly
from one sample to the next in the first solid
solution series, A-B, but the trend is marked and
there is no doubt that the expansion takes place.
The plot does not exhibit a linear relationship
between weight percent composition and the
lattice constant. The curve reaches a maximum
and then begins to fall off between point 6 and 7
at about 13 weight percent MnCI 2• 2H20 in the
solid phase. This phenomenon has been observed
in metallic solid solutions33 but this is the first
time that it has been reported in crystal systems.
The solid solution series, A to B Fig. 5, does
not follow Vegard's additivity law, nor should it
be expected to, for as shown by J ette34 this law
may be considered analogous to Raoult's law of
liquid solutions. It has been well established that
Raoult's law holds for solutions only when the
molecular species involved are very much alike
chemically and physically. Therefore, Vegard's
law should be applied only to cases of solid solution
in which the components are similar in chemical
and crystal structure. This is borne out by the
previous work of Walden and Cohen,5. in which
the solid solutions formed did not follow this law.
If the MnC!Z· 2H20 is in an ordered arrange
ment in the ammonium chloride lattice, new
33 E. R. Jette and F. Foote, Am. Inst. Mining Met. Eng.
No. 670 (1936).
"' E. R. Jette, Trans. Am. Inst. Mining Met. Eng. 111,75
(1934). reflection lines should be observed on the x-ray
films for these solid solutions or at least the
relative intensities of the reflection lines should
change.35 Debye-Scherrer and precision camera
films taken for each sample in this solid solution
series showed no new lines. Furthermore visual
examination of the films revealed no marked
change In relative intensities of the lines,
see Table IX. Therefore, the distribution of
TABLE X.
CALCIUM RADIATION
6NH.Cl·MnCJ, '211,0
NH.Cl (SAMPLE No.8)
PLANE
LINE AND
No. SOURCE
100"
2 11013-
110"
3 110"
4 Ill"
6 200" REL. PLAKE REL.
Exp. INTEN- LINE AND Exp. INTE!'\-
SIN20 SITY No. SOt::RCE SI:-.l"2 (} SITY
8 004" 0.1744 .)
0.1859 4
9 400" .1931 2
.3754 6
.3756 13
.5627 3
.7505 9 13 40413-" .3676 6
14 44013-" .3854 6
15 404"
16 440"
17 444"
22 008"
23 800" .3684 10
.3859 10
.5615 8
.7019 8
.7733 10
TABLE XI.
CALCIUM RADIATION
2NH.Cl·MnCJ, '2H,O
NH.Cl (SAMPLE No. 26)
PLANE REL. PLANE REL.
LINE AND Exp. INTEN- LINE AND Exp. INTEN-
No. SOURCE SIN2 (J SITY No. SOURCE SIN2 (J SITY -----------------1
100"
2 11013-
110",
3 110"
4 111"
5 20013-
200"
6 200"
8 210" 0.1859 4
.3754 6
.3756 10
.5627
.7509
.7505
.9388 3
3
9
9 5 002" 0.1654 6
8 20213-" .3640 5
9 220~-a .3990 6
10 202"
11 220" .3642 10
.3980 10
15 222" .5638 9
18 40013-" .7958 3
21 400"
22 204"
25 402" .7958 10
.8602 5
.9599 10
35 M. von Laue, Ann. d. Physik 78, 167 (1925).
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MnCIz· 2H20 must be entirely random in the
solid solutions.
Much has been written in regard to double
salts as to whether or not they were "true"
compounds or merely a portion of a solid solution
series which corresponds to a stoichiometric
relationship, e.g., C1endinnen and Rivett12,36 con
cluded from their work that these double salts
are really eolid solutions. In line with this, the
results of our investigation on the substances
present at D and E, Fig. 5, indicate that there
exists grounds for reasonable doubt for calling
these "true" compounds. The existance of the
complete series of solid solutions between D and
E makes it impossible to definitely demonstrate a
finite existence range for either end member. If
such an existence range is to be used as the
criterion of a true compound then these end
members cannot be definitely so designated on
the basis of the existing data. We have, neverthe
less, used the'term compound for these substances
throughout this paper on the basis that they
correspond to simple formulae (see Table IV for
complete chemical analysis), that they give
distinctly different x-ray diffraction patterns
from NH4C!· MnCIz·4H 20 and each other, and
that they do appear to have existence ranges as
indicated by the somewhat vertical portions of
the curve at the corresponding compositions of
these substances. It would perhaps be better to
call these' 'compounds of variable compositions"37
in accordance with a similar procedure used in
the metallic systems where the formation of
superstructure lines is now attributed to "inter
mediate phases" rather than intermetallic com
pounds. Many examples are now listed in the
literature of compounds having variable compo
sitions.37 This has been discussed by Hagg in a
general way.3S The picture of such compounds
has been extremely useful in explaining the
structure of silicates, as for example, the forma
tion of NaAISi0 4 from Si02 by the substitution
of aluminum for silicon and the interstitial
addition of sodium.39
The regular distribution of the MnCl 2• 2H20 in
the ammonium chloride lattice increases the axial
36 F. W. J. C(pndinnen and A. C. O. Rivett, J. Chem. Soc.
123, 1634 (1923).
37 C. W. Stillwell, Crystal Chemistry (McGraw-Hill, 1938),
pp. 154-157,201-203,330-333.
38 G. Hagg, Zeits. f. Krist. 91, 114 (1935).
39 T. F. W. Barth and E. Posnjak, Zeits. f. Krist. 81,376
(1932) . ratio of the unit.cell from 1.00 to 1.05 and then to
1.09 which are just off-cubic. The unit cell is then
tetragonal and the diffraction lines of ammonium
chloride are split into two for planer indices
containing (hkl) with two unlike numbers, such
as 100, 110, 120, etc., but remains single for (hkl)
all similar, (111) planes. This is apparent from
Tables X and XI in which ammonium chloride
diffraction lines are compared with those of the
two "compounds." Kusnecov14 undoubtedly
made the mistake of using one set of these
tetragonal lines from which he computed the
lattice constants and found a contraction of the
ammonium chloride unit cell. For, if one system
atically picks out all the lines which appear
displaced from those of ammonium chloride
towards higher angles of reflection (larger sin2 ()
values), it will be found that these can be indexed
on the assumption of cubic symmetry and there
will be shown a contraction of the ammonium
chloride lattice. Thus, in Table X or XI, if we
used the 400,440, 800 plane reflections or the 220,
400, 402 plane reflections, respectively, for the
6NH 4C!· MnCI 2• 2H20 and 2NH 4Cl· MnCI 2• 2H20
we could calculate out a unit cell side which is
smaller than that of ammonium chloride. How
ever, if we chose the other set of lines, 004, 404,
008 and 202, 204, respectively, we could equally
well demonstrate an increase in the unit cell side.
Kusnecov14 in his x-ray studies missed com
pletely the slight expansion of the ammonium
t:hloride lattice with entrance of MnCI 2• 2H20
which exists in the solid solution series A-B. The
decrease in lattice constant of ammonium chlo
ride that he found at concentrations 11.6, 27.6,
32.8,47.0 weight percent manganous chloride are
undoubtedly due to measurements, at least from
27.6 weight percent and up, on diffraction lines of
the tetragonal compounds and their solid solu
tions, on the mistaken assumption that they were
ammonium chloride diffraction lines. The possi
bility of making such an error has been pointed
out above. It illustrates quite clearly the danger
of using only a few of the diffraction lines on an
x-ray photogram for the purpose of computing
la ttice constan ts.
We wish to thank Professor Paul F. Kerr of
Columbia University for his invaluable help in
the microscopic examination of several of our
samples, and Mr. Morris Krasnoff for his
assistance in drawing the plots and diagrams.
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