MELTING POINT OF SEPARATE!)
LITHIUM ISOTOPIS

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MICHIGAN STATE UNIVERSITY

Juiian Anthony Crawford
1958

 

 

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L I B R A R Y
Michigan State

University

MELTING POINT OF
SEPARATED LITHIUM ISOTOPES

by
Julian Anthony Crawford

AN ABSTRACT

Submitted to the College of Science and Arts
Nflchigan State University of Agriculture and
Applied Science in partial fulfillment of
the requirements for the degree of

MASTER OF SCIENCE

Department of Physics and Astronomy

1958

Approved

 

11

ABSTRACT

The melting points of the separated isotopes
lithiumpb and lithium-7 were determined by a melting—
wire technique. The samples were extruded at room
temperature in the form of wires O.h mm in diameter and
3 cm in length. Samples were placed two at a time in
an oil bath and the temperature was slowly raised through
the melting point. Occurrence of melting was detected
by interruption of a current through the samples. The
difference in melting point of the two isotopes was
found to be 0.23:: 0.07 C-deg. The absolute melting
points of the isotopes and of natural lithium were found

to be: Li6

, 180.u : o.2°c; L17, 180.7 : o.2°c;

Li-natural, 180.7 : o.2°c. The melting point difference
is smaller by a factor of ten than that predicted on the
basis of the Lindemann theory. It is concluded that the
lattice of the solid has become so imperfect at tempera-

tures near the melting point that the Lindemann scheme

affords a very poor description.

MELTING POINT OF
SEPARATED LITHIUM ISOTOPES

by
Julian Anthony Crawford

A THESIS

Submitted to the College of Science and Arts
Michigan State University of Agriculture and
Applied Science in partial fulfillment of
the requirements for the degree of

MASTER OF SCIENCE

Department of Physics and Astronomy

1958

I II ‘- P.4-

iv

ACKNOWLEDGMENTS

I wish to express my appreciation to Professor
D. J. Montgomery for his suggestion of this problem and
for his guidance and encouragement throughout the work.
I would also like to thank Professor B. H. Dickinson for
his advice during the early stages of the work. The
isotope loan fees were met in part by an All-College
Research Grant awarded to Dr. J. C. Lee for l95h-SS.
Dean Thomas H. Osgood was instrumental in making this
arrangement, and has otherwise encouraged and facili-
tated the program. Dr. P. S. Baker, of the Stable Isotope
Research.and Production Division of the Oak Ridge National
Laboratory, has contributed generously of his facilities
and experience in aiding the procurement and preparation
of the separated isotopes. Partial support of this work
was provided by a research contract granted to Michigan
State University by the Metallurgy and Materials Branch
of the Division of Research of the Atomic Energy Commission.

I.
II.

III.

IV.

TABLE OF CONTENTS

INTRODUCTION . . . . . . . . .

EXPERIMENTAL PROCEDURES . . .

A.
B.
C.
D.

E.

Choice of Material . . .
Procurement of Samples .
Preparation of Specimens
Experimental Apparatus .

Thermocouple Calibration

THEORETICAL CONSIDERATIONS . .

RESULTS AND DISCUSSION . . . .

LIST OF FIGURES . . . . . . .

BIBLIOGRAPHY . . . . . . . . .

O‘U'lU'lf-J

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19
22
26
1.0
1.1

I. INTRODUCTION

The production of electromagnetically-enriched
isotopes by atomic-energy projects has made isotopic
mass available as a new tool for the study of physical
properties of many substances. The essential point in
utilizing isotopes of the same element is that the mass
can be changed while the atomic force field is kept almost
exactly the same. The isotopic mass thus affords a
powerful method for the verification and extension of
theories of the properties of matter. This aspect of
the production of iéotopes was realized upon their discovery,
but the low enrichments and the small mass differences
of the isotOpes then available prevented significant effects
from appearing in phenomena other than gaseous or chemical.
The discovery of deuterium and methods of producing it
in quantity in the early 1930's made possible the measure-
ment of strong isotopic effects resulting from the great
relative mass difference of the hydrogen isotopes, and
many physical measurements were made on deuterium and its
compounds. The special nature of hydrogen, however,
precluded the results from aiding the understanding of
metals and most compounds.

The effect of isotopic mass on physical properties

of metals is usually small. As early as 1919, Richards(l)

reported that ordinary lead and uranium lead do not differ
in their melting temperatures by more than about 0.06 C-deg,
the uncertainty of his experimental measurements. However,
the relative mass difference was only about one-half percent.
The measurements by Soddy<2> on the densities of several
isotopic species of lead gave negative results for the
atomic volume to within an experimental accuracy of about

3 parts in 10,000.” Johnson(3) suggested that the diffusion
rate in solid metals should be influenced by atomic mass.
His experiments show that the relative abundance of the
various isotopes of nickel is altered by diffusion into
'copper in approximately the way that would be expected

if the diffusion rate varies inversely with the square root
of atomic mass. Chemla and Sue(h) have recently proposed
that the isotopic enrichment obtainable by solid-state
diffusion can be enhanced by the presence of an electric
field. The isotOpic effect on the superconducting transition
temperature is appreciable, as discovered independently

by Maxwell‘S) and Reynolds(6) and their cO-workers, and
discussed by Frdhlich(7). The experimental evidence for

an isotopic effect in superconductivity demonstrates

the importance of the interaction of electrons and lattice
vibrations in determining the behavior of superconducting
material. Tuyn‘a) and Justi(9) studied the electrical
resistances of uranium lead and normal lead at several

temperatures between 70K and 2730K. The results of the

two investigators are contradictory, so that it is difficult
to decide whether an isotopic effect is indicated or not.
Justi's results indicate an isotopic effect Opposite in

sign to that expected on the Graneisen theory. However,

his results depend upon a more limited number of measure-
ments than do those of Tuyn. The results obtained by Tuyn,
though not analyzed as to evidence of an isotopic effect,
indicate a somewhat better agreement with the predictions

of the Graneisen theory than could be accounted for by
random scatter of the data.

Nmre recently, McCaldin(lO) in l95h reported studies
of the isotopic effect on thermoelectric power, temperature
coefficient of resistance, and the alpha-gamma allotropic
transformation in FeSh and Fe57. The small relative mass
difference prevented him from getting conclusive results
on the thermoelectric power and the allotropic transfor-
mation, but he was able to confirm the existence and the
direction of the change in resistance. ‘Covington and

(11) have measured the difference in lattice

Mbntgomery
constants of L16 and Li7 and Snyder, Leffler and Montgomery(12)
have determined the difference in electrical conductivity.
Montgomery, Leffler, and Smith‘lB) found a difference in

the thermoelectric power of the separated isotopes of lithium
in conformity with the theoretical prediction of

(111)

Sondheimer

Perhaps the region of phenomena where studies with
varying isotopic mass can make their most useful contri-
bution is that where the nucleus moves from one position
of quasi-equilibrium to another, such as in solid or molten
lithium.around the melting point. In view of the great
need for adequate understanding of melting phenomena, it
was decided that a measurement of the difference in melting
points between the two isotopes might be particularly
valuable. Mbreover, if the difference is substantial,
it would be worthwhile to determine the temperature-
composition phase-equilibrium diagram for the separated
lithium isotopes in the solid-liquid region. Apart from its
intrinsic interest, establishment of this diagram would
show whether an isotope-enrichment process could be based
on fractional crystallization from the melt.

The present work is limited to the determination of
the melting-point difference, together with an estimation
of the absolute values of the melting points. These last
data are themselves useful for the light they might
shed on the discrepancies appearing in the literature as

to the melting point of natural lithium.

II. EXPERIMENTAL PROCEDURES

A. Choice of Material

Prior to the development of production—type mass
spectrographs at the Oak Ridge National Laboratory (ORNL)
and other installations of this kind, it was not possible
to obtain bulk quantities of highly-enriched stable isotopes
other than those of hydrogen. In early l9u6 ORNL started
a program for the enrichment of all naturally-occurring
stable isotopes, and by the end of that year had begun
shipments of samples. At present stable isotOpes of the
majority of the elements are available for sale or, in
some cases, for loan. Among the elements not supplied
are those with only one naturally-occurring stable
isotope; the majority of the radioactive elements; the
inert gases; certain rare earths; and a few other, such
as the highly toxic ones.

The investigation of the melting point of separated
isotopes was part of a broad program using the isotopic
mass as a probe for the study of the solid state. Lithium,
with natural isotopes Li-6 and Li-7 in reasonable abundance
ratio (Li-6, 7.52%; Li-7, 92.h8%), and a large relative
mass difference [(Li-7 —Li-6)/%(Li-7 + Li-6) I 111%] , was
selected as the most promising material for the initial
studies. Examination of the OBNL Inventory of Electromag-
netically Enriched Isotopes showed that both of these

isotopes were available in high enrichments and in adequate
amounts.

From the standpoint of theory, lithium is attractive
in that it has a rather simple structure, both atomic and
crystalline. It has low atomic number, and it crystallizes
in the body-centered cubic form at all but the lowest
temperatures. From the standpoint of experiment, on the
other hand, lithium offers difficulties in its handling
because of its high chemical reactivity. Nonetheless,
it was decided that the advantages of high relative mass
difference, ready availability, and simplicity of structure

outweigh the disadvantages of experimental difficulties.

B. Procurement of Samples

When the present work was begun in 1955, electromag-
netically-separated isotopes were available for distribution
only on loan as approved by the U. S. Atomic Energy
Commission. Requests for loan were made to the AEC by
using Form ABC-100. The requested amount of Li-6, the
rarer isotope, was 500 milligrams; that of Li-7, the more
common isotope, 1000 milligrams. For samples of this size
the loan fee was $50 per sample. For preparation of the
lithium in the elemental form, a special service charge of
$60 per sample was made. The total charge was thus $220,
which was met by an All-College Research.Grant, Physics
and Astronomy No. u53, initially given to Dr. J. C. Lee

for the academic year l95h-55. The samples were shipped

from ORNL on 19 May 1955. When these samples arrived,

it was found that the concentrations of impurities were

too high to allow meaningful results to be obtained.

The impurities appear to be introduced during the thermo-
chemical reduction of lithium chloride to elemental

lithium by means of metallic barium in stainless steel
containers. Dr. P. S. Baker, of ORNL, who supervised the
preparation of the lithium, suggested that vacuum distilla-
tion would be the best method of purifying the metallic
lithium, and agreed to have his organization perform the
distillation, at the nominal charge of $50 per sample.

The material was accordingly returned for purification
about 22 July 1955, without any measurements having been
made on it. The redistilled material was shipped from
ORNL on 3 November 1955, in approximately double the

amount initially requested, following the suggestion of
Dr. Baker that it would be advantageous to have additional
material to make up for the attrition during processing

if further distillation were to be attempted. The redistilled
Li-6 sample, SS 5(a), was of low isotopic purity (96.1%
Li-6, 3.9% Li-7), and was not used for melting—point
determination. The analysis of the redistilled Li-7 sample

is as follows:

11-] Lot No. 668LJ) - redistilled 1028 mg‘+ 1000 mg
Isot0pic Analysis (mass and atomic percent):
Li-6, 0.2 t 0.1%; Li-7, 99.8 t 0.1%

Spectrographic Analysis (element and weight percent,
precision.t 50%; T = trace):

Ag T Fe 0.3 Ni 0.02

Al 0.02 K 0.02 Pb 0.01
B8. 0.01 Mg 0.02 Si <0.05T
Ca 0.2 Mn <0.0l Sn <0.0l
Cr (0.0MT Mo <0.0l Sr (0.01
Cu 0.01 Na 0.02 V <0.0l

The spectroscopic analysis shows a large amount of
iron present (Fe I 0.3%). It is believed that this high
amount can be largely discounted in view of the sampling
procedure, which involved cutting the material with a
steel knife. The only other impurity in high concentration
is calcium (0.2%). The source is unknown. In the vacuum
distillation, the hardest element to remove is strontium,
because of the similarity of its vapor-pressure curve to
that of lithium. It is gratifying to note that it appears
only in very slight amount. It is this Li-7 sample (668j)
which was used for melting point determinations.

During the progress of the experiments, the AEC policy
on distribution of stable isotOpes was changed, and it
became possible to purchase certain samples, in particular
L1-6 of high isotopic purity. An allocation for 3 grams
of 99 percent Li-6 as well as one for 10 grams of 96 percent

Li-6, was authorized about 31 January 1956. The Li-6

sample, from Lot SS 5(b) containing 99.3% Li-6, was ordered
about l.Nbrch.and shipped 15 Nbrch. The cost was $30 per
gram, plus $15 handling fee, for a total of $105. The

analysis, as supplied by ORNL, is as follows:

Li-6 Lot No. SS 510) 000

 

Isotopic Analysis:
Li-é, 99.3 t 0.2%; Li-7, 0.7: 0.1%

SPeCPTOBPaPhic Analysis (element and weight percent,
presumed precision i 100%):

Al <.OlT Fe .05 Pb <.01
Ba .01 K <.01 Sn <.01
Be <.001 Mg .01 Sr .01
Ca .25 MD <.01 V <.01
Cr <.01FT Na .02 Zn <.25
Cu .02 Ni <.01

It is this Li-6 sample SS 5(b) which was used for melting-
point determinations.

The natural lithium was produced by the Lithium
Corporation of America, Minneapolis. It is their low;
sodium grade, in the form of 3/8-inch diameter rods, with

the following specifications:

Na 0.005%
K 0.01
C8. 0002

N 0.06
Fe 0.001

The isotopic Analysis is that of ordinary natural lithium.
Mr. Theodore L. Brown and Professor be.T. Rogers,

of the Chemistry Department of Nflchigan State University,

10

kindly furnished the natural lithium and the information
on its specifications for the initial experiments. Larger
amounts were subsequently ordered from the Lithium.Corpora-

tion of America.

C. Preparation of Specimens

 

All lithium samples were shipped and stored in oil.
Nevertheless, they became coated with a dark layer, probably
lithium nitride for the most part. The coating can be
scraped or cut off and the clean metal obtained, provided
the fresh surface is protected either by keeping it in a
nonreacting atmosphere (e.g., carbon dioxide) or by covering
it with a nonreactive substance (e.g., petrolatum).

The lithium was extruded from a steel press in the
form of O.h-mm diameter wire. It emerged through a layer
of petrolatum which forestalled surface contamination until
the samples were inserted in the temperature bath. The
samples averaged 2.5 cm in length, and were handled with
petrolatum-coated tweezers while being inserted in the
holder.

The later experiments were run with annealed material.
Prior to being inserted into the press, the lithium was
heated to its melting point in a beaker of mineral oil and
then allowed to cool slowly back to room temperature.

This procedure resulted in more uniform wires.

11

D. Egperimental Apparatus

The apparatus for this experiment can be divided
into three parts: the temperature bath, the sample
holder, and the measuring devices. Photographs of the
apparatus are shown in Figures 1 and 2.

The temperature bath consisted of a series of
containers and insulation as shown in Figure 3. There
were two different oil baths, the small one containing
mineral oil in which the samples were melted, and the
large one containing lowavolatility motor oil in which
the heaters were immersed. A pair of glass Jars, nested
one within the other and separated by a layer of sand,
served to separate the two oil baths and provide a means
of heat transfer between them. The large bath, contained
in an iron tank, was enclosed in a box with sides of
asbestos board. The tank was insulated on the sides and
the bottom with several inches of loosely packed vermiculite.
A ventilating fan removed the fumes from the hot 011.

Two Watlow No. we-123, 115-volt, 1000-watt immersion
heaters were used to heat the main oil bath. They were
controlled by a 100 - 550° F thermostat. The top of the
main tank was covered with a sheet-metal lid which
contained a large variable-speed stirrer. Insulation of
the oil bath from.the room was completed by covering the
lid with several layers of glass-wool padding and putting

an asbestos-board cover on the box.

2.3332 - ._ .3“.

 

Fig. 2.‘ Sample holder

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Fig. 3.-Uiagra- of temperature bath.

 

 

15

Initially a sample holder was built to carry five
lithium wires simultaneously. Each of the five positions
was identified by a separate pulse signal which occurred
when the sample wire broke. However, consistent results
could not be obtained with this arrangement. A two-wire
holder was then built with particular attention paid to
obtaining uniformity of conditions for the pair of samples.

A sketch of the sample holder is shown in Figure A.
The frame was constructed from l/h-inch and l/8-inch
black phenolic plastic. The holder was designed so that
it could be inserted directly into the temperature bath
from outside the apparatus without having to remove any
insulation. The wire samples were suspended between pairs
of small spring clips projecting from the side of the
holder toward the center. The jaws of the clips were
located equidistant from.the cylindrical center line
of the holder. On this center line, and level with
the jaws of the clips,was located one junction of a
thermocouple. Directly above the center of this arrange-
ment was a small slowespeed stirrer to minimize thermal
gradients in the oil.

The spring clips formed part of a pulse circuit
used to detect the occurrence of melting. The insertion
of a lithiumpwire sample between a pair of clips closed
the circuit, allowing a l-ma current to flow through the

sample. A small hanger was placed on each sample wire to

l6

 

 

 

 

 

 

 

 

 

 

 

Pig. hubiagram of sample holder.

l7

overcome the effect of the surface film in preventing
breakage of the sample. When the sample melted and
opened the circuit, a small pulse was recorded on the
temperature record.

Figure 5 shows a block diagram of the measuring
circuit. A copper-constantan thermocouple made from
27-gauge wires was used to measure the temperature. The
copper loads were covered with Teflon to provide durable
insulation in the hot oil. A mixture of crushed ice and
water provided a reference temperature. The thermocouple
had a sensitivity of about 55 microvolts per degree at
1800 C. A Leeds and Northrup No. 7553 type K-3 Universal
Potentiometer (stated accuracy 0.02% of voltage) backed
off most of the thermocouple voltage, which was about
8000 microvolts at the melting point. Copper leads and
copper or brass contacts were used in the potentiometer
and the switch circuits to reduce the possibility of
spurious thermal voltages. The voltage difference between
the thermocouple and the potentiometer was fed into a
Leeds and Northrup No. 9835 B Stabilized D-C Microvolt
Amplifier (stated accuracy O.h% of the reading). The
amplified signal drove a Leeds and Nerthrup Model S,
60000 Series Speedomax type-G Recorder (stated accuracy
0.5% of full scale). The pulse circuit previously mentioned
was connected directly to the input of the recorder.

This combination offered a continuous record of temperature

18

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against time, and gave an automatic indication of melting
with a maximum sensitivity of 50 av (less than one degree)
full scale. It was possible to detect accurately differences
as small as % av, or less than 0.010 G. Our estimate of

the overall accuracy of the temperature measurement is

t 0.01;0 C. A.sample strip chart record is shown in

Figure 6.

E. Thermocouple Calibration

The copper-constantan thermocouple was calibrated
against a Leeds and Northrup No. 8163 Thermohm platinum
resistance thermometer. The hot junction of the thermo-
couple was fastened alongside the coil of the resistance
thermometer, and the combination was immersed to a depth
of 9 or 10 inches in mineral oil surrounded by the oil of
the main temperature bath. The thermocouple remained in
the same recording circuit as previously described. The
resistance thermometer was connected through a Leeds and
Northrup No. 8068 Mercury Commutator switch to a Leeds and
Northrup No. 8067 Mueller Temperature Bridge. The resistance
and the emf were measured for a series of equilibrium
temperatures ranging from 178° C to 1820 C. A plot of
resistance against temperature was made using the constants
of the resistance thermometer. From this plot and the
experimental data the variation of thermocouple emf with
temperature was determined, as shown in the calibration curve

of Figure 7.

20

 

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w YI+9 I... ‘ ...... e w ‘4 . e c. I .9 _ .49.“. . ... .u. e I. 9 . 9 _
. .... ...... bee». . vs... I.. ... . ... ... . o 9 . ... ~ .. 9 . .
..a . . . . - 9 . . . . ... I . .- . o . .. . .....
IlInf‘lo71huoI1414‘I'IeI VLAIQIIO I. .9 nIIII IL” A”- Ahoy]. TV Ole ? I IreIIWITHI b!‘.*.uIeI IQII It.” YO. IV- v IIIOI.r.OsI 9. I 1- I .II 0+ fi “
. 9.9 ... I.» . 9. I v. .I.. . . I. .I .9. .. . .... r9. .. ...oI.. _ 9
9* a e. 9.9... e o. . . 9 a . I 9 . ”pet a. ..”.I 9 .~I .. . 9. ....94... I . .
to I I. e I.+.*v”.. r 9. e . .9v.9. .. .. .o I .9 . vr I .. ... o0 . I. I. F ... I 9 I . 9 . 9 . 9
.. . .L. ..NI.> IPQ. IIIII ILL. .. 19.. .H .IM .HHL. .I I .IL .I v . .rr IIII.I.r E . . .... I III I III: I IIrI.II.I. III-III ..... ILIrI-I .9...-

 

 

 

 

 

 

 

 

 

III. THEORETICAL CONSIDERATIONS

When heat is supplied to a solid, there is an increase
in the amplitude of vibration of the atoms about their
equilibrium positions. Naively stated, each atom then
requires more room, and consequently the solid expands.

As the temperature is increased, the long-range interatomic
forces become ineffective and atoms begin leaving their
original equilibrium positions. When this happens frequently
enough, the solid loses its rigidity and melts.

In 1910 Lindemann‘lS) postulated a relation between
the Einstein characteristic frequency vE and the melting
temperatureT},. He assumed that a solid consists of a
set of simple harmonic oscillators arranged in a tetra-
hedral lattice, and that melting occurs when the amplitude
of thermal vibration of the atoms attains one-half the
separation of nearest neighbors minus the sum of their
radii; that is, the solid melts when the atoms touch.
Idndemann.assumed simply that the atomic radius is some
constant fraction of the atomic spacing. These assumptions
are equivalent to the assumption that at the melting point
the mean amplitude of thermal vibration Xm is a constant

fraction a of the interatomic distance d; that is,

Xm= ad (1)

23

In a tetrahedral configuration, d is related to the

atomic volume V'by

d=€/§M=V2—e’A/pN (2)

where N is Avogadro's number, A is atomic mass and f) is
the density.
For a classical harmonic oscillator the average total

energy is

E = é-bxfim = kT (3)
where T is the absolute temperature, k is Boltzmann's
constant, xmax is the.maximum amplitude of the oscillator
at temperature T and b is the force constant which depends
only on the atomic field. Quantum mechanically, the
average total energy would be

E = é-bxfim = 'g'z'hv + ___h_u__ (u)

63h1y4(T __ I

where h is Planck's constant and I) is the frequency of
vibration. Figure 8 is a plot of the mean vibrational
energy ibxemax against kT (both quantities are normalized
through division by by for Li-7). At absolute zero the
difference in zero-point energy shifts the curve for Li-o
about 8% above that for Li-7. As the temperature increases,
the difference becomes smaller, approaching zero at high

(11) have used this

temperatures. Covington and Montgomery
model to account for the difference in lattice constants

of Li-6 and L1-7.

 

 

 

 

 

O l g L l
O l 2

kT/h ow

Fig. 8,-Plot of the mean vibrational energy fixzmax
against kT (both quantities normalized with respect

to thi-7)‘

Under the assumption that the mean vibrational
amplitudes are equal at the melting point, the inter-
section of a horizontal line with the curves in the
neighborhood of the melting point for natural lithium
gives the melting points of the individual isotOpes.

To get a value analytically for the difference in melting
points equation (u) is written separately for each isotope
and the right-hand sides are equated. The result can be
solved numerically for A Tm, the melting point difference.
With 322°K for the Einstein characteristic temperature,
and MSBOK for the melting point of lithium, the predicted

temperature difference ZSTm turns out to be about 3 K-deg.

IV. RESULTS AND DISCUSSION

The results of the measurements are given in Table I.
Here the first column gives the date (in 1957) on which
the experiment was performed. The next three columns give
the thermal electromotive force between the hot junction
of the copper-constantan thermocouple and its cold junction
maintained at 0°C, when breaking of the various lithium
wires occurs. The fifth column lists the observed
differences in thermocouple voltages between Li-o and Li-7
samples whenever the samples tested were of these materials;
no entry is made for the cases where both wires were of
the same material, or where Li-nat was under test. The
sixth column gives the average heating rate, expressed
in rate of rise of thermocouple voltage, in the neighborhood
of the melting point. The seventh column lists the sample-
wire diameter, and the last column gives the weight of
the hanger used to insure breaking upon melting. The data
are broken into sets, as indicated by subheadings. In a
few cases some serious anomaly existed in the data, and
such points were discarded in analyzing the data. These
points are indicated by an "x" immediately preceding column

1.

TABLE I

EXPERIMENTAL DATA ON MELTING POINTS OF LITHIUM

27

 

 

Thermocouple Voltages

Heating Wire

Hanger

 

 

Date Li-6 Li-7 Li-n Diff. Rate Diem. Weight
1957 (11V) (uv) (1w) (11v) (pV/min) (mm) (ms)
Standard Measurements, u00 mg

6-7 8220 8228 - 8 5.6 0.1; ~ 1;00
6-7 8226 8231; - 8 3.5 0.1; ~ 1;00
6-7 8218 8223 - S 11.0 0.1; ~ 1;00
6-10 8225 8235 - 10 3.8 0.1; ~ 100
6-10 8219 8233 - 11; 2.5 0.1; ~ 1;00
6-10 8219 8228;— - 9% 2.2 0.1; ~ 1;00
6-12 8217 8232 - 15 1;.2 0.1; ~1;00
6-12 8215 8225 - 10 1.6 0.1; ~1;00
6-12 8218 8231 - 13 1;.0 0.1; ~1100
6-12 8219 8232 - 13 5.0 0.1; ~1;00
6-12 8218 8232 - 11; 2.6 0.1; ~ 1;00
6-13 8216 8228 - 12 3.8 0.1; ~1;00
6-13 8215 - - - 3.1; 0.1; ~ 1;00

8217
6-13 - gggg - - 11.5 0.1; ~ 1100
6-13 - - gig - 1;.2 0.1; ~1;00
6-13 - - 8228 - 5.0 0.1; ~ 1;00
8230
6-11; - - 8228 - 3.2 0.1; ~ 1;00
8231
6-11; 8216 - 8230 - 2.8 0.1; ~1;00

TABLE I - Continued

28

 

 

 

Thermocouple Voltages Heating Wire Hanger
Date Li-o Lia? Li-n Diff. Rate Diam. Weight
1957 (MV) (HV) (HY) (9V) (uV/hin) (mm) (mg)
6-11; - 8230 8231 - 2.2 0.1; ~ 1;00
6-11; 8212 8216 - 6 7.0 0.1; ~ 1;00
6-11; 8216 8233 - 17 2.6 0.1; .- 1;00
10-8 8160 8186 - 26 6.7 0.1; ~ 1;00
10-8 8206 8218 - 12 9.5 0.1; ~1;00
10-8 8213 8221; - 11 3.6 0.1; ~1;00
10-9 - - 8221 - 3.3 0.1; ,- 1;00
8227
10-10 - - 8213 - 2.7 0.1; ~1;00
8228
10-10 8211; - - - 5.5 0.1; ~1;00
8216%
10-10 - 8225 - - 2.9 0.1; ~ 1;00
‘ 8228%
10-10 823% - - - 5.3 0.1; ... 1;00
8216
10-12 - 8226 - - 1;.9 0.1; ~1;00
82265
10-12 8210 - - - 5.7 0.1; ~ 1;00
8211; '
10-12 82101: - - - 3.9 0.1; ~1;00
8212
10-12 8213i 8226-:— - 13 3.0 0.1; ~1;00
10-12 82131; 82273 - 11; 5.1 0.1; ~1;00
10-12 8209% 8225—2 - 16 5.8 0.1; ~1;00
10-15 8217 8229 - 12 1;.0 0.1; ~ 1;00

TABLE I - Continued

29

 

Date

Thermocouple Voltages
Li-n

Li-o

Li-7

Diff.

Heating Wire

Rate

Hanger

Diam. Weight

 

1957 (1W) (1W) (11V) (11v) (IN/min) (Hun) (mg)

10-15 8208 8221;% - 16% 2.6 0.1; ~ 1;00

10-15 8215% 8228 - 12—;— 2.7 0.1; ... 1;00

10-15 8218 8231 - 13 3.7 0.1; .- 1;00

10-16 8216-:— 82282 - 12 3.9 0.1; ... 1;00

10-16 8215-g— 8220-é - 5 1.6 0.1; .- 1;00

10-17 8211 - " " hob, 0014 N LL00
8220%

10-17 8197 - - - 2.0 0.1; ~ 1;00
8197

10-17 8205-1— - - - 3.6 0.1; .- 1;00
8206;

10-21 8212 - - - 1;.6 0.1; ~ 1;00
821ué

10-21 - 8221; - - 1;.5 0.1; ~ 1;00

8229
10-21 - 8226 - - 2.1 0.1; ~ 1;00
8228

10-23 8218 - - - - 0.1; ~ 1;00
82212

10-26 8216 - - - 7.1; 0.1; ,- 1;00
8220

10-26 8220% - - - 3.8 0.1; ~ 1;00
8221;

10-26 8217 - - - 5.8 0.1; ~ 1;00
8219

10-26 82111L - - - 6.3 0.1; ~ 00
8211: h

10-26 8213 - - - 6.0 0.1; ~ 1;00

8217

TABLE I - Continued

3O

 

 

 

Thermocouple Voltages Heating Wire Hanger
Date Li-6 Li-7 Li-n Diff. Rate Diam. Weight
1957 (uV) (HV) (uv) (uV) (uV/min) (mm) (mg)
10-29 - 8227 - - 3.1 0.h .~.h00
8228
10-29 - 8229 - - 6.0 0.u «1&00
8229
10-29 - 8223i - - 3.2 0.u -.h00
8227;
10-29 - 8228l - - 6.0 0.h «vhoo
8228
10-30 - - 8222 - 6.6 0014 N 11.00
8227%
10-30 - - 82261 - 6.0 0.u nahoo
8229§
10-30 - - 8222i - 6.6 0.h -«u00
8228
10-30 - - 8217 - 5.2 0.h -u00
8222
Weight Effect
11-2 8209 - - - 8.2 0.u uoo
8217
11-2 8199_ - - - 7.5 0. 300
8205i h
11-2 82201 - - - 5.0 0-h 200
8221§
11-2 8209i - - - 3-h 0.u 200
8228
11-2 8216 - - - 6.7 0.u 300

8217

TABLE I - Continued

31

WW

 

Thermocouple Voltages Heating Wire Hanger
Date Li-6 Li-7 Li-n Diff. Rate Diam. Weight
1957 (uV) (HV) (uV1 (uV) (WV/min) (mm) (mg)
11-2 8203% - - - 6.3 0.h hoo
8213
11-5 8216% - - - 7.2 0.u 200
8219
11-5 8211 - - - 5.6 0.h 200
821h%
11-5 8218? - - - 5.2 0.1 100
8221§
11-5 8220 - - - 2.8 0.8 50
8221%
11-5 8225 - - - 5.2 0.8 50
8226%
11-5 8226 - - " 701 00,4 50
8228
11-6 8216 - - - 5.1 0.h 100
8220%
11-6 - 82h2i - - h-O 0.h 50
8211;
11-6 - 82u3% - - 6.6 Ooh SO
82u6
1.1-6 - 8229 - " 2.8 0.1.]. 100
8233
11-6 - 823a - - h-S 0.h 100
8236%
11-7 - - 8222 - 6.0 0.u 50
8229%
11-7 - - 8226% - 6.7 0.1 50
11-7 - - " 7.0 00L} 25

TABLE I - Continued

32

 

 

 

 

 

Thermocouple Voltages Heating Wire Hanger

Date Li-6 Lia? Li-n Diff. Rate Diam. Weight

1957 (uV) (0v) (uV) (uV) (uV/min) (mm) (mg)

1.1-? - - 8230 - 7.6 0.1.} 100
823k

11-7 - - 823 - 6.h 0.8 100
823 1

11-7 - - 822h% - 6.1 0.u 200
8229:

11-9 - - 8229 - 10.8 O.h 300
8231

Diameter Effect

11-9 - - 8225 - 6.8 O.h 300
82382 1.0 300

ll-12 - - 8222 - 6.8 1.0 625
823h% 0.8 100

11-12 - - 8235 - 9.2 0.u 100
82u6% 1.0 250

11-12 - - 82351 - 1.5 0.u 100

11-12 - - 8229 - h.0 O.h lOO
82u0 1.0 MOO

Standard Measurements, 100 mg_

ll-l3 8223.3 8233.3 - 10 7.3 0.8 100

11-13 8225.1 8238.7 - 13.6 6.3 0.8 100

11-13 8228.0 8233.8 - 9.8 5.8 0.h 100

TABLE I - Continued

33

 

 

 

 

Thermocouple Voltages Heating Wire Hanger
Date Li-6 Li-7 Li-n Diff. Rate Diam. Weight
1957 (1W) (1W) (1W) (1W) (Mr/min) (mm) (mg)
11-13 8223.0 8211.0 - - 6.5 0.1 100
11-13 8222.3 - - - 5.2 0.1 100
11-11 8221.5 8231.5 - 13 1.0 0.1 100
11-11 8221.0 8233.0 - 9 3.0 0.1 100
11-11 8226.1 8211.2 - 17.8 1.1 0.1 100
11-11 8226.9 8238.0 - 11 5.2 0.1 100
11-19 8221.7 8237.2 - 15.5 6.6 0.1 100
11-19 8227.0 8231.7 - 1.7 7.2 0.1 100
11.19 8220.3 8236.1 - 15.8 8.0 0.1 100
11-19 8221.1 8230.1 - 5.9 7.9 0.1 100
11-19 8221.6 8233.2 - 8.6 7.8 0.1 100
11-19 8222.6 8231.2 - 11.6 7.8 0.1 100
11-19 8232.8 8211.8 - 12 7.1 0.1 100
11-20 8217.5 8227.7 - 10.2 5.5 0.1 100
11-20 8222.8 8211.2 - 21.1 5.1 0.1 100
11-20 8230.9 8235.2 - 1.1 7.0 0.1 100
Standard Measurements, 200 mg and 100 mg
11-20 8219.0 8227.1 - 8.1 6.7 0.1 200
11-20 8223.0 8232.8 - 9.8 6.5 0.1 200
11-20 8218.6 8233.1 - 11.5 2.6 0.1 200
11.21 8221.5 8221.9 - 3.1 1.6 0.1 100
11-21 8203.0 8221.7 - 21.7 5.7 0.1 100

3h

The interpretation of data on melting points as obtained
by the melting-wire technique adOpted in the present work
is complicated by the following factors: the possible
existence of an appreciable temperature difference between
the measuring thermocouple and the specimen under test,
the difference having its source in the interaction of the
specimen location and the heating rate; and the existence of
a substantial difference between the "true" melting point
and bath temperature when breaking occurs, the difference
having its source in the incomplete compensation between
support of the specimen by the coating formed on its outside,
and load on the specimen by the weight hung on it to overcome
this support.

Much of the preliminary experimentation was carried out
in order to obtain temperature uniformity between the two
sample locations. Statistical analysis of the final results
showed that the effect of location is not significant, and
moreover that the effect of heating rate is not important
provided that it lies between 1 and 8 uv/min. These limits
were maintained in the final experiments following their
establishment tentatively in preliminary runs.

Estimation of the possible difference between melting
point and breaking temperature is much more troublesome.
Scatter diagrams for the breaking emf against hanger weight
for 0.1-mm wire diameter showed identical trends for the
threenaterials Li-6, Li-7, and Li-nat. The effect amounts

to a lowering in emf of about 8 av, equivalent to about

35

0.11 C-deg, from the lOO-mg weight to the 100-mg weight.
Increasing the thickness of wire at constant hanger weight
would be expected to increase the breaking emf, and this
effect is indeed found; in fact, at 300-mg load an increase
in diameter from 0.1 mm to 1.0 nmiproduces a rise in emf
of about 15 av, corresponding to a temperature difference
of 0.27 C-deg. It might be possible to combine the variables
of diameter and weight into a single variable corresponding
to an "equal loading" of some kind, for instance, equal stress
on metal (pr0portional to weight divided by square of the
diameter), equal stress on coating (proportional to weight
divided by diameter), and so on. But without an adequate
theory for failure, data on the mechnical properties of
lithium, and extensive experiments with the present apparatus,
further analysis does not appear worth while.

The conclusion---which must remain tentative---to be
drawn from examination of the present data is that for
wire diameters of 0.1 mm and 1.0 mm the breaking emf does
not vary by much more than iiéutv for loads that are heavy
enough to keep the coating from supporting the wire to
indefinitely high temperatures, and light enough to keep the
hanger from causing creep to produce breakage at unreason-
ably low temperatures. Hence absolute values for melting
points cannot be reported to better than t:0.l C-deg on
the basis of uncertainties in the method itself, apart
from the effects of chemical impurities and errors in

calibration and instrumental inaccuracies.

36

On the other hand, the difference in melting points

 

between isotopes can be determined with much higher precision.
Examination of the data shows that the difference in breaking
emf's between isotopes is nearly independent of hanger
weight and wire diameter. On physical grounds this result
would be expected, unless the effect of isot0pic mass on
ultimate strength, creep rate, and other mechanical properties
is pronounced.
Analysis of all the data leads to the following results

for the actual samples of lithium isot0pes:

Melting point for lithium-6: 180.1 t 0.100

Melting point for lithium-7: 180.3 i: 0.1%
Difference in melting points: 0.23 t 0.07 C-deg.

Here the indicated limits of error refer to those discussed
above for the melting points, and to the statistical standard
deviation for the difference in melting points. The
instrumental and calibration errors are negligible in each
case with.respect to the indicated limits.

IsotOpic and chemical impurities need next to be
considered. The isot0pic impurities produce negligible
effects under the assumption of a straight-line extrapolation
for melting-point as a function of isotopic composition;
indeed, the isotopic contamination is considerably less than
one percent, and even a fairly strong dependence of melting

point on isotopic composition would not change the results.

37

The effect of chemical impurities is harder to assess, with
respect both to the effect of a given amount and to the actual
amounts present in the samples. If the usual assumption is
made that for small concentrations of impurities, the freezing-
point depression is pr0portional to the atomic fraction of
impurities, and if further the melting point is affected in

the same way as the freezing point, it is possible to correct
for the effect of impurities. Douglas and his colleagues(16)
have measured the melting point of natural lithium very
carefully, and in this work have been able to estimate the
constant for the freezing-point depression.

The analyses for the samples, as provided by Oak Ridge
National Laboratory, were made spectrographically. The
accuracy is given as only 1750 per cent. From certain other
experimental work performed in the Physics Department at
Ruchigan State University, some question has arisen as to
the accuracy of the analyses. It was attempted to check
the results by use of the spectrograph in the Department of
Agricultural Chemistry at Michigan State University, but
difficulty was experienced in preparing samples which would
give satisfactory spectra. Hence there remains some
uncertainty in analysis. The samples of both isotopes,
however, have had simdlar chemical treatment, and are reported
to have nearly identical chemical analyses. Again there
appears an uncertainty in the absolute value of the melting
points, but the uncertainty in difference remains in all

likelihood affected only slightly.

38

When the reported analysis is combined with the results
of Douglas g§_gl, and the uncertainty due to chemical

impurities is taken into account, the values become finally:

Melting point for lithium-6: 180.1 s 0.2°C
Melting point for lithium-7: 180.7 1 0.2°c

Difference in melting points: 0.23 i 0.07 C-deg.

The melting point for natural lithium does not differ
significantly from that for lithium-7, according to the
present data. Nonetheless, it is of interest to compute
the melting point for natural lithium on the basis of a
linear interpolation between the values given above. The
figure turns out to be 180.6SOC, which is in perhaps
fortuitously good agreement with the value of 180.51 t 0.03°C
reported in reference 16. These investigators were able

to use a thermal-arrest technique, and had large samples of
exceptionally high purity. Hence their result is of high
reliability.

The value of 0.23 t 0.07 C-deg found experimentally is
an order of magnitude lower than the value of about 3 C-deg
predicted on the Lindemann theory. It appears that this
theory is inadequate to treat any of the details of the
fusion process. Such a finding is not surprising, of course,
since the Lindemann theory attempts only to suggest a
mechanism for fusion and has little thermodynamic basis,

predicting as it does the occurrence of a phase change, but

39

not the coexistence of two phases at the melting point.
Still, the success of the Lindemann theory for a wide range
of substances calls for some speculation as to the source
of the discrepancy between theory and experiment. We tend
to look for an explanation along the lines that near the
melting point so many lattice defects appear that the
average potential well in which the lithium ion moves is
flattened, with consequent lowering of the natural frequency
and the effective characteristic temperature. Then the
ratio of actual temperature to characteristic temperature
is increased, the effects of quantization and hence the
difference in melting points thus becoming smaller.

In any event the hope of utilizing the difference in
melting points as a basis for isotopic enrichment appears
slight. Consequently extension of the work might more
profitably take the form of determination of melting
points on compoundscf the lithium isotopes, or on other
elements such as calcium and magnesium. It does not appear
profitable to attempt to determine the solid-liquid phase-
equilibrium diagram for the lithium isotopes in the absence

of some motivation from the direction of metallurgy theory.

10

LIST OF FIGURES

Figure Page
1. View of Apparatus . . . . . . . . . . . . . . . l2
2. View of Sample Holder . . . . . . . . . . . . . l3
3. Diagram of Temperature Bath and Insulation . . 11
1. Diagram of Sample Holder . . . . . . . . . . . 16
5. Block Diagram of Measuring Circuit . . . . . . l8
6. Sample Strip Chart Record . . . . . . . . . . 20

7. Calibration Curve for Copper-Constantan
Thermocouple 0.000000000000021

8. Plot of the Mean Vibrational Energy 36x2!“ax
againstkT................2’4

l.

2.

3.

9.

10.

ll.

12.

11

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"111111111 111111“