LATTICE CONSTANYS OF SEPARATED
[SOTOPES OF LETHIUM

Thesis for ”12 Degree 05 M. S.
MICHESAN STATE UNIVERSETY

Edward James Covington
1956

L4 1.:

IHIllllllllllllHlIIIHIIIHIIHIJIIIIIIIl‘lllllllllllllllll‘l

1 31293017640206 r

germ-fur: Fray; q r1:

LATTICE CONSTANTS OF SEPARATED

ISOTOPES 0F LITHIUM

By

Edward James ggvington

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 0? SCIENCE

Department of’Physics

1956

fine

 

 

 

 

_.__=—-
__.—..._

ABSTRACT

The lattice constants of the separated isotopes lithium - 6 and
lithium.- 7 are determined at room temperature with.a llh.6—mm.Phillips
camera on a Norslco xpray diffraction unit. Essentially single crystals
are worked with by melting the specimens and allowing them to solidify
slowly. Films are measured on an optical linear comparator and the
extrapolation method of Nelson and Riley used. No consistent differences
in lattice constants between lithium - 6. lithium - 7. and natural
lithium were observed, and it is concluded that within one part in one

thousand the lattice constants are the same.

iii

ACKNOWLEDGMENT

To Professor D. J. Montgomery I express my appreciation for the
suggestion of the problem and for his guidance during the entire work.

Thanks are extended to Dr. George Beard of the Physics Department
who did much to get the preliminary apparatus in working condition.

I am grateful to Professor C. D. Hause of the Physics Department
for making available some of the measuring equipment in the spectroscopy
and the optics laboratories. Dr. J. C. Lee. formerly of the Physics
Department. made it possible to obtain samples of separated isotopes on
his All-College Research Grant, and I wish to express my gratitude to
him and to the All-College Research Committee.

I wish to thank Dean Thomas H. Osgood. Dean of the School for
Advanced Graduate Study. for his interest in the work, and for his
support during its inception when he was head of the Physics Department.

Through the courtesy of Dr. Carl Brubaker of the Chemistry Depart-
ment. I was able to use the x-ray unit in Iedzie Laboratory and also to
obtain some capillary tubes.

Special acknowledgment is due Dr. A. I. Erickson and Dr. H. Mort-
land of the Soil Science Department for the use of the diffraction unit
and film-deveIOping facilities in that department.

Mr. Theodore L. Brown and Professor Max T. Rogers of the Chemistry
Department kindly supplied us with samples of purified natural lithium.
Dr. P; 8. Baker. in charge of special materials. separation development.

and isotope utilization for the Stable Isotope Research and Production

iv

Division of the Oak Ridge national Laboratory. has contributed most
generously of his facilities and experience to aid as in procuring

samples of the separated isotopes. I am grateful to him and to the

Atomic Energy Commission for their assistance.

TABLE OF CONTENTS

I. IMODUCTIONOOOOOOOOOO0.00.00.00.00 ..... .00000001

11. x-my DIWCTIONOOOOOOOOOOOOIOOOOOOOOOOOOOOOOQO 2

III. Powm cm mnonoooooOOOOOOOOOOOOOOOOOOOOOOO 3

IV. EXPERIMENTAL PROCEDURES......................... 8
Procurement of Samples..................... 8
Preparation of Specimens...................12
Exposures and DevelOping...................13

Film Interpretation........................13

v. RESULTSmDISCUSSIONOOOOOOOOOOOOOOOOOOOIOOOOOOZ‘

v1. SUGGESTIONSmmm"MOOOOOOOOOOOOOOOOOOCOO28

BIBLIOGRAPHYOOOOO...000.00.00.00..00...OOOOOOOOOOOCOOOOOOBO

I. INTRODUCTION

The determination of the lattice constants of the lithium isotopes
is directed towards testing and extending present theories in solid
state physics. The constants can also be used in determining the ideal
densities of the metals. The lithium isotopes six and seven were chosen
in view of their large relative mass difference (lhfi) and their avail-
ability in reasonably large amounts. Moreover. lithium has a simple
crystal structure (body-centered cubic) which makes the diffraction film
interpretation easy, and a simple electronic structure. which facilitates
theoretical analysis. For most purposes in solid state physics, the
difference in lattice constants is of greater interest than the precise
absolute value themselves. The problem is thus simplified. since
accurate absolute determination of lattice constants requires highly-
developed techniques and very precise control over the experimental

variables.

II. XrRAI DIFTRACTION

xrrays are electromagnetic radiations which lie between the ultra-
violet and gamma rays in the electromagnetic spectrum. The xpray region
itself is ordinarily taken to lie between 0.02 and 100.A. The rays'used
for diffraction work lie between 0.5 and 2.5L. Like visible light they
show themselves as having a dual nature. that is. they can behave like
waves or like particles. Xprays differ from visible light in that they
have a shorter wavelength and a larger photon energy. It is because
the wavelength of the xprays is of the order of magnitude of the unit
cell dimension that diffraction patterns occur. a crystalline material
acting much like a grating.

When the x-ray photon impinges on matter and approaches an electron.
the electron begins to vibrate owing to the periodically changing
electric field of the x—ray waves. When the electron accelerates. it
is itself a source of waves of the same wavelength. These waves radiate
from the electron. and we may then consider that the photon has been
deviated from the direction of the primary radiation. This process
is known as “coherent" scattering; it has taken place without a change
in wavelength.

When a plane wave of xerays than meets a row of equally-spaced
atoms. all atoms act as sources of scattered waves. All the electrons
in an atom act as wave sources. but the nucleue.because it has a mass
much greater than that of the electron. is not involved in the scatter-
ing phenomena. It is the constructive combination of all the waves
which results in the diffraction phenomena. The number of new waves
sent out depends on the number of electrons present. and thus the

intensity will be roughLy proportional to the atomic number.

III. POWDER CAMERA METHOD

The method of investigation of a polycrystalline metal is about
the same as for a powder. A source of nearly monochromatic x-rays is
led into a cylindrical camera where it is allowed to hit a cylindrical
sample. suspended and rotating at the center of the cylinder. The
diffracted rays then strike a photographic film which is placed on the
inside of the cylinder. As shown in ll'ig. l. the diffracted rays leave
the specimen in the form of a cone of semi-apex angle 29. whereQ is the
angle between the incident ray and the reflecting plans. By Dragg's
equation we have then that hh=2d$ih 9 ,
where ‘n 7- order of reflection

7s: wavelength of incident radiation
d: interplanar spacing
B: incident angle.
Now for a cubic crystal the interplanar spacing d. is related to the

lattice constant (1., by the relation

Q0
d =
hK‘l \'h1*K1*i‘l

where h,K,i are the Miller indices. For a body-centered lattice the

 

final relation is

 

hNJW‘s- K‘J'?
2 sin 9

where the form factor is such that the reflection vanishes unless the sum

o..=

K4401 is even. The cone of rays leaves the crystal and intersects the
cylindrical film along the generatrix of the cone and cylinder. The
angle 29 is determined by measuring the distance between symmetric

1‘etlections along the film axis. Now if the reflections do not lie on

 

 

 

 

 

 

 

 

   

2 3 4
_\V- [-r;_\ _ PM I-
L \ V r was I
FLUORESCENT
\ SCREEN
\
\ 4-
‘ /
\ /
TARGET \ k /
\\ \
l \ \ \ l/I’ // 3
\ 7’
| l 24> \\\\ ‘\ x, I /’\29
._._..'_ __—-—>—. .— —.’— %/——_—___L ______
X-RAYS I \ ‘~\
I \ ‘~\
\\ ‘~\\
COLLIMATOR \ ‘ z
\
\
\\

FILM

 

Fig. 1. Schematic diagram of x-ray powder camera .

the axis, the angle 9 must be found by a different means. In Fig. 2.

it is seen that

 

cos zo= C0$@COSO< . (1)
no... (3 3 Ti radians. (2)
TCLTHK-t %. (3)
Substituting (2) and (3) into (1).
cos 29: cos(;";) cos(tam" A) . (a)
Hence = i cos"[cos( 5%,) cos(ta1\‘-}_)] , (5)
Now n7~=2dsine,
, d- m. .
'- " zs'me (6)

Substitutinge from (5) into (6).

 

 

 

 

d: “R
2 sin[-'z— cos"{cos(y-’:_) cos(mn" an] .
Since d - ‘ 0,.
- 4.9+ KN i"
Q.= nx‘lh‘MC‘hl“

 

(
2 sin [1-2 cos"{cos(fi) cos(ton“ at)” .

This expression for 0.. must be used for any reflections which do not
lie on the film axis.

When the film is measured it is really 9 which is to be determined
by measuring linear distances. To find the change 8d as a result of a

change 83 . we differentiate Bragg's law:
dsf a 2..)-
n 9 2

dco'5686 + s'mGSd =0
j§+cot9 89=O
.'. Ead— :- ~COIe S9,

 

 

 

 

 

 

 

 

 

Fig. 2 . Determination of 29 from spots not
lying on the film axis.

or. % =— CDT. 0 89
for the cubic lattice. From this expression it is clear that the pre—
cision measurements are obtained for large values of G .
Tor precision determinations employing the powder camera there are
a number of sources of error. These are:
(1) effective camera radius uncertainty
(2) film shrinkage
(3) eccentricity of the specimen
(h) absorption
(5) vertical divergence of the beam .
A detailed discussion of each of these is given in Klug and
Alexander(6 )and need not be elaborated here. Under a later section

on "Film Interpretation” each factor will be considered when appropriate.

IV. EXPERIMENTAL PROCEDURES

Procurement of Samples

Prior to the development of production-type mass spectrographs at
the Oakzfiidge National Laboratory 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 l9h6 OBNL started a
program for the enrichment of all naturally-occurring stable isotOpes,
and by the end of that year had begun shipment of samples. At present
stable isotopes of the majority of 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
radioactive elements: the inert gases: certain of the rare earths;
and a few others.

The investigation of the lattice constants of separated isotopes
was one part of a broader program on the use of the isotopic mass as
a probe for study of the solid state. For the general study a metal
was desired. Lithium. with the natural isotopes Li-6 and Li-7 in
reasonable abundance ratio (Li-6. 7.52%: Li-7. 92.h8$), and the large
relative mes difference (Li-7 - Li—6)/ $(Li-7 + Li—6)= 14$. was an
obvious choice. Examination of the ORNL Catalog showed that both
isotopes were available in very 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 is an
alkali. and 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 outweighed the disadvantages of experimental difficulties.
When the present work was begun in 1955. electromagnetically—
separated isotopes were available for distribution only on loan as
approved by the‘U. 3. Atomic Energy Commission. Requests for loan
were made to the ABC by using Porm.LEC-100.* The requested amount of
lithium-6. the rarer isotope. was 500 milligrams: that of lithium-7.
the more common isot0pe. 1000 mg. with 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‘ell-College Research Grant.
Physics and.Astronomy No. #53. initially given to Dr. J. C. Lee for
the academic year 1954 - 1955. The samples were shipped from OakZBidge
Rational Laboratory on 19 May 1955. The analyses. as furnished by GRNL
were as follows:
Li:§ Lot No. FYijgbd) 53949;
Isotopic Analysis (mass number and atomic percent): 6. 95.7: 7. “.3.

SpectrOgraphic Analysis (element and weight percent. precisioni:100%):

A1 0.03 re 0.5 Ni 0.1
Ba < 0.05 K 0.03 Ni 0.3
Ca 0.2 Mg 0.02 Pb 0.06
Or 0.1 Mn 0.02 Sn 0.01
Cu 0.05 MO Oel

 

‘ The procedure in effect after 13 April 1956 is quite different. Loans
of isotopes may be obtained only under unusual conditions. and under a
complicated set of rules. Purchases may be made simply. by submitting two
completed Iorms.AlC-39l with the purchase order to the supplier. Dr. C. Pt
Keim. Director. Stable Isotopes. Research and Production Division. Oak
Ridge national Laboratory. Post Office Box I. 0ak:Ridge. Tennessee.

10

Li- Lot No. H668”) - not redistilled 1000 g
Isotopic Analysis (mass number and atomic percent): 6. 0.21‘ 0.1: 7. 99.8: 0.L

Spectrographic Analysis (element and weight percent. precision+100$):

A1 < 0.01T K < 0.01-P Pb 0.15
s. 0.25 Mg 0.5 Sn < 0.01
Ga 0.1 H! < 0.0103 Sr 1.0
01' < 0.015” H0 < 0.01 V < 0.01
Cu 0.15 Re 0.5 Zn < 0.5 T
1'0 0e]. 31 0001 (T " trace)

Unfortunately the concentration of impurities was considered to be too
high to allow meaningful results to be obtained. The impurities appear
to be introduced during the thermochemical reduction of LiCl to Li by
means of metallic Ba. in stainless steel containers. Dr. P. S. Baker.
who supervised the preparation of the lithium. suggested that vacuum
distillation would be the best method of purifying the metallic lithium.
and agreed to have his organization perform the distillation. at a
nominal service charge of $50 per sample. The material was accordingly
returned for purification about 22 July 1955. without any measurements
having been made on them.

The redistilled material was shipped from ORRL on 3 November 1955.
in approximately double the amounts 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 we were to
attempt further distillation. The new samples had the following analysis:
Li:§_ Lot No. 835‘s} - redistilled 1005 mg
Isotopic Analysis (mass number and atomic percent): 6. 96.1: 0.1: 7. 3.91:0.1.

Spectrographic Analysis (element and weight percent. precisiontSOfi):

A1 (0.01 T I < 0.02 T Pb < 0.02T
Ba < 0.02 T Mg 0.02 Si 4 0.05
Ga 0.05 Mn < 0.01 Sn < 0.01
Cr < 0.01 T 140 < 0.01 Sr < 0.01
Cu 0.01 Na 0.03 V < 0.02

11

Li-Z Lot No. 668 ”I - :edistilled 1028 g-t 1000 gs
Isotopic Analysis (mass number and atomic percent): 6. 0.23 0.1: 99.83: 0.1.

SpectrOgraphic Analysis (element and weight percent. precisioni’50fi):

Ag T r. 0.3 Ni 0.02
A1 0.02 x 0.02 Pb 0.01
Ba 0.01 Mg 0.02 Si < 0.05m
Ca 0.2 Mn < 0.01 Sn < 0.01
Cr 40.0w Mo < 0.01 s:- < 0.01
Cu 0.01 Na 0.02 v <0.01

With both isot0pe samples. the iron appears in very great amount
(Li-6. lb: 0.5%; 1.1-7. Fe=0.3%). It is believed that these high
amounts 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 in the lithium-7 (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.

The natural lithium was produced by the Lithium Corporation of
America. Minneapolis. It is their low—sodium grade. in the form of

BIB-inch diameter rods with the following specifications:

Na 0.005 73
K 0.01

Ca 0002

N 0.06
l'e 0.001 .

Mr. Ted Brown and Professor Max T. Ragers. of the Chemistry Depart-
ment of Michigan State University. kindly furnished the natural lithium

and the information on its specifications.

Preparation of Specimens

All the lithium samples were kept immersed in oil. Nevertheless.
they became coated with a dark layer. which was probably lithium nitride
to the greatest extent. The coating can be scraped off and the clean
metal obtained. provided that the fresh surface is protected by covering
it with a nonreactive substance.

Initially the lithium was extruded from a steel die in such a way
that paraffin oil or petrolatum (vaseline) coated the 0.2-mm dia.wire.
The short lenths of wire were then sealed in capillary tubes of wall
thickness 0.01 mm. It was necessary to seal the lithium since it reacts
readily with air to form lithium nitride (L138). lithium oxide (LizO).
lithium hydroxide (LiOH). and lithium carbonate (Lizcoa). Specimens
were then exposed after annealing at 100°C for one hour. or a long time
at room temperature. A few Specimens would give sharp reflections while
others would not. This was judged to be due to large grains in unfavor-
able orientations.

Specimens were then prepared in the same manner as above. but in
place of annealing they were immersed in oil and brought up to 186°C.
All the melted specimens gave sharp reflections. but breakage of tubes
in this way was quite considerable. Care must be taken when melting the
specimens to position them so that they solidify again in a cylindrical
form. Many specimens tended to resemble a twisted ribbon upon solid-
ification. Large grains were obtained in this way. and spots rather than

continuous lines resulted on the film.

13

Exposures__acnd Develpping

A 114.6-mm diameter camera was used on a Phillips diffraction unit
for all exposures. Copper radiation was used since this has a wave-
length for highest angle diffraction of cubic materials of the lattice con-
stant involved (12). All x-radiation of a particular wavelength is
accompanied by a continuous spectrum of wavelengths which tends to fog
the entire film. The characteristic radiation itself is composed of

K“ and K? . The intensity of K is comparable to K‘ and the reflections

(i
tend to overlap. so it is desirable to eliminate the Kawavelength.

This is accomplished by making use of the element which exhibits strong
absorption Just to the short-wavelength side of the K“ line of copper
(Z=29). Thus a filter of nickel (2= 28) was used for all the exposures.

The specimens were rotated during the exposures. which were for
about 22 hours at 35 kv and 20 ma. A Brown zit—hour temperature recorder.
reading to a Zl'ahrenheit degree. was set next to the unit.

Kodak No-screen x-ray film was used and developing was done in a
Spectrographic developer. Recommended developing and fixing times were
followed.

Film Interpretaptaigg

It is now necessary to consider the sources of error in the powder

camera method listed previously. The 110.6-mm dia.camera employs the

asymmetric (Straumanis) method of film position as shown in Fig. 3.

The camera dimensions are such that 1 mm distance on the film axis
0..

 

 

 

 

 

 

1h
is equivalent to an angle of 1°. This film position consequently enables

one to correct for uniform shrinkage without the use of fiducial marks.

The eccentricity of the sample is reduced to the vanishing point.
it is believed. by means of a precise centering arrangement.

It has been seen that high Bragg angles tend to give the most pre-
cise measurements. Therefore only those reflections above 60c’wsre
used. It is important to get at least one reflection above 80°.

Since lithium (2:3) has low absorbing power and the lines in the
backhreflection area were used. the absorption factor is not large.
Thrther reduction of this source of error is obtained by making the
specimen diameter small.

The factor of vertical divergence of the beam can be ignored since
the slit was small.

All films were measured on a Gaertner linear optical comparator
which could be read to 0.001 mm. The necessary accuracy for the
measurements was 0.01 mm.

As previously mentioned the specimens were melted before exposure.
Large crystalline regions were formed which gave rise to symmetrical
spots on the film instead of continuous rings. A typical film is shown
in rig. L». Fig. 5 shows the effect that a 0.6-mm dia, specimen has on the
size of the reflections. Under magnification the diffuse spots disappear
into the grainy emulsion of the film. Because of this. the Spots were
pin pricked under low magnification to obtain well—defined measuring
points.

With slow cooling of the lithium during specimen preparation. preferred
orientation of the grains was present and subsequently would alter the
intensity of some reflections. Since at high angles the intensity is

less. in many cases a reflection would be completely absent.

{—.___.,7i,, ___x.___

 

Fig. 4. Typical film taken
with a 0.2-mm dia.
specimen.

 

 

 

 

 

Fig. 5. Film showing effect
of a 0.6 mm dia. specimen
on spot size.

15

16

When the films are measured and lattice constants determined. it
is necessary to use an extrapolation function of some kind. since the
lattice values will decrease for smaller values of9 . Optimum results
are obtained if certain conditions are fulfilled. If a thin specimen
is used. the absorbing power is small and the slope of a plot of lattice
constants versus an extrapolation function will be minimised. A
reflection at least7’80o will fix the one end of the plot with a high
degree of accuracy. .A linear relationship which holds for low angles
would also be desirable.

When the eccentricity error is negligible. it has been found that the

| cos-{‘0 cos-{‘6

lattice constants versus —2 m + __e._—)(13) is linear between
9:. 30°to 90°. This linearity to 6=~30° would seem important for crystals
of high symmetry since the number of reflections for 6760°are few.
In these determinations however. it seemed that these low angle
reflections should be given such little weight that only values where
0>603were employed.

0n the following pages data from a typical film are shown. The
specimen was the lithium-6 isotope. from a lot obtained for a different

purpose."I The first measurements were to determine the film shrinkage.

(See Fig. 6).

 

 

 

 

 

 

 

 

 

i“ 4’ 4’ «15'
L e .1

Fig. 6.

 

 

 

‘ Lot 5550:). L1-6. 99.3: 0.2%: 1.1—7. 0.7: 0.2g.
Chief Impurities: Ga. 0.25%; r.. 0.05%; zn,<0.25$.

17

Spot 1 Spot 2 Spot 3
(1) 5.1954 mm —. 51.0290 mm r—v 150.7350 mm
(2) 5.1955 51.0284 150.4338
(3) 5.1910 51.0308 150.4336
(4) 5.1946 51.0270 150.7353
(5) 5.1955 51.0268 150.7326

 

 

mean I 5.1944 mean = 51.0284 mean = 150.7341
Because the maximum range on the comparator was 200 mm it was

necessary to reposition the film to take the rest of the measurements.

Spot 3 Spot 4 Spot 5 Spot 6
(1) 6.5280 ——- 7.0452 +120.4648 —. 120.9800
(2) 6.5365 —» 7.0432 120.4661 —. 120.9780
(3) 6.5305 —» 7.0475 120.4698—i.120.9779
(4) 6.5355 —" 7.0453 120.4641 —~ 120.9770
(5) 6.529o——l-> 7._0422 120.4656 _, 120.9793

 

 

mean=6.5299 mean=7.0447 mean=120.466l mean2120.9784
Thus we see that
A¢51.0284 - 5.1944=45.8340
33150.7341 - 51.0284299.7057
08120.9784 - 6.5299=114.4485
D=120.4661 - 7.0447=113.4214.
Now m-§(A+c)+s
=%(16o.2825)+99.7057
=80.l412+99.7057
E=179.85 mm.
Hence the film has shrunk 0.15 mm. All measured linear distances
must then be multiplied by 180.00/179.85 to correct for the film

shrinkage during development.

18

Since the (400) reflection was used in this determination. we
shall work with these values first. As seen in Fig. 6. the (400)

reflections happen to fall on the film axis. Thus. correcting for

shrinkage :

c .-. (130-001 314.4485) _ .
179.85 - (1 0008) (114.45)

C = 114.54 mm
D: (1.0008) (113.42)
B: 113.51 mm.
The d. wavelength is shorter thanatz: consequently the linear distances.
of the reflections for at. are larger. Thus we let
44).: 114.54.
44"..” 1113-51.
where 40*3600- 49;

49.: 360.00 - 114.54 49.: 360.00 - 113.51
= 245-46 = 246.49
0,: 61.365° ' 0,1: 61.62°
31110.: 0.877690 81n91=0.879815.

The expression for 0.. in this instance is
nle “1*K1+l‘l
2 sine '
ror the (400) reflection. \lh"+ (+1“ -.- 4.00000;
Cu Kg“: 1.5405“

 

2

Cu K“:- 1. 544331 .

19

Thus we now get

6:3 ‘61:

1. 40 0 4.00000

Q ._. Q _ (1.54433) (4.00000)
° 2( .877690 "' 2( .879815

Q.‘ 3.51041 Cu K... (400) 0.: 3.51061 Cu xdz.(400),

The measurements of the (411. 330) reflection are now considered.

b——A

 

8—.-

 

 

 

 

 

 

 

a 2 3 4
36 O |
I n
(4u.eeo) C) (40.330)
Fig. 7.
Spot 1 Spot 2 Spot 3 Spot 4

(1) 63.3483 —. 64.0162 -7 148.2478 —,- 148.8977
(2) 63. 3445—:- 64.0143 148.2461T 148.8950

(3) 63.3461—-- 64.0145 148.2448T 128.8962
(4) 63.3449—o-64.0135 148.2440—.148.8950

 

(5) 63.3463 ——» 64.0162 148.2439 _. 148.8985
L F

 

mean: 63. 3460 mean=64.0149 mean=l48.2453 mean=148.8965
Following the same procedure as above. we get
q... 3.5100 A Cu K... (411, 330)
Q...- 3.5109 A Cu K“ (411. 330).
The (420) reflection for this film did not lie on the film axis. so

this calculation is more lengthy. Consider Fig. 8.

 

 

A

“*1
I2 34
i‘. H

e
VLF—.426 147.0

C

 

 

 

 

 

 

Fig. 8.

Spot 1 Spot 2 Spot 3 Spot 4
(1) 48.6491—v 50.0866 V9139” —- 92.8412
(2) 48.6500—- 50.0851 91.3933 —' 92.8408
(3) 48.6465—-- 50.0861 91.3943 —. 92.8400
(4) 48.6512—- 50.0890 91.3968—- 92.8432
(5) 48.64827» 50.0866 91.3975 -—-' 92.8402

means-48.6490 mean=50.0867 mean-=91. 3954 mean:92.84ll

Spot 5 Spot 6
(1) 90.2448 - 95.0012
(2) 90.2453 95.0015
(3) 90.:&2_ 95.0007

 

mean=90.2449 mean=95.0011 _
Correcting for film shrinkage we get.
A= 44.22 mm
B= 41.34 mm
C= 4.76 mm.

Referring to rig. 2. we can let As 2:. . 13-21:. . and CaZy. where again

20

21

the subscript "1" is reserved for the O(. wavelength. Thus. 11‘: 22.11.

:12: 20.67. and ya 2.38.

From equation (7) we can now find 4a and $1.

45‘: g cos"[cos ( Egg—$715) cos(10.fi‘ éfifl
= g cos"[ (.05 (.3859) cos,(ton"(.0415))]
= 3003‘}. 926460) (05 (.0415)]

§co6|k.926460) (.9991393
icos"(.925662)

‘i’ ‘ (03880)
.1940 radians

‘h
9. = (1.5708 - .1940) radians

: 1.3768 radians
= (1.3768) (57.296)°
9,: 78.885°.
Similarly. we find that $2: .1815 radians and 91:79.65.
The values of (1. are found to be
q,= 3.5105 Cu K,“ (420)
(1.: 3.5109 Cu K‘zwzo) ,
The results are summarized in Table I. All values of the extrapolation

function were obtained from Nelson and Riley. On the extrapolation

 

 

 

 

 

Table I. j
8 a. h.K,L c°s°°+ “"9
61 . 365 3 . 5104 400 o. 238
61.62 3.5106 400 0.234
68.595 3. 5100 411.330 0.127
68. 925 3 .5109 411 .330 0. 123
78.885 3.5105 420 0.32
79.60 3.5109 420 0.28

curve (Fig. 9) the line of best fit was determined by the method of

22

least squares. After the extrapolated value was found it was necessary
to correct for thermal expansion. For lithium. a change of 1°C during
the exposure amounts to a linear expansion of 0.00016). at room tempera—

ture.

V. RESULTS AND DISCUSSION

While the analysis for the lithium-6 isotope given previously is
that for sample 5(a). only results for sample 5(b) (the analysis of
which is on page 16) will be given. Measurements were first taken
using the 5(b) sample since more of this sample was obtainable. Unp
fortunately time did not permit measurements to be taken using sample
5(a). However. the analyses do show how distillation reduced the amount
of impurities in the metal.

.Analysis of the experimental data gives the following results for
the lattice constants of the samples of lithiumeé (sample 5-b) and
lithiump7 (sample 668$). corrected to ZOG’C, but not corrected for
impurities:

Li-7 3.5097 A»

The results for lithium-7 have the greatest reliability. since they
were obtained from several films. The results for lithiump6 were
obtained from several films. but showed the highest scatter for values
obtained from different reflections. Since the isotopic concentration
of natural lithium is 92.5 percent Li-7. and that of our sample of
lithium-7 is 99.8 percent Li-7. we believe that our value for this
isotope is our best estimate for the absolute value for natural lithium.
From the analyses furnished by the suppliers of the samples. it
is possible to correct the lattice constants to those for the pure
material. if a generalized Vegard's Law is accepted. This law says
that the lattice constant of a binary mixture forming a solid solution
is a linear function of the molecular fractions of the components.
For the small amount of impurities present (less than 0.25 per cent)

Jhx:
it is likely that a solid solution is formed. What isnlikely is

25

that the law is obeyed: almost all binary alloys violate it to some
degree or other. and there are several serious exceptions. namely.
copper-manganese and silver-gold. In these cases minima in lattice
constant as a function of composition exist. Nonetheless. we have no
better guide. and in all probability the generalized Vegard's Law
leads to an upper limit of error. Moreover. the corrections are found
to be smaller than the other uncertainties. The new values. obtained
from the amounts of impurities and from their lattice constants. and
taking into account experimental errors. are:

1.1-6 3.5107 1’ .0010
1.1-? 3.5092 1!". .0007

One film of the natural lithium sample was measured. The value
of a¢,obtained for this sample. corrected to 20°C but not corrected
for impurities) was 3.5111A. Correcting for impurities so is found to
be 3.5110A. This result shall be discounted since only one film was
measured.

we are now able to calculate the density for lithhwn-7. For the
bodybcentered cubic structure there are two atoms per cell. If we
multiply this number by the mass of each atom. the mass of a unit cell
is obtained. The mass of each atom is given by uln. where M is the
atomic weight of lithium-7 and R is Avogadro's number. Since the mass
can be written as age . we have

M

3
N=Q°€
.3...

where e is the density.

Now

e g 2(mmso) _
(c. .0241 x 1o‘313.so 9?. mos)3
3

:, e = 0.539l gmcm’

The predicted value for the density of lithium-7, using the experimentally
obtained value for so, is .5391 an cat-.3

To gain an idea of the validity of the absolute value of the
constants. we cite the results of the other modern determinations for

natural lithium:

Aruja and Perlitz (10) 1940 3.5090 A
Lonsdale and Hume-Rothsry (11) 1945 3.5094 A
Pearson (14) 1954 3.5087 A
(Present investigator Li-7 1956 3.5092 A)

The samples of Aruja and Perlitz were commercial lithium. of unknown
purity: moreover. their extrapolation procedure has been criticized by
Lonsdale and Hume-Bothery. and we believe that their value is too low.
On the other hand. the samples of Lonsdale and Hume-Rothsry may have
contained sodium. according to Pearson, and are too high. But Pearson's
data upon direct examination. appear to lead to a slightly higher value
than he cites: perhaps 3.5090 A. Pearson's samples. however. are by
far the purest used. In any event. the agreement is well within the
experimental uncertainties of the various investigators.

At the present stage of investigation. we can conclude the following:
The lattice constant for lithium-6 appears to be higher than lithium-7
fractionally by 4X10“: but the. experimental uncertainty is such that
they may be identical. Lithium—6 is not more than 10x 10." larger than
lithium-7. while lithium-7 is not more than 0.5x 10.» larger than lithium-

6.

27

So far as theory is concerned. there is no adequate model to des-
cribe the effect under investigation. Theory on the basis of an Einstein
or Debye model predicts that lithium-6 is larger fractionally by about
3s 10"}; Gr'Lg-neisen - Mie theory predicts 4% 10.4.. The precision of
our measurements is not better than 51ledr. Hence no inconsistency

has been shown.

Similar results have been obtained for L18 1" and L11 1' 9by Thewlis(l5).
The greater scattering power of this crystal makes high precision more
readily obtainable. and Thewlis reports that the compound with the

lighter isotope has a larger lattice constant by the fractional difference
2)t10~¥. whereas London (referred to by Thewlis. loc. cit.) has calculated

4%
the value 3.31.10 e

VI. SUGGESTIONS FOR FUTURE WORK

Impurities must be reduced to be sure that the absolute values are
precise. With lithium it appears that only repeated vacuum distillation.
in a metal still will produce a sample of adequate purity. The effects
of nonuniform film shrinkage could be eliminated. by using a camera
with a set of fiducial marks. The temperature must be known and it
should be held constant. If the temperature varies a few degrees the
fourth place in the lattice constant is affected. Even a few tenths
of a degree variation will affect the fifth place. It was found that
two films taken with the sample would vary in their reflections; that
is. the spots would be smeared out and more diffuse. This was probably
caused by a large temperature variation. It is also true that the
higher the temperature. the weaker the diffracted intensities. It would
seem desirable then to work at low temperatures. Thus. for high angles
the decrease in intensity is minimized by decreasing the thermal agitation
in the lattice.

Since there are so few reflections in the high angle region.
possibility of not using the filter was investigated. If this could be
done the exposure time would be reduced as well as getting more re-
flections to work with. It was found however. that the general fogging
was much more intense and the@ reflections were barely distinguishable.

While the control of the temperature during exposures is necessary.
the control of the temperature and humidity during film measurements
is also important. The light source should be fluorescent so that heat
is not a disturbing factor. The film base will also suffer dimensional
variations with the humidity.

A serious difficulty can arise in the case of the xpray film. To

29

increase the sensitivity of the film. both sides have a layer of silver
bromide. This is characteristic of the Kodak ”No-Screen“ x-ray film.
These images will be superimposed when the x-rays are normal to the film.
that is. for reflections along the "equatorial axis". However. when

the reflections are off axis. such as we have in some cases, the center
is shifted slightly. It would be desirable then to use a film with a
single layer of emulsion.

The absorption of x-rays increases with grain size in the emulsion.
so if the films are measured with a magnification which is too great.
the weak lines are lost in the background. If the lines are sharp
enough. one might consider the possibility of using a microphotemeter.
Also. since the intensities ofd. to dzis about 2: 1. it is probable
that measurements using ck. should be more accurate.

Finally isotopes of elements other than lithium are available in
quantities large enough for lattice constant determination. Many of
them are less inclement to the experimenter than lithium. because of

their lower chemical reactivity and their higher scattering power.

29

BIBLIOGRAPHY

Book references:

1.

2.

3.

4.

6.

7.

8.

9.

Charles S. Barrett, Structure 2;,Metals. (Mc Grew-Hill Book Company,
Inc.. New York. 1952).

M. J. Buerger..x-ray 052stallographz. (John Wiley and Sons. Inc..
New York. 1942).

George L. Clark:. Applifi X-rays. (Mc Grew-Hill Book Company. Inc..
New York. 1955).

Andre Guinier. X—ra ngstalloggaphig Technology. (Hilger and Watts
Ltd.. London. 1952).

Clifford Am Hampel. Rare Metals Handbook. (Reinhold Publishing
Corporation. New York. 1954).

H. P. Klug and L. 3. Alexander. X-ra Diffraction Procedures. (John
Wiley and Sons. Inc.. New York. 1954 .

H. S. Peiser. H. P. Rooksby. and A. J. C. Wilson. Xeray Diffraction
_y,Pol cr stalline Materials, (The Institute of Physics. London.
1955). .

Stable Isotopes Research and Production Division. In enter {fig
ElectroggggeticallyeEnriched Isotopes. (Oak Ridge Regional .-
Laboratory. Oak.Ridge. Tennessee, 1950; revised February. 1955).

\\
Stable Isotopes Research.and.Production Division..lnventogz gag
Price List of Electropggnetically-Enriched_ and Other Stable»
Isotopes. “(Oaszidge Rational Laboratory. Oaszidge, Tennessee,
April 1956). g

\

Journal references:

10.
11.
12.
13.
14.

15.

1:. Aruja and H. Perlitz. Phil. Mag. 39. 55 (1940).

I. Lonsdale and W. Hume-Rothsry. Phil. Mag..1§ (7). 799 (1945).
L. Muldawer and R. Peder, Rev. Sci. Instru. 26 (9). 827 (1955).
J. H. Nelson and D. P. Riley. Proc. Phys. Soc. (London)'§z, 160 (1945).
w. 3. Pearson. Can. J. Phys. 33. 708 (1954).

J. Thewlis. Acta Cryst. 8.‘3§ (1955).

PHYSICS-MA r‘

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