The self-diffusion of alpha-uranium

JOLTRNAL OF NUCLEAR

RETRIALS

5, No.

1 (1962) 5-11,

AORTA-HOL~,A~D

PUBLISHING

CO.,

AMSTERDA~~

THE SELF-DIFFUSION OF ALPHA-URANIUM i_

Received

25 April 1961

I)glool = I,8 X 10-l* cmZ/sec DLO~O~ = 0,72 x lo-l4 cm+ee Dlanll = 0,66 x IO-l* cmz/sec

The self-diffusion coefficient of alpha-~~iurn was measured as a function of erysta~lo~aphic direction at, 640’ C, using the decrease in surface activity method. The average of two measurements made in each direction are:

L’anisotropie de diffusion est loin importante qu’on 18 pr&oyait. -_

D[IOO~= 1.8 x lo-l4 cmz/sec L)fol~l = 0.72 x lo-14 cmz/sec z)lo~ll = 0.66 x IO-14 cmz/sec

d’&re

aussi

Der Selbst-Diff~ions-Koeffizient VOXI Alpha-Uran wurde ala Funktion der ~istalIo~fisch8n Richtungen bei 640” C gemessen. Benutzt wurde die Method% der Abnahme der ~~~~ehenaktivi~t. Die D~o~schnittswerte von 2 illessungen in jeder Richtung sind:

The anisotropy in diffusion is not nearly so large as had been anticipated.

L)[IOOI= 1.8 X lo-14 cmz/sec Le coe~aient d’autodi~sion de ~ur~ium a Bt,B D~ol~l = 0.72 X lo-l4 cmafsee mesure & 640’ C pour diff&entes directions cristalfoDfwrl = 0.66 X IO-l4 cm*jsec graphiques en utilisant la mdthode de d&roissanee de Die Anisotropie der Diffusion iat nieht upheld l’activitci supe~cielle. Pour chaque direction, la so gross, wie angenommen wurde. moyenne de deux mesures est

1,

Introduc~on

Because of the value of the data to both theory and practice, measurements were undertaken of the self-vision coe~cients in the three principal directions in alpha-uranium single crystals.

Alpha-uranium exhibits marked anisotropy in its physical and mechanical properties which is a result of its exceedingly asymmet~~al o~horhombic lattice structure, determined by Jacobs and Warren 1) and shown by Tucker 2) to consist of widely spaced corrugated planes of relatively close-packed atoms. It might be expected that the self-elusion coe~cients would also vary with direction in alpha-uranium crystals. For example, if diffusion occurred by a simple vacancy mechanism, the rate of diffusion within the corrugated planes of close-packed atoms might be quite different from that pe~endi~ular to these planes. Such anisotropy of diffusion might be related to the anisotropic growth of alphaura~um single crystals in a reactor flux 3). t This work was supported AT (30-l) 2102.

by the Atomic

2. Preliminary Considera~ons and Experimental Details Since alpha-uranium is unstable at temperatures above 667” C 4) the measurement of the diffusion ~oe~cients is limited to relatively low tem~ratures. The order of magnitude of the self-di~usion coe~cients at a temperature just below the alpha-beta transformation temperature was estimated by conducting a preliminary experiment in which a thin film of gold was deposited on a cathodie~ly cleaned disc of polycrystalline uranium, 2.5 cm in diameter by

Energy Commission, 5

Division

of Research, under Contracts

R. RESNICK

6 about

0.6 cm thick.

SEIGLE

for two

the specimen being the cathode, causes a current flow of 15 to 30 mA during sputtering. Reversing

layers

the

successively

annealing

L. L.

months in an evacuated quartz capsule at 640” C, approximately

After

AND

1 x 1O-4 cm

thick

were

ground from the specimen surface.

The thickness of each layer was calculated from the weight loss of the disc after grinding the grindings analyzed

for gold. From the data obtained, coefficient

of gold in uranium

to be 2.3 x lo-l4 self-diffusion

and

spectra-photometrically

cm2/sec,

the diffusion

was calculated

indicating

that the

coefficients in alpha-uranium

were

probably no larger than lo-l4 cms/sec. This is an extremely low value for experimental measurement by most techniques. For example, a radio tracer deposited on the surface would penetrate only 0.0025 cm in two months. This low diffusion rate, in combination with the high toxicity of U233 isotope chosen as a tracer, led to a decision to employ a decrease in surface activity method for determining the self-diffusion coefficients rather than one of the more commonly employed sectioning techniques. The diffusion specimens were fabricated from small single crystals of alpha-uranium, one of

polarity

several

times

during

the

early

st’ages of sputtering helped to remove adsorbed gases from the walls of the system. Following

the

sputtering

chamber was evacuated

operation,

the

to a pressure of about

5 x 10m6mm Hg and the U233 evaporated from the tungsten filament which is now heated by an ac power supply. The evaporation usually proceeded for a few minutes, at which time the filaments burned out. Very thin, adherent deposits ranging from 1 x 10-5 to 3 x 10-S cm in thickness were obtained. The diffusion specimens were then sealed in evacuated quartz capsules and annealed at 640” C for periods varying between 41 and 74 days. All procedures which involved handling of the U233 alloy were carried out in a dust-tight glove box maintained under a negative pressure by a filtered exhaust system. The high toxicity of U233 requires that exceptional care be taken WATER

which was supplied by the Argonne National Laboratory, and the rest grown by the graincoarsening method of Fisher 5) from high-purity also furnished by Argonne. The uranium.

~I/B”O.D 55/50

KOVAR TUBE JOINT

crystals were oriented on a two-cricle goniometer and a flat surface ground normal to one of the crystallographic directions. This followed by electropolishing to remove

was the

deformed surface layer. A thin film of an alloy of 5 y0 u233 in natural uranium was evaporated onto the ground surface using an apparatus patterned after one described by Davis 6) and shown schematically in fig. 1. A two-stage operation is involved ; the first being cathodic sputtering of the single crystal in order to remove any traces of surface oxides, and the second being evaporation of the isotope. During sputtering, a slow flow of deoxidized and dried argon is passed through the chamber. the pressure being maintained between 15 to 50 microns of Hg, as measured with a thermocouple gauge. A dc voltage of 2-3 kilovolts applied across the specimen and the tungsten filament,

COPPER COUPLING

I”DIA. x I/4”THIC COPPER POT

_~

118”O.O

COPPER TUBING TO VACUUM

COPPER

CLIPS

-

/-=

ARGiJN

MOLYBDENUM

COUPLING

TO METAL

Fig. 1.

SEAL

Schematic diagram of sputtering-evapolittic,rl apparatus.

THE

during

all handling

tamination 3.

operations

to avoid

OF

con-

the

penetration

of the Diffusion

diffusion

anneals,

the diffusion

conditions

Coefficients the

depth

the residual alpha activity

the specimen surface. The surface activity determined

by

an

autoradiographic

at was

method

foil interposed between the emulsion and the surface. An identical pair of exposures were made of the surface of a bulk sample of the 5 o/o Paa alloy used to form the original deposit. The sequence of exposures is illustrated schematically in fig. 2. The surface activity of each specimen was then determined by counting the number of alpha particle tracks in the emulsion using a Zeiss petrographic microscope fitted with a dark field condenser and having an optical grid set in the eyepiece. The procedure for computing

EMULSION

Fig.

Cdl

2.

Schematic

representation

emulsion exposures. is exposed

standard

without the foil; anneal is exposed diffusion

of nuclear

track

(a) a standard alloy of 5 O! U233

to the emulsion with the foil interposed;

(b) the same

couple

is exposed

to the emulsion

(c) the diffusion couple after diffusion with the foil interposed; after

diffusion

without

anneal

the foil.

for

is

where D is the self-diffusion concentration

(1) coefficient,

Q is the

of isotope times the thickness of

the initial deposit, and C is the surface concentration at time t. The four nuclear track exposures illustrated in fig. 2 are used to calculate Q and C. Q is evaluated from exposures 5(b) and 5(d) as follows: It is assumed to begin with that the average percentage of Uaaa in the diffusion zone is equal to 5 xC~+J&, where Csb is the track density measured on exposure 5(d), and Cub is the track density measured on exposure 5(b). This implies that the U2aa in the diffusion couple is uniformly distributed over the diffusion zone. Since this is obviously not the case, the value of Q obtained is clearly an approximation. The approximation, however, does permit the calculation of a diffusion coefficient which can then be used to obtain a more accurate Q and in turn a more accurate D, as explained further on. The range, R,, of alpha particles in uranium can be calculated from the Bragg-Kleeman relation ‘) : lo--JR,?

s

= 8.56x 10-d cm

(2)

R, in this equation is the range of Uzaa alpha radiation in air, I+J~ is the square root of the

(bl

(Cl

equation

DE---nt c2

RB=3.19x ‘NTA

from the alpha track

Q2

of

using Eastman Kodak type NTA nuclear track emulsions, which are sensitive to alpha particles, as the radiation detector. Two exposures were made on each couple ; of approximately 1 minute duration with the emulsion in direct contact with the specimen surface, and of one-half hour’s duration with an 0.009 mm thick nickel

(01

coefficients

set up in this experiment

of the deposited U2aa was measured

by determining

7

ALPHA-URANIUM

densities is as follows: The solution to the diffusion

of the surroundings.

Calculation After

SELF-DIFFUSION

(d) the

is exposed

atomic weight and cl, the density of alpha uranium. The estimated percentage of Uzaa in the diffusion zone is used to determine the thickness of the initial deposit, t= R, Csb/Cub assuming all of the Uzas lies within the depth R, from the surface. Q is then equal to

Cst,xRsxo.gs

c ub

gr/cm2.

The surface concentration after diffusion is evaluated from exposures 5(a) and 5(c). The nickel foil between the photographic emulsion

8

R.

and the specimen alpha radiation. from

RESNICK

AND

emitted

a narrow zone at the specimen

surface

sufKcient

uranium

L.

energy

to penetrate

after

leaving

the

the foil and enter the

emulsion.

The depth of this surface zone was

calculated

to be 1.32 x IO-4 cm by the use of cub

exposures 5(a) and 5(b). It is required that this depth

be

SEIGLE

serves as a barrier to the Only those particles

possess

L.

shallow

relative

to

diffusion so that the concentration

the

depth

z=

of

measured is

representative of the surface concentration. The surface concentration C = 0.95C,t/C,t gr/cms, where C,r is the track density measured on exposure 5(c), and C,n is that measured on exposure 5(a). Substituting the quantities & and C in eq. (l), we get:

for

0

Q4Rs ~~P~Rs-a)ila 0

where @

. e-d’i4Dt

ys = ---iGF-

is the number of emitting ~enters~~n~3 in the diffusion couple, and where yu = constant, is the number of emitting centers/cm3 in the standard alloy, Thus,

(3) The value of D computed from eq. (3) is only a first approximation due to the assumption of a uniform distribution of isotope in the diffusion zone but may be used to obtain a more accurate D by allowing for the variation of Uzaa concentration

with distance,

as follows:

cub -zz

c sb

& ,s” e-dx14Dt(Rs - df 6d

C ub

-zz c sb A

-&

ZDt(e-Rs’/4Dt- l)+ R, 7 e-d’/4Dt Sd 0

‘%b

Ad

The fraction of the total number of alpha particles emitted by the particle of uranium, P, at depth, d, which reach the surface is

F=

I-

co9 2

0

=+(1-g

The number of alphas reaching the surface per unit time from the layer Ad in thickness at depth d equals AC= aFyAd per unit area. y =number of emitting centers per ems, and cy=rate of alpha emission of Uam.

RR2~11

Rs2yu

1

.

Substituting the approximate value of D into eq. (4), a new value of & is obtained which can be used in eqs. (1) to (3) to calculate a second approximation to D, etc. The numerical values indicated that the third approximation was suitably precise. 4.

Results and Discussion

The measurements of the self-diffusion coeflicients were made twice in each of the three crystallographic directions, using different annealing times, The counting data are presented in table 1. The diffusion coefficients~ including

THE

TABLE

sk pecimen

Time of diffusion anneal

count,s~unit area/second exposure time

(days)

Cs,,

Csf

46 48 74 41 44 55

0.1276 0.0523 0.1390 0.0410 0.0411 0.0089

0.0014 0.0009 0.0017 0.0008 0.0006 0.0002

TABLE

Time of diffusion anneal

;

Cub

1

of

&f

0.0343 0.0525 0.0343 0.0441 0.0343 0.0473

coefficients

2

material

8.8 x lo-13

650’ C. There

and reports

a value

and 2.8x lo-12 om2/sec at

is su~oient

all the values presently

2

Corrected self-diffusion

Specimen

between

d&a

9

ALPHA-URANIUM

polycrystalline

1

Nuclear track counting /

OF

SELF-DIFFUSION

reported

measured

agreement to indicate

values

between that

are correct

the

to at

least an order of magnitude. 5.

Investigation The

counting

calculated

using

of Errors errors the

in Cut, and method

6&b

described

were by

Yagoda 7) to be 10 ye, and the error in C,r and G’!,f5 %. Since R, is obtained from the empirical Bragg-Kleeman relation, eq. (2), the error in this value is not known. Assuming it is no more than 10 %, the error in the relative value of the self-diffusion coefficients could be 80 y@ from these sources alone. Other sources of error may be present in the experiment which are much more di~eult to appraise. These are (a) the possible existence of

(days)

the values of each successive approximation, are given in table 2. Although there may appear

substructure in the single crystals, and (b) the presence of a diffusion-inhibiting layer at the interface between the crystals and the deposited layer of isotope. If the single crystals which served as the diffusion medium contained subboundaries, or if these had formed during the diffusion anneal, it is conceivable that diffusion could have taken place along such boundaries. Secondly, if a very thin layer of oxide were formed at the interface

to be a paucity of data, it should be understood that each measurement represents an extraordinary amount of time and effort. Contrary to

between the base crystal and the evaporated layer of isotope, in spite of the extra care taken during the preparation of the diffusion couples,

expectations, no marked anisotropy of diffusion is indicated by the results. The small difIerences found are easily within the experimental error of the measurements, as will be shown in the next section. The results are in general agreement with the value of D=2.3 x IO-14 cm@/sec measured for the diffusion of gold in polycrystal uranium by the standard sectioning technique. Kidson *), at Chalk River, Canada, has made a number of measurements on very coarsegrained polyorystals at 047’ C and reports D values between 1.5 and 3.2 x IO-13 cm‘Qec. Adda 9) of the French Atomic Energy Installation at Saclay, has also made measurements on

then the diffusion coefficients measured might be that of uranium through a uranium oxide, instead of self-diffusion in metallic uranium. In order to check the first possibility, a back reflection Laue X-ray photogram was taken on the [OlO] crystal after diffusion. This was compared with a photogram taken on the same crystal before fabrication of the diffusion couple for evidence of polygonization. The examination revealed that the spots were single and remained so after diffusion. Fig. 3(a) is the X-ray pattern taken before diffusion and 3(b) after diffusion. However, Jaumot and Smith 10) have found evidence of abnormal diffusion in zinc at low

11001 [lOOI PlOl PlOl 10011 10011

46 48 74 41 44 66

2.9 2.7 1.5 1.5 2.0 0.91

2.2 2.0 0.97 0.80 1.2 0.43

1.9 1.7 0.80 0.64 0.96 0.35

10

R.

RESNICK

AND

L.

L.

SEIGLE

original

surface

interface

could

to such

approach

involved

an extent

not be observed.

the

measuring the self-diffusion

of gamma-uranium and comparing

that

The second

by the described

the measured

technique

diffusion

coeffi-

cients with those obtained by other investigators using standard

sectioning

measurements

in

the

techniques.

gamma

Several

phase

agreed

reasonably well with those of other investigations 11J2J3 ) as shown in fig. 4. It may therefore be concluded that a serious diffusion-inhibiting barrier does not exist, at least not one which is effective at higher temperatures.

(4

6.

Conclusions

Although the precision of these measurements is probably not high, a marked diffusional anisotropy does not appear to exist in alphauranium. Variations larger than the 5 y0 to 10 y0 found by other investigators l”J4J5) in

w

\X

O\

04 Fig.

3.

(a) Laue

back-reflect,ion

\

X-ray

patt,ern of

‘X

01

[OIO] crystal before fabrication of the diffusion couple; (b) [OlO] crystal after diffusion.

temperatures in single crystals which exhibited sharp Laue spots. Hence, the absence of gross substructure is no guarantee that imperfections have not influenced the diffusion rates. This is a very difficult issue to resolve. Two approaches were taken to check the second possible experimental defect, i.e., the formation of a diffusion-inhibiting oxide layer. One consisted of fabricating diffusion couples from polycrystalline uranium with a natural uranium deposit using the identical technique to that for the U-U233 couples. These natural uranium couples could eventually be taken outside the dryboxes for metallographic examination. Unfortunately, the process of metallosranhic mountinn and nolishing marred the

\

Cl

‘x n

\

\ A\

okm2/sec

‘x

0’ \

q\

Id’

X\

III 0-BOCHVAR &..& X -ADDA AND KIRIALENKO 13) A-ROTHMAN et O-PRESENT

0 Fig. 4.

8 7.4

Summary

I

7.8

INVESTIGATION

I

I

8.2 8.6 I/T°KxlO*

of self-diffusion gamma

12’

uranium.

I

9.0

measurements

on

THE

cadmium

SELF-DIFFUSION

and zinc could easily be present, but

order of magnitude differences are not indicated. It appears that the diffusion rate in the [loo] direction

is somewhat

higher

than the other

two, but this difference is barely large enough to be outside of the possible limits of error of the method.

OF

References 1) C. W. Jacobs and B. E. Warren, Jnl. A.C.S. 59 (1937)

2588

2) C. W. Tucker, Jr., Trans. ASM 42 (1950) 762 3) L. L. Seigle and A. J. Opinsky, Nuclear Science and Engineering 5)

E.

S. Fisher, Trans. AIME

6)

W.

D. Davis,

7)

H.

J. Nucl.

38

B. Blumenthal,

Knolls

Report,

Yagoda,

Inc.,

Mat.

23 882

Power Laboratory

1100

Radioactive

New York,

2 (1960)

209 (1957)

Atomic

KAPL

Nuclear Track Emulsions

Acknowledgments

and Dr. H. H. Chiswik of Argonne National Laboratory for supplying a uranium single crystal and several ingots of high-purity uranium, and also for assistance with the crystallographic orientation of the crystals. They are also grateful to Dr. L. S. Castleman of General Telephone & Electronics Laboratories for many helpful discussions. The support of the U.S. Atomic Energy Commission is gratefully acknowledged.

2 (1957)

4)

(USA)

The authors are indebted to Mr. E. S. Fisher

11

ALPHA-URANIUM

Measurements (John Wiley

with

and Sons

1949) p. 83

8) G. Kidson, Private communication 9) 10) ii)

Y.

Adda,

Private

communication

F. E. Jaumot and R. L. Smith, Trans. AIME (1956)

164

A.

Bochvar,

A.

Sergeev,

V.

Second

G. Kuznetsova Geneva

206

and U.

Conference

8.

(1958)

15/P/2306 12)

Y.

Adda

(1959) 13)

8. J. Rothman, Trans.

14)

AIME

E. 8. Wajda, Acta

15)

and A.

Kirialenko,

Nucl.

Mat.

1

Met.

L. T. Lloyd and A. L. Harkness, 218 (1960)

Met.

605

G. A. Shirn and H. B. Huntington,

3 (1955)

39

G. A. Shirn, E. S. Wajda Acta

J.

120

1 (1953)

513

and H. B. Huntington,