Diffusion of vanadium in niobium, zirconium and vanadium

DIFFUSION

OF VANADIUM

IN

It.P. AGARWALA,~

NIOBIUM,

ZIRCONIUM

s. P. MURARKA?

and M.

AND

VANADIUM*

S. ANANDt

Diffusion of vanadium has been studied in niobium, zirconium and vanadium crystals using radioactive tracerandresidualactivity technique. In niobiumandalphazirconium, thediffusioncoefficients (cme/sec) have been given: Dvjxb(lOOO”-14OOOC) = 2.21 exp (-S5,000/RT) and

Dv/,_sr(600”-850°C)

= 1.12 x IO-* exp (-22,90O/RT)

In beta zirconium and vanadium, little deviation from linearity in the plots of log D vs.l/T have been detected and the diffusion coefficients (cmP/sec) have, therefore, been described in two temperature ranges as: D~~/~_zr(870”-1200”C) = 7.59 x 10-a exp (-45,80O/RT) Dv~~.sr(12000-1400”C)

= 0.32 exp (-57,20O/RT) = 0.107 exp (-64,60O/RT)

Dvlv(1050”-1400°C)

= 10.45 exp (-76,80O/RT)

All these data are discussed in light of Kidson’s

DIFFUSION

and

Dr/v(7000-1300’C)

DU VANADIUM

DANS

model and the impurity

LE NIOBIUM,

content of t,he host metals.

LE ZIRCONIUM

ET LE VANADIUM

On Btudie la diffusion du vanadium dans des cristaux de niobium, de zirconium et de vanadium par la technique de traceurs radioactifs et d’activite residuelle. Dans le niobium et le zirconium alpha, on donne pour les coefficients de diffusion (cm*/s): Dv1xs(1000~-1400~C) et

Dv/,_sr(6000-850°C)

= 2,21 exp (-85 = 1,12

OOO/RT)

* lo-* exp (-22

900/RT)

Dens le zirconium beta et le vanadium, on d&s&e une petite deviation Q la linesrite du diagramme de log D en fonction de l/T et les coefficients de diffusion (cmr/s) ont done et,8 decrits dans deux domaines de temperatures: Dr/,q_sr(8700-1200°C) v/b-srD(1200”-1400°C)

= 7,59

. 10-a exp (-45

= 0,32 exp (-57

800/RT)

200/RT)

et

v/vD(700”-1300°C)

= 0,107 exp (-64

600/RT)

Dv/v(1050’-14OO’C)

= lo,45 exp (-76

800/RT)

On discute ces resultats a la lumiere du modele de Kidson et de la teneur en impure&

DIFFUSION

VON

VANADIUM

IN NIOB,

ZIRKONIUM

UKD

des mitaux

hates.

VANADIUM

Die Diffusion von Vanadium wurde in Niob, Zirkonium und Vanadium mit.tels radioaktiven Tracern und der Methode der Restaktivitiit untersucht. Die Diffusionskoeffizienten (in cm*/sec) in Niob und in Slpha-Zirkonium betragen und

D~~x~(1000”-1400~C)

= 2,21 exp (-85

OOO/RT)

Dv/a_sr(6000-8500C)

= 1,12. 10-Sexp

(-22

900/RT).

In Beta-Zirkonium und Vanadium wurden kleine Abweichungen vom linearen Verlauf der Arrheniusgeraden gefunden. Die Diffusionskoeffizienten werden daher in zwei Temperaturbereichen angegeben: Dv/,~_s~(870~-1200”C) Dv/~-sr(1200”-14000C)

= 7,59 .1O-3exp (-45 = 0,32 exp (-57

Dr~v(700”-1300°C)

= 0,107 exp (-64

600/RT)

Dv/r(1050°-14OO’C)

= lo,45 exp (-76

800/RT).

Siimtliche Daten werden im Rahmen des Kidson’schen gungsgehalt der Wirt,skristalle diskutiert. * Received March 14, 1967; revised June 6, 1967. t Bhabha Atomic Research Centre, Chemistry Division, ACT-4 METALLURGICA, 5

VOL.

SOO/RT)

F?OO/RT)

16, JANUARY

1968

Models und im Hinblick

Trombay, 61

Bombay-i4,

India.

auf den Verunreini-

ACTA

62

METALLURGICA,

INTRODUCTION

The appearance of non-linearity in the plots showing temperature dependence of diffusivities in beta zirconium,“) beta titanium,(s) gamma uraniumt3) and vanadium(4*5) has induced an interest to study diffusion and its mechanism in body centered cubic metals. The vacancy mechanism of diffusion which had been commonly accepted even for these metals, thus requires a reconsideration. Kidson(Q explained this non-linearity for self diffusion in beta zirconium on the assumption that non-thermal vacancies are introduced by the strains around the interstitial impurities. This model, however, is not able to explain the non-existence of this behaviour in otherwise impure metals especially of body centered cubic structure and was also not acceptable for the diffusion in gamma uranium.‘3) Lazarusc7) has discussed the diffusion in body centered cubic transition metals and pointed out that this anomalous diffusional behaviour in these elements may not be truly characteristic of the pure metal. In view of this, attempt has been made to throw further light on this issue by studying the tracer diffusion of vanadium in niobium, zirconium and vanadium using residual activity technique.@) EXPERIMENTAL

Vanadium and niobium single crystals of) in. dia. x $ in. high were obtained from Semi Elements Inc. Zirconium specimen of $ in. dia. x &in. high were machined from a rod of ) in. dia. and the end faces were prepared flat and parallel. The spectrographic analysis of vanadium, niobium and zirconium used in these investigations is given in Table 1. For volume diffusion studies in zirconium, specimens were annealed in vacuum for several hours at 12OO”C, to develop grains of nearly 1000 p. One of the end faces of vanadium, niobium and zirconium was then prepared for radioactive deposition as described earlier.fgJ TABLE 1. Chemical and spectrographic analysis of zirconium, vanadium and niobium Zirconium Imp. H R Ti

Vanadium

ppm 6:: 40 25

2

500 100

:b W Al CU

160 50 50 25 25

Other total impurities due to Cu, B, Co, Pb, Mg, MO, Bi, Mn, Ni and Sn are < 100 ppm.

Imp. H 0 I\’ Ts Ti Fe

ppm <5 800
Niobium Imp. H 0 ?J Ta. Ti Fe

ppm <5 100
Other impurities like Co, Be, B, Sb, Mn, Mg, Pb, Cr, Sn, Si, Ni, Bi, Ca, Cu, Zn, Ag, MO and Al not detected

VOL.

16,

1968

Carrier free vanadium-48 activity was obtained from Radiochemical Centre Amersham in the form of VOCl, in dilute HCl (1 N). The solution (2.5 cc containing 750 pg of vanadium-48) was highly active, and was diluted 250 times in order to get suitable range of activity for diffusion studies. Also the acid concentration reduced to almost neutrality. 301, (i.e. 0.03 cc) of this solution was placed over each specimen by a micropipette. The care was observed that solution spreads uniformly over the whole surface area without trickling down the cylindrical surface. The solution was dried and the specimen were preannealed at 200°C for about an hour in order to homogenise the deposited activity level over the surface and to anneal out any residual strains left over in the specimens used. Finally, diffusion annealings were carried out in purified helium atmosphere. For annealing6 above llOO”C, vacuum furnaces were used. Temperature was measured using Pt Pt-10 y0 Rh thermocouples, and was controlled to within &5”C. Total amount of vanadium oxychloride over the specimen surface was nearly 0.128 pg, corresponding to 0.036pg of vanadium; 0.012 pg of oxygen and 0.08 ,ug of chlorine. Assuming that all of chlorine and oxygen is held by the host lattice during diffusion and that the diffusion is up to a maximum depth of 200 microns the impurity level of chlorine or oxygen thus present will not exceed 2.5 ppm in the host lattice. In the case of minimum penetration of 10 ,u, the impurity level of chlorine does not exceed 45 ppm in any metal and that of oxygen even less than 7 ppm. Impurities as low as this will have negligible influence on the diffusion rate of vanadium and we assume that measured diffusivities will represent true diffusion coefficients very closely, specially in view of other uncertainties in measurements and level of impurity content in these metals, contributing to a larger degree of error. Residual activity technique(s) was used to study diffusion profiles. The total activity was measured by counting 0.99 MeV y-radiation of vanadium-48 (half life 16 days) on a 27~geometry NaI(T1) scintillation counting set up. Under the conditions of the experiments,(lO) the solution of Fick’s second equation for volume diffusion is C(x, t) = con&. exp (-x2/4Dt)

(1) The concentration has been determined using Gruzin’s analysis@) for the residual activity method. for which pI,

-

‘2

n

= con& C(x,) = const. exp ( -xn2/4Dt)

(2)

AGARWALA,

MURARKA

DIFFUSIOK

ANAXD:

AND

OF

V TN Wb,

Zr

AL\‘D T-

63

o -1400115hrs. . - llOO/ZOhrs. e - 910 / 66 hrs.

X2,x I.0

I 20

I 40

, 60

I 90

X”,X

FIG. 1. Characteristic

plots of log C

(

106(FOR140&.B110~C.l

I IlO

, 120 IdtFOR

c = - -$$

I 160

I 140

1 190

I 200

I 220

9lo”C.k

vs. 5,’ for the diffusion of vanadium

”

in zirconium.

less than 1 per cent of latter. Thus C(z,) is determined from the slope of I, vs. x, curves. Figures 1, 2 and 3 show the characteristic plots of log C vs. xR2 for diffusion in zirconium, vanadium and niobium respectively. Diffusion coefficients were calculated from the slopes of these curves for all temperatures. At lower ~mperatures (600°, 650” and 700%) in v. phase of zirconium a little drop in concentration at the surface has been noticed. This is similar to observations of the drop at surfaces in many other cases and

Where p is the linear absorption coefhcient in cm-l, 1%is the surface activity in counts per unit time, x, is the thickness of the material removed in cm and t is the time in sec. The values of p for 0.99 MeV y-rays of vanadium-48 in vanadium, zirconium and niobium are 0.36 cm-l, 0.39 cm-l and 0.51 cm-l respectively. These are so small that ,uI, is negligible, within the range of experimental error, compared to (-dI,/dx,). Even at the highest temperature of diffusion anneal, this is

1-6

15 14 t

O-

1400

/ 15 hrs.

. -

1100

/ 2Ohrs.

@-

700

IlOlhn.

13-

X:X

FN.

2. Characteristic

plots of log C

C =

107 FOR

- 2

70d

R

C.

vs.

I x,,~

for

the diffusion of vanadium

in vanadium.

64

METALLURGICA,

AC'TA

VOL.

16,

1961

0 -

1400/S

hrs

.-

1300/16

hrs

; _i I

0 - lOOO/lOO hrs

X',x 10" [FOR 14OCiC d13OOk)

1

I

0

5

;O

;5

1

I

I

I

I

I

I

/

I

20

25

30

35

40

40

50

55

60

X:X

lOOdC1

x,* for the diffusion of vanadium in niobium.

FIG. 3. Characterist.ic plots of log c

can be attributed to be due to the near surfa.ce effect.(lO) In these cases the diffusion coefficient8 were calculated from higher penetration depth8 where a good fit of log c vs. x,,~ was observed. RESULTS AND

10'1 FOR

DISCUSSION

Table8 2 and 3 list the diffusivities of vanadium in zirconium (a and @ phases), vanadium and niobium at different annealing temperatures. It is seen that diffusivity values are smallest for the diffusion in niobium. Figure 4 shows the plot of log D VS. 1/T for the diffusion of vanadium in niobium single crystals. A straight line is obtained and the diffusion coefficient (cm2/8ec) can therefore be represented by the relation : D = 2.21 exp (-SS,OOO/RT) In the experimental temperature range of lOOO”14OO”C, no non-linearity in Arrhenius plot could be detected. These result8 are thus analogous to those obtained for the diffusion of iron, cobalt? and nickelo2) in niobium. The activation energy of diffusion of V in Nb is less by about 12 kcal/mole a8 compared to it8 self diffusion(11*13)value in niobium whereas diffusivities are about 100 t,imes greater than

self diffusion coefficients. However vanadium and niobium form continuous solid solutions and additions of vanadium to niobium decrease the lattice parameter of niobium.04) From these, one would have expected rather greater value of activation energy for diffusion of vanadium in niobium, contrary to the present results. Figure 5 gives the plot of log D vs. l/T for the diffusion of vanadium in u and @ phases of zirconium. An increase in diffusivity by about 25 time8 is observed a8 the phase changes from a to 8. This change in diffusivity at the transition temperature is rather less pronounced than that observed in the case of diffusion of tin,(la) chromium,(reJ 8ilveP) or even zirconiumo5*riJ in zirconium. Table 4 compares the ratio of the extrapolated diffusivities of various species in cxand p phases of zirconium at 863°C. It is noted from Table 4 that diffusivity of vanadium in b.c.c. phase of zirconium is very much smaller than that of other impurities in the same phase. In the closed packed hexagonal phase, the diffusivities of tin and vanadium are of the same order, while those TABLE

TABLE 2. Diffusivities of vanadium in zirconium Temp. Aplha-phase

Beta-phase

Temp.

D

(“C)

(cm*/sec)

850 810 750 700

650 600

4.84 3.02 1.43 7.60

x x x x

4.36 x 2.08 x

IO-13 lo-la lo-‘* lo-‘* lo-l4 lo-‘*

Temp. (“C) 1400 1300 1200 1100 1000 900 870

W)

D (cm2/sec) 1.11 4.14 1.30 4.16 1.08 2.01 1.43

I

j

x x x x x x x

10-e 10-g 10-g 10-l” 10-10 lo-” lo-‘1

1400 1300 1200 1100 1000 900 810 700

3. Diffusivities of vanadium in vanadium and niobium Niobium

Vanadium

D

(cm*/sec) 7.95 2.27 3.97 6.00 8.30 7.53 1.00 3.08

x x x x x x x x

IO-‘0 lo-“’ lo-” lO-12 10-13 10-14 10-14 10-16

Temp. (“C) 1400 1350 1300 1250 1200 1150 1100 1050 1000

D

(cmz/sec) 6.30 3 16 1:41 5.61 1.80 7.08 2.30 5.62 1.78

x x x x x x x x x

lo--‘* lo-‘? lo-‘* 1O-13 10-13 lo-” IO-l4 lo-l5 10-15

AGARKALA.

RIVRARBA

AND AiSAND:

DIFFUSIOS

-60

OF

V IS

Nb,

Zr ASD

V

65

t

-70 I -8.0 c

0

o-

p PHASE

.-

mPHASE

-110

F J

t -12,oc !

-14 0

-130 c -14.5 -140 -150

I

I -155

I 55

, 65

I 60

7b +

I 75

I 80

\

I 85

1 9-o

I

10'

FIG. 4. Temperature dependence of diffusivity of vanadium in niobium.

of chromium, silver and zirconium are about 10 times higher. In alpha zirconium the straight line fit of log D VS. l/T (Fig. 5) is observed. The diffusion coefficient, (cm2/sec) in this phase can be described by D VinZrtaj = 1.12 x 1O-8 exp (-22,90O/RT)

In beta zirconium, however, the diffusivities at 1300” and 1400°C appear to be more than expected from the log D vs. l/T plot in the temperature range of 870”-1200°C. Two different lines can be drawn to describe the diffusivity of vanadium in j3 zirconium, in the temperature ranges of 870”-1200°C and 1200”-1400°C. It’ is possible that this nonlinearit,y of t,he Arrhenius plot continues even at higher temperatures, as has been observed in the diffusion of zirconium and niobium in zirconium.“) The two ranges are arbitrarily divided and diffusivity (cm2/sec) in these ranges can be described as DV inp-Zr(8iOc-12OOT)

=

7.59 x 1O-3 exp (-45,80O/RT)

I

I

I

I

I

I

I

4

5

6

7

8

9

10

TG

=

0.32 exp (-57,20O/RT)

Figure 6 shows the plot of log D vs. 1/T for the diffusion of vanadium in single crystals of vanadium. The data are best fitted on a curve with a changing slope. Though this deviation from linearity is very small, no single value of activation energy and

.re

x 10’

FIG. 5. Temperature dependence of diffusivity of vanadium in zirconium.

diffusion frequency factor can describe the diffusivities throughout the experimental temperature range. The diffusivity (cm2/sec) has therefore been described in two temperature ranges as : D\~/V~iClW-1050"~)

=

0.107 exp (-64,60O/RT)

and Dv/v(1050”-1*00~c) = 10.45 exp (--‘iS,SOO/RT) The value of activation energy at higher temperature is close to the one predicted on empirical or semiempirical relations.‘1E-20) Table 5 lists the various results of self-diffusion studies in vanadium together with the purity of vanadium used and the temperature ranges. Both Peartc5) and Lundy et aZ.(*) have reported nonlinearity in Arrhenius plot. In the range of lOOO’1400°C the diffusivities of vanadium, obtained in our investigations are about 7 times higher than those reported by Peartt5) and about 2-7 times higher than TABLE

4. Diffusivities of various impurities in alpha

and

beta phases of Zr at 863°C

and DV inP-Zr(1000”-1400°C)

I

1

n

Imp.

Zr Sn Cr Ag Nb 1’

D cm*/sec at 863°C a-phase 2.88 5.75 4.05 3.25

x x x x

lo-‘* 10-13 10-12 lo-‘*

4.47 x 10-13

p-phase 6.24 1.52 4.81 2.68 1.00 1.00

x x x x x x

lo-lo lo-“’ lo-‘0 lo-” 10-10 lo-”

Ratio Dal& 217 264 118 83 G

Ref. 15 15 9 16 1 Present

ACTA

66

METALLURGICA,

+-

PEART.

0-

PRESENT RESULTS

l

----

-

1

LUNDY AND MC LEASTSCWARE

FIT

-EXPERIMENTAL

‘1

l

0.

-13 -

‘1 Q

-16 -14: -15

~IJRVE

\

‘\

\ \\

0

I

I

I

I

I

6

7

8

9

10

ii

:

a\ \ 11

I

I

12

13

14

x 12

FIG. 6. Temperature dependence of diffusivity of vanadium in vanadium.

those reported by Lundy et LzZ.(~)In all these investigations, single crystals of vanadium were used having different impurity content (Table 1). The diffusivities at lower temperatures increase as the impurity content increases. The difference in diffusivity may thus be attributed to the varying purity of material rather than to the difference in the method of deposition of the tracer. In our results, at 14OO”C-7OO”C, a maximum error of 8.6O/,15o/o in D is estimated compared to those of Lundy et al. and Peart where the former has reported nearly 5% error at 1400°C and 40% at 1OOO’C and latter &l%. Considering all these, agreement between the results in these investigations is satisfactory. Diffusion studies in niobium(ll) as well as in

I-OL.

16,

1968

molybdenum(21) and tant,alum’22) yielded straight line plots of log D vs. l/T. whereas non-linearity in Arrhenius plots of diffusion in B-Zr:cl) p-Ti.t2) y-U(3) and V’4*5)has been observed. This apparent, diversity among the body centred cubic metals is interesting. The probable explanation based on the non equilibrium number of defects introduced due t.o transition from one phase to another does not apply t,o vanadium. Theoretically this non-linear behaviour of diffusion in Arrhenius plots is not favoured, though itf is not altogether ruled out. Kidson@) has been able to explain the data of self diffusion in zirconium assuming the existence of non-thermal vacancies associat,ed with impurities (preferably oxygen) at lower temperatures. The diffusivity has been obtained as the sum of two exponential factors describing the charact,eristics of diffusion through thermal or intrinsic vacancies and that t,hrough non-thermal or extrinsic vacancies. According to this model diffusivity (cm2/sec) of vanadium in /kirconium and vanadium can be described as D r,~_zr~eio~_l~oooc~ = 8.32 exp (-71,450/W + 7.59 x 1O-3 exp (-45,80O/RT) and DV/V(iClCl”-1400”~)

=

55.59 exp (--83,21O/RT)

+ 8.61 x 1O-3 exp (-59:500/RT)

The above equations represent the experimental diffusivities at all temperatures within 4?, for beta zirconium and 10% for vanadium. In these cases the extrinsic diffusion activation energy is high (more than 4 of the intrinsic value), and cannot be said to represent simply the energy of migration of vacancies as would have been expected, if a large excess of non-thermal vacancies were present, in association with impurities at low temperatures. Kidson’s model@) does not appear, therefore, to explain the data. However, when w-e compare the

TABLE 5. Self diffusion studies in vanadium Purity of vanadium used 99.989% (0,, N, & H, all less than 5 ppm.) 99.724% (02-880 ppm X,--800 ppm C-600 ppm Hz-l20 ppm) 99.920/b

Temperature range of investigation (“C)

D0 (cm2/sec)

Q

(Cal/mole)

Ref.

73,650

6

1356-l 833

2.14 x 102

94,140

5

below 1400

1.1 x 10’

61,000

4

91,500

4

64,600

Present

76,800

Present

MO-1356

above 1600 700-1050 1050-1400

0.3

58 0.105 10.45

diffusion at different impurity contents, the enhancement, of diffusion with increasing impurity content in vsnadium is observed which supports Kidson’s model. As the deviation from linearity W&S small in the above invest&&ions of vanadium and &conium, a least squares fit of the data was tried to yield the expression D,,, -= 1.77 exp (-68,40O/RT)cm2/sec which describes the experiment& diffusivities within 1220; and

of impurities. Does it mean th& the impurities are playing the role of non-linearit,y introducers in ziroonium, titanium, uranium or vanadium ? In vien of the results with three different purities of vanadium z this seems to be true.

cmz/sec %/z*(p) = 1.32 x 10w2exp (-47,0OO/RT)

1, J. I. FEDE~ER and T. 8. ~;WXDP, Trans. Am. I?zst. Min. Engra 227, 592 (1963). 2. G. B. GIBBS, D. GRAHAMand D. H. ToM~~~N,Phil. Mag, 8,1269 (1963).

ACKNOWLEDGMENTS

Authors thank Analytical and Spe&roscopy Divisions of this es~bl~shme~t, for analysis of metals, REFERENCES

with all observed diffusivities within &20%. At present we could not establish, whether this deviation is more at, higher temperature. Errors estimated in our invest~igations vary from a minimum of S.6o/oto a maximum of 15%. In spite of this common expe~rnen~~l error, no deviation from linearity has been observed in the diffusion of vanadium in niobium and also in the earlier investigations on niobium, tantalum or tungsten. In all these investigations the impurity contents in the above met&s were larger tbsn those of vanadium or zirconium. Impurities thus does not seem to introduce this non-linearity in Arrhenius plots In these metals. Recently(=) a little departure from non-linearity in Arrhenius plots (6 kcaljmole deviation in activation energy of niobium diffusion in tantalum) over the temperature range of 920”25OO’C was observed, where the diffusivities increased lOlo folds between 920’ and 2500°C. Whether this is due t.5k&e mndom errors_ or impurity content (more t,han 3~Oppm~ in tantalum, could not be established. Howover, the Arrhenius relationship applied here exceptionally well than in case of beta zirconium, beta titanium or even gamma urebnium nnd vanadium. Tantalum7 niobium and tungsten are much stronger than zirconium: titanium, uranium or vanadium and are very much less susceptible to change their st,rength properties with small addition

3* A842 (1964).

4. T. S. LUNDY and C. J. MCHARGUE, !l’rans. Am.

Inst. Min. Eng?V8283, 243 (1965). R. F. PEART, J. Phys. Chcrn.Solids 26, 1853 (1965). :: G. Y. KIDSON, Can. J. Fhys. 41,1563 (1963). 7. D. LAZKRUS,AEC. AGO. No. 41920, Rept. No. COU-1198. 204 (1964). P.L.G~uzrx, DokLAkad. NaukSSSR86,289 (1952). and M. S. ANAND, i: R. P. AGIARWALA, S. P. MUXARKA Trans. Am. Inst. Min. Emgrs 233, 986 (1965). S. P. MURARKA and M. S. AXAXD, 10. R. P. AOARWALA, Acta Met. 12,871 (1964). Acta Me& ti. R. F. PEART, D. GRAHAM r*nd D. H. TONLI.XX’, 519 (1962). 12. K. HIRANO, 8. L. AVER~ACE, M. COZXESand R. P. AGARWALA,unpublished work. and L. S. CABTLEMAN,Trans. Am. Inst. N&I. 18. R. RESNICEC Engrs 218, 307 (1960). 14. M. HANSEN, Go?zst&ution‘of Binary Albg?ls, p. 1022. ~~G~W-~ill (1958). 15. P. L. GRUZX~~,V. S. EMEX,YANOV,C. G. RSABO~A and G. B. FEDQWW, Proc. 2nd U.N. Int. Canf, Peaceful Uses of Atomic Energy, Geneva, 10, 187 (1958). 16. M. C. NAIK and R. P. A~ARWALA, Proc. NucE. Radiat. Chew Symp. Chemistry Committee, Dept. of Atomio Energy, India 282 (1966). 17. G.V.K1nso~rtndJ.5IcG~~~~,~~~~J.Phys.;(S,f146~1961). 18. A. D, LEC~ERE, P7q. Me&E P&s. 1st edition, 1, 366 (1949). 19. N. H. NACHTRIEB and G. 8. HANDLER, Acta Met. 2, 795 (1954). 20. S. P. MUXAEKA and R. F. AGARWALA,Report AEET/233 (1965). 12{3), 21. L. IT. PATLINOY and 1’. 5. RTKO~, Fa’z%a. &rietiadE. 459 (1964). 22. R. L. EAQER and D. B. LANGDIVIIR. Php. Rec. 89, 890, 911 (1953). 23. R. E. PAWEILand T. S, Lvx~r-, J. Phys. Chem. Solids 26,937 (1965).