Self-diffusion in B.C.C. and ordered phases of an equiatomic iron—cobalt alloy

Vol. 43, No. 3, pp. 1183 1188, 1995 Copyright ~k: 1995 Elsevier ScienceLtd Printed in Great Britain. All rights reserved 0956-7151/95 $9.50 + 0.00

Acta metall, mater.

~

Pergamon

0956-7151(94)00331-9

S E L F - D I F F U S I O N IN B.C.C. A N D O R D E R E D P H A S E S OF A N E Q U I A T O M I C I R O N COBALT A L L O Y YOSHIAKI IIJIMAt and CHAN-GYU LEEz ~Department of Materials Science, Faculty of Engineering, Tohoku University, Aoba, Sendai 980-77, Japan and -'Department of Materials Science and Engineering, Chang-won National University, Chang-won 641-773, Republic of Korea (Received 1 6 M a y

1994)

Abstract--Self-diffusion coefficients of 59Fe and ~7Co in an Fe 50.8 at.% Co alloy have been determined in the temperature range between 877 and 1238 K by use of the sputter-microsectioning technique. Above the order~lisorder transformation temperature (1003 K), the Arrhenius plots of the self-diffusion coefficients of both components show a slight deviation from linearity due to the magnetic spin ordering of the alloy. Below 1003 K the Arrhenius plots become curved downward remarkably owing to the B2 type of atomic ordering. The temperature dependence of the self-diffusion coefficients D~ and Dco across the phase transformation temperature can be expressed by DF~--7.0x 10 4exp{-(241kJmol-l)[l+0.16s2+0.21u2]/RT}m2s

i

and Dco=0.31 x 10 4exp{

(201kJmol-t)[l+0.29s2+0.27u2]/RT}m2s

t

where s is the ratio of the spontaneous magnetization at T to that at 0 K, and u is the long range order parameter. Both the magnetic spin ordering and the atomic ordering of the alloy yield an increase in the activation energies for self-diffusion.

1.

INTRODUCTION

Iron and cobalt form wide concentration ranges of solid solutions with the b.c.c, lattice at lower temperatures and with the f.c.c, lattice at higher temperatures [1]. The Curie temperature of the b.c.c, phase increases from 1043 K for pure iron to about 1240 K at 25 at.% Co, beyond which the magnetic transformation temperature coincides with the b.c.c.-f.c.c. phase transformation temperature between 25 and 69 at.% Co. The Curie temperature in the f.c.c, phase with higher cobalt contents rises from 1163 K at 73 at.% Co to 1396 K for pure cobalt. The relatively high Curie temperatures in this system make it especially appropriate for diffusion measurements in both the ferromagnetic and the paramagnetic states of both the b.c.c, and the f.c.c, structures. Furthermore, an ordered lattice of the B2 type exists in the b.c.c, region around the equiatomic composition. A diffusion study on the ordered phase is also attractive. Hence, the equiatomic alloy of Fe and Co undergoes the b.c.c.f.c.c, phase transformation at 1258 K and the B2 type order-disorder transformation at 1003 K. The Curie temperature of the alloy is 1258 K. Thus, the temperature dependence of the self-diffusion coefficients in the alloy is expected to show drastic changes across these transformation temperatures.

Okada [2] and Hirano and Cohen [3] have determined diffusion coefficients of 59Fe in an Fe 50.4 at.% Co alloy and 6°Co in an Fe-49.6 at.% Co alloy, respectively, using the residual activity method. Fishman e t al. [4] have studied the self-diffusion and isotope effect on it in the equiatomic F e - C o alloy using radioactive tracers (5SFe, 59Fe, 57Co and 6°Co) and the serial mechanical sectioning technique. According to these studies [2-4], the Arrhenius plots of self-diffusion coefficients of both components show linearity in the f.c.c, phase and in the b.c.c, phase, respectively, with a drastic increase of about two orders of magnitude at the transition from the f.c.c. phase to the b.c.c, phase, while below 1003 K the Arrhenius plots curves become downward remarkably owing to the atomic ordering. However, the temperature dependence of the diffusion coefficients in the ordered phase has not been represented by equations, because the experiments in the ordered phase [2-4] have been limited in narrow temperature ranges. An isotope effect coefficient for 55Fe and SgFe is 0.66 for the f.c.c, phase and 0.52 for the b.c.c, phase and below 1003K it decreases remarkably with decreasing temperature, i.e. with increasing degree of order [4]. These authors [2-4] have used the conventional mechanical sectioning techniques, thereby limiting the measurable diffusion coefficient to larger than

1183

1184

IIJIMA and LEE: SELF-DIFFUSION IN B.C.C. AND ORDERED PHASES

10 16m 2 s-i. To extend the lower limit of the diffusion coefficient the sputter-microsectioningtechniquc is useful, because it enables us to measure sub-micron diffusion profiles of radioactive tracers in solids and also to determine diffusion coefficients as small as 10 2~m 2 s-i [5]. Iijima et al. [6] and Lfibbehusen and Mehrer [7] have applied the sputter-microsectioning technique to measure self-diffusion in ~-iron and furthermore compared the self-diffusion coefficients obtained by the conventional mechanical sectioning technique and by the sputter-microsectioning technique. Consequently, these authors [6, 7] have demonstrated that the apparent self-diffusion coefficient in the paramagnetic ~-iron by the former technique is 1.3 1.9 times larger than that by the latter technique, where the value of self-diffusion coefficient lies in the range of 10-~6-10 t4 m2s 1, The reason for it is that the former technique requires long diffusion profiles which are often affected by the enhancement effect due to the dislocation diffusion. At lower temperatures the enhancement effect becomes more serious. Therefore, old diffusion data by the conventional mechanical sectioning techniques should be replaced with new data by the sputter-microsectioning technique especially when the temperature dependence of diffusion coefficients is ambiguous at low temperatures. The aim of the present work is to examine the temperature dependence of the self-diffusion coefficients of both components in the b.c.c. disordered phase and in the B2 type ordered phase of the equiatomic F ~ C o alloy using the sputtermicrosectioning technique in detail. 2. EXPERIMENTAL

An ingot of Fe 50.8at.% Co alloy was made by vacuum-melting high purity electrolytic iron (99.96%) and cobalt (99.97%) in an alumina crucible and casting into a steel mold 20 mm in diameter. The ingot was hot-forged and machined to 10mm in diameter. To cause grain growth and reduce the contents of carbon, nitrogen and oxygen, the rod was annealed at 1700 K for 173 ks in a stream of hydrogen gas purified by permeation through a palladium alloy tube at 700 K and passed through a liquid nitrogen trap. The resultant grain size was about 4 mm. The rod was cut to make the disc specimen 2 mm in thickness. The flat face of the specimen was ground on abrasive papers and polished with fine diamond paste. To obtain a stress-free surface, the specimen was annealed at 1053 K for 10.8 ks in a stream of the purified hydrogen gas. For diffusion below 923 K, the specimen was pre-annealed at 873 K for 2.42 Ms to attain an equilibrium ordered state at the diffusion temperatures. The radioisotope ~gFe (7 -rays, 1 . 0 9 5 and 1.292 MeV; half-life time, 45.6 d) was supplied in a form of FeC13 in a 0.5 kmol m 3 HC1 solution from Dupont NEN Research Products, U.S.A. The radioisotope 5VCo (7-ray, 0.122 MeV; half-life time, 270 d)

X = / I 0 -'~ m2for A and B zo 40 6o 8o ~oo 12o 14o 16o 18o

o

I

i

i

i

i

•%. L

m

i

i

~eFe--> FeCo

O_~O~o~o ~ ° ~ o ....•

~'~...

~

r\.

(,Z38 K, 5ks)

~.\

(1206 K,3ks)

.~ %%% C (993K 168ks)

\ o

D (98i K, 6i.2 ks) i ;~ i

i 4i0 60 i 8i0

i ,oo ,o ,4o ,~o ,oo X~I Id'"~ fo~ c o~d D

~o

Fig. 1. Examples of penetration profiles for diffusion of 59Fe in Fe 50.8 at.% Co alloy. was supplied in a form of CoCI2 in a 0.1 kmol m 3 HCI solution from Amersham International plc, U.K. The two isotopes were mixed so that the ratio in the activities of 5VCo/59Fe was about 3, and they were put into 0.1 x 10-6m 3 of dimethylsulfoxide. Then, the radioisotopes were electroplated from the dimethylsulfoxide on the mirror-like surface of the specimen. The specimen was diffused a~ temperatures in the range 877-1238 K for 3.0 684 ks in a stream of the purified hydrogen gas in furnaces controlled within _+1 K.

o 20

X 2 / I d l 2 m 2 for A and B 40 60 8o ~oo tzo 14o 16o tso i

i

i

i

i

i

E

5TCo~ FeCo

~

-.>

(12~,8 K,3 ks }

\o

\

(1206K,3 ks)

o

x o3

%. •\°~. °

~ C {993K, 16.8 ks)

\ D (981 K, 61.2 ks) 2Jo 410

610

I

8o

X ~/10'"

I

o•

I

z•

I

4o

I

ooLso

g for C and D

Fig. 2. Examples of penetration profiles for diffusion o f 57Co

in Fe 50.8 at.% Co alloy.

IIJIMA and LEE: SELF-DIFFUSION IN B.C.C. AND ORDERED PHASES The serial radio-frequency sputter-microsectioning method was employed to measure the penetration profiles of the radioisotopes in the specimen. The details of the method were described elsewhere [6, 8]. For each specimen 15-30 successive sections were sputtered. A constant fraction more than 60% of the sputtered-off material was collected on an aluminium foil. The intensities of the radioactivities of the two isotopes in each section were measured by a well-type Tl-activated NaI detector with a 1024-channels pulse height analyzer.

1185

T/K 400

IZO0

I(~ I~

tO00

800

I

I

[

~

o Fishrn<]n, Gupto and Lieber mon (1970)

::]% I(~ 15

U Okoda ( 1 9 6 6 )

o =~ o~'~!

id '~` "Tu~EId':'

~o

C~

3. RESULTS AND DISCUSSION

3. I. Self-diffusion coefficients in an Fe-50.8at. % Co alloy

Idls

For the one-dimensional volume diffusion of a tracer from an infinitesimally thin surface layer into a sufficiently long rod, the solution of Fick's second law is given by

id2~ 1(522

I 8

I 9

l(X, t) 3c C(X, t)

I 10

I II

I 12

13

T-'/I0-" K-' = [M/x/~t]exp(--X2/4Dt)

(1)

where I(X, t) and C(X, t) are the intensity of the radioactivity and the concentration, respectively, of the tracer at a distance X from the original surface after a diffusion time t. D is the volume diffusion coefficient of the tracer and M is the total amount of the tracer deposited on the surface before the diffusion. Figures 1 and 2 show the typical plots of In I(X, t) vs X 2 for the diffusion of 59Fe and SVCo, respectively, in the Fe 50.8 at.% Co alloy. The linearity observed in Figs 1 and 2 proves that equation (1) holds, and thus it can be said that the volume diffusion has been concerned. The diffusion coefficients calculated from the slope of the plot are listed in Table 1, and the Arrhenius plots of 59Fe and ~7Co in the alloy are shown in Figs 3 and 4, respectively, in comparison with those by the previous authors [2-4]. As shown in Fig. 3, in the b.c.c, phase between 1003 and 1258 K, the diffusion coefficient of iron by the present

Fig. 3. Arrhenius plots of diffusion coefficients of iron in F~50.8 at.% Co alloy in comparison with those by other authors. work is in agreement with that by Fishman et al. [4]. However, the experimental data by Okada [2] is lower than those of the former two. Below the orderdisorder transformation temperature (1003 K), the diffusion coefficient of iron by Fishman et al. [4] is larger than that by the present work. For cobalt diffusion in the alloy, a similar tendency is observed in Fig. 4. In the b.c.c, phase the diffusion coefficient

T/K 1400

1200

i 0 ~3

I

I000

800

I

I

570 o __~FeCo • Present work

i(~ 14

o Fishmon, Gupta ond Liebermafl (1970) •, Hirano and Cohen(19727,

'%

I{~15

I(~ Is T a b l e 1. Self-diffusion coefficients o f 59Fe a n d 57C0 in e q u i a t o m i c Fe~Co alloy T(K)

t(s)

1238 1236 1236 1206 1185 1164 1145 1145 1129 1104 1091 1060 1015 993 981 954 923 877

3 . 0 0 x 103 3 . 0 0 x 103 3 . 0 0 x 103 3 . 0 0 x 103 3 . 0 0 x 103 3.00x103 3 . 0 0 x 103 3.00xlO 3 3 . 6 0 x 103 3.60xl03 6 . 0 0 x 103 7 . 2 0 x 103 9 . 6 0 x 103 1.68 x 104 6 . 1 2 x 104 7.20 x 104 4 . 1 4 x 105 6 . 8 4 x 105

Dw(m2s ~)

Dco(m2s

~)

8.84x10 7 . 4 8 x 10 6 . 9 4 x 10 4 . 1 4 x lO 1.79x10 1.01 x l O 7 . 4 0 x 10 6.23xi0 3 . 3 4 x 10 1.70xlO 1.44 x 10 4 . 5 0 x 10 1.00 x 10 3.08 x 10 1.01 x 10 2 . 4 0 x lO 2 . 9 4 x 10 2 . 0 8 x 10

7 . 9 4 x 10 6 . 1 5 x 10 5.88 x 10 3.52 x 10 1 . 6 6 x 10 8.36x10 6 . 2 0 x 10 5 . 2 6 x 10 2 . 7 8 x 10 1 . 4 3 x 10 1.20 x 10 4 . 2 4 x 10 9 . 2 0 x 10 2 . 8 5 x 10 9.85 x 10 2.25 x 10 3 . 1 4 x 10 2.73 x 10

15 ~5 ~5 15 ~5 t6 16 ~6 16 16 ~s ~7 t~

=5 =5 15 ~5 ~5 15 ~6 ~6 16 16 16 17 t7 m ~8 19 20 2~

TM

19 ~9 ~'0 21

Dw,/Dco 1.1l 1.22 1.18 1.18 1.08 1.21 1.19 1.18 1.20 1.19 1.20 1.06 1.09 1.08 1.03 1.07 0.94 0.76

o,~

o_

i(~ j7

"E

\o

I(~ la

)o

I(j m

idz°

id 2~ I(~zz

I 8

I 9

I I0

I 11

I 12

[ 13

T-'/ IU 4 K-' Fig. 4. Arrhenius plots of diffusion coefficientsof cobalt in Fe 50.8 at.% Co alloy in comparison with those by other authors.

1186

IIJIMA and LEE: SELF-DIFFUSION IN B.C.C. AND ORDERED PHASES

of cobalt by the present work is in agreement with those by Fishman et al. [4] and by Hirano and Cohen [3]. However, below 1003 K, the former is smaller than those of the latter two [3, 4]. Okada [2] and Hirano and Cohen [3] have used the residual activity method which is less feasible than the serial sectioning method, in particular for the 7 radiation with high energy as in the case of 6°Co and 59Fe [9]. Furthermore, in the serial mechanical sectioning technique used by Fishman et al. [4] the mean penetration distance in the diffused specimen, 2(Dt) j/2, is much longer than that obtained by the sputter-microsectioning technique. As a result, the apparent diffusion coefficients obtained by the conventional mechanical sectioning techniques are usually affected by the enhancement effect due to the dislocation diffusion [6, 7]. As shown in Table 1, the ratio of DF¢ to Dco is about 1.2 in the disordered b.c.c, phase, while in the ordered phase it decreases gradually with decreasing temperature, and it is 0.76 at 877 K. The temperature dependence of the ratio is the same as that observed by Fishman et al. [4], although in the experiments by Fishman et al. [4] the ratio less than unity at low temperatures has not been definite. The ratio by the present experiment is well in the range between 0.4917 and 2.034, which is derived theoretically for the six jump vacancy mechanism in the B2 ordered structure [10].

3.2. Effect o f magnetic spin ordering on se[f-d!ffusion in the Fe-50.8at. % Co alloy Above 1003 K in Figs 3 and 4, the Arrhenius plots of the self diffusion coefficients by the present work show a slight deviation from linearity, although the previous authors [2-4] have regarded them linear. According to the equilibrium phase diagram [1], the Curie temperature of the equiatomic Fe~Co alloy is 1258 K. Thus an apparent bending of the Arrhenius plot of the self-diffusion coefficients in the alloy can be expected just below 1258 K, as in the case of the self-diffusion in iron above and below the Curie temperature [6, 7]. However, very slight curvature below 1258 K is observed in Figs 3 and 4. According to a thermodynamical study on the chemical and magnetic interchange energies in Fe-Co alloys [11], the Curie temperature of the hypothetical b.c.c, random F e ~ o alloys increases with increasing cobalt content from 1043 K for pure Fe to 1396 K for pure Co, and it is estimated to be 1400 K for the equiatomic composition. Therefore, an apparent curve of the Arrhenius plots would be observed in a higher temperature region near 1400K, if the self diffusion experiment in the hypothetical b.c.c, random equiatomic Fe-Co alloy were carried out. Equations describing the temperature dependence of the self-diffusion coefficients in ~-iron over the whole temperature range across the Curie temperature have been proposed by

-2.6

-2.7

"x/ ¢ C ) -2_8 -2:9

~

o~

-3,0

-3.1 --

- : 5 . 2 L_

I'--3.3

I 0.5

-3.4 0.2

I 0,4

I ~ 0.5 0.6

I 0.7

0.8

S2

Fig. 5. Plots of TIn(D/D~) vs s 2 for self-diffusion in the ferromagnetic Fe 50.8 at.% Co alloy. several workers. Ruch et al. [2] have proposed an equation D = D~exp[-QP(1 + c~sZ)/RT].

(2)

D p and QP are the frequency factor and the activation energy for the self-diffusion, respectively, in the paramagnetic state, s is the ratio of the spontaneous magnetization at T to that at 0 K. The constant expresses the extent of the influence of the magnetic transformation on diffusion. Equation (2) can be rewritten as T I n { D ( T ) / D ~ } = - Q P / R - {,~QP/R}s 2.

(3)

If the values of D p and Qp are known, the value c~can be estimated from the slope of the straight line in the plot of T ln{D(T)/D p } vs s 2, where the experimental value of s(T) for iron has been obtained by Potter [13] and Crangle and Goodman [14]. For the analysis of the self-diffusion in ~-iron the present authors [6] have used this method successfully. Since the Arrhenius plot of self-diffusion coefficients in the paramagnetic c~-iron showed linearity, the values of D~ and Qp have been determined directly from it [6]. For the self-diffusion in e-iron the value of ~ has been estimated to be 0.156. 0 ~

I

I

i

I

"k

]-\

mC)

o 57c0

\o.,

E

E3 - 2 . o __c F - -2.5

-3.0

0

0.11

I _

02

0.3

0.4

0.5

ij z

TIn(D/D m) vs u 2 f o r serf-diffusion in the ordered Fe-50.gat.% Co alloy.

Fig. 6. Plots o f

IIJIMA and LEE:

1187

SELF-DIFFUSION IN B.C.C. AND ORDERED PHASES

Table 2. Frequencyfactor and activation energiesfor self-diffusionin equiatomic Fe Co alloy Activation energy Diffusing Frequency factor Paramagneticphase Ferromagneticphase ordered phase atom D0P(10-4 m2s ') QP Qr= QP(I + ~ z ) Q°=QP(I+~+fl) Fe 7.0 241 280 330 Co 0.31 201 259 314 Unit of lhe energy is kJ m o l i For the present case, the paramagnetic phase of the equiatomic Fe~Co alloy does not exist [1]. Hence, the values of D p and Qp cannot be determined experimentally. Assuming appropriate values of D0p for diffusion of 59Fe and 57Co in the Fe-50.8 at.% Co alloy and using D obtained by the present work, T In{D(T)/D~ } was calculated as a function of s 2, and plotted in Fig. 5, where s ( T ) for pure iron [13, 14] was used, assuming that the temperature dependence of s(T) of the alloy is the same as that of pure iron. To estimate s(T) in the alloy the hypothetical Curie temperature of the equiatomic Fe~Co alloy (MOO K) [11] was converted to the Curie temperature of pure iron (1043 K). The parameters D~, c~ and QP are determined under the conditions that in equation (3) the residual sum of squares for the method of least squares is m i n i m u m (Fig. 5). The following parameters are obtained; for diffusion of 59Fe, D P = ( 7 . 0 + 0 . 1 ) × 10 4m2s 1, :t = 0 . 1 6 4 0.01 and Qp = 241 4- 2 kJ tool ', and for diffusion of STCo, D P = (0.314- 0.01) x 10 4m2s l, ~ = 0 . 2 9 4 0.01 and Q p = 2 0 1 4 - 2 k J m o l 1. The value of for diffusion of 59Fe in the alloy is nearly equal to 0.156 for self-diffusion in a-iron [6] and that for diffusion of 5VCo in the alloy is near to 0.23 for diffusion of cobalt in a-iron [15] but smaller than 0.54 for diffusion of cobalt in an Fe-12 at.% Co alloy [16]. 3.3. Effect o f atomic ordering o f self-diffusion in the Fe-50. 8 at. % Co alloy Below 1003 K the equiatomic F e - C o alloy forms the B2 type ordered phase. The temperature dependence of self-diffusion coefficients across the orde~disorder transformation temperature can be expressed as [17, 18] D = D 0 e x p [ - Q ( 1 +fiu2)/RT]

(4)

as in the case of the paramagnetic-ferromagnetic transformation in equation (2). Do and Q are the frequency factor and the activation energy for diffusion in the disordered phase, u is the long range ordering parameter, fl is the constant expressing the extent of the influence of the atomic ordering on diffusion. For the ordered phase of the equiatomic F c - C o alloy both effects of the magnetic spin ordering and the atomic ordering must be taken into consideration. From equations (2) and (4) the next equation can be written D -- Dl]exp[-QP(1 4- ~s2)(l 4-flu-)/RT].

(5)

The second order t e r m ~fls2bl 2 is negligible if both e and fi are much smaller than unity, as in the present case. Hence D = D~exp[-QP(1 + e s 2 + f l u 2 ) / R T ] . Putting D~ exp[-- QP(I + es2)/"RT] = D m 1003 K, and rewriting equation (6) as T ln{D(T)/D m} = - Q P / R - {flQP/R}u 2

(6) below (7)

we can estimate fi from the slope in the plot of T ln{D(T)/D"} vs u 2 shown in Fig. 6, where we use the value of u for the equiatomic F e - C o alloy determined by the neutron diffraction experiments [19, 20]. Although only the points at 877 K are deviated from the linearity, the constant fl can be estimated to be 0.21 4- 0.01 and 0.27 _+ 0.01 for diffusion of SgFe and STCo, respectively, in the Fe-50.8 at.% Co alloy. The deviation at 877 K in Fig. 6 is probably due to some enhanced diffusion by dislocations. Using the values of D~, Qp, ~ and fi estimated as above, thc solid lines in Figs 3 and 4 are drawn. The fittings of the lines with the experimental points are excellent. The frequency factor and activation energies for the selfdiffusion in the equiatomic Fe Co alloy are summarized in Table 2. In the complete ferromagnetic state of the alloy the activation energies Qf = Qp(1 4- e) for diffusion of Fc and Co are 280 and 259 kJ mol ', respectively. Furthermore, in the complete ordered state the activation energies Q0 = Qp(1 + e + fl) for diffusion of Fe and Co are 330 and 314 k J m o l ,, respectively. 4. CONCLUSIONS Using the sputter-microsectioning technique, selfdiffusion coefficients in an Fe-50.8 at.% Co alloy have been determined in the temperature range from 877 to 1238 K. The temperature dependence of the diffusion coefficients across the order-disorder transition temperature is represented by D F e = 7 . 0 X 10 4 e x p { - - ( 2 4 1 k J m o l 1) x [1 + 0.16s 2 + 0.2lu2]/RT}m 2 s -1 and DCo=0.31 x 10 4 e x p { - ( 2 0 1 k J m o l

1)

x [1 + 0.29s 2 + 0.27u2]/RT}m 2 s -1 where s is the ratio of the spontaneous magnetization at T to that at 0 K, and u is the long range ordering parameter. The increase in activation energies due to the magnetic spin ordering is 16 and 29% for the diffusion of iron and cobalt, respectively, in the alloy.

1188

IIJIMA and LEE:

SELF-DIFFUSION IN B.C.C. AND ORDERED PHASES

Moreover, the increase in activation energies due to the atomic ordering is 21 a n d 2 7 % for the diffusion of iron a n d cobalt, respectively, in the alloy. Acknowledgement One of the authors (C.-G.L.) wishes to acknowledge the support of the Ministry of Education for the Korea Research Foundation (1993).

REFERENCES 1. T. Nishizawa and K. Ishida, Bull. Alloy Phase Diagrams 5, 250 (1984). 2. K. Okada, Radioisotopes 15, 169 (1966). 3. K. Hirano and M. Cohen, Trans. Japan Inst. Metals 13, 96 (1972). 4. S. G. Fishman, D. Gupta and D. S. Leiberman, Phys. Rev. B 2, 1451 (1970). 5. H. Mehrer, Solute Defect Interaction, Theory and Experiment (edited by S. Saimoto, G. R. Purdy and G. V. Kidson), p. 162. Pergamon Press, Toronto (1986). 6. Y. Iijima, K. Kimura and K. Hirano, Acta metall. 36, 2811 (1988). 7. M. Liibbehusen and H. Mehrer, Acta metall, mater. 38, 283 (1990).

8. Y. Iijima, K. Kimura and K. Hirano, Proc. Tenth Symp. Ion Sources and Ion-Assisted Tech. (edited by T. Takagi), p. 297. Ionics, Tokyo (1986). 9. S. J. Rothman, Diffusion in Crystalline Solids (edited by G. E. Murch and A. S. Nowiek), p. 1. Academic Press, New York (1984). 10. M. Arita, M. Koiwa and S. Ishioka, Acta metall. 37, 1363 (1989). 11. G. Inden, Z. Metallk. 68, 529 (1977). 12. L, Ruch, D. R. Sain, H. L. Yeh and L. A, Girifalco, J. Phys. Chem. Solids 37, 649 (1976). 13. H. H. Potter, Proc. R. Soc. A 146, 362 (1934). 14. J. Crangle and G. M. Goodman, Proc. R. Soc. Lond. A321, 477 (1971). 15. Y. Iijima, K. Kimura, C.-G. Lee and K. Hirano, Mater. Trans. JIM 34, 20 (1993). 16. C.-G. Lee, Y. Iijima and K. Hirano, Defect and Diffusion Forum 66---69, 433 (1989). 17. L. A. Girifaleo, J. Phys. Chem. Solids 24, 323 (1964). 18. L, A. Girifalco, Statistical Physics of Materials, p. 274. Wiley, New York (1973). 19. B. G. Lyashenko, D. F. Litvin, I. M. Puzey and J. G. Abov, J. Phys. Soc. Japan 17, Suppl. B-III, 49 (1962). 20. V. I. Goman'kov, D. F. Litvin, A. A. Loshmanov, B. G. Lyashchenko and I. M. Puzei, Soy. Phys. Cryst. 7, 637 (1962).