Thermodynamics of the Ni3Ga phase with the L12 superlattice structure

Scripta

METALLURGICA

Vol. i0, p p . 2 0 1 - 2 0 4 , P r i n t e d in the U n i t e d

THERMODYNAMICS OF THE

Ni3Ga PHASE WITHTHE

1976 States

Pergamon

Press,

Inc.

L12 SUPERLATTICE STRUCTURE

Y. A. Chang and Y. Hsiao Materials Department College of Engineering and Applied Science University of Wisconsin-Milwaukee Milwaukee, Wisconsin 53201 (Received

December

15, 1975)

Since the publication of the theoretical equations by Gyuk, Liang and Chang (1,2) to describe the compositional dependence of the thermodynamic properties of substantially ordered 3:1 intermetallic phases exhibiting the Cu3Au-type (LI2) structure, data have become available for the a'-NisGa phase. Katayama, Igi and Kozuka (3) measured the activities of Ga in the ~-NiGa and e'-Ni3Ga and ~'-NisGa + 8'-NiGa two-phase field as well as in the homogeneous region from 1125 to 1325 K using a solid-oxide electrolyte galvanic cell technique. Pratt, Bird and Martosudirdjo (4), on the other hand, measured the activities of Ga in these alleys from 660 to 1250 K also using a solid-oxide electrolyte galvanic cell technique. The primary purpose of the present communication is to test the validity of the theoretical equations of Gyuk, Liang and Chang using the experimental data detel-mined by these two groups of investigators since extensive data were not available in the literature for any of the intermetallic phases exhibiting the L12 structure at the time the theoretical equations were presented. Secondly, using this theoretical model it is intended to check the consistency of these two sets of experimental data obtained as has been done by Kou and Chang (5) for ordered 81-NiZn intermetallic phases exhibiting the L1 structure, o The theoretical equation in describing the compositional dependence of the activity of Ga in the a'-Ni3Ga phase is (1,2), 1 l-4z 3 3-4X-4z £n aGa = 8[X 2 - z(x + 2z) + 2~ 2] + [ £n ~ + [ £n 3-4~ aGa, 0 3 3 ~ ~-X-Z * [ [ 8 ( z - a - 2 X ) - £n -] X*Z ~ - a

(1)

4

1

where 8 = f(e) = and

4a 2

~ - 4a 4

£n

~ - 4e + 4e 2 4

a is a disorder parameter at the stoichiometric composition, X = x~ .ha - 0.25 = 0.0; expressing the fraction of Ga atoms which have gone to the N1-sublattice sites; z is the composition-dependent disorder parameter and is a function of a and X. A l t h o u g h Eq. (1) i s r a t h e r complex, n e v e r t h e l e s s i t c o n t a i n s o n l y one p a r a m e t e r a ; knowing w h i c h , we can r e a d i l y compute t h e v a r i a t i o n o f a c t i v i t y o f Ga w i t h d e v i a t i o n s from s t o i c h i o m e t r y . The d a t a d e t e r m i n e d b y Katayama, e t a l . , and P r a t t , e t a l . , a r e c o r r e l a t e d w i t h Eq. ( i ) n u m e r i c a l l y u s i n g a d i g i t a l c o m p u t e r , The v a l u e s o f a a t d i f f e r e n t t e m p e r a t u r e s a r e o b t a i n e d by means o f b e s t f i t s b e t w e e n t h e e x p e r i m e n t a l d a t a and t h e t h e o r e t i c a l l y computed c u r v e s • Fig. 1 shows t h a t t h e P r a t t , e t a l . a t 875 K a r e and a = 0.0013 a t 873 K. a r e e s t i m a t e d b a s e d on t h e

v a l u e s o f £n a_ as d e t e r m i n e d by Katayama, e t a l a t 1225 K and by i n good a g r e e m e n t w i t h t h e computed v a l u e s u s i n g a = 0 . 0 0 9 a t 1225 K In e v a l u a t i n g t h e s e d a t a , t h e p h a s e b o u n d a r i e s o f t h e ~ ' - N i s G a p h a s e p h a s e d i a g r a m o f H e l l n e r (6) and E l l i o t t (7), since activity values •

b a

.

201

202

THERMODYNAMICS OF N i 3 G a

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No.

2

were d e t e r m i n e d i n t h e a + a ' and e ' + 6' t w o - p h a s e f i e l d s . The p h a s e b o u n d a r i e s a r e n o t w e l l known and t h e v a l u e s u s e d a r e e s t i m a t e d t o have an u n c e r t a i n t y o f a t l e a s t ± 0.5 at%. Having o b t a i n e d t h e v a l u e s o f a a t t h e s e two t e m p e r a t u r e s , we can c o r r e l a t e e n t h a l p y d a t a as a f u n c t i o n o f c o m p o s i t i o n u s i n g t h e f o l l o w i n g e q u a t i o n :

HGa

HGa,0 RT

2 ÷ 3a

-

= B [,:~ 3

+ ¥

[-x

4

+ a -

3 2(×

+

32

+ 4a2) 1/2

the partial

]

2X2 ÷ 4a 2 + 3/4 X

2(X 2 + 4U2) I/2

(2)

The theoretical values for the compositional variation of the partial entropy may be obtained from Eqs. (i) and (2) and the standard relationship between free energy, enthalpy and entropy. Figs. 2 and 3 show that the experimental values of AH~ba and AS~ a obtained from the temperature . d e p e n d e n c e o f t h e a c t i v i t y d a t a r e p o r t e d by Katayama, e t a l . a~ 1223 K a r e i n good a c c o r d w i t h the theoretically computed v a l u e s u s i n g a v a l u e o f u = 0.009. A t t e m p t s t o c o r r e l a t e t h e compos i t i o n a l d e p e n d e n c e o f ~H~ and ~SGa as o b t a i n e d by P r a t t , e t a l . a t 873 K w i t h t h e t h e o r e t i c a l ha. curves are not successful since thexr data scatter badly with composition. Knowing t h e v a l u e s o f a d e r i v e d from a c t i v i t y d a t a a t 1223 and 873 K, we may compute t h e v a l u e o f Tc o , t h e c r i t i c a l t r a n s i t i o n t e m p e r a t u r e from an o r d e r e d s t a t e t o a d i s o r d e r e d s t a t e , for the s t o l c h l o m e t r l c alloy using the following equation (8): T

c,o _ 0.2055 T 1 - ~ - .16 -a

£n 3___ (I - 4u)(l - 4u/3) 16 u2

(3)

The value of a = 0.009 at 1223 K y i e l d s a value of Tc, o = 2033 K while that of a = 0.0015 at 873 K yields a value of a = 2048 K, in excellent agreement with each other. Since both groups of investigators have determined the activity values of the stoichiometric alloy, their data are presented in Fig. 4 for comparison. The solid line show~ in this figure is believed to best represent the temperature dependence of the activity values since they are based on the smoothed values of £n aGa obtained at 1223 and 873 K from Fig. I. The slightly higher activity values of Pratt, et al., from those based on the smoothed data is undoubtedly due to a small change in the composition from stoichiometry. Since the activity values change drastically at the stoichiometric co.mposition, any small variation in composition will cause a correspondingly large change in activity values. Based on the experimental evidence presented in Figs. I-4 and the values of To, o derived from both sets of experimental data at different temperatures, it is reasonable to conclude that the theoretical model is adequate in describing the thermodynamic behavior of this type of substantially ordered intermetallic phases. Furthermore, the two sets of experimental data are compatible with each other. Acknowledgment Financial support of the National Science Foundation (Grant No. (~H-36123) is greatly acknowledged. References I.

I Gyuk, W. W. Liang, and Y. A. Chang, J. Less-Com. Metals, 38, 249-256 (1974).

2.

Y . A . Chang, in "Treatise on Materials Science and Technology," i, edited by H. Herman, 173-259, Academic Press, New York (1974).

3.

I. Katayama, S. Igi and Z. Kozuka, J. Japan Inst. Metals, 38, 332-338 (1974).

Vol.

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No. 2

THERMODYNAMICS OF Ni3Ga

203

4.

J.N. Pratt, J. M. Bird, and S. Martosudirdjo, Final Technical Report, United States Army, Contract DAJA37-72-C-3034, March 1975, Department of Physical Metallurgy and Science of Materials, University of Birmingham, England.

5.

S. Kou and Y. A. Chang, Met. Trans., 6A, 245-248 (1975).

6.

E. Hellner, Z. Metallk., 41, 480 (1950).

7.

R.P.

8.

T. Muto and Y. Takagi, "Solid State Physics," I, edited by F. Seitz and D. Turnbull, 195-282 (1955).

Elliott, Constitution of Binary Alloys, McGraw-Hill Book Co., New York (1965).

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Figure I Comparison between Theory and Experiment for the Activities of Ga at 1223 and 873 K.

Figure 2 Comparison between Theory and Experiment for the Partial Enthalpies of Ga at 1225 K.

204

THERMODYNAMICS

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Figure 3

Comparison b e t w e e n Theory and E x p e r i m e n t f o r t h e P a r t i a l

Entropies

o f Ga a t 1223 K.

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Figure 4

Correlation Pratt,

of Activity

et al.

Data o f Ga R e p o r t e d by Katayama, e t a l .

as a F u n c t i o n o f T e m p e r a t u r e .

and

No.

2