Intrinsic diffusion and vacancy wind effects in Ag-Cd alloys
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T H E o r i g i n a l a n a l y s i s by D a r k e n I of i s o t h e r m a l diffusion in b i n a r y s y s t e m s has o v e r the y e a r s p r o v i d e d a convenient b a s i s for the d e t e r m i n a t i o n of i n t r i n s i c d i f fusion c o e f f i c i e n t s and to r e l a t e i n t r i n s i c and t r a c e r diffusion c o e f f i c i e n t s through t h e r m o d y n a m i c data. A m o d i f i c a t i o n of D a r k e n ' s a n a l y s i s was p r o p o s e d b y Manning 2 to include a v a c a n c y wind t e r m in the e q u a tions r e l a t i n g the K i r k e n d a l l shift to the t r a c e r diffusion c o e f f i c i e n t s . In a l a t e r p a p e r , Manning 3 showed how v a c a n c y f l u x e s can affect i n t r i n s i c diffusion and d e r i v e d r e l a t i o n s b e t w e e n i n t r i n s i c and t r a c e r c o e f f i c i e n t s which i n c o r p o r a t e d v a c a n c y wind e f f e c t s . F o l lowing the t r e a t m e n t of Manning, D a y a n a n d a 4 d e v e l o p e d an a n a l y s i s f o r an e x p e r i m e n t a l d e t e r m i n a t i o n of v a c a n c y wind c o n t r i b u t i o n s to i n t r i n s i c f l u x e s . In his a n a l y s i s , the a t o m i c m o b i l i t i e s of the c o m p o n e n t s a s well a s the v a c a n c y wind p a r a m e t e r m a y be d e t e r m i n e d with the a i d of a p a i r of independent diffusion c o u p l e s with m a r k e r p l a n e s of i d e n t i c a l c o m p o s i t i o n , r e g a r d l e s s of the n u m b e r of c o m p o n e n t s . The use of D a r k e n ' s r e l a t i o n s without v a c a n c y wind c o r r e c t i o n t e r m s h a s b e e n found i n a d e q u a t e in the c a s e of a C u - Z n a l l o y s b y Schmatz, Domian, and A a r o n s o n s who a p p l i e d D a r k e n ' s e q u a t i o n s with M a n n i n g ' s m o d i f i c a t i o n to d e t e r m i n e the t r a c e r diffusion c o e f f i c i e n t s of c o p p e r and zinc, D~u and D*Zn. They found that the * * Dzn/Dcu ratios evaluated from Manning's equations at v a r i o u s zinc c o n c e n t r a t i o n s a g r e e d w e l l with the corresponding ratios determined from tracer diffusivit i e s . However, i n d i v i d u a l v a l u e s of D*Zn and D~u e v a l uated f r o m M a n n i n g ' s r e l a t i o n s d i f f e r e d s i g n i f i c a n t l y f r o m t h o s e e x p e r i m e n t a l l y d e t e r m i n e d b y t r a c e r diffusion studies. Kohn et alfi d e t e r m i n e d t r a c e r a s well a s i n t r i n s i c diffusion c o e f f i c i e n t s in the F e - N i and F e - C o s y s t e m s at 1200~ The K i r k e n d a l l s h i f t s o b s e r v e d b y t h e m in t h e s e s y s t e m s w e r e found to be g r e a t e r than t h o s e p r e N. R. IORIO is with Westinghouse Electric Corp., Tampa, Fla. M. A. DAYANANDA and R. E. GRACE are Associate Professor and Professor, respectively, School of Materials Science and Metallurgical Engineering, Purdue University, West Lafayette, Ind. 47907. Manuscript submitted September I
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