Atomic mobilities and vacancy wind effects for diffusion in ternary Silver-zinc-cadmium solid solutions
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his now c l a s s i c p a p e r on the s u b j e c t of d i f f u s i o n in b i n a r y m e t a l l i c s y s t e m s , D a r k e n 1 e m p h a s i z e d the n e e d to d i s t i n g u i s h b e t w e e n i n t r i n s i c d if f u s io n and m a s s flows d e m o n s t r a t e d by the K i r k e n d a l l e f f e c t . In a d d i tion to this i m p o r t a n t c o n t r i b u t i o n to the a r e a of m a s s t r a n s p o r t in the p r e s e n c e of c h e m i c a l c o n c e n t r a t i o n g r a d i e n t s , D a r k e n 1 a l s o p r o v i d e d an a n a l y s i s which r e l a t e s i n t r i n s i c and t r a c e r d i f f u s i o n c o e f f i c i e n t s t h r o u g h t h e r m o d y n a m i c i n f o r m a t i o n . In g e n e r a l , h o w e v e r , the c o m p o n e n t s of a b i n a r y a l l o y diffuse at d i f f e r e n t r a t e s , and in the p r e s e n c e of a c h e m i c a l c o n c e n t r a t i o n g r a d i ent this l e a d s to a net flow of m a t t e r d u r i n g diffusion. When diffusion p r o c e e d s by the v a c a n c y m e c h a n i s m , the n et flow of m a t t e r in one d i r e c t i o n is b a l a n c e d by a net flow of v a c a n c i e s in the o p p o s i t e d i r e c t i o n . Manning ~ has shown that c o n s i d e r a t i o n of the net v a c a n c y flow, o m i t t e d in the o r i g i n a l D a r k e n a n a l y s i s , is r e la ted to the v a c a n c y wind e f f e c t and g i v e s r i s e to a d d i tional t e r m s in the D a r k e n e q u a t i o n s r e l a t i n g the i n t r i n s i c diffusion c o e f f i c i e n t s , i n t e r d i f f u s i o n c o e f f i c i e n t and K i r k e n d a l l shift to the t r a c e r d i f f u s i o n c o e f f i c i e n t s . F o l l o w i n g M a n n i n g ' s t r e a t m e n t , Dayananda 3 d e v e l o p e d an a n a l y s i s with which 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 can be e x p e r i m e n t a l l y d e t e r m i n e d . In his t r e a t m e n t , 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 as well as 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 use of a p a i r of i n d e p e n d e n t d if f u si o n c ou p l es 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 . On the b a s i s of both the Manning and Dayananda a n a l y s e s , the t h e o r e t i c a l and e x p e r i m e n t a l c o n t r i b u t i o n s of the v a c a n c y wind e f f e c t to the i n t r i n s i c f l u x e s can be determined for each component. A t t e m p t s to v e r i f y the m o d i f i e d e x p r e s s i o n s of ManP. T. CARLSON is Research Staff Member, Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tenn. 37830. M. A. DAYANANDA and R. E. GRACE are Associate Professor and Professor respectively, School of Materials Engineering, Purdue University, West Lafayette, Ind. 47907. Manuscript submitted September 19, 1974. METALLURGICAL TRANSACTIONS A
ning which include t e r m s a r i s i n g
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