Diffusion composition path patterns in ternary systems

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a n a l y s i s of diffusion b e h a v i o r in t e r n a r y s y s t e m s is u s u a l l y r e p o r t e d in t e r m s of the v a r i a t i o n with c o m p o s i t i o n of the m a t r i x of f o u r p h e n o m e n o l o g i c a l c o e f f i 9 c m n t s , w r i t t e n D.k.. O c c a s x o n a l l y K~rkendall m a r k e r m o t i o n s a r e alsoZ~reported, 4,~ and in a few i n s t a n c e s i n t r i n s i c diffusion c o e f f i c i e n t s m a y be c a l c u l a t e d , s The t r a n s l a t i o n of such c o m p l e x i n f o r m a t i o n a s the c o m p o s i t i o n d e p e n d e n c e of a m a t r i x of p h e n o m e n o l o g i c a l c o e f f i c i e n t s into a p h y s i c a l p i c t u r e of how the a t o m i c s p e c i e s in the s y s t e m move r e l a t i v e to each o t h e r and the l a t t i c e is v e r y i n d i r e c t . F o r e x a m p l e , the r e l a t i v e v a l u e s of the ~k.. zj c o e f f i c i e n t s depend upon which s p e c i e s is c h o s e n a s the dependent c o m p o s i t i o n a l v a r i a b l e , k; the r e s u l t that Da~l > D~2 d o e s not n e c e s s a r i l y i m p l y that c o m p o n e n t 1 m o v e s f a s t e r than 2 t h r o u g h the s y s t e m , and g i v e s no i n s i g h t w h a t e v e r into the b e h a v i o r of c o m ponent 3. 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 f u s i v i t i e s m a y help to c l a r i f y t h i s s i t u a t i o n , but the i n f o r m a t i o n r e q u i r e d h a s not g e n e r a l l y b e e n d e t e r m i n e d in t e r n a r y diffusion s t u d i e s . The p h e n o m e n o l o g i c a l i n t e r p r e t a t i o n is a f t e r a l l b a s e d upon an a s s u m p t i o n of a p r o p o r t i o n a l i t y b e t w e e n c a r e f u l l y defined f l u x e s and f o r c e s . F r o m the e a r l y o b s e r v a t i o n that the " c o n s t a n t s " in t h i s p r o p o r t i o n a l ity, t h e D~j, a r e b y no m e a n s c o n s t a n t , e,7 the continued a p p l i c a t i o n of the p h e n o m e n o l o g i c a l t h e o r y h a s l e d to m o r e and m o r e c o m p l i c a t e d d e s c r i p t i o n s of the i n t e r p e n e t r a t i o n of a t o m i c s p e c i e s . 8'9 The untangling of t h e s e c o m p l e x i t i e s h a s not y e t r e a c h e d the s t a g e w h e r e in it is p o s s i b l e to c o m p a r e d i r e c t l y the diffusion b e h a v i o r of a s p e c i e s at a given c o m p o s i t i o n in a c o n c e n t r a tion g r a d i e n t in a t e r n a r y s y s t e m with the b e h a v i o r of that s p e c i e s in a h o m o g e n e o u s a l l o y of the s a m e c o m p o s i t i o n . The n u m b e r of s e p a r a t e e x p e r i m e n t s r e q u i r e d to g e n e r a t e the i n f o r m a t i o n to m a k e such a 9

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R. T. DeHOFF, is Professor, Department of Materials Science and Engineering, University of Fla. 32611. K. J. ANUSAVICE, Affiliated with United States Atomic Energy Commission, Savannah River, Georgia. C. C. WAN, is Postdoct

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