Atomic mobilities and vacancy wind effects in multicomponent alloys
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g r a d i e n t s o f c o m p o n e n t s o t h e r t h a n i do not e x p l i c i t l y a p p e a r i n E q . [1], it h a s b e e n s h o w n by M a n n i n gz t h a t E q . [1] i s e q u i v a l e n t t o t h e g e n e r a l t h e r m o d y n a m i c d i f f u s i o n e q u a t i o n g i v e n by n ~j di : - ~ Lij (i = 1 , 2 . . . n ) [2] 1=1 0x w h e r e t h e c r o s s - c o e f f i c i e n t s , Lij (i ยข j), a r e n o n z e r o q u a n t i t i e s a n d a r i s e e n t i r e l y f r o m the v a c a n c y w i n d e f f e c t . M a n n i n g has also d e r i v e d e x p r e s s i o n s f o r all Lij c o e f f i c i e n t s , b o t h d i a g o n a l a n d n o n d i a g o n a l , i n t e r m s o f 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 , D~(i = 1 , 2 , . . n ) , w h i c h c a n be d e t e r m i n e d by n i n d e p e n d e n t m e a s u r e ments. When Jiv i n E q . [1] a n d t h e n o n d i a g o n a l c o e f f i c i e n t s i n E q . [2] a r e z e r o , d i f f u s i o n i n t h e n - c o m p o n e n t s y s t e m c a n be d e s c r i b e d i n t e r m s o f o n l y n m o b i l i t y c o e f f i c i e n t s /3i, a n d t h e /3 i c a n be d e t e r m i n e d f r o m a n e x p e r i m e n t i n v o l v i n g m a r k e r m o t i o n s t u d i e s in a s i n g l e diffusion couple. 3 In t h e p r e s e n t p a p e r , t h e description o f a l l o y d i f f u s i o n i n t e r m s o f t h e 13i i s d e v e l o p e d f u r t h e r . A n a n a l y s i s b a s e d o n m a r k e r m o t i o n s t u d i e s in diffusion c o u p l e s is a p p l i e d to r a n d o m a l l o y s i n c l u d i n g a n o n z e r o v a c a n c y w i n d c o n t r i b u t i o n Jiv in E q . [1]. This analysis a l l o w s t h e determination of atomic m o bilities a n d v a c a n c y w i n d t e r m s f o r all c o m p o n e n t s in a r a n d o m m u l t i c o m p o n e n t a l l o y . It i s s h o w n t h a t a pair of independent diffusion couples with t h e i r m a r k e r p l a n e s i d e n t i f i e d by t h e s a m e c o m p o s i t i o n w i l l s u f f i c e f o r t h e d e t e r m i n a t i o n o f a l l k i n e t i c d a t a a t that c o m m o n composition r e g a r d l e s s of t h e n u m b e r of diffusing species. F o r a r a n d o m a l l o y m o d e l M a n n i n g4 h a s s h o w n that t h e v a c a n c y w i n d e f f e c t is directly p r o p o r t i o n a l to t h e v a c a n c y f l u x , dr. H e n c e , o n e c a n w r i t e that
Jiv = - elNi [3iJv
[3]
w h e r e N i is t h e a t o m f r a c t i o n o f c o m p o n e n t i a n d t h e c o n s t a n t o f p r o p o r t i o n a l i t y , or, i s a f u n c t i o n of c o m p o s i t i o n a n d c r y s t a l s t r u c t u r e ; ot i s d e s i g n a t e d a s t h e v a c a n c y w i n d p a r a m e t e r in t h i s p a p e r . S u b s t i t u t i o n o f E q . [3] i n EQ. [1] y i e l d s :
Atomic Mobilities and Vacancy Wind Effects in Multicomponent Alloys
Ji = - C i ~ i
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B u t , Jv i s g i v e n i n t e r m s o f i n t r i n
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