Intrinsic diffusion and vacancy flow effects in vanadium-titanium alloys
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I n t r i n s i c diffusion coefficients and v a c a n c y flow p a r a m e t e r s have b e e n d e t e r m i n e d in the v a n a d i u m - t i t a n i u m s y s t e m f r o m 900 to 1500~ The e x p e r i m e n t a l r e s u l t s r e f l e c t a g r e a t e r i n f l u e n c e of the v a c a n c y flow p h e n o m e n o n on the i n t r i n s i c flux of each s p e c i e s than that p r e d i c t e d on the b a s i s of the r a n d o m alloy model. The p r i n c i p a l a s s u m p t i o n s of the r a n d o m alloy model a r e that a single vacancy m e c h a n i s m is the o p e r a t i v e diffusion m e c h a n i s m and that a l l diffusing s p e c i e s find t h e m s e l v e s in r a n d o m e n v i r o n m e n t s with the a b s e n c e of p r e f e r r e d s i t e s for e i t h e r a t o m s or v a c a n c i e s . Solvent diffusivity e n h a n c e m e n t c a l c u l a t i o n s have been p e r f o r m e d , however, and s u g g e s t that e x i s t e n c e of two competing, v a c a n c y mec h a n i s m s in this s y s t e m . The o b s e r v e d d i s c r e p a n c i e s between t h e o r e t i c a l and e x p e r i m e n t a l v a l u e s a r e e x a m i n e d in light of the o c c u r r e n c e of a combined m o n o v a c a n c y - d i v a cancy m e c h a n i s m . In addition, other n o n r a n d o m effects a r e d i s c u s s e d which r e s u l t in violations of the r a n d o m alloy model a s s u m p t i o n s and which lead to d i f f e r e n c e s b e t w e e n t h e o r e t i c a l and e x p e r i m e n t a l q u a n t i t i e s . I N an e a r l y paper, D a r k e n ~ developed an a n a l y s i s 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 which d e m o n s t r a t e d that c h e m i c a l diffusion coefficients, in the f o r m of i n t e r d i f f u s i o n and i n t r i n s i c diffusion coefficients, could be c a l c u l a t e d f r o m t r a c e r diffusion and t h e r m o d y n a m i c a c t i v i t y data. Some y e a r s l a t e r , M a n n i n g2 p r o p o s e d a modification to D a r k e n ' s t r e a t m e n t for a v a c a n c y m e c h a n i s m to include a d d i t i o n a l t e r m s in the equations which r e l a t e i n t r i n s i c coefficients and K i r k e n d a l l m a r k e r shifts to t r a c e r diffusion coefficients. Since, in g e n e r a l , the components of a b i n a r y alloy diffuse at different r a t e s , a net flow of m a t t e r r e s u l t s d u r i n g diffusion i n 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 e n t . If, in addition, 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 net 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 opposite d i r e c t i o n . The net flux of v a c a n c i e s is r e l a t e d to the v a c a n c y flow effect, and it is this effect which gives r i s e to the t e r m s added to D a r k e n ' s o r i g i n a l e x p r e s s i o n s . F o l l o w i n g a l a t e r t r e a t m e n t by Manning, 3 which extended the t h
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