The application of first order mixing statistics to the variation of the diffusivity of carbon in austenite
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was shown r e c e n t l y I that the c o m p o s i t i o n d e p e n dence of the d i f f u s i v i t y , D, of c a r b o n in a u s t e n i t e at a given t e m p e r a t u r e can be e x p l a i n e d in t e r m s of the s i m p l e blocking m o d e l f o r i n t e r s t i t i a l s o li d s o l u t i o n s . In this m o d e l a r e p u l s i v e p o t e n ti a l e x i s t s b e t w e e n s o l ute a t o m s in the s o l v e n t l a t t i c e such that a c e r t a i n n u m b e r of n e a r e s t n e i g h b o r i n t e r s t i t i a l s i t e s a r e r e s t r i c t e d f r o m occupancy by f u r t h e r i n t e r s t i t i a l a t o m s . In c a l c u l a t i n g the c o m p o s i t i o n d e p e n d e n c e of D, the n u m b e r of a v a i l a b l e s i t e s f o r f o r w a r d or b a c k w a r d diffusion jumps along the c o n c e n t r a t i o n g r a d i e n t was d e t e r m i n e d . T h i s n u m b e r is a function of c o m p o s i t i o n ; it e f f e c t i v e l y i n t r o d u c e s a c o m p o s i t i o n dependence into the i n t r i n s i c m o b i l i t y of the diffusing a t o m s . The g r e a t e r p a r t of the c o m p o s i t i o n d e p e n d e n c e of D i s , h o w e v e r , due to the v a r i a t i o n of c a r b o n a c t i v i t y in a u s t e n i t e with c o m p o s i t i o n . D a r k e n 2 showed that the d i f f u s i v i t y , D, of an i n t e r s t i t i a l solute depends on i t s a c t i v i t y c o e f f i c i e n t ~ and c o n c e n t r a t i o n C in the f o r m
D = BkT(1 + Cd in y/dC)
[1]
w h e r e T is the t e m p e r a t u r e , k i s B o l t z m a n n ' s c o n stant, and B is the m o b i l i t y of the solute a t o m . Howe v e r , S m i t h ' s a t t e m p t s to r e c o n c i l e the o b s e r v e d d ependence of D on c o m p o s i t i o n with an equation d er i v e d by F i s h e r , H o l l o m o n , and T u r n b u l l a
and with Eq. [1] a s s u m i n g a c o m p o s i t i o n independent m o b i l i t y B, was u n s u c c e s s f u l . H o w e v e r , a s D a r k e n h i m s e l f pointed out, 2 t h e r e is no r e a s o n why B should not v a r y with c o m p o s i t i o n . In the t r e a t m e n t of S i l l e r and M c L e l l a n , ~ e s s e n t i a l l y the c o n c e n t r a t i o n d e p e n d e n c e of the m o b i l i t y was c a l c u l a t e d f r o m the g e o m e t r i c a l b l o c k i n g m o d e l of i n t e r s t i t i a l s o l u t i o n s . In this m o d e l the r e p u l s i v e i n t e r a c tion b et ween solute a t o m s is m a n i f e s t e d in the fact that s o m e of the n e a r e s t - n e i g h b o r i n t e r s t i t i a l s i t e s s u r r o u n d i n g a given solute a t o m a r e r e s t r i c t e d f r o m o c c u p a n c y by f u r t h e r solute a t o m s . T h i s c a u s e s an e n h a n c e m e n t in the diffusion r a t e which i n c r e a s e s with c o m p o s i t i o n . D e s p i t e the s i m p l i c i t y of the s o l u t e - s o l u t e r e p u l s i v e i n t e r a c t i o n s and the fact that o v e r
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