Homogenization by diffusion
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D I F F U S I V E p r o c e s s e s n a t u r a l l y lead to h o m o g e n i z a t i o n - a n isolated stable s y s t e m will approach u n i f o r m i t y as a c o n s e q u e n c e of the second law. Indeed, all diffusion m e a s u r e m e n t s made u n d e r c o n v e n t i o n a l l a b o r a t o r y conditions a r e e q u i v a l e n t to p a r t i a l h o m o g e n i z a t i o n . 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 s t r u c t u r e that h a s been built up around the p r o c e s s of s o l i d - s t a t e diffusion 1-s i s t h e r e f o r e of r e l e v a n c e in a d i s c u s s i o n of the decay of m i c r o s e g r e g a t i o n . Application of this knowledge i n v o l v e s the t r a n s p o s i t i o n of concepts and q u a n t i t i e s p r e v i o u s l y explored u s i n g , say, infinite c o u p l e s to s y s t e m s with i n i t i a l c o n d i t i o n s i m p o s e d through p r i o r treatment: casting, working, or second-phase dissolution. G e n e r a l l y , these a r e finite s y s t e m s . The p r a c t i c a l s i g n i f i c a n c e of the d e g r e e of h o m o g e n e ity of a l l o y s is e v i d e n t throughout the m e t a l s i n d u s t r y . S u c c e s s f u l heat t r e a t m e n t of m a t e r i a l s is often s t r o n g l y dependent on the d i s t r i b u t i o n of alloying e l e m e n t s , as a r e the p r o p e r t i e s of the f i n a l m a t e r i a l s . In the s i m p l e s t a n a l y s i s , the p r o b l e m of h o m o g e n i z a t i o n r e d u c e s f o r m a l l y to a closed--although often t o r t u o u s - - m a t h e m a t ical p r o b l e m . However, t h e r e e x i s t a n u m b e r of i n t e r e s t i n g a s well as t e c h n o l o g i c a l l y s i g n i f i c a n t p h y s i c a l a s p e c t s of the p r o c e s s , which a r i s e when the i n t e r a c tions of s o l u t e s with c r y s t a l l i n e d e f e c t s - - o r with o t h e r solutes--are considered. H e r e , we will r e v i e w the p r i n c i p l e s of diffusion in solids in the context of the p r a c t i c a l p r o b l e m of the r e m o v a l of p e r i o d i c m i c r o s e g r e g a t i o n r e s u l t i n g f r o m a l loy s o l i d i f i c a t i o n , as d i s c u s s e d in the p r e c e d i n g c o n t r i bution. The f i r s t p a r t of t h i s p a p e r will e m p h a s i z e ' b i n a r y ' effects, i.e., those which o c c u r in t w o - c o m p o nent a s well as in h i g h e r o r d e r s y s t e m s . The l a t t e r p a r t will deal with p h e n o m e n a which a r e e x c l u s i v e to t e r n a r y and higher o r d e r s y s t e m s : " u p h i l l " diffusion in stable s o l u t i o n s , and p r e c i p i t a t i o n as an i n t e r m e d i a t e stage in h o m o g e n i z a t i o n . The a p p l i c a t i o n s and e x a m p l e s c h o s e n , by e d i t o r i a l r e q u e s t , deal p r i m a r i l y with f e r r o u s s y s t e m s , but it would be difficult to w r i t e a p a p e r of this kind which did not p o s s e s s a hi
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