Discontinuous precipitation in aluminum-base zinc alloys
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T H E R E a r e many e x a m p l e s of solid state phase t r a n s f o r m a t i o n s o c c u r r i n g w h e r e a single phase t r a n s f o r m s d i s c o n t i n u o u s l y into two new p h a s e s , one of which has the s a m e c r y s t a l s t r u c t u r e as the p a r e n t p h a s e . 1-1~ P e r h a p s the m o s t well d o c u m e n t e d t r a n s f o r m a t i o n of this n a t u r e is that o c c u r r i n g in the P b - S n s y s t e m w h e r e e x t e n s i v e s t u d i e s have b e e n made on the n u c l e a t i o n , growth, and morphology of the l a m e l l a r p r o d u c t , the l e a d - r i c h a and t i n - r i c h / 3 p h a s e s . 5-~~ P r e c i p i t a t i o n in this s y s t e m is g e n e r a l l y thought to s t a r t by n u c l e a t i o n of the /3 p h a s e along g r a i n b o u n d a r i e s followed by m o v e m e n t of the g r a i n b o u n d a r y to m i n i m i z e the n e w l y c r e a t e d s u r f a c e e n e r g y b e t w e e n ot and/3. Continued n u c l e a t i o n , b o u n d a r y m o t i o n , and s u b s e q u e n t b r a n c h i n g of the /3 phase e v e n t u a l l y r e s u l t s in the d e v e l o p m e n t of a c e l l u l a r s t r u c t u r e which grows at a c o n s t a n t r a t e into the m a t r i x ot p h a s e . S e g r e g a t i o n is quite likely a c c o m p l i s h e d by diffusion along the advancing i n c o herent cellular interface. T h e s e c h a r a c t e r i s t i c s hold t r u e also in s y s t e m s w h e r e both c o n t i n u o u s and d i s c o n t i n u o u s p r e c i p i t a t i o n o c c u r s i m u l t a n e o u s l y . However, the p r e s e n c e of the c o n t i n u o u s p r e c i p i t a t e has an affect on the growth of the d i s c o n t i n u o u s p r e c i p i t a t e . A a r o n s o n and C l a r k ~ have shown that in the A1-Ag s y s t e m the d r i v i n g f o r c e for (and t h e r e f o r e the r a t e of) d i s c o n t i n u o u s p r e c i p i tation is i n v e r s e l y p r o p o r t i o n a l to the extent to which continuous p r e c i p i t a t i o n has o c c u r r e d . The o v e r a l l r a t e equation g o v e r n i n g m o s t d i s c o n tinuous phase t r a n s f o r m a t i o n s can be e x p r e s s e d in the f o r m X : 1 - e x p ( ~ t n)
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w h e r e X is the v o l u m e f r a c t i o n t r a n s f o r m e d , t is t i m e , and b and n a r e c o n s t a n t s whose v a l u e s depend upon the n u c l e a t i o n and growth r a t e s of the t r a n s f o r m a t i o n p r o d u c t . Many d i s c o n t i n u o u s r e a c t i o n s occur by the r a p i d i n i t i a l exhaustion of a v a i l a b l e n u c l e a t i o n s i t e s (usually g r a i n b o u n d a r i e s ) followed by a growth stage in which no f u r t h e r n u c l e a t i o n o c c u r s . T h i s b e h a v i o r has b e e n t e r m e d " s i t e s a t u r a t i o n " , and is p a r t i c u l a r l y UMESH K. MALHOTRAis Development Engineer, Tarrytown Technical Center, Linde Division, Union Carbide Corp., Tarrytown, N.Y. KARL B
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