Effects of growth mechanism on solution kinetics
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m a t h e m a t i c a l m o d e l s that have b e e n p r o p o s e d for the p r e d i c t i o n of the s o l u t i o n k i n e t i c s of s e c o n d - p h a s e p a r t i c l e s have b e e n f o r m u l a t e d to handle s t r u c t u r e s that w e r e e q u i l i b r a t e d in the t w o - p h a s e f i e l d p r i o r to solution t r e a t m e n t . 1-s It i s quite p r o b a b l e , h o w e v e r , that m o s t s o l u t i o n t r e a t m e n t s a r e c a r r i e d out u n d e r conditions w h e r e c o n c e n t r a t i o n g r a d i e n t s e x i s t in the m a t r i x p r i o r to the s o l u t i o n t r e a t m e n t . Singh and F l e m i n g s 6 have p r e s e n t e d a m o d e l for the s o l u t i o n t r e a t m e n t of c a s t i n g s w h e r e the i n i t i a l s o l u t e c o n c e n t r a t i o n g r a d i e n t (due to c o r i n g ) s l o p e d a w a y f r o m the s e c o n d - p h a s e p a r t i c l e s and the c o n c e n t r a t i o n - d i s t a n c e (CD) p r o f i l e could be a p p r o x i m a t e d b y a sine function. A a r o n 7 h a s p r e s e n t e d a m o d e l for the solution t r e a t m e n t of s e c o n d - p h a s e p a r t i c l e s which had not r e a c h e d t h e i r m a x i m u m s i z e d u r i n g a growth h e a t t r e a t m e n t in the t w o - p h a s e f i e l d . T h i s s o l u t i o n m o d e l c o n t a i n s an i n i t i a l solute c o n c e n t r a t i o n g r a d i e n t that s l o p e s t o w a r d the s e c o n d - p h a s e p a r t i c l e s . A a r o n a s s u m e d the i n i t i a l g r a d i e n t ( r e s u l t i n g f r o m the growth p r o c e s s ) to be l i n e a r and t i m e - i n d e p e n d e n t d u r i n g solution. He a l s o a s s u m e d that the g r a d i e n t that d e v e l o p e d d u r i n g s o l u tion was l i n e a r and t i m e - d e p e n d e n t d u r i n g the s o l u t i o n process. It was the p u r p o s e of the p r e s e n t i n v e s t i g a t i o n to s t u d y the e f f e c t s of growth m e c h a n i s m and d u r a t i o n of the growth p r o c e s s on s u b s e q u e n t solution k i n e t i c s . Both 1) d i f f u s i o n - c o n t r o l l e d g r o w t h (DCG) with e q u i l i b r i u m i n t e r f a c e c o m p o s i t i o n s and e r r o r function CD p r o f i l e s and 2) i n t e r f a c e - r e a c t i o n - c o n t r o l l e d g r o w t h (IRCG), w h e r e the s o l u t e c o n c e n t r a t i o n in the m a t r i x d e c r e a s e d u n i f o r m l y with growth t i m e (negligible g r a d i e n t s ) , w e r e c o n s i d e r e d a s i n i t i a l c o n d i t i o n s for the s o l u t i o n k i n e t i c s . The c a l c u l a t i o n s which w e r e c a r r i e d out w e r e b a s e d upon the p l a n a r , finite m o d e l p r e s e n t e d p r e v i o u s l y by T a n z i l l i and H e c k e l . 4 T h i s n u m e r i c a l m e t h o d m o d e l was a d a p t e d to the p r e s e n t s t u d y by p r o v i d i n g for the input of s o l u t e CD p r o f i l e s ( n u m e r i c a l e r r o r
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