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SHARP AND M. C. F L E M I N G S

A t h e o r y i s given which r e l a t e s the c o m p o s i t i o n of i n t e r d e n d r i t i c " e u t e c t i c " f o r m i n g d u r ing u n i d i r e c t i o n a l s o l i d i f i c a t i o n to s o l i d i f i c a t i o n v a r i a b l e s . T h i s t h e o r y shows that the c o m p o s i t i o n of the s o l i d f r e e z i n g f r o m the i n t e r d e n d r i t i c liquid is not equal to the e u t e c t i c c o m p o s i t i o n but is e x a c t l y e q u i v a l e n t to the c o m p o s i t i o n of the a l l o y which would j u s t grow with a p l a n a r front at the s a m e g r o w t h r a t e a n d t e m p e r a t u r e g r a d i e n t . It is shown that t h i s l e a d s to a m e t h o d for d e t e r m i n i n g the c r i t i c a l v a l u e s of t e m p e r a t u r e g r a d i e n t and g r o w t h r a t e for i n t e r f a c e s t a b i l i t y of o f f - e u t e c t i c c o m p o s i t e s . E x p e r i m e n t a l r e s u l t s for the b i n a r y A1-Cu s y s t e m and the t e r n a r y A 1 - C u - N i s y s t e m give good a g r e e m e n t with theory.

WHEN c e l l s o r d e n d r i t e s grow into a m e l t of a b i n a r y a l l o y the s o l u t e is r e j e c t e d l a t e r a l l y and p r o g r e s s i v e e n r i c h m e n t of s o l u t e o c c u r s in the i n t e r d e n d r i t i c liquid (if h < 1) until the e u t e c t i c c o m p o s i t i o n i s r e a c h e d . At the e u t e c t i c t e m p e r a t u r e the r e m a i n i n g liquid s o l i d i f i e s a s a two p h a s e s o l i d . Although the liquid c o m p o s i t i o n is then a t the e u t e c t i c c o m p o s i t i o n , the s o l i d which f r e e z e s out i s not, and m a y d i f f e r s u b s t a n t i a l l y f r o m it. C o n s i d e r c e l l s o r d e n d r i t e s of a b i n a r y a l l o y f r e e z i n g u n i d i r e c t i o n a l l y a s s c h e m a t i c a l l y shown in F i g . 1. We a s s u m e that 1) e q u i l i b r i u m p e r t a i n s at a l l liquid s o l i d i n t e r f a c e s , 2) the effect of i n t e r f a c e c u r v a t u r e on the l i q u i d u s t e m p e r a t u r e i s n e g l i g i b l e , and 3) s o l u t e diffusion in the l i q uid i s s u f f i c i e n t l y r a p i d that t h e r e i s n e g l i g i b l e u n d e r cooling in i n t e r d e n d r i t i c s p a c e s . T h e s e a r e the b a s i c a s s u m p t i o n s that have been u s e d in r e c e n t p a p e r s in q u a n t i t a t i v e d e s c r i p t i o n of solute r e d i s t r i b u t i o n in d e n d r i t i c s o l i d i f i c a t i o n . 1'2 Now a s s u m e f u r t h e r that i s o t h e r m s a r e p l a n a r . F r o m a s s u m p t i o n (3) alone i s o c o n c e n t r a t e s m u s t a l s o be e s s e n t i a l l y p l a n a r . Then, at any point in the liquid b e t w e e n the d e n d r i t e s , the c o n c e n t r a tion g r a d i e n t in the g r o w t h d i r e c t i o n is given by ~x

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