Macrosegregation in ternary alloys
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G e n e r a l e x p r e s s i o n s a r e given to d e s c r i b e m a c r o s e g r e g a t i o n in t e r n a r y alloys r e s u l t i n g from m a s s flow of i n t e r d e n d r i t i c liquid d u r i n g s o l i d i f i c a t i o n . B a s i c p a r a m e t e r s d e t e r m i n i n g whether a given alloy e l e m e n t s e g r e g a t e s p o s i t i v e l y o r n e g a t i v e l y a r e given, and it is shown that alloy e l e m e n t s which form a s e c o n d phase, e . g . , an i n c l u s i o n , can often be expected to s e g r e g a t e p o s i tively where other alloy e l e m e n t s s e g r e g a t e n e g a t i v e l y . N u m e r i c a l e x a m p l e s a r e given for a l loys from the a l u m i n u m rich c o r n e r of the A1-Cu-Ni s y s t e m and qualitative e x a m p l e s a r e given for the F e - S i - O s y s t e m . E x p e r i m e n t a l m e a s u r e m e n t s of m a c r o s e g r e g a t i o n in the A1-Cu-Ni s y s tem a r e in a g r e e m e n t with t h e o r y . I N a r e c e n t s e r i e s of p a p e r s , a n a l y t i c a l and e x p e r i m e n t a l work has b e e n r e p o r t e d on m a c r o s e g r e g a t i o n in b i n a r y a l l o y s . 1-3 A g e n e r a l c o n c l u s i o n r e a c h e d in that work was that a v a r i e t y of a p p a r e n t l y different types of m a c r o s e g r e g a t i o n r e s u l t from the s a m e b a s i c c a u s e - - m a s s flow of i n t e r d e n d r i t i c liquid to feed s o l i d i fication and t h e r m a l c o n t r a c t i o n s . In this p a p e r we extend our c o n s i d e r a t i o n s to t h r e e component a l l o y s . Our m a j o r i n t e r e s t is to c o m p a r e s e g r e g a t i o n b e h a v i o r of those c o m p o n e n t s that a r e p r e d o m i n a n t l y in solid solution in the p r i m a r y phase, with s e g r e g a t i o n b e h a v i o r of those c o m p o n e n t s that a r e p r e d o m i n a n t l y in s e c o n d a r y p h a s e s . The f o r m e r e l e m e n t s will be r e f e r r e d to as " s o l i d solution c o m p o n e n t s " and the latt e r as " i n c l u s i o n f o r m i n g c o m p o n e n t s " . MACROSEGREGATION EXPRESSIONS G e n e r a l . In d e r i v i n g the g e n e r a l m a c r o s e g r e g a t i o n e x p r e s s i o n s for three component s o l i d i f i c a t i o n , we follow an e s s e n t i a l l y i d e n t i c a l p r o c e d u r e to that p r e viously e m p l o y e d for two component alloys. We cons i d e r a s m a l l volume e l e m e n t at c o o r d i n a t e s x, y , z within a solidifying ingot. No solid m a t e r i a l e n t e r s o r l e a v e s the e l e m e n t d u r i n g s o l i d i f i c a t i o n . Solute e n t e r s or l e a v e s only by liquid flow; m a s s flow in or out of the e l e m e n t by diffusion is neglected. Liquid c o m position and t e m p e r a t u r e within the e l e m e n t a r e unif o r m at any t i m e , t. E q u i l i b r i u m is m a i n t a i n e d at the l i q u i d - s o l i d i n t e r f a c e ; hence, liquid c o m p o s
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