Inhomogeneities and their control via solidification
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is a p p r o p r i a t e that the f i r s t p r e s e n t a t i o n a t t h i s s y m p o s i u m is c o n c e r n e d with the i n i t i a l s t a g e in the p r o d u c t i o n of a h o m o g e n e o u s m a t e r i a l , that i s , by the p r o c e s s of s o l i d i f i c a t i o n f r o m the m e l t . The c o m p l e x i n t e r a c t i o n s wh i ch t a k e p l a c e when a liquid b e c o m e s soli d m a y p r o d u c e s t r u c t u r a l i n h o m o g e n e i t i e s of m a n y t y p e s . Since t h e s e o f t e n r e m a i n t h r o u g h o u t the life of the m a t e r i a l , it is i m p o r t a n t to a p p r o a c h the p r o b l e m of h o m o g e n e i t y c o n t r o l at its s o u r c e . T h e t h e o r e t i c a l b a s i s u n d e r l y i n g o u r p r e s e n t s t a t e of the a r t has beert t r e a t e d e l s e w h e r e , 1-5 and only a s h o r t s u m m a r y of f i r s t p r i n c i p l e s is p r e s e n t e d h e r e . D i s c u s s i o n then c e n t e r s a r o u n d the i n h o m o g e n e i t i e s w h i c h a r e a b y p r o d u c t of n o r m a l ingot s o l i d i f i c a t i o n and the s t r u c t u r a l a l t e r a t i o n s on a m i c r o s c o p i c and m a c r o s c o p i c s c a l e w h i c h can be a d v a n t a g e o u s in p r o d u c i n g a h o m o g e n e o u s m a t e r i a l . It is a n t i c i p a t e d that the m a n y s t e p s b e t w e e n the i n i t i a l s o l i d i f i c a t i o n and a f in al h o m o g e n e o u s p r o d u c t can be r e d u c e d if the d e f e c t s w h i c h a c c o m p a n y s o l i d i f i c a t i o n can be c l e a r l y s p e c i f i e d so that they m a y be c o n t r o l l e d w h e r e p o s s i b l e . GROWTH T h e p h a s e d i a g r a m d e n o t e s the k i n d , n u m b e r , and v o l u m e f r a c t i o n of p h a s e s which a r e p r e s e n t when s o l i d i f i c a t i o n o c c u r s u n d e r " e q u i l i b r i u m c o n d i t i o n s " . By e q u i l i b r i u m , it is u n d e r s t o o d that t h e liquid and so l i d a r e of u n i f o r m c o m p o s i t i o n , and t h i s g e n e r a l l y r e q u i r e s that the l i q u i d - s o l i d r e a c t i o n t a k e s p l a c e i n f i n i t e l y s l o w l y . H o w e v e r , g r o w t h is often m o r e r a p i d so that s o l u t e o r s o l v e n t r e j e c t e d at the i n t e r f a c e b e t w e e n soli d and liquid (s/l) d o e s not have s u f f i c i e n t t i m e to d i f f u s e away f r o m the i n t e r r a c i a l r e g i o n and is not u n i f o r m l y r e d i s t r i b u t e d t h r o u g h o u t the r e m a i n i n g l i q uid (and solid). Th e r e s u l t is a buildup of s o l u t e o r s o l vent at the s/l i n t e r f a c e which i n c r e a s e s with an i n c r e a s e in the r a t e of s o l i d i f i c a t i o n , V, and the e f f e c t i v e f r e e z i n g r a n g e of the alloy,*/~Reff , and d e c r e a s e s with *The effectivefreezingrangeis givenby the expression-Cisrn(1-ko)/ko,where m is the liquidus slope,k0 the equili
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