The growth of off-eutectic composites from stirred melts
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A L I G N E D eutectic m a t e r i a l s p r o d u c e d by c o n t r o l l e d s o l i d i f i c a t i o n techniques have m a n y advantages for u s e as c o m p o s i t e m a t e r i a l s . A m a j o r d i s a d v a n t a g e , howe v e r , is that the volume f r a c t i o n of the s t r o n g e r phase is f r e q u e n t l y l i m i t e d to s m a l l v a l u e s . 1'2 M o l l a r d and F l e m i n g s ~ have r e c e n t l y shown that this difficulty can be o v e r c o m e by an o f f - e u t e c t i c s o l i d i f i c a t i o n technique. It is p o s s i b l e with this technique not only to i n c r e a s e o r d e c r e a s e the v o l u m e f r a c t i o n of e i t h e r phase, but one may also add s m a l l additions of s o l u t e s in o r d e r to produce solid s o l u t i o n and p r e c i p i t a t i o n h a r d e n i n g of one or both p h a s e s . 4 A c c o r d i n g to M o l l a r d and F l e m i n g s , 5 the conditions n e c e s s a r y for aligned growth at o f f - e u t e c t i c c o m p o s i t i o n s a r e steep t e m p e r a t u r e g r a d i e n t , slow growth r a t e , and the a b s e n c e of convection. The l a t t e r r e q u i r e m e n t is a f a i r l y s e v e r e r e s t r i c t i o n on this technique. The only e x p e r i m e n t a l c o n f i g u r a t i o n in which both solute and t h e r m a l c o n v e c tion m a y be e l i m i n a t e d 6 is a v e r t i c a l a r r a n g e m e n t in which the heat s o u r c e is at the top and the solute m a t e r i a l i n c r e a s e s the liquid d e n s i t y for ko < 1 and d e c r e a s e s it for ko > 1. Hence, in m a n y eutectic s y s t e m s it is not p o s s i b l e to e l i m i n a t e convection. The p u r p o s e of the p r e s e n t work is to p r e s e n t some t h e o r e t i c a l a r g u m e n t s which indicate that o f f - e u t e c t i c growth should be p o s s i b l e in the p r e s e n c e of convection and that the convection itself affords some advantages.
E U T E C T I C REACTION WITH MIXING A t h e o r e t i c a l t r e a t m e n t i n c l u d i n g o f f - e u t e c t i c growth for a l a m e l l a r eutectic in a n o n c o n v e c t i n g s y s t e m h a s been g i v e n by J a c k s o n and Hunt.7 They show that the l a m e l l a r spacing, ~, v a r i e s with growth r a t e , V, a c c o r d i n g to the following equation
2D [aLafB x2v - P(C;--ca)L--,;,-c[a
rna,m/3 = s l o p e s of the ~ and fl l i q u i d u s (defined positive) f a , f B = v o l u m e f r a c t i o n s of a and fl p h a s e s Ca,C/~ = the e u t e c t i c c o m p o s i t i o n s of the solid p h a s e s as shown in Fig. 1. p =~ 1
sin2(nTrfa) n3ff3
L ~c~l L (T~l . a a = AS a s i n 0 ~ ; a/~ = ~ - - ~ s m ~
(~al, aBl = s u r f a c e
e n e r g i e s between the liquid and the ~ and fl p h a s e s
ASa, AS• = e n t r o p i e s of solidification of ot and fl phases 0 a , 0~ = the contact a n g l e s of the o~ and/3 plates at the ol/~ i n t e r f a c e . In the t h e o r e t i c a l t r e a t m e n t of J a c k s o n and Hunt, it is a s
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