Interface undercoolings during the growth of Pb-Sn eutectics
- PDF / 579,357 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 15 Downloads / 195 Views
IN
a p r e v i o u s p a p e r , ~ d e t a i l e d c o m p a r i s o n was m a d e b e t w e e n l a m e l l a r s p a c i n g s m e a s u r e d in A1-CuA12 and P b - S n e u t e c t i c s , and those p r e d i c t e d f r o m the J a c k s o n and Hunt 2 t h e o r y . J a c k s o n and Hunt 2 showed that for l a m e l l a r e u t e c t i c s the i n t e r f a c e u n d e r c o o l i n g ( a T ) i s a function of both v e l o c i t y (v) and l a m e l l a r s p a c i n g (~t). In o r d e r to obt a i n a unique solution for AT o r ~ in t e r m s of the growth velocity, s o m e a s s u m e d c o n d i t i o n s m u s t be applied. In the p a s t , t h r e e such c o n d i t i o n s have been p r o p o s e d , 2-4 and t h e s e w e r e d e s c r i b e d in Ref. 1 a s i) Growth at the e x t r e m u m . ii) Growth w h e r e r a = S~. iii) Growth at the m i n i m u m rod u n d e r c o o l i n g . T h e s e c o n d i t i o n s a r e i l l u s t r a t e d on s c h e m a t i c plots of a T v s r a a n d S a in Fig. 1. ( r e a n d S a a r e the halfwidths of an a rod or an a l a m e l l a r r e s p e c t i v e l y . ) It was shown 1'2 that each of t h e s e c o n d i t i o n s applied to the J a c k s o n - H u n t a n a l y s i s p r e d i c t s r e l a t i o n s h i p s which have b e e n e x p e r i m e n t a l l y s u b s t a n t i a t e d on n u m e r o u s o c c a s i o n s in the p a s t . T h e s e a r e ~2v = c o n s t a n t and ATv-~/~ = c o n s t a n t (The c o n s t a n t s a r e both f u n c t i o n s of v o l u m e f r a c t i o n . ) Using the p r e d i c t e d v a r i a t i o n of ~tev with c o m p o s i tion, a c r i t i c a l method was developed ~ for e v a l u a t i n g l a m e l l a r growth t h e o r y . When applied to the Ai-CuA12 s y s t e m , it i n d i c a t e d that the e x p e r i m e n t a l l y d e t e r m i n e d v a r i a t i o n of )tzu with c o m p o s i t i o n 1 was too l a r g e to be c o m p a t i b l e with the t h e o r y . T h i s d i s c r e p a n c y was a t t r i b u t e d to the n e g l e c t of k i n e t i c t e r m s in the J a c k s o n and Hunt a n a l y s i s . Good a g r e e m e n t between t h e o r y and e x p e r i m e n t a l v a l u e s of ~t2v was found for P b - S n , however, and a t t e m p t s w e r e made to a s s e s s the r e l a t i v e m e r i t s of the t h r e e growth conditions. ~'5 U n f o r t u n a t e l y , any of the conditions could d e s c r i b e the m e a s u r e d v a r i a t i o n of h2v with c o m p o s i t i o n , and hence this was not p o s s i b l e . In o r d e r to d i s t i n g u i s h f u r t h e r b e t w e e n the p r o p o s e d conditions, i n t e r f a c e u n d e r c o o l i n g s a r e m e a s u r e d and c o n s i d e r e d in the p r e s e n t work. Two p r e v i o u s e x p e r i m e n t a l d e t e r m i n a t i o n s have been made of u n d e r c o o l ings in the P b - S n eutectic. 6'7 The r e s u l t s obtained, however, w e r e v e r y d i f f e r e n t - - i n fact differing by m o r e than a f a c t o r of t h r e e
Data Loading...
