On the eutectoid reaction in Cu-Al and Fe-C
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T E A T , where T E is the eutectold t e m p e r a t u r e (565~ F i g s . l(a) and (b) m a y be c o m b i n e d to yield a plot of s v e r s u s v (Fig. 2). C&R plotted the t r a n s l a t i o n v e l o c i t y (R) v e r s u s s p a c ing (s). T h e s e e x p e r i m e n t a l data a r e also given in Fig. 2. The a u t h o r s c o m p a r e d the R - s data with the t h e o r e t i cal v - s r e l a t i o n s h i p , i m p l i c i t l y a s s u m i n g that R = v. D i s c u s s i o n : If indeed R = v, the data for i s o t h e r m a l and the i s o v e l o c i t y growth should coincide. However, Fig. 2 i l l u s t r a t e s that they do not. We will f i r s t c o n s i d e r the i s o t h e r m a l data. Over the e n t i r e r a n g e of i s o t h e r m a l data a n o n l i n e a r r e l a t i o n s h i p between v and s is o b s e r v e d . F o r v ' s s m a l l e r than ~ 0 . 7 5 V m a x the i s o t h e r m a l data fit a s t r a i g h t line a c c o r d i n g to shy = c o n s t a n t with n ~ 4. Near Vmax the l i n e a r i t y is lost v e r y a b r u p t l y . This i s o t h e r m a l dependence of s on v is e x a c t l y as expected f r o m our t h e o r y . 3'4 The i s o v e locity data do not fit the expected r e l a t i o n s h i p and show a deviating t r e n d . The c o n c l u s i o n is that the t r a n s l a t i o n v e l o c i t y and the growth r a t e a r e not equal. This m u s t be due to n o n p a r a l l e l l i s m of the l a m e l l a e to the t r a n s lation d i r e c t i o n , s i n c e the t r a n s l a t i o n v e l o c i t y is s m a l l e r than Vmax. N o n p a r a l l e l l i s m has b e e n m e n tioned by C&R (their Fig. 9) and has also b e e n found by other a u t h o r s f i ' ' ~ As a r e s u l t the growth r a t e (v) is l a r g e r than the t r a n s l a t i o n velocity. B e c a u s e the n o n p a r a l l e l l i s m i n c r e a s e s with the t r a n s l a t i o n v e l o c i t y the deviation f r o m the t h e o r e t i c a l l y expected b e h a v i o r i n c r e a s e s with R. This e x p l a i n s the t r e n d in the d e v i a tion of the i s o v e l o c i t y data. In t h e i r d i s c u s s i o n C&R a r g u e that v o l u m e diffusion is the r a t e c o n t r o l l i n g m e c h a n i s m for growth in Cu-A1. That s t a t e m e n t is b a s e d on the s i m i l a r i t y of e x p e r i m e n t a l and c a l c u l a t e d v - T c u r v e s . However, c o m p a r i s o n with c u r v e s c a l c u lated a c c o r d i n g to the b o u n d a r y diffusion model yield an even b e t t e r fit (volume diffusion leads to v s = K D v A C , b o u n d a r y diffusion to v s 2 = K ' D b A C ) . In fact the method is not a c c u r a t e enough to d i s t i n g u i s h b e t w e e n the two m e c h a n i s m s . E a r l i e r c a l c u l a t i o n s by Asundi and West n a r e p e r h a p s m o r e r e l e v a n t . Again, the C a h n - H a g e l a n a l y s i s cannot s i m p l y be applied to the b o u n d a r y model. It only i n d i c a t e s that v o l u m e diffusion is p o
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