The dendrite arm spacings of aluminum-copper alloys solidified under steady-state conditions
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A N D D. H. KIRKWOOD
A l u m i n u m - c o p p e r a l l o y s of d i f f e r e n t c o m p o s i t i o n have b e e n s o l i d i f i e d under s t e a d y - s t a t e c o n d i t i o n s with known growth v e l o c i t i e s and t e m p e r a t u r e g r a d i e n t s . S p e c i m e n s w e r e quenched d u r i n g s o l i d i f i c a t i o n to r e v e a l the d e n d r i t e growth m o r p h o l o g y and to allow the s o l u t e content at d e n d r i t e t i p s to b e a n a l y z e d . P r i m a r y and s e c o n d a r y a r m s p a c i n g s have b e e n m e a s u r e d a s a function of the d i s t a n c e d behind the g r o w i n g d e n d r i t e t i p s , the tip v e l o c i t y R the t e m p e r a t u r e g r a d i e n t in the liquid GL and the s o l u t e content. The p r i m a r y a r m s p a c i n g AI is d e s c r i b e d f o r each a l l o y b y the e m p i r i c a l r e l a t i o n : kl = kGLa R - b w h e r e k is a c o n s t a n t , and both a and b a r e c l o s e to 89; kl is a l s o found to i n c r e a s e with s o l u t e content. The s e c o n d a r y a r m s p a c i n g k~ f o r e a c h a l l o y i n c r e a s e s with t i m e 0 s p e n t in the l i q u i d / s o l i d r e g i o n , b e i n g d i r e c t l y p r o p o r t i o n a l to On w h e r e n is c l o s e to ~ ; i n c r e a s i n g s o l u t e content h o w e v e r c a u s e s a r e d u c t i o n in A2. It is s u g g e s t e d t h a t the o b s e r v e d " c o a r s e n i n g " of the s e c o n d a r y a r m s is p r i m a r i l y a c o a l e s c e n c e phenomenon.
MOSTof the
p u b l i s h e d w o r k 1-4 c o n c e r n i n g d e n d r i t e a r m s p a c i n g s in a l l o y s h a s involved the p o s t - m o r t e m e x a m i n a t i o n of s o l i d i f i e d ingots in which the s o l i d i f i c a tion conditions have b e e n only p a r t i a l l y c o n t r o l l e d . G e n e r a l l y the m e a s u r e d p a r a m e t e r h a s b e e n the l o c a l c o o l i n g r a t e , s o r the l o c a l s o l i d i f i c a t i o n t i m e , 4 and the l o c a l d e n d r i t e t i p v e l o c i t y and t e m p e r a t u r e g r a d i e n t a r e unknown. N e v e r t h e l e s s t h e s e e x p e r i m e n t s have c o n t r i b u t e d g r e a t l y to our u n d e r s t a n d i n g of d e n d r i t e m o r p h o l o g y and it is g e n e r a l l y a g r e e d that both c o o l ing r a t e and a l l o y content affect the s t r u c t u r e of c a s t a l l o y s . Of t h e s e the cooling r a t e is d o m i n a n t and i n c r e a s i n g the cooling r a t e is found to r e d u c e both the p r i m a r y and s e c o n d a r y a r m s p a c i n g s . M o r e r e c e n t l y s it has b e e n a l s o shown that s e c o n d a r y a r m s p a c i n g s i n c r e a s e with t i m e s p e n t in the l i q u i d / s o l i d r e g i o n . A few a t t e m p t s have b e e n m a d e to c o n t r o l s o l i d i f i cation more precisely by establishing steady-state growth c o n d i t i o n s with c o n t r o l l e d growth v e l o c i t i e s
