The formation of modulated structures in Ni-V alloys
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T H E p r e c i p i t a t i o n of c o h e r e n t o r d e r e d p h a s e s in num e r o u s a l l o y s y s t e m s is a c c o m p a n i e d by the d e v e l o p m e n t of p e r i o d i c o r m o d u l a t e d m i c r o s t r u c t u r e s . In NiA1 a l l o y s , the p e r i o d i c s t r u c t u r e has b e e n a t t r i b u t e d to elastic interactions between ordered particles, ~ wherea s , in N i - T t a l l o y s , the p e r i o d i c s t r u c t u r e has been a s s o c i a t e d with the s p i n o d a l d e c o m p o s i t i o n p r o c e s s . 2'3 In F e - N i - C u a l l o y s which u n d e r g o s p i n o d a l d e c o m p o s i t i o n , p e r i o d i c m i c r o s t r u c t u r e s a r e a l s o o b s e r v e d . 4 De F o n taines p o i n t s out that the m o d u l a t e d , o r p e r i o d i c , m i c r o s t r u c t u r e s m a y be r e g a r d e d a s " t y p i c a l " s p i n o d a l m o r p h o l o g y but that p e r i o d i c i t y d o e s not n e c e s s a r i l y i m p l y s p i n o d a l d e c o m p o s i t i o n and s p i n o d a l d e c o m p o s i tion d o e s not n e c e s s a r i l y i m p l y p e r i o d i c i t y . De F o n t a i n e f u r t h e r p o i n t s out that the s p i n o d a l d e c o m p o s i t i o n p r o c e s s cannot apply to s y s t e m s in which the d e c o m p o s i t i o n of the s u p e r s a t u r a t e d s o l i d s o l u t i o n g i v e s r i s e to a m o d i f i e d c r y s t a l l a t t i c e . Thus, although p e r i o d i c m i c r o s t r u c t u r e s which exhibit s p i n o d a l m o r p h o l o g y m a y a r i s e in a l l o y s f o r m i n g o r d e r e d p r e c i p i t a t e s , the s p i n odal d e c o m p o s i t i o n r e a c t i o n cannot be d i r e c t l y a p p l i e d to account for t h e s e m i c r o s t r u c t u r e s . O r d e r i n g p r o c e s s e s have b e e n a n a l y z e d by Cook, e t a l . 6 and by Ling and S t a r k e 7 in a m a n n e r s i m i l a r to C a h n ' s a n a l y s i s of s p i n o d a l d e c o m p o s i t i o n . 8 In the a n a l y s i s of o r d e r i n g p r o c e s s e s the c o m p o s i t i o n f l u c t u ation is d i v i d e d into two c o m p o n e n t s ; a d o m a i n wave c o m p o n e n t which has a wavelength equal to the d o m a i n s i z e and a l o n g - r a n g e - o r d e r wave c o m p o n e n t which has a wavelength dependent upon the a r r a n g e m e n t of a t o m s in the unit c e l l of the o r d e r e d s t r u c t u r e . L i m ited e x p e r i m e n t a l v e r i f i c a t i o n of t h i s concept has been p r o v i d e d b y Okamoto and T h o m a s 9 and by Ling and S t a r k e . 7 M i c r o s t r u c t u r e s which r e s e m b l e the t y p i c a l s p i n o d a l m o r p h o l o g y , but containing an o r d e r e d p h a s e , have b e e n o b s e r v e d in a v a r i e t y of o t h e r s y s t e m s including NisV, 1~ NizV, n Ni3Ti, 3 and CuAu. ~2 Continuous o r d e r i n g t h e o r y p r o v i d e s the t h e o r e t i c a l b a s i s for int e r p r e t i n g the m e c h a
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