The lattice dimensions of the AB 2 Laves phases
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Laves Phases
EDWARDS
A c o m b i n e d g e o m e t r i c / c h e m i c a l m o d e l i s p r o p o s e d to a c c o u n t f o r the o b s e r v e d l a t t i c e d i m e n s i o n s of t h e cubic AB2 L a v e s p h a s e s . T h e s e c o m p o u n d s a r e t r e a t e d a s a h y b r i d s t r u c t u r e b e t w e e n the s i m p l e m e t a l l i c b e e and fcc s t r u c t u r e s , the i n t e r a t o m i c s p a c i n g s depending on the a t o m i c d i a m e t e r s of t h e p u r e A a n d B m e t a l s and on the d i f f e r e n c e in t h e i r e l e c t r o n e g a t i v i t i e s . T h e m o d e l i s s u c c e s s f u l enough to i n d i c a t e that the e l e c t r o n e g a t i v i t y concept could w e l l find w i d e r q u a n t i t a t i v e a p p l i c a t i o n s in a l l o y c h e m i s t r y than it h a s in t h e p a s t . T h e t r e a t m e n t u s e d a l s o l e a d s to q u a l i t a t i v e e x p l a n a t i o n s f o r t h e r e l a t i v e f r e quency of o c c u r r e n c e of cubic and h e x a g o n a l L a v e s p h a s e s , the i n c i d e n c e of a l l o t r o p y in t h e s e c o m p o u n d s , the n o n a p p e a r a n c e of L a v e s p h a s e s in c e r t a i n a p p a r e n t l y f a v o r a b l e a l l o y s y s t e m s , and t h e m i n i m u m A - m e t a l content found in p h a s e s showing a r a n g e of h o m o g e n e i t y .
A s a g r o u p , t h e AB2 L a v e s p h a s e s (having one of t h e c l o s e l y r e l a t e d MgCu2-, M g Z n z - , o r M g N i z - t y p e s t r u c tures) are the most frequently occurring intermetallic p h a s e s . Although they have been the s u b j e c t of e x t e n s i v e study and d i s c u s s i o n , m u c h r e m a i n s to be d i s c o v e r e d about such f u n d a m e n t a l c o n s i d e r a t i o n s a s the r e a s o n s f o r t h e i r a p p e a r a n c e o r n o n a p p e a r a n c e in a given a l l o y s y s t e m , and the i n t e r p l a y of p a r a m e t e r s g o v e r n i n g t h e c r y s t a l t y p e and l a t t i c e d i m e n s i o n s a s s u m e d by the s o m e 270 known e x a m p l e s of t h e s e b i n a r y compounds. Among n o t a b l e t r e a t m e n t s of t h e s u b j e c t m a d e in r e cent y e a r s a r e t h o s e by N e v i t t , 1 R u d m a n , 2 and P e a r son, 3 and t h e s e have r e i n f o r c e d the view that the s i m p l e m e c h a n i c a l m o d e l , b a s e d on the c l o s e p a c k i n g of h a r d s p h e r e a t o m s of r a d i u s r a t i o RA / R B = (3/2) 1/2 , o r 1.225, i s not s u f f i c i e n t to c h a r a c t e r i z e the L a v e s p h a s e s . T h i s t r a d i t i o n a l b a s e l i n e for c o n s i d e r a t i o n of the c o m p o u n d s h a s i t s e l f b e e n q u e r i e d ; thus Rudman, u s i n g a m o d e l b a s e d on the a t o m i c v o l u m e s and e l a s t i c c o n s t a n t s of the m e t a l s c o n c e r n e d , p r e f e r s an " i d e a l " r a d i u s r a t i o R A / R B = 21/3 = 1.26, r a t h e r than 1.225. W h a t e
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