Enhanced lever rule for high-precision phase diagram determination
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BENNETT AND G.C. C A R T E R
A d e s c r i p t i o n is g i v e n o f t h e c o n d i t i o n s u n d e r w h i c h h i g h - p r e c i s i o n p h a s e b o u n d a r y d e t e r m i n a t i o n s r e s u l t f r o m t h e application o f t h e l e v e r r u l e . T h i s high precision r e s u l t s f r o m a m u l t i p l i c a t i o n f a c t o r to t h e l e v e r rule r a t i o , w h i c h is p r e s e n t o n l y f o r e x p e r i m e n t s s a m p l i n g o n e e l e m e n t a l s i t e at a t i m e . T h e m u l t i p l i c a t i o n f a c t o r is l a r g e r f o r s m a l l e r solubility l i m i t s . P r e c i s i o n o f t e n t h s o f a p e r c e n t c a n be r e a d i l y a t t a i n e d u n d e r t h e i n d i c a t e d c o n d i t i o n s . A n e x a m p l e i n v o l v i n g the n~In n u c l e a r m a g n e t i c r e s o n a n c e f o r t h e d e t e r m i n a t i o n o f t h e s o l u b i l i t y o f A u I n u in A u A I 2 is p r e s e n t e d .
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more traditional methods of determining the relative amount of constituent p h a s e s of a two-phase a l l o y such as quantitative metallography o r X - r a y diff r a c t i o n , all a t o m i c s i t e s a r e s a m p l e d at t h e s a m e t i m e . T h i s i s b e c a u s e a s m a l l r e g i o n of t h e s a m p l e , o r t h e e n t i r e s a m p l e , is s t u d i e d in t h e s e " b u l k " m e a s u r e m e n t s . Currently t h e r e exist v a r i o u s types of a t o m i c , or l o c a l , m e a s u r e m e n t s with w h i c h one can s t u d y o n e o f t h e elemental c o m p o n e n t s at a t i m e . T h e s e m e a s u r e m e n t s , in w h i c h o n l y o n e o f t h e c o n s t i t u e n t e l e m e n t s is s a m p l e d , i n v o l v e e l e c t r o n i c o r n u c l e a r transitions for a s i n g l e component of an alloy. A m o n g such experiments a r e M 6 s s b a u e r effect, soft X - r a y spectroscopy, electron spectroscopy for c h e m ical a n a l y s i s (ESCA), a n d n u c l e a r magnetic resonance. W e w i l l d e s c r i b e i n t h i s p a p e r how t h e s e l o c a l m e a s u r e m e n t s can give a p r e c i s e determination of t h e amount of s e c o n d p h a s e p r e s e n t , when for the t r a d i t i o n a l e x p e r i m e n t s t h e d e t e c t i o n l i m i t s of t h e a p p a r a tus have been exceeded. Fig. 1 s h o w s a schematic p h a s e d i a g r a m with s i n g l e p h a s e r e g i o n s a , a n d (3, a n d a t w o - p h a s e r e g i o n , a + /3. B r i e f l y , t h e l e v e r r u l e s t a t e s that a t t e m p e r a t u r e , t , a n d c o m p o s i t i o n , c , in t h e t w o - p h a s e r e g i o n , t h e r e l a tive fractions, f(c~), of p h a s e a , with composition c a , a n d p h a s e ~ w i t h c o m p o s i t i o n c/3 a r e , r e s p e c t i v e l y , 1 cfl - c
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T h e s y m b o l s a r e d e f i n e d i n F i g . 1.
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