Thermodynamic analysis of the liquidus in ternary systems involving small contents of one component

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the c h e m i c a l p o t e n t i a l s of the c o m p o n e n t s in the liquid and the solid p h a s e s of an alloy s y s t e m have b e e n d e t e r m i n e d as functions of c o m p o s i t i o n and t e m p e r a t u r e , the c o n d i t i o n s for c o e x i s t e n c e of two o r m o r e p h a s e s , i.e. e s p e c i a l l y the liquidus and the solidus m a y be c a l c u l a t e d f r o m the c o n d i t i o n that the c h e m i c a l p o t e n t i a l s of the c o m p o n e n t s in c o e x i s t ing p h a s e s m u s t be e q u a l . ' A p p r o p r i a t e m e t h o d s for c o m p u t e r i z e d c a l c u l a t i o n s have b e e n s u g g e s t e d by s e v e r a l a u t h o r s . 2-9 In g e n e r a l , c o m p l e t e data for the c h e m i c a l p o t e n t i a l s of the c o m p o n e n t s a r e not a v a i l able. Thus, c a l c u l a t i o n s a r e p o s s i b l e only by use of a p p r o x i m a t i o n s and e s t i m a t e s . Many e x p e r i m e n t a l data and e s p e c i a l l y e s t i m a t e s on the b a s i s of f a i r l y s i m p l e m o d e l s involve c o n s i d e r a b l e u n c e r t a i n t i e s . The r e l i a b i l i t y of c a l c u l a t e d p h a s e d i a g r a m s is, t h e r e fore, l i m i t e d . A l t e r n a t i v e l y , when phase d i a g r a m s have b e e n d e t e r m i n e d e x p e r i m e n t a l l y by use of c l a s s i c a l m e t h o d s , the p r o c e d u r e m a y be r e v e r s e d , i.e. one m a y deduce t h e r m o d y n a m i c data for the i n d i v i d u a l p h a s e s f r o m i n f o r m a t i o n conveyed in a phase d i a g r a m . In addition, t h e r m o d y n a m i c c a l c u l a t i o n s m a y be used in o r d e r to u n d e r s t a n d c e r t a i n c o n s p i c u o u s f e a t u r e s of p h a s e d i a g r a m s . Fig. i shows p a r t of an i s o t h e r m a l s e c t i o n of the p h a s e d i a g r a m C u - F e - S at 1350~ 1~ The o n e - p h a s e field of liquid C u - F e a l loys is c o n s i d e r a b l y e n l a r g e d upon addition of s m a l l a m o u n t s of s u l f u r c o r r e s p o n d i n g to a s h r i n k a g e of the t w o - p h a s e field y F e + liquid alloy. In this context, one m a y a s k for an " e x p l a n a t i o n " of the r a t h e r l a r g e effect b r o u g h t about by s m a l l additions of s u l f u r . Fig. 2 shows i s o t h e r m a l c o n t o u r l i n e s of the l i q u i d u s s u r f a c e in the Gibbs t r i a n g l e of the s y s t e m B i - A g - Z n at v a r i o u s t e m p e r a t u r e s . U p o n addition of s m a l l a m o u n t s of Zn to s i l v e r r i c h B i - A g a l l o y s , the r e g i o n of the liquid alloy is e n l a r g e d and a c c o r d i n g l y the twophase field for c o e x i s t e n c e of liquid alloy with n e a r l y p u r e solid Ag is n a r r o w e d . 13 This effect is s i m i l a r to the effect of an addition of s u l f u r to C u - F e a l l o y s shown in Fig. 1. On the o t h e r hand, in the c a s e of BiAg alloys c o n t a i n i n g l e s s

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