The free energies of mixing of melts in the systems 2FeO-SiO 2 -2MnO-SiO 2 and 2.33FeO-TiO 2 -2.33MnOTiO 2

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s i m p l e s t t h e o r e t i c a l a p p r o a c h to m i x i n g in t e r n a r y oxide m e l t s a s s u m e s r a n d o m m i x i n g of the c a t i o n s , and the n u m b e r of c a t i o n i c s p e c i e s a s s u m e d d e p e n d s on w h e t h e r o r not it i s c o n s i d e r e d that oxya n i o n s o c c u r in the m e l t s a s the p r o d u c t s of a c i d - b a s e r e a c t i o n s . If o x y a n i o n s f o r m , a s in s i l i c a t e m e l t s , the s i m p l e s t m o d e l is t h a t of i d e a l s i l i c a t e m i x i n g , in which it is a s s u m e d that, when the b i n a r y s i l i c a t e s x A O 9 SiOs and x B O 9 SiOs a r e m i x e d to f o r m a t e r n a r y s i l i c a t e m e l t , the f r e e e n e r g y d e c r e a s e a r i s e s s o l e l y f r o m i d e a l m i x i n g of the A ~" and B z* cations.Z T h i s a s s u m p t i o n p e r m i t s c a l c u l a t i o n of the a c t i v i t i e s of AO, BO and SiOs in a t e r n a r y m e l t f r o m k n o w l e d g e of the f r e e e n e r g i e s of f o r m a t i o n of m e l t s in the b i n a r y s y s t e m s AO-SiOs and BO-SiOs. A l t e r n a t i v e l y , if it is a s s u m e d that o x y a n i o n s a r e not f o r m e d , a s might be the c a s e in t e r n a r y t i t a n a t e s A O - B O - T i O s , the s i m p l e s t m o d e l i s that of r e g u l a r t e r n a r y m i x i n g , 2 in which r e g u l a r m i x i n g of A s+, B 2+ and T i 4§ is a s s u m e d . T h i s p e r m i t s c a l c u l a t i o n of the a c t i v i t i e s of AO, BO and TiOs in a t e r n a r y m e l t f r o m knowledge of the r e g u l a r solution interaction parameters for the three constituent b i n a r y oxide s y s t e m s . A s an u n d e r s t a n d i n g of s l a g - m e t a l e q u i l i b r i u m r e q u i r e s a knowledge of the t h e r m o d y n a m i c p r o p e r t i e s of the s l a g s y s t e m s , it is i m p o r t a n t to d e t e r m i n e the e x t e n t s to which t h e s e p r o p e r t i e s can be p r e d i c t e d b y s i m p l e t h e o r e t i c a l m o d e l s and to i d e n t i f y the c a u s e s of any o b s e r v e d d e v i a t i o n s f r o m the m o d e l s . T o w a r d s t h i s end, the p r e s e n t w o r k w a s u n d e r t a k e n a s p a r t of a continuing s t u d y of the t h e r m o d y n a m i c s of m i x i n g in t e r n a r y oxide m e l t s . A p r e v i o u s i n v e s t i g a t i o n of m i x i n g in the s y s t e m 2CoO 9S i O s - 2 F e O 9SiOs at 1450~ s h o w e d that the f r e e e n e r g i e s of m i x i n g w e r e s o m e w h a t m o r e n e g a t i v e than t h o s e which would b e p r e d i c t e d by i d e a l s i l i c a t e m i x ing, with the m a x i m u m d e v i a t i o n b e i n g - 4 . 2 kJ p e r m o l e of o r t h o s i l i c a t e 2 M O . SlOe. 3 A s the r a d i i of Co s§ and F e s+, (0.74 and 0.76A r e s p e c t i v e l y ) , a r e e s s e n t i a l l y i d e n t i c a l , t h i s n e g a t i v e d e v i a t i o n could not r e a s o n a b l y be a t t r i b u t