A criticism of the Flood-Grjotheim ionic treatment of slag-equilibria
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F. ELLIOTT,
DAVID
C. LYNCH.
AND
TRACY
B. BRAUN
The a n a l y s i s by Flood and Grjotheim I of the e q u i l i b r i a between a m e t a l and a fused slag utilizes the ionic behavior of the slag or salt, and it employs a r e v e r s i b l e t h e r m o d y n a m i c cycle. However, in the o r i g i n a l a n a l y s i s there appears to be an e r r o r in the use of free energy. A c o r r e c t e d t r e a t m e n t has been developed which involves a m o d e s t change and s i m p l i f i c a t i o n in the o r i g i n a l formulation. The r e v i s e d a n a l y s i s shows the i m p o r t a n c e of the t h e r m o d y n a m i c b e h a v i o r of ionic s p e c i e s in the slag, which may be nonideal. Data from the l i t e r a t u r e on s l a g - m e t a l e q u i l i b r i a , for example: [Fe z+] + M n = F e ( l ) +[Mn2ยง a r e analyzed by the new f o r m u l a t i o n to obtain e x p r e s s i o n s for r a t i o s of activity coefficients such as (VS2-/~O2-), (~,Mn2./VFe 2*) and [(ypo~-)z/(VO 2-)a] in t e r m s of slag c o m p o sition the l a s t two having been found to depend s t r o n g l y on the oxygen-ion content of the slag.
IN
1952 Flood and Grjotheim t put forward a method of a n a l y s i s by which a r e l a t i o n s h i p can be e s t a b l i s h e d b e tween the e q u i l i b r i u m quotient for a s l a g - m e t a l , or s l a g - g a s , r e a c t i o n and the ionic n a t u r e of the slag. The method has been used by o t h e r s 2'3 who have found the method useful for t r e a t i n g e q u i l i b r i a with a m e t a l phase and s t r o n g l y b a s i c slags. For s o m e time the p r e s e n t authors have been c o n c e r n e d about what a p p e a r s to be a fundamental e r r o r in the F l o o d - G r j o t h e i m t r e a t m e n t , and a r e v i s e d t r e a t m e n t has been developed. F o r t u nately, the c o r r e c t e d i n t e r p r e t a t i o n involves a r e l a tively modest change, and the p r i m a r y c h a r a c t e r of the r e s u l t is p r e s e r v e d ; that is, r e a c t i o n s involving anionic species a r e e x p r e s s e d in t e r m s of the cationic population of the slag and vice v e r s a . The e s s e n t i a l aspect of the t r e a t m e n t of the e q u i l i b r i u m of a r e a c t i o n between a m e t a l phase and the slag, or a gas phase and the slag, is that the r e a c t i o n is a n a lyzed by a cyclic r e v e r s i b l e p r o c e s s for which the sum of all of the changes in Gibbs free e n e r g y m u s t be zero. It a p p e a r s that the fault in the F l o o d - G r j o t h e i m a n a l y sis as has been r e p o r t e d I and used z'3 a r i s e s b e c a u s e the change in standard f r e e energy r a t h e r than the f r e e energy was used in two steps of the a n a l y s i s . The s a m e steps in the r e v e r s i b l e cyclic p r o c e s s are also used in this r e v i s e d a n a l y s i s . However, a s i m p l i f i c a t i o n is possible in two steps in the cycle by u s i n g r e a c t i o n s i n volving pu
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