Thermodynamics of slag-metal equilibrium
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1. INTRODUCTION
IN
1950 Flood and Muan 4 d e r i v e d a r e l a t i o n s h i p b e tween an a n i o n i c exchange e q u i l i b r i u m q u o t i e n t and the c a t i o n i c c o m p o s i t i o n of a m o l t e n s a l t m i x t u r e . B a s e d on this d e r i v a t i o n Flood and G r j o t h e i m 2 d e m o n s t r a t e d that as a f i r s t a p p r o x i m a t i o n a l i n e a r r e l a t i o n s h i p e x i s t s b e t w e e n the l o g a r i t h m of the e q u i l i b r i u m q u o t i e n t for s l a g - m e t a l exchange r e a c t i o n s and the ionic c o m p o s i t i o n of the b a s i c slag. An e x a m p l e of such a cation exchange e q u i l i b r i u m is the following: [Fe(A)] + Mn = Fe + [Mn(A)]
[I]
w h e r e the u n d e r l i n e d c o m p o n e n t s a r e in a m i x e d liquid m e t a l phase and those in s q u a r e b r a c k e t s a r e in a m i x e d fused s l a g phase. H e r e (A) s t a n d s for a m i x t u r e of i d i f f e r e n t a n i o n s , A i , such as F-, O 2-, PO~-, SiO~and so forth. B e c a u s e of the ionic n a t u r e of the slag, the net ionic r e a c t i o n can be w r i t t e n : [Fe z*] + Mn = Fe + [Mn2+].
[II]
A c c o r d i n g to the FG t r e a t m e n t , 2 the e q u i l i b r i u m q u o t i e n t was e x p r e s s e d as:
t r e a t m e n t m a d e i t p o s s i b l e to p r e d i c t t h e e q u i l i b r i u m quotient when the composition of a basic slag was k n o w n . T h e s e types of a n a l y s i s have p r o v e d u s e f u l in
N 2+ Mn g'
--
2+
NFe 9 Mn
[11
w h e r e N~In and N~e a r e the ionic f r a c t i o n s of Mn 2ยง and F e 2+ in the e q u i l i b r i u m s l a g m i x t u r e , and Mn is the c o n c e n t r a t i o n of m a n g a n e s e in dilute s o l u t i o n in the i r o n phase. The l i n e a r r e l a t i o n s h i p d e r i v e d by FG for this cation exchange r e a c t i o n is: log K' = N~- 9log g~ + NO~- 9 logKb + N~O ~- 9 log K'po, + N~io~- ' log Ksio,' + f(~).
[2]
H e r e N~ r e p r e s e n t s the e q u i v a l e n t f r a c t i o n defined as: ' zini N i - ~zin i i
s e v e r a l systems.2-24 When W a r d 16 had at his d i s p o s a l a c t i v i t y d a t a for s u l f u r and oxygen in the m e t a l p h a s e , he v e r i f i e d the F G l i n e a r r e l a t i o n s h i p by t r e a t i n g the o x y g e n - s u l f u r d i s t r i b u t i o n b e t w e e n m e t a l and s l a g as an a n i o n exchange e q u i l i b r i u m . T h e t h e r m o d y n a m i c d e r i v a t i o n of the l i n e a r r e l a t i o n s h i p can be p e r f o r m e d by two " m e t h o d s " b a s e d on d i f f e r e n t s t a n d a r d s t a t e s . We will f i r s t b r i e f l y r e peat the two " m e t h o d s " u s e d by F l o o d and c o w o r k e r s , then p r e s e n t a s t a t i s t i c a l d e r i v a t i o n , 8 and f i n a l l y c o m p a r e t h e s e with the " n e w " t r e a t m e n t by ELB.
2. THE F G - E X C H A N G E T R E A T M E N T BASED ON THE " M I X E D A C T I V I T Y " C O N C E P T [3]
TORMOD FO
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