The clustering of alumina inclusions
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T H E growth of continuous c a s t i n g and v a c u u m p r o c e s s i n g o p e r a t i o n s over the past decade has i n c r e a s e d the need of the s t e e l m a k e r to have an adequate u n d e r s t a n d i n g of, and c o n t r o l o v e r , deoxidation p r a c t i c e s . A l u m i n u m is the most c o m m o n l y used d e o x i d i z e r in the p r o d u c t i o n of killed s t e e l s b e c a u s e it is t h e o r e t i cally p o s s i b l e to attain an e x t r e m e l y low oxygen content (> (pct O), it c a n be a s s u m e d t h a t (aAI)K i --~ (aA1)~ =o a n d that the a c t i v i t y c o e f f i c i e n t of oxygen, f o , is c o n s t a n t . T h e n : (pct O)h. VA120a (r Fe/A120~ z]= In [(pet O)eq 3RT Ki
[A.6]
w h e r e (pct O)h :o = (pct O)eq. S i n c e [(pet O ) h i / ( p c t O)eq] - 1, Eq. [A.6] c a n b e a p p r o x i m a t e d b y :
t c r i t = 4800
[A.15]
5 O
w h e r e the u n i t s of 5, r , Ki, a n d Kj a r e /~m. If, o n the o t h e r h a n d , K/ < Xj p a r t i c l e i w i l l g r o w . T h e t i m e , t*, n e c e s s a r y for the i n c l u s i o n to g r o w f r o m r a d i u s r o to radius 2r o is: 2r~ t* = 4800 f
5
~ d r .
[A.16]
O
(pct O)Ki - (pct O)eq = VA1203 (y Fe/A1203 (pct O)eq ~i 3RT
[A.7] S i m i l a r l y , for a p a r t i c l e w h o s e r a d i u s of c u r v a t u r e i s ~cj,
ACKNOWLEDGMENT T h e a u t h o r s w i s h to e x p r e s s t h e i r a p p r e c i a t i o n to the A m e r i c a n I r o n a n d S t e e l I n s t i t u t e ( P r o j e c t No. 7 3 - 2 6 8 ) f o r f i n a n c i a l s u p p o r t of the w o r k r e p o r t e d .
VA1203 tr Fe/A1203 (pct O)hj - (pct O)eq -
3RT
(pct O) eq Kj [A.8]
REFERENCES I. H. A. Sloman and E. L. Evans:./. Iron Steel Inst., 1950, vol. 165, pp. 81-90.
a n d s u b t r a c t i n g E q . [A.8] f r o m [A.7], (pct O)Ki - (pct O)~3-VA1203 aFe/A1203 ( p c t O )
(~i-- ~j)"
3RT
[A.9] T h e d i f f u s i o n flux of o x y g e n a w a y f r o m the i n t e r f a c e of p a r t i c l e i, Ji, is g i v e n b y the e x p r e s s i o n : Ji = - D
OC ~ D P F e ( p e t O ) h i ~-~ - 100 [ 5
(pct O)hj] -
[A.10]
w h e r e D i s the d i f f u s i o n c o e f f i c i e n t of o x y g e n i n l i q u i d i r o n , P F e i s the d e n s i t y of i r o n , a n d 5 is the " d i f f u s i o n d i s t a n c e " . By the c o n s e r v a t i o n of m a t t e r at the i n t e r face, f o r a c y l i n d r i c a l o r s p h e r i c a l p a r t i c l e w i t h radius, ri, J i = [ ( C o ) h i -- (CO) A1203] ~ t i
[A.11]
w h e r e ( C o ) h i is the d e n s i t y of o x y g e n i n the l i q u i d a d j a c e n t to t h e p a r t i c l e a n d (CO)A120 ~ i s the d e n s i t y of o x y g e n in the a l u m i n a . E q u a t i o n [A.11 ] c a n b e r e w r i t t e n to g i v e :
Ji =
[PFe(P ct O)K i 100
48PA1203 d r i 102 ] d t "
[A.12]
C o m b i n i n g E q s . [A.9], a n d [A.10], a n d [A.12) y i e l d s : d r i = ( K j - ~i) dt
135
METALLURGICAL TRANSACTIONS B
[A.13]
2. K. Torsselland M. Olette: Comptes Rendus, 1969,vol.
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