The deoxidation thermodynamics of cerium and lanthanum in liquid iron

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[11 [2] [3] [4] [5] [6]

a r e obtained f r o m the s t a n d a r d f r e e e n e r g i e s of f o r m a tion of G s c h n e i d n e r e t a l . ~'2 and the f r e e e n e r g i e s of solution of c e r i u m , l a n t h a n u m and oxygen s in iron, where [ ] r e p r e s e n t s a c o m p o n e n t in solution in i r o n and 1 w / o r e p r e s e n t s the one wt pet s t a n d a r d state. The f r e e e n e r g i e s of s o l u t i o n of l a n t h a n u m and c e r i u m in i r o n m a y be c a l c u l a t e d a p p r o x i m a t e l y f r o m t h e i r r e s p e c t i v e phase d i a g r a m s 4's which a r e r e p r o duced in Figs. 1 and 2. The solution of c e r i u m and l a n t h a n u m in i r o n m a y be r e p r e s e n t e d b y the equations: Ce (,) = [Ce] l w / o

[7]

Lat, ) = Inn] l w / o

[8]

Fig. 1--The iron-lanthanum phase diagram.

and the f r e e e n e r g i e s of solution, AG-ce and AGLa a r e given by the r e l a t i o n s h i p s : AG-ce = R T In (0.5585 Y~e/140)

[9]

and AG--La = R T In (0.5585 y~.a/139)

[10]

respectively. In the evaluation of V~_a at 1900 K, the Raoultian a c tivity of iron, a F e , of s o l u t i o n s in the composition r a n g e 5 to 100 pct Fe at 1.900 K, a r e e s t i m a t e d f r o m the liquidus curve of the i r o n - l a n t h a n u m phase d i a g r a m a s s u m i n g r e g u l a r solution b e h a v i o r . The R a o u l tian activity of l a n t h a n u m , aLa, is then calculated u s ing the Gibbs-Duhem r e l a t i o n s h i p , the r e f e r e n c e a c tivity of lanthanum b e i n g d e r i v e d f r o m the eutectic

Fig. 2--The iron-cerium phase diagram. point in Fig. 2 at 1445~ and 5 wt pct l a n t h a n u m . The c a l c u l a t e d activity of l a n t h a n u m is shown as a function of the atom fraction, XLa , in Fig. 3. The slope of the aLa vs XLa curve at infinite dilution of lanthanum, yoLa, is taken to be a p p r o x i m a t e l y 15.7. E v a l u a t i o n of Eq. [10] gives: AG-La = -- 5.5 T cal

A. VAHED,formerly a Research Engineer at McMaster University, is now with FalconbridgeNickel Mines Ltd., Dominican Republic. D. A. R. KAY is Professor, Department of Metallurgyand Materials Science, McMaster University, Hamilton, Ontario. Manuscript submitted May 10, 1974. METALLURGICALTRANSACTIONSB

[11]

Eq. [11] is c o n s i s t e n t with the work of P e r m y a k o v et a l f l who also calculated the f r e e e n e r g y of solution of l a n t h a n u m in iron f r o m an i r o n - l a n t h a n u m phase d i a g r a m . A value for Y~ = 2.5 at 1900 K, can be obtained in a VOLUME 6B,JUNE 1975-285

CeO2(s, : [Ce]lw/o + 2[O]lw/o

[16]

equal to 3.5 x 10 -8 at infinite dilution of the a l l o y i n g element. When his r e s u l t s w e r e i n t e r p r e t e d on the b a s i s of Ce203 as the deoxidation product, the plot of K~e v s wt p c t of Ce shown in Fig. 4 is obtained, w h e r e :

log

K~e = 2 log [w/o O] + 3 log [w/o Ce]

[17]

The v a l u e of log K~e at infinite d i l u t i o n of c e r i u m is then:

log g c o : 2 log [ho] + 3 log [hco ] :