Refining by fractional melting
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f s ) k -1
fl]
w h e r e CO is i n i t i a l c o m p o s i t i o n . " P o t e n t i a l r e f i n i n g r a t i o " is defined a s - C s / C o where CS is a v e r a g e solid A. L. LUX is Senior Research Scientist, Consolidatcd Aluminum Corp, Science Centcr, St. Louis, MO 63141, and M. C. FLEMINGSis Ford Professor of Engincering,Massachusetts Institute of Tcchnology, Cambridgc, MA 02139 This papcr is based on doctoral thesis work of A. L. Lux. Manuscript submitted May 31, 1978. METALLURGICALTRANSACTIONSB
composition.* T h i s is obtained by i n t e g r a t i o n of Eq. *The "potential"ratio becomesthe actualrefiningratio if liquidand solidare completelyseparated.
Ill: CS
Co
_
1-
(1-fs)
k
[21
fs
The t e m p e r a t u r e at which the given f r a c t i o n solid is r e a c h e d is r e a d i l y c a l c u l a t e d s i n c e C~ in Eq. [lJ is l i n e a r l y r e l a t e d to this t e m p e r a t u r e by the slope of the s o l i d u s of the phase d i a g r a m . F i g u r e s 1 to 3 plot the r e s u l t s of Eqs. [1] and [2] in t h r e e d i f f e r e n t ways, for a m o d e l Sn-2.5 pct Pb alloy. F i g u r e 1 shows f r a c tion s o l i d vs t e m p e r a t u r e , F i g . 2 is a v e r a g e solid comp o s i t i o n vs f r a c t i o n solid, and F i g . 3 is p o t e n t i a l r e fining r a t i o vs f r a c t i o n solid. A l s o shown in these f i g u r e s a r e c o m p a r a b l e c u r v e s a s s u m i n g complete diffusion in the solid ( e q u i l i b r i u m s o l i d i f i c a t i o n ) . The f o r e g o i n g " f r a c t i o n a l s o l i d i f i c a t i o n " c u r v e s apply for m e l t i n g as well as s o l i d i f i c a t i o n p r o v i d e d no liquid is r e m o v e d f r o m the s y s t e m d u r i n g the m e l t i n g p r o c e s s . However, s t a r t l i n g l y d i f f e r e n t r e s u l t s a r e 240 . . . . . . . .
FRACT,ONA[ MEt f NG ,,,,, 250
~
220
~
210
--
EOL]IL IARIUM S C L I D F CAT O N - P
200 CRACTIONA s SOL IDIFICA" ,0 N - NO SOt ID DIFFUSION
I 190[
180
I __
2
4
. L_ .6
8
I0
FRACTION SOLID, fs
Fig. 1--Fraction solid us temperature for Sn-2.5 pct Pb alloy, for equilibrium solidification, no solid diffusion, and for "fractional melting".
ISSN 0360-2141/79/0312-0079500.7510 9 1979AMERICANSOCIETY FOR METALS AND TIIE METALLURGICALSOCIETYOF AIME
VOLUME 10B, MARCH 1979-79
o b t a i n e d if a f r a c t i o n a l m e l t i n g p r o c e s s i s conducted s o the liquid is c o n t i n u o u s l y d r a i n e d f r o m the s o l i d d u r i n g h e a t i n g and if h e a t i n g is s u f f i c i e n t l y slow that c o m p l e t e d i f f u s i o n i s obtained in the s o l i d . F i g u r e s 1 to 3 show p l o t s f o r t h i s r a d i c a l l y new r e f i n i n g p r o c e s s , b a s e d on q u a n t i t a t i v e c a l c u l a t i o n s given b e low. Note in F i g . 1 that in t h i s new p r o c e s s a much h i g h e r f r a c t i o n s o l i d e x i s t s at a given t e m p e r a t u r e and that, in f a c t , o v e r 0.8 of the o r i g i n a l s a
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