The measurement of liquid diffusion coefficients in the Al-Cu system using temperature gradient zone melting
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AND
J. D. HUNT
The p o s s i b i l i t y of m e a s u r i n g liquid diffusion coefficients in m e t a l s using t e m p e r a t u r e gradient zone melting has been investigated. A technique has been developed for introducing i n t r i n s i c d r o p l e t s . When c o r r e c t i o n s to the s i m p l e theory have been made the value of the liquid diffusion coefficient a g r e e s well with previous work. "!" I.,IQUID diffusion coefficients a r e needed in the a n a l y s i s of many solidification p r o b l e m s . T e m p e r a t u r e gradient zone melting (TGZM) p r o v i d e s a potentially a t t r a c t i v e technique f o r the m e a s u r e m e n t of these coefficients 1 p a r t i c u l a r l y in metals or m a t e r i a l s which f r e e z e with v e r y s m a l l kinetic u n d e r coolings. When a droplet of liquid in a solid is p l a c e d in a t e m p e r a t u r e gradient, the d r o p l e t moves. The motion is a r e s u l t of the composition gradient a r i s ing f r o m the t e m p e r a t u r e difference at e i t h e r end of the d r o p l e t . The velocity is given by the continuity of m a t t e r equation at the i n t e r f a c e (neglecting solid state diffusion and t h e r m a l t r a n s p o r t ) Vn(C S - CL) = DL-~ac~
[1]
where Vn is the velocity n o r m a l to the i n t e r f a c e , Cs and CL a r e the concentrations in atom f r a c t i o n of the s o l i d and liquid, DL the liquid diffusion coefficient and Oc/an the composition gradient n o r m a l to the i n t e r face. The composition gradient in the d r o p l e t is a l m o s t constant because in a metal t h e r e is local equilibrium around the i n t e r f a c e . That is G = m 0c 0-x
[2]
where G is the t e m p e r a t u r e gradient and m is the liquidus slope and x is the distance axis in the d i r e c tion of the t e m p e r a t u r e gradient. Thus V(Cs - CL) = DL ~0c x
Is]
V(Cs - CL) = DL G m
[4]
or
where V is the velocity of the i n t e r f a c e in the x d i r e c tion. The diffusion coefficient can be calculated p r o v i d e d the t e m p e r a t u r e or composition of the droplet, the t e m p e r a t u r e gradient within the d r o p l e t and the distance d r o p l e t has moved is known. The technique has the advantage that the s a m e d i r e c t i o n a l growth a p p a r a t u s used in many s o l i d i f i c a t i o n e x p e r i m e n t s may M. P. WATSONand J. D. HUNT are Student and UniversityLecturer, respectively,Department of Metallurgyand Scienceof Materials, University of Oxford, England. Manuscript submitted December 13, 1976. METALLURGICALTRANSACTIONSA
be used for the m e a s u r e m e n t s . Another advantage is that a n a l y s i s of composition is not n e c e s s a r y p r o vided a c c u r a t e phase d i a g r a m information is a v a i l able.
EXPERIMENTAL Aluminum (99.99 pct) containing copper rich zones was investigated in the present work. In the initial experiments copper wires were incorporated in pure aluminum specimens. Aluminum was cast into graphite specimen tubes 17 c
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