Experimental determination of ternary partition coefficients in Fe-Ni-X alloys
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THE
definition of partition coefficients in ternary systems is similar to that for binary systems although the solidus and liquidus are surfaces rather than lines, l For ternary systems such as Fe-Ni-X, where X is a third element, the solidus and liquidus temperatures for a given composition are dictated not only by the Ni content but also by the concentration of element X. The equilibrium ternary partition coefficient o f element X (K x) can be written as
Zr
= C~/C~
[1]
where C x is the concentration o f X in solid Fe-Ni and C g is the concentration of X in molten Fe-Ni in equilibrium with the solid. Coates e t al 2 have shown that the concept of constitutional supercooling can be applied to ternary single phase alloys. With the right choice o f thermal gradients and growth rates ternary alloys can be solidified cellularly. Such a cellular solidification will result in the segregation of the solute elements from the dendrite cores to the dendrite edges9 If diffusion in the solid is negligible the segregation profile can be calculated with the classical Scheil equation: C x = KxCX(1
-f)
K x-'
[2]
where C x is the concentration of the solid forming at the solid-liquid interface, KXo is the equilibrium partition coefficient of element X, C x is the bulk composition and fs is the fraction solidified. F r o m Eq. [2] at the onset of solidification, f~ = 0, and the equilibrium partition coefficient K x is the ratio of C x, the concentration of the first solid to freeze, to the bulk composition C x. The solute distribution during dendritic solidification may be modified by solid state diffusion effects. In such cases the analytical Scheil equation cannot be used to monitor the changing dendrite core composition. Brody and Flemings 3 proposed a numerical plate C. NARAYAN is Research Assistant and J. I. GOLDSTEIN is T. L. Diamond Professor of Metallurgy, Department of Metallurgy and Materials Engineering, Lehigh University, Bethlehem, PA 18015. Manuscript submitted February 18, 1981.
model to characterize dendritic segregation when diffusion in the solid is important. Figure 1 shows the plate model that they developed for binary alloys. The volume element indicated in the figure is used to monitor the concentration between the dendrite core and the dendrite edge. The plate model can be readily adapted for ternary systems. The solute redistribution may also be modified by coarsening effects. Experiments with Al-rich alloys 4 have, however, shown that coarsening is negligible for primary dendrites. In addition, a recent study by Kadalbal e t a P h a s shown that solute redistribution in primary dendrites of directionally solidified dendritic monocrystals o f Ni-A1-Ta is mainly affected by solid state diffusion and not by dendrite coarsening. This study uses a directional solidification experiment to grow dendritic structures in Fe-Ni-X alloys. The measured segregation in the primary dendrites is used to evaluate the ternary partition coefficients. A correction based on the numerical plate model is used to calculate
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