Microsegregation in directionally solidified Pb-8.4 at. pct Au alloy
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INTRODUCTION
VARIATIONS in mechanical and physical properties in cast and wrought metallic alloy components are mainly determined by the extent of chemical inhomogeneity. Microsegregation, the localized chemical inhomogeneity over distances which are of the order of primary arm spacings, can sometimes be eliminated by subsequent heat treatment. Usually these localized solute enrichments result in the formation of interdendritic precipitates, frequently very detrimental to mechanical properties. The embrittling sigma phase in superalloys is one such example. IJl While microsegregation in commercial alloys is of considerable interest, its basic understanding can only be obtained from carefully controlled directional solidification experiments on well characterized binary alloys. Several theoretical dendrite growth models have been proposed in the literature to understand the dependence of dendritic microstructure on solidification parameters. These models have attempted to make quantitative predictions of dendrite characteristics: dendrite tip radius (rt), composition of liquid at the dendrite tip (C,), dendrite tip temperature (T,), and primary arm spacing (hi), for a given alloy composition (Co), growth velocity (R), and thermal gradient at the liquid-solid interface (G). [2-91 During directional solidification (cellular/dendritic liquidsolid interface) of a binary alloy melt with a solute content less than the maximum solute solubility in the primary phase, the composition of interdendritic liquid is expected to vary from C, at the dendrite tip to Ce, the eutectic composition, at the base of the dendrite. This interdendritic solute profile determines the observed microsegregation across primary dendrites, and composition (Cs,) and volume fraction (f~) of the interdendritic two phase (eutectic-like) solid formed during directional solidification. Dendrite tip compositions predicted from the dendrite growth theories can be used to predict microsegregation across primary dendrites or in the interdendritic liquid. Brody et al. [2.~olproposed a theoretical model characterizing microsegregation patterns based on the following assumptions: (1) there is no undercooling before nucleation, or from curvature or kinetic effects; (2) there is no convection S.N. TEWARI is Associate Professor, Department of Chemical Engineering, Cleveland State University, Cleveland, OH 44115. Manuscript submitted February 12, 1987. METALLURGICALTRANSACTIONS A
in the liquid and thus no mass flow in or out of the interdendritic volume element; (3) diffusion in the liquid in the volume element is complete; and (4) local equilibrium at the solid-liquid interface prevails. They also incorporated limited solid state diffusion, called "back diffusion", and predicted the interdendritic solute profile as a function of fraction solid from the dendrite tip to the eutectic-like region at the base of dendrites. The fraction of eutectic (fe) and the minimum solute content at the center of dendrite arms (kC,) measured in aluminum copper alloys, were sho
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