Thermosolutal convection and macrosegregation
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INTRODUCTION
T E M P E R A T U R E and composition profiles in the melt near the tips of the primary dendrite array, both in the interdendritic mushy region and in the bulk melt ahead, for directional solidification of a Pb-10 wt pct Sn alloy at a thermal gradient (G~) of 110 K cm -~ are shown in Figure 1. As shown schematically, the location of the tips corresponds to the distance marked zero. The interdendritic solutal profiles in this figure were obtained from the experimentally determined I~l thermal profiles during steady-state directional solidification of the alloy by assuming local equilibrium. Tip compositions, C,, are estimated from a theoretical model. [2] The solute content of the bulk liquid is assumed to decrease exponentially from C, to the melt composition, C0, over a characteristic distance equal to D~/R, where D~ is the solutal diffusivity in the melt and R is the growth speed. The temperature and composition dependence of the Pb-Sn binary alloy melt density reported by Poirier t3] has been used in calculating the density profiles in the melt shown in Figure I. For directional solidification with the melt on top and solid below, with gravity pointing down, the density profile in the interdendritic melt and in the melt immediately ahead of the tips promotes natural convection (higher density melt on top of that with lower density). For dendritic arrays growing with small solute build up at the tips, the interdendritic density profile plays a crucial role in determining the extent of natural convection. In a recent article, 141 we described the influence of thermosolutal convection in the interdendritic melt on the longitudinal macrosegregation for dendritic arrays and its relationship with the formation of channel segregates. However, the solute buildup at the tip is much larger for the cellular arrays which form at lower growth speeds, S.N. TEWARI, Professor, and RAJESH SHAH, Graduate Student, are with the Chemical Engineering Department, Cleveland State University, Cleveland, OH 44115. M.A. CHOPRA, formerly Research Associate, NASA-Lewis Research Center, Cleveland, OH, is Development Engineer with IBM, Austin, TX 78758. Manuscript submitted June 22, 1992. METALLURGICAL TRANSACTIONS A
for example, 2 /xm s ~ for cells vs 10 /xm s -1 for dendrites (compare C~ with C) in Figure 1). This not only produces a larger density inversion in the melt ahead of the tips at lower growth speeds (density of the melt ahead of the tip increases by Apz before beginning to decrease, compared with an increase of only Apj), but the inversion also exists over larger distance (compare Dt/Rz with D~/Rj in Figure 1). Thermosolutal convection in the bulk melt will therefore be very important for the cellular morphologies. Convection near the tips can also penetrate into the mushy region. This will result in longitudinal (parallel to the growth direction) and transverse macrosegregations, solutal inhomogeneities over length scales much larger than the primary arm spacings, during directional solidification. In this art
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