Coriolis effects on the stability of plane-front solidification of dilute Pb-Sn binary alloys
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INTRODUCTION
D U R I N G directional solidification of alloys, it is frequently desired to produce large single crystals with very low densities of macrosegregation defects and other imperfections. In principle, this can sometimes be achieved by "plane-front" solidification, in which the melt-solid interface remains perfectly planar. In such a case, the solidification process would be steady in a reference frame moving with the interface, and the only spatial variation would be in a direction normal to the interface. However, in real systems, several instabilities can cause departures from the nominally steady and one-dimensional plane-front case. First, the solid-liquid interface may be subject to the so-called morphological instability, which has been studied extensively since the early work of Mullins and Sekerka. m This instability causes deformation of the nominally planar interface, ultimately leading to formation of a two-phase "mushy zone" of dendrites and interdendritic liquid. Departures from one-dimensionality and steadiness in the mushy zone result in nonuniform distribution of solute in the solidified material. Second, the density of a binary or multicomponent melt depends on both temperature and composition. When an alloy is solidified by cooling from below, rejection of solute(s) at the growing interface is potentially destabilizing if the solute-enriched liquid just above the interface is less dense than the warmer overlying bulk liquid. Under some conditions, this adverse solute gradient overcomes the stabilizing temperature gradient, leading to convection in the melt. This fluid motion provides another transport mechanism, besides molecular diffusion, for redistributing solute(s) into the bulk liquid from the relatively enriched region near the interface. Convection in the melt is often referred to as thermosolutal convection or, because the diffusivities of heat and solute are different, as doubly diffusive convection. A L P A R S L A N OZTEKIN, Research Assistant, and ARNE J. PEARLSTEIN, Associate Professor, are with the Department of Mechanical and Industrial Engineering, University of Illinois at UrbanaChampaign, Urbana, IL 61801. Manuscript submitted April 15, 1991. METALLURGICAL TRANSACTIONS B
Convective and morphological instabilities in a binary alloy undergoing directional solidification were first studied by Coriell e t al. r2j using a linear stability analysis. These authors showed that motion may occur due to either morphological or convective instabilities and that the buoyancy force does not sensibly alter the criterion for onset of morphological instability, which occurs at higher wavenumbers than does the buoyancy-driven instability. Subsequent work was reviewed by Glicksman e t al. t31 and Sekerka and CoriellJ 41 More general discussions of the effects of convection on plane-front and dendritic solidification have been given recently by Worster, I51 Davis, t61 Huppert, 171 Polezhaev, tSl and Miiller. 191 Buoyancy-driven convection in the melt has been shown to be the dominan
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