Effects of shear flow and anisotropic kinetics on the morphological stability of a binary alloy
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INTRODUCTION
DURING alloy solidification, a smooth crystal-fluid interface may become unstable, leading to cellular or dendritic growth. Linear morphological stability theoryt~,21 describes the conditions under which the interface becomes unstable. A number of recent reviews of morphological stability are available. I3,4,51The original treatment of morphological stability by Mullins and Sekerka[1,2] assumed local equilibrium at the crystal-melt interface and isotropy of the crystal-melt surface tension; this is an excellent approximation for many metals at low growth velocities. However, many materials, including such metals as gallium and bismuth, grow with facets, indicating strong anisotropy and deviations from local equilibrium. The stability of faceted growth has also been reviewed. I6,71The effect of anisotropy of surface tension and interface kinetics on morphological stability has been treated in a quasistatic approximation to the diffusion field; kinetic anisotropy causes traveling waves along the crystal-melt interface.tS] Yuferev[91 showed that for growth in which the interface is near a singular orientation, there is an enhancement of morphological stability; more detailed calculations for a binary alloyIlOl and for growth into a supersaturated solutionEHl have recently been carried out. The linear stability theory of Mullins and Sekerkar~.2] assumed a quiescent melt; there has been extensive research on the effect of various types of fluid flow on morphological stability (see the recent review by DavisI121). Delves t~31 showed that a shear flow along the interface generally stabilized the interface with respect to perturbations of the interface shape along the flow direction; stability with respect to perturbations perpendicular to the flow direction is unaffected. Thus, a shear flow introduces an anisotropy similar to that introduced by anisotropy of surface tension and interface kinetics; perturbations in directions perpendicular and parallel to the flow direction have different staS.R. CORIELL, B.T. MURRAY, A.A. CHERNOV, and G.B. McFADDEN are with the National Institute of Standards and Technology, Gaithersburg, MD 20899. A.A. CHERNOV is on leave from the Institute of Crystallography, Russian Academy of Sciences, 117333 Moscow, Russian Federation. This article is based on a presentation made at the "Analysis and Modeling of Solidification" symposium as part of the 1994 Fall meeting of TMS in Rosemont, Illinois, October 2-6, 1994, under the auspices of the TMS Solidification Committee.
METALLURGICAL AND MATERIALS TRANSACTIONS A
bility characteristics. Huang e t al. [141 have experimentally studied the effect of a parallel shear flow in the succinonitrile-acetone system; they found an enhancement of morphological stability and an inclination of the cells toward the downstream flow direction. In this article, we consider morphological stability of the planar interface during solidification of a binary alloy at constant velocity. For an isotropic interface, the positive temperature gradient (temp
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