Convection-induced distortion of a solid-liquid interface
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I.
INTRODUCTION
D U R I N G unidirectional growth of a crystal by a Bridgman or similar process, convection in the liquid phase can be driven by several forces. In the presence of gravitational forces, the most important source of convective flow is ordinarily the density differences due to temperature and composition differences within the sample. Additional flow can be driven by the volume change which accompanies the phase change, and if any free surfaces (liquid-vapor or liquid-liquid) are present, surface energy gradient (Marangoni) flows are possible. The latter two types of flow are present even in the absence of gravitational forces. In the presence of gravitational forces, density-induced convective flow can be avoided during crystal growth if special conditions are met. In a pure material it is sufficient that the temperature increases with height (for a normal material which expands with increasing temperature) and that no gradients be present in the horizontal directions. If a solute is present, the solidification process will lead to composition differences ahead of the solid-liquid interface. If the rejected solute is lower in density than the solvent, the composition differences can lead to a thermosolutal convective instability. The conditions which lead to this instability are not simply that the density in some region increases with height: the conditions are determined by an analysis of the behavior of elements of the fluid which are displaced vertically. ~.2.3 When convective flow occurs, it redistributes both heat and solute in the liquid phase, and thus causes the temperature and concentration fields in this phase to differ from those which would be calculated on the basis of diffusive transport alone. As a result, the composition of the crystal as it grows will be less homogeneous than would be possible in the absence of convection. A steady state flow pattern can result in lateral segregation while a non-steady flow pattern will produce additional longitudinal non-uniformity. Because convective flow can modify the temperature and solute fields in the liquid adjacent to the solid-liquid interface, it can cause local variations in the conditions which determine the morphological stability 4 of the solid-liquid interface. Thus, for example, it can lead to the growth of crystals which contain localized regions of cellular microstructure within an otherwise cell-free matrix. When a R. J. SCHAEFER and S. R. CORIELL are with the Metallurgy Division, National Bureau of Standards, Gaithersburg, MD 20899. This paper is based on a presentation made at the symposium "Fluid Flow at Solid-Liquid Interfaces" held at the fall meeting of the TMS-AIME in Philadelphia, PA on October 5, 1983 under the TMS-AIME Solidification Committee. METALLURGICALTRANSACTIONSA
highly uniform crystal is needed, it may thus be essential to keep these convective effects under control. In this paper we present observations of convective phenomena during the solidification of a transparent "alloy" system, succinonitrile contain
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