ABSTRACT
An investigation is made of pattern formation on an initially planar interface of solid growing uniformly into the liquid phase during the unidirectional solidification of a dilute binary alloy. Two and three-dimensional nonlinear stability analyses are performed on the governing model system analogous to those originally developed for the study of Bénard convection cells. The main result of these analyses is the identification of regions in a solidification speed-liquid temperature gradient parameter space corresponding to a planar interface, nodes consisting of circular depressions of liquid into the solid phase, bands, and hexagonal cells, the latter only existing if the variation of interfacial surface free energy with solute concentration is taken into account. Then the associated problem of the melting of such an alloy is considered by performing the two-dimensional nonlinear stability analysis on its governing system obtaining a similar bifurcation diagram. For this model the diffusion of solute in the solid phase is taken equal to that in the liquid phase (the two-sided model) whereas for solidification it was taken equal to zero (the one sided model). These results are shown to be in accord with relevant experimental evidence.
