A theoretical investigation of the development of interfacial cells during the solidification of a dilute binary alloy: Comparison with the experiments of Morris and Winegard

Abstract

An investigation is made of the development of hexagonal cells on an initially planar interface of solid growing uniformly into the liquid phase during the unidirectional solidification of a dilute binary alloy. The model employed postulates three-dimensional diffusion of solute and heat under the simplifying assumptions that there is no convection in the liquid phase, no solute diffusion in the solid phase, both these phases are infinite in extent, latent heat is negligible, and the thermal fields satisfy Laplace's equation in each phase. A nonlinear stability analysis is performed analogous to that originally developed for the study of Bénard convection cells. The main results of this analysis are that, for a fixed value of the liquid temperature gradient, the structure of the planar interface evolves from nodes (circular depressions) to bands (elongated cells) to dome-shaped hexagonal cells as the solidification speed is increased. These results, which can only be obtained provided the variation of interfacial surface free energy with solute concentration is taken into account, are in excellent agreement with the experimental observations of Morris and Winegard [J. Inst. Metals 97 (1969) 220; J. Crystal Growth 5 (1969) 361] in regard to interface morphologies and solute segregation under their solidification conditions.