Interface dynamics, instabilities, and solute bands in rapid directional solidification

Abstract

In rapid solidification experiments on metallic alloys structures have been observed which are periodic along the growth direction. The origin of these banded structures has been ascribed to an oscillatory instability of the solid-liquid interface characterized by large variations of the interface velocity; this instability was predicted by several authors incorporating nonequilibrium effects into the classic Mullins-Sekerka analysis. In this paper the rapid solidification of a binary alloy, directed by a moving temperature field, is studied with the phase-field model; in a region of the parameter space an oscillatory instability is evidenced, which reflects in alternating low and high concentration solute bands. The equations of the model are numerically solved to show under what conditions (i.e., isotherm velocity and temperature gradient) the banded structure can be observed. In many respects the results agree with the linear stability analysis of the free-boundary equations performed by Merchant and Davis [G. J. Merchant and S. H. Davis, Acta Metall. Mater. 38, 2683 (1990)]; we detected also significant deviations which trace their roots to the diffuse solid-liquid interface characteristic of the phase-field model, opposed to the zero dimension interface of the free-boundary model.