Interface dynamics and banding in rapid solidification

Rapid-solidification experiments on metallic alloys in the last decade have provided widespread observations of a novel ‘‘banded structure.’’ We report the results of numerical and analytical studies of the interface dynamics underlying the formation of this structure in a model of directional solidification which includes both solute and heat diffusion and nonequilibrium effects. The thrust of these studies is on the unsteady dynamics of the planar interface and thermal effects. The main conclusion is that the origin of banding can be related to relaxation oscillations of the solidification front, characterized by large variations of the interface velocity, which are dramatically affected by latent-heat diffusion. Without the latter, the oscillations are found to be reasonably well approximated by the phenomenological model of Carrard et al. [Acta Metall. 40, 983 (1992)], and the band spacing is inversely proportional to the temperature gradient. In contrast, with latent-heat diffusion the band spacing is insensitive to the temperature gradient, but is controlled instead by the interplay of solute and heat diffusion. The smallness of the solutal diffusivity to thermal diffusivity ratio is exploited to explain analytically this effect and to derive considerably simpler equations of interface motion that provide an efficient numerical means to study the nonplanar interface dynamics expected to cause dark bands. A reasonable agreement with experiment is found for the spacing of banded structures dominated by light-band microsegregation-free regions in Al-Fe alloys.