Effect of latent heat on oscillatory and cellular mode coupling in rapid directional solidification

At large rates of solidification, some metallic alloys exhibit periodic microstructures along the growth direction in which layers free of lateral segregation alternate with cellular, dendritic, or eutectic phases. We investigate the formation of microstructures such as these bands by studying the nonlinear dynamics of the rapidly solidifying interface for a dilute binary alloy. The model employed in these studies has a velocity dependent segregation coefficient and liquidus slope, a linear form of attachment kinetics, and the effects of latent heat release and full temperature distribution. Huntley and Davis performed a linear stability analysis on this model which revealed two modes of instability to the planar solid/liquid interface: (i) a steady cellular instability, and (ii) an oscillatory instability driven by disequilibrium effects. In this paper we investigate the nonlinear interaction between these two instabilities by performing a weakly nonlinear analysis on their coupling. The bifurcation analysis results in coupled Landau equations that govern the behavior of the disturbance amplitudes. The theoretical predictions are applied to several physical systems that exhibit large-transition-rate microstructures. Although bands are not described with this analysis, our results give insight into the influence of latent heat on the nonlinear dynamics and suggest where banding behavior may be found.