EFFECT OF LATENT-HEAT ON OSCILLATORY AND CELLULAR-MODE COUPLING IN RAPID DIRECTIONAL SOLIDIFICATION

At large rates of solidification, some metallic alloys exhibit periodi c microstructures along the growth direction in which layers free of l ateral segregation alternate with cellular, dendritic, or eutectic pha ses. We investigate the formation of microstructures such as these ban ds by studying the nonlinear dynamics of the rapidly solidifying inter face for a dilute binary alloy. The model employed in these studies ha s a velocity dependent segregation coefficient and liquidus slope, a l inear form of attachment kinetics, and the effects of latent heat rele ase and full temperature distribution. Huntley and Davis performed a l inear stability analysis on this model which revealed two modes of ins tability to the planar solid/liquid interface: (i) a steady cellular i nstability, and (ii) an oscillatory instability driven by disequilibri um effects. In this paper we investigate the nonlinear interaction bet ween 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 influe nce of latent heat on the nonlinear dynamics and suggest where banding behavior may be found.