Abstract
An investigation is made of the weakly nonlinear morphological stability of a uniformly moving planar solid-liquid interface during the controlled unidirectional solidification of a dilute binary substance by the process of liquid phase electro-epitaxy (LPEE). A prototype model equation for LPEE is considered which postulates two-dimensional diffusion and electromigration of solute under a fixed temperature gradient and electric current. The results of this nonlinear analysis, which can be represented in a plot of temperature gradient versus the component of solidification growth rate due to diffusion for a particular imposed electric field, are then compared with those obtained in the absence of that electric current, the latter being a model for thermal liquid phase epitaxy (LPE). If the electric current is increased beyond a certain critical value for a solid substrate such that the electric field enhances the overall solidification growth rate, then the subcritical instability always present during LP...
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