Interface kinetics in phase-field models: Isothermal transformations in binary alloys and step dynamics in molecular-beam epitaxy

Abstract

We present a unified description of interface kinetic effects in phase-field models for isothermal transformations in binary alloys and steps dynamics in molecular-beam-epitaxy. The phase-field equations of motion incorporate a kinetic cross-coupling between the phase field and the concentration field. This cross-coupling generalizes the phenomenology of kinetic effects and was omitted until recently in classical phase-field models. We derive general expressions (independent of the details of the phase-field model) for the kinetic coefficients within the corresponding macroscopic approach using a physically motivated reduction procedure. The latter is equivalent to the so-called thin-interface limit but is technically simpler. It involves the calculation of the effective dissipation that can be ascribed to the interface in the phase-field model. We discuss in detail the possibility of a nonpositive definite matrix of kinetic coefficients, i.e., a negative effective interface dissipation, although being in the range of stability of the underlying phase-field model. Numerically we study the step-bunching instability in molecular-beam-epitaxy due to the Ehrlich-Schwoebel effect, present in our model due to the cross-coupling. Using the reduction procedure we compare the results of the phase-field simulations with the analytical predictions of the macroscopic approach.