A multi-phase field model for mesoscopic interface dynamics with large bulk driving forces

Abstract

We develop a multi-phase field model for diffuse interface dynamics with large bulk chemical driving forces for phase transformation using the double-obstacle potential. We show how the classical prefactor functions for the bulk driving force significantly overestimate the velocity of multi-order-parameter junctions. We introduce a novel prefactor that properly distributes the forces for phase transformation among an arbitrary number of coexisting thermodynamic phases and order-parameters (i.e., melt patches and solid grains). The accuracy of the model is examined and we describe techniques to ensure accuracy for use with and without large bulk driving forces, including interface correction procedures that prevent profile deformation, and a recursive predictor–corrector technique for inter-parameter transfer at junctions. We explore the predictions of our models for a number of two-dimensional model configurations, including the shrinking circle, the moving tri-junction, and a shrinking circular crystal embedded in a fine-grained polycrystalline medium. The predictions for a moving tri-junction under increasingly large bulk driving forces (or length scales) are particularly notable, as the steady-state geometry of junctions deviate systematically from Young’s law for a given length scale. We provide an ansatz for the junction geometry in the case where a single-order-parameter phase (e.g., melt) consumes a multi-order-parameter phase (e.g., polycrystalline solid); an accurate solution for the opposite case remains elusive at present.