Phase-Field Models for Microstructure Evolution

TLDR

The phase‑field method is a powerful computational approach for modeling mesoscale morphological and microstructure evolution in materials. This paper reviews recent advances in phase‑field modeling of processes such as solidification, phase transformations, grain growth, thin‑film domain evolution, surface patterning, dislocation microstructures, crack propagation, and electromigration. It represents microstructures with conserved and nonconserved continuous field variables whose evolution follows the Cahn‑Hilliard diffusion and Allen‑Cahn relaxation equations, enabling prediction of arbitrary morphologies without explicit interface tracking.

Abstract

▪ Abstract The phase-field method has recently emerged as a powerful computational approach to modeling and predicting mesoscale morphological and microstructure evolution in materials. It describes a microstructure using a set of conserved and nonconserved field variables that are continuous across the interfacial regions. The temporal and spatial evolution of the field variables is governed by the Cahn-Hilliard nonlinear diffusion equation and the Allen-Cahn relaxation equation. With the fundamental thermodynamic and kinetic information as the input, the phase-field method is able to predict the evolution of arbitrary morphologies and complex microstructures without explicitly tracking the positions of interfaces. This paper briefly reviews the recent advances in developing phase-field models for various materials processes including solidification, solid-state structural phase transformations, grain growth and coarsening, domain evolution in thin films, pattern formation on surfaces, dislocation microstructures, crack propagation, and electromigration.