Modeling Grain Boundaries using a Phase Field Technique

TL;DR

This paper introduces a phase field model for simulating grain boundary behaviors like impingement and coarsening, providing analytical solutions and linking to microscopic models.

Contribution

It presents a novel two-dimensional phase field model that captures grain boundary phenomena with analytical solutions and connects to established microscopic theories.

Findings

Analytical solutions for stable grain boundaries in bicrystals.

Calculation of rotation rates for free grains.

Grain boundary energy matches the Read-Shockley model.

Abstract

We propose a two dimensional frame-invariant phase field model of grain impingement and coarsening. One dimensional analytical solutions for a stable grain boundary in a bicrystal are obtained, and equilibrium energies are computed. We are able to calculate the rotation rate for a free grain between two grains of fixed orientation. For a particular choice of functional dependencies in the model the grain boundary energy takes the same analytic form as the microscopic (dislocation) model of Read and Shockley.