Phase-field approximation of sharp-interface energies accounting for lattice symmetry

TL;DR

This paper introduces a phase-field model for sharp-interface energies that captures lattice symmetries in polycrystals, enabling realistic grain boundary simulations and reconstructions with correct energy scaling for small misorientations.

Contribution

It develops a novel phase-field approximation that incorporates lattice symmetry and accurately models grain boundary energies in polycrystals.

Findings

Surface energy scales as θ|log θ| for small misorientations.

Model effectively simulates grain growth and boundary reconstruction.

Applicable to imaging data analysis of polycrystalline materials.

Abstract

We present a phase-field approximation of sharp-interface energies defined on partitions, designed for modeling grain boundaries in polycrystals. The independent variable takes values in the orthogonal group $\mathrm{O}(d)$ modulo a lattice point group $\mathcal{G}$, reflecting the crystallographic symmetries of the underlying lattice. In the sharp-interface limit, the surface energy exhibits a Read-Shockley-type behavior for small misorientation angles, scaling as $\theta|\log\theta|$. The regularized functionals are applicable to grain growth simulation and the reconstruction of grain boundaries from imaging data.