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arXiv · 2601.07497

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

Sergio Conti·Vito Crismale·Adriana Garroni·Annalisa Malusa
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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.

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Sergio Conti, Vito Crismale, Adriana Garroni, Annalisa Malusa. 2026-01-12. Phase-field approximation of sharp-interface energies accounting for lattice symmetry. https://arxiv.org/abs/2601.07497

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