preprint

Inserted: 13 jan 2026

Year: 2026

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 $θ
\logθ
$. The regularized functionals are applicable to grain growth simulation and the reconstruction of grain boundaries from imaging data.