Modeling grain boundaries in solids using a combined nonlinear and geometrical method

TL;DR

This paper introduces a phenomenological model combining nonlinear and geometrical methods to analyze grain boundaries in solids, providing detailed defect descriptions with minimal tuning and aligning with crystallographic theories.

Contribution

It develops a Ginzburg-Landau-like approach for crystalline phases that captures defect structures at the lattice scale without extensive parameter tuning.

Findings

Model results agree quantitatively with crystallographic theories.

Universal features of frustration and competition effects near defects.

Applicable to symmetric tilt boundaries in crystalline materials.

Abstract

The complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg-Landau-like) description of crystalline phases based on symmetries and fairly general stability arguments. This method allows a very detailed description of defects at the lattice scale with virtually no tunning parameters, unlike usual phase-field methods. The model equations are directly inspired from those used in a very different physical context, namely, the formation of periodic patterns in systems out-of-equilibrium ({\it e.g.} Rayleigh-B\'enard convection, Turing patterns). We apply the formalism to the study of symmetric tilt boundaries. Our results are in quantitative agreement with those predicted by a recent crystallographic theory of grain boundaries based on a geometrical quasicrystal-like construction. These results suggest that frustration and competition effects near defects in crystalline arrangements have some universal features, of interest in solids or other periodic phases.