Modeling of grain boundary dynamics using amplitude equations

TL;DR

This paper models grain boundary dynamics using amplitude equations derived from density functional theory, capturing coupled motion and grain rotation, and discusses the relation to geometrical models and elastic behavior.

Contribution

It introduces an amplitude equations framework for grain boundary dynamics that reproduces geometrical predictions and analyzes coupling modes and grain rotation.

Findings

Recover predictions of coupled grain boundary motion by Cahn and Taylor

Identify both $10 angle$ and $10 angle$ coupling modes

Confirm amplitude equations capture linear elasticity accurately

Abstract

We discuss the modelling of grain boundary dynamics within an amplitude equations description, which is derived from classical density functional theory or the phase field crystal model. The relation between the conditions for periodicity of the system and coincidence site lattices at grain boundaries is investigated. Within the amplitude equations framework we recover predictions of the geometrical model by Cahn and Taylor for coupled grain boundary motion, and find both $\langle100\rangle$ and $\langle110\rangle$ coupling. No spontaneous transition between these modes occurs due to restrictions related to the rotational invariance of the amplitude equations. Grain rotation due to coupled motion is also in agreement with theoretical predictions. Whereas linear elasticity is correctly captured by the amplitude equations model, open questions remain for the case of nonlinear deformations.