Modeling of grain boundary dynamics using amplitude equations

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 $⟨100⟩$ and $⟨110⟩$ 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.

arXiv comment21 pages. We extended the discussion on the geometrical nonlinearities in Section 5

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• Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene
• Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model
• Gradient elasticity in Swift-Hohenberg and phase-field crystal models
• Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation
• Effect of shear-coupled grain boundary motion on coherent precipitation
• Snaking without subcriticality: grain boundaries as non-topological defects