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.

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

References in corpus (5)

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• Phase-field crystal modeling of equilibrium bcc-liquid interfaces
• Phase Field Modeling of Fracture and Stress Induced Phase Transitions
• Phase field modelling of grain boundary premelting using obstacle potentials
• The influence of short range forces on melting along grain boundaries