Phase-field-crystal models and mechanical equilibrium

Abstract

Phase field crystal (PFC) models constitute a field theoretical approach to solidification, melting and related phenomena at atomic length and diffusive time scales. One of the advantages of these models is that they naturally contain elastic excitations associated with strain in crystalline bodies. However, instabilities that are diffusively driven towards equilibrium are often orders of magnitude slower than the dynamics of the elastic excitations, and are thus not included in the standard PFC model dynamics. We derive a method to isolate the time evolution of the elastic excitations from the diffusive dynamics in the PFC approach and set up a two-stage process, in which elastic excitations are equilibrated separately. This ensures mechanical equilibrium at all times. We show concrete examples demonstrating the necessity of the separation of the elastic and diffusive time scales. In the small deformation limit this approach is shown to agree with the theory of linear elasticity.

References in corpus (8)

• Phase-field Crystals with Elastic Interactions
• Phase-field crystal study of grain-boundary premelting
• Melting at dislocations and grain boundaries: A Phase Field Crystal study
• Renormalization group theory for the phase field crystal equation
• Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model
• Phase Diagram and Commensurate-Incommensurate Transitions in the Phase Field Crystal Model with an External Pinning Potential
• Nonlinear Driven Response of a Phase-Field Crystal in a Periodic Pinning Potential
• Thermal fluctuations and phase diagrams of the phase field crystal model with pinning

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