Complex order-parameter phase-field models derived from structural phase-field-crystal models

Abstract

The phase-field-crystal (PFC) modeling paradigm is rapidly emerging as the model of choice when investigating materials phenomena with atomistic scale effects over diffusive time scales. Recent variants of the PFC model, so-called structural PFC (XPFC) models introduced by Greenwood et al., have further increased the capability of the method by allowing for easy access to various structural transformations in pure materials [Phys. Rev. Lett. 105, 045702 (2010)] and binary alloys [Phys. Rev. B. 84, 064104, (2011)]. We present an amplitude expansion of these XPFC models, leading to a mesoscale complex order-parameter (amplitude), i.e., phase-field representation, model for two dimensional square-triangular structures. Amplitude models retain the salient atomic scale features of the underlying PFC models, while resolving microstructures on mesoscales as in traditional phase-field models. The applicability and capability of this complex amplitude model is demonstrated with simulations of peritectic solidification and grain growth exhibiting the emergence of secondary phase structures.

15 pages, 6 figures

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• Closing the gap between atomic-scale lattice deformations and continuum elasticity
• Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview
• Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model
• Controlling grain boundaries by magnetic fields
• Phase ordering, transformation, and grain growth of two-dimensional binary colloidal crystals: A phase field crystal modeling
• Multiscale analysis of crystal defect formation in rapid solidification of pure aluminium and aluminium-copper alloys
• Angle-adjustable density field formulation for modeling crystalline microstructures
• Magnetically induced/enhanced coarsening in thin films
• Amplitude expansion of the phase-field crystal model for complex crystal structures
• Magnetic APFC modeling and the influence of magneto-structural interactions on grain shrinkage
• Gradient elasticity in Swift-Hohenberg and phase-field crystal models