Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview

Abstract

Comprehensive investigations of crystalline systems often require methods bridging atomistic and continuum scales. In this context, coarse-grained mesoscale approaches are of particular interest as they allow the examination of large systems and time scales while retaining some microscopic details. The so-called Phase-Field Crystal (PFC) model conveniently describes crystals at diffusive time scales through a continuous periodic field which varies on atomic scales and is related to the atomic number density. To go beyond the restrictive atomic length scales of the PFC model, a complex amplitude formulation was first developed by Goldenfeld et al. [Phys. Rev. E 72, 020601 (2005)]. While focusing on length scales larger than the lattice parameter, this approach can describe crystalline defects, interfaces, and lattice deformations. It has been used to examine many phenomena including liquid/solid fronts, grain boundary energies, and strained films. This topical review focuses on this amplitude expansion of the PFC model and its developments. An overview of the derivation, connection to the continuum limit, representative applications, and extensions is presented. A few practical aspects, such as suitable numerical methods and examples, are illustrated as well. Finally, the capabilities and bounds of the model, current challenges, and future perspectives are addressed.

57 pages, 15 figures

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Cited by in corpus (5)

• A phase field crystal theory of the kinematics of dislocation lines
• The elastic inclusion problem in the (amplitude) phase field crystal model
• 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
• Explicit temperature coupling in phase-field crystal models of solidification