Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation

Abstract

The phase-field crystal (PFC) model describes crystal structures at diffusive timescales through a periodic, microscopic density field. It has been proposed to model elasticity in crystal growth and encodes most of the phenomenology related to the mechanical properties of crystals like dislocation nucleation and motion, grain boundaries, and elastic or interface-energy anisotropies. To overcome limitations to small systems, a coarse-grained formulation focusing on slowly varying complex amplitudes of the microscopic density field has been devised. This amplitude-PFC (APFC) model describes well elasticity and dislocations while approximating microscopic features and being limited in describing large-angle grain boundaries. We present here seminal concepts for a hybrid multiscale PFC-APFC framework that combines the coarse-grained description of the APFC model in bulk-like crystallites while exploiting PFC resolution at dislocations, grain boundaries, and interfaces or surfaces. This is achieved by coupling the two models via an advanced discretization based on the Fourier spectral method and allowing for local solution updates. This discretization also generalizes the description of boundary conditions for PFC models. We showcase the framework capabilities through two-dimensional benchmark simulations. We also show that the proposed formulation allows for overcoming the limitations of the APFC model in describing large-angle grain boundaries.

24 pages, 9 figures

References in corpus (12)

• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• Phase-field Crystals with Elastic Interactions
• Phase-field crystal study of grain-boundary premelting
• An Efficient Algorithm for Solving the Phase Field Crystal Model
• Renormalization group theory for the phase field crystal equation
• Multiscale modeling of polycrystalline graphene: A comparison of structure and defect energies of realistic samples from phase field crystal models
• Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model
• A coarse-grained phase-field crystal model of plastic motion
• Free energy of the bcc-liquid interface and the Wulff shape as predicted by the Phase-Field Crystal model
• Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks
• Modeling of grain boundary dynamics using amplitude equations
• Improved time integration for phase-field crystal models of solidification