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

TL;DR

This paper introduces a hybrid multiscale framework combining the phase-field crystal (PFC) and amplitude-PFC (APFC) models to efficiently simulate crystal structures, dislocations, and grain boundaries across different scales.

Contribution

It presents a novel coupling method for PFC and APFC models using spectral discretization, enabling detailed resolution of interfaces while maintaining computational efficiency.

Findings

Successfully couples PFC and APFC models in 2D simulations

Overcomes APFC limitations in large-angle grain boundary modeling

Demonstrates improved multiscale crystal simulation capabilities

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.