  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.
