  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.
