  We investigate the equilibrium properties of bcc-liquid interfaces modeled
with a continuum phase-field crystal (PFC) approach [K. R. Elder and M. Grant,
Phys. Rev. E 70, 051605 (2004)]. A multiscale analysis of the PFC model is
carried out which exploits the fact that the amplitudes of crystal density
waves decay slowly into the liquid in the physically relevant limit where the
freezing transition is weakly first order. This analysis yields a set of
coupled equations for these amplitudes that is similar to the set of equations
derived from Ginzburg-Landau (GL) theory [K.-A. Wu et al., Phys. Rev. E 73,
094101 (2006)]. The two sets only differ in the details of higher order
nonlinear couplings between different density waves, which is determined by the
form of the nonlinearity assumed in the PFC model and by the ansatz that all
polygons with the same number of sides have equal weight in GL theory. Despite
these differences, for parameters (liquid structure factor and solid density
wave amplitude) of Fe determined from molecular dynamic (MD) simulations, the
PFC and GL amplitude equations yield very similar predictions for the overall
magnitude and anisotropy of the interfacial free-energy and density wave
profiles. These predictions are compared with MD simulations as well as
numerical solutions of the PFC model.
