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.Comment: 12 pages, 2 figure

We develop and analyze a two-mode phase-field-crystal model to describe fcc ordering. The model is formulated by coupling two different sets of crystal density waves corresponding to <111> and <200> reciprocal lattice vectors, which are chosen to form triads so as to produce a simple free-energy landscape with coexistence of crystal and liquid phases. The feasibility of the approach is demonstrated with numerical examples of polycrystalline and (111) twin growth. We use a two-mode amplitude expansion to characterize analytically the free-energy landscape of the model, identifying parameter ranges where fcc is stable or metastable with respect to bcc. In addition, we derive analytical expressions for the elastic constants for both fcc and bcc. Those expressions show that a nonvanishing amplitude of [200] density waves is essential to obtain mechanically stable fcc crystals with a nonvanishing tetragonal shear modulus (C11-C12)/2. We determine the model parameters for specific materials by fitting the peak liquid structure factor properties and solid-density wave amplitudes following the approach developed for bcc [K.-A. Wu and A. Karma, Phys. Rev. B 76, 184107 (2007)]. This procedure yields reasonable predictions of elastic constants for both bcc Fe and fcc Ni using input parameters from molecular dynamics simulations. The application of the model to two-dimensional square lattices is also briefly examined.

The weak anisotropy of the interfacial free energy ␥ is a crucial parameter influencing dendritic crystal growth morphologies in systems with atomically rough solid-liquid interfaces. The physical origin and quantitative prediction of this anisotropy are investigated for body-centered-cubic ͑bcc͒ forming systems using a Ginzburg-Landau theory where the order parameters are the amplitudes of density waves corresponding to principal reciprocal lattice vectors. We find that this theory predicts the correct sign ␥ 100 Ͼ ␥ 110 and magnitude ͑␥ 100 − ␥ 110 ͒ / ͑␥ 100 + ␥ 110 ͒Ϸ1% of this anisotropy in good agreement with the results of molecular dynamics ͑MD͒ simulations for Fe. The results show that the directional dependence of the rate of spatial decay of solid density waves into the liquid, imposed by the crystal structure, is a main determinant of anisotropy. This directional dependence is validated by MD computations of density wave profiles for different reciprocal lattice vectors for ͕110͖ crystal faces. Our results are contrasted with the prediction of the reverse ordering ␥ 100 Ͻ ␥ 110 from an earlier formulation of Ginzburg-Landau theory ͓Shih et al., Phys. Rev. A 35, 2611 ͑1987͔͒.

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