Paper detail

Phase-field-crystal model for fcc ordering

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 non-vanishing amplitude of [200] density waves is essential to obtain mechanically stable fcc crystals with a non-vanishing 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.