Phase-field-crystal model for fcc ordering

Abstract

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.

Phase-field-crystal study of grain boundary premelting and shearing in bcc iron

“…45, exhibiting the discrepancy between PFC and MD. In PFC γ sl /B = 2.67 whereas in MD γ sl /B = 1.59, where B denotes the bulk modulus.…”

“…Various methods have been developed to change the kernel of the freeenergy in order to stabilize a variety of two and three dimensional periodic and crystal structures 45,79,80 . Here we focus on bcc structures, therefore we restrict the summation to the N = 12 principal reciprocal vectors Notice that by the condition of having a real density field ψ the N complex amplitudes are not independent but are complex conjugate (denoted by a star) for antiparallel RLVs.…”

“…In this paper, we investigate GB premelting and shearing and their relationship using the PFC method [40][41][42][43][44][45][46] . We use the simplest PFC model 40,41 with the same freeenergy function as the Swift-Hohenberg model of pattern formation 47 , which favors hexagonal and bcc ordering in two and three dimensions (2D and 3D), respectively.…”

“…With appropriate rescaling of length and energy, the PFC model can be expressed in a form that involves a single small dimensionless parameter ǫ. In the context where PFC is derived from DFT, ǫ is uniquely determined by liquid-structure factor properties 44,45,54 . More generally, decreasing this parameter makes the freezing transition more weakly first order and increases the width of the solid-liquid interface in units of lattice spacing.…”

“…To benchmark our results, we compare the disjoining potentials computed by PFC and MD simulations. The MD simulations are carried out using the same EAM potential 55 that was previously used to calibrate PFC model parameters for Fe 44,45,54 . With appropriate rescaling of length and energy, the PFC model can be expressed in a form that involves a single small dimensionless parameter ǫ.…”