The phase-field crystal (PFC) method is an emerging coarse-grained atomistic model that can be used to predict material properties. In this work, we describe procedures for calculating isothermal elastic constants using the PFC method. We find that the conventional procedure used in the PFC method for calculating the elastic constants are inconsistent with those defined from a theory of thermoelasticity of stressed materials. Therefore, we present an alternative procedure for calculating the elastic constants that are consistent with the definitions from the thermoelasticity theory, and show that the two procedures result in different predictions. Furthermore, we employ a thermodynamic formulation of stressed solids to quantify the differences between the elastic constants obtained from the two procedures in terms of thermodynamic quantities such as the pressure evaluated at the undeformed state.

We introduce a new approach to represent a two-body direct correlation function (DCF) in order to alleviate the computational demand of classical density functional theory (CDFT) and enhance the predictive capability of the phase-field crystal (PFC) method. The approach utilizes a rational function fit (RFF) to approximate the two-body DCF in Fourier space. We use the RFF to show that short-wavelength contributions of the two-body DCF play an important role in determining the thermodynamic properties of materials. We further show that using the RFF to empirically parametrize the two-body DCF allows us to obtain the thermodynamic properties of solids and liquids that agree with the results of CDFT simulations with the full two-body DCF without incurring significant computational costs. In addition, the RFF can also be used to improve the representation of the two-body DCF in the PFC method. Last, the RFF allows for a real-space reformulation of the CDFT and PFC method, which enables descriptions of nonperiodic systems and the use of nonuniform and adaptive grids.

We present a structural phase-field crystal (XPFC) model [Greenwood et al. PRL 105, 045702 (2010)] that yields a stable dc structure. The stabilization of a dc structure is accomplished by parameter, which controls the heights of the peaks in the two-body DCF, is described by a Gaussian function. Furthermore, the dependence of interfacial energy on peak widths of the two-body DCF, which controls the excess energy associated with interfaces, defects, and strain, is described by an inverse power law. These relationships can be used to parameterize the PFC model for the dc structure to match solid-liquid interfacial energies to those measured experimentally or calculated

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