The phase field crystal (PFC) method has emerged as a promising technique for modeling materials with atomistic resolution on mesoscopic time scales. The approach is numerically much more efficient than classical density functional theory (CDFT), but its single mode free energy functional only leads to lattices with triangular (2D) or BCC (3D) symmetries. By returning to a closer approximation of the CDFT free energy functional, we develop a systematic construction of two-particle direct correlation functions that allow the study of a broad class of crystalline structures. This construction examines planar spacings, lattice symmetries, planar atomic densities and the atomic vibrational amplitude in the unit cell of the lattice and also provides control parameters for temperature and anisotropic surface energies. Solid-state transformations form the basis of many problems in materials science and physical metallurgy [1]. They involve complex structural changes between parent and daughter phases and couple atomic-scale elastic and plastic effects with diffusional processes. These phenomena are presently impossible to compute at experimentally relevant time scales using molecular dynamics simulations. On the other hand, meso-scale continuum models wash out most of the relevant atomic scale physics that leads to elasticity, plasticity, defect interactions and grain boundary nucleation and migration. Phase field studies of precipitate and ledge growth [2-4] must thus re-introduce these effects phenomenologically. There is presently no continuum method to efficiently simulate solid-state transformations on diffusional time scales that self-consistently computes elastic and plastic effects at the atomic scale.Classical density function theory (CDFT) provides a formalism that can accurately describe the emergence of crystalline order from a liquid or solid phase through a coarsegrained density field [5]. Unfortunately, this approach requires very high spatial resolution and is highly inefficient for dynamical calculations [6]. A recent model, coined the phase field crystal (PFC) model, has been gaining widespread recognition as a hybrid method between CDFT and traditional phase field methods. PFC models capture most of the essential physics of CDFT without having to resolve atomically sharp atomic density peaks [7][8][9][10][11]. In spite of their successes, however, only PFC free energy functionals minimized by triangular (2D) or BCC (3D) lattices have been seriously studied. While there have been attempts to extend the PFC model to describe other crystal symmetries such as square [12,13] and FCC [6,14,15] lattices, these have been somewhat ad-hod and not self-consistently connected to material properties. PFC modeling is presently lacking a generalized free energy formulation that allows the study of important phase transformations between different crystalline states.This Letter proposes a new CDFT/PFC model based on two-point direct correlation function that is systematically constructed to be minimized by arbitrary...

We introduce and characterize free-energy functionals for modeling of solids with different crystallographic symmetries within the phase-field-crystal methodology. The excess free energy responsible for the emergence of periodic phases is inspired by classical density-functional theory, but uses only a minimal description for the modes of the direct correlation function to preserve computational efficiency. We provide a detailed prescription for controlling the crystal structure and introduce parameters for changing temperature and surface energies, so that phase transformations between body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal-close-packed (hcp), and simple-cubic (sc) lattices can be studied. To illustrate the versatility of our free-energy functional, we compute the phase diagram for fcc-bcc-liquid coexistence in the temperature-density plane. We also demonstrate that our model can be extended to include hcp symmetry by dynamically simulating hcp-liquid coexistence from a seeded crystal nucleus. We further quantify the dependence of the elastic constants on the model control parameters in two and three dimensions, showing how the degree of elastic anisotropy can be tuned from the shape of the direct correlation functions.

We develop a phase field crystal model for structural transformations in two-component alloys. In particular, the interactions between components are described by direct correlation functions that are an extension of those introduced by Greenwood et al. [Phys. Rev. Lett. 105, 045702 (2010)] for pure materials. These correlation functions result in broad density modulations that can be treated with high numerical efficiency, hence enabling simulations of phase transformations between a wide range of crystal structures. A simplified binary alloy model is shown to describe the equilibrium properties of eutectic and peritectic binary alloys in two and three dimensions. The robustness and versatility of this method is demonstrated by applying the model to the growth of structurally similar and dissimilar eutectic lamella and to segregation to defects.