Phase-field crystal model for a diamond-cubic structure

Abstract

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

Fluctuations and Universality in a Catalysis Model with Long-range Reactivity

“…Recent studies of adding non-zero long-range interactions in an equilibrium Ising ferro-magnet [5] showed that the universality class of the critical point changed abruptly from Ising to mean-field. Motivated by this result, we recently modified the ZGB model by introducing an adjustable probability (a) that an O atom and a CO molecule adsorbed far apart on the surface can react to form CO 2 and desorb [2]. This move is attempted only if the adsorbed species cannot find an opposite species within its four nearest-neighbor sites.…”

Mapping the phase transitions of the ZGB model with inert sites via nonequilibrium optimizing methods

“…As presented below, this question has been considered by several authors in recent years. For instance, some authors have included the diffusion of the adsorbed species (carbon monoxide molecules or oxygen atoms) on the catalystic surface [2][3][4][5][6], and others have studied the model with the desorption of molecules from the surface [7][8][9][10][11]. In this paper, we include to the original model the existence of inert sites (or impurities) over the surface (see, for example, Ref.…”

Angle-adjustable density field formulation for the modeling of crystalline microstructure

“…A fast-growing and widely applied version of such a theory is the phase field crystal (PFC) method 1,2,[7][8][9][10][11][12][13][14] , with applications across a variety of solid and soft-matter systems, particularly for the elastoplastic phenomena that are inaccessible to traditional methods [15][16][17][18][19][20][21][22][23] . Most PFC models are constructed for systems of isotropic interactions, with lattice symmetry controlled by microscopic length scales 1,2,[7][8][9][10][11][12][13][14][24][25][26] . They are applicable to metallic-type materials or colloidal systems with excluded volume or steric interactions that are dependent on interparticle distance, but would be a crude approximation if applied to a broader range of material systems with directional interaction depending on both bond lengths and angles.…”