An In-Depth Examination of a Thermodynamic Framework for the Phase-Field Crystal Model.

Abstract

In this dissertation, we examine the phase-field crystal (PFC) model, which is a simulation method for modeling atomistic phenomena on diffusive time scales. We develop thermodynamic relationships that are used to derive procedures for calculating equilibrium material properties from the PFC model.

The first set of relationships links the PFC free energy to thermodynamic state variables and are based on the thermodynamic formalism for crystalline solids [Larche and Cahn, Acta Metall., 21 1051 (1973)]. These relationships are employed to examine the thermodynamic processes associated with varying the input parameters of the PFC model. The equilibrium conditions between bulk solid and liquid phases are imposed on the relationships to obtain a procedure for determining solid-liquid phase coexistence. The resulting procedure is found to be in agreement with the common-tangent construction commonly used in the PFC community. We apply the procedure to an eighth-order-fit (EOF) PFC model that has been parameterized to body-centered-cubic (bcc) Fe [Jaatinen et al., PRE 80, 031602 (2009)] and demonstrate that the model does not predict stable bcc structures with positive vacancy densities.

The second set of relationships is built on the recent work of Pisutha-Arnond et al. [Pisutha-Arnond et al., PRB, 87 014103 (2013)], and is applied to develop a thermodynamically consistent procedure for determining elastic constants from the PFC model. To implement these procedures, we present two alternative deformation methods, one in real space and the other in Fourier space, that are computationally more accurate and efficient than the method conventionally used in the PFC community. The procedure for determining elastic constants is implemented with the Fourier space deformation method to calculate bulk mechanical properties from the EOF-PFC model.

Finally, we present a structural PFC model [Greenwood et al. PRL 105, 045702 (2010)] that yields a stable dc structure. The stabilization of a dc structure is accomplished by constructing a two-body direct correlation function (DCF) approximated by a combination of two Gaussian functions in Fourier space. A phase diagram that contains a dc-liquid phase coexistence region was constructed for the model. We examine the energies of the (100), (110), and (111) solid-liquid interfaces.