Related papers: Phase field model of interfaces in single-componen…
The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…
In this paper the relationship between the density functional theory of freezing and phase field modeling is examined. More specifically a connection is made between the correlation functions that enter density functional theory and the…
We present a new multiphase-field theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical…
In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic…
We investigate the multi-order parameter phase field model of Steinbach and Pezzolla [I. Steinbach, F. Pezzolla, A generalized field method for multiphase transformations using interface fields, Physica D 134 (1999) 385-393] concerning its…
Using a generalized order parameter gradient expansion within density functional theory, we derive a phase-field-crystal model for liquid crystals composed by apolar particles in three spatial dimensions. Both the translational density and…
We present a phase field model of solidification which includes the effects of the crystalline orientation in the solid phase. This model describes grain boundaries as well as solid-liquid boundaries within a unified framework. With an…
The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional theory (DDFT), for both single-component and binary systems. The derivation is based on a truncation up to the three-point direct correlation…
The expression of the free energy density of a classical crystalline system as a gradient expansion in terms of a set of order parameters is developed using classical density functional theory. The goal here is to extend and complete an…
The statics and dynamics of a surface separating two phases of a relativistic quantum field theory at or near the critical temperature typically make use of a free energy as a functional of an order parameter. This free energy functional…
Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits…
A modified phase field crystal model in which the free energy may be minimised by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where…
In a recent class of phase field crystal (PFC) models, the density order parameter is coupled to powers of its mean field. This effectively introduces a phenomenology of higher-order direct correlation functions acting on long wavelengths,…
We develop a phase-field model for evaporation from a porous medium by explicitly considering a vapor component together with the liquid and gas phases in the system. The phase-field model consists of the conservation of mass (for phases…
Phase field crystals (PFC) are a tool for simulating materials at the atomic level. They combine the small length-scale resolution of molecular dynamics (MD) with the ability to simulate dynamics on mesoscopic time scales. We show how PFC…
Phase field crystal (PFC) theory, extensively used for modelling the structure of solids, can be derived from dynamical density functional theory (DDFT) via a sequence of approximations. Standard derivations neglect a term of form…
The phase-field crystal (PFC) model describes crystal structures at diffusive timescales through a periodic, microscopic density field. It has been proposed to model elasticity in crystal growth and encodes most of the phenomenology related…
The solidification of polycrystalline materials can be modelled by orientation-field models, which are formulated in terms of two continuous fields: a phase field that describes the thermodynamic state and an orientation field that…
We propose a two dimensional frame-invariant phase field model of grain impingement and coarsening. One dimensional analytical solutions for a stable grain boundary in a bicrystal are obtained, and equilibrium energies are computed. We are…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…