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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…

Soft Condensed Matter · Physics 2019-09-04 Andrew J. Archer , Daniel J. Ratliff , Alastair M. Rucklidge , Priya Subramanian

Structural phase transformations in (001)-oriented (1-x)Pb(Mg1/3Nb2/3O3)-32%PbTiO3 (PMN-x%PT) crystals have been investigated by x-ray diffraction. A C->T->MC sequence was observed in both the field-cooled (FC) and zero-field-cooled (ZFC)…

Materials Science · Physics 2009-11-10 Hu Cao , Feiming Bai , Jiefang Li , D. Viehland , Guangyong Xu , H. Hiraka , G. Shirane

This paper develops three linear and energy-stable schemes for a modified phase field crystal model with a strong nonlinear vacancy potential (VMPFC model). This sixth-order phase-field model enables realistic crystal growth simulation.…

Numerical Analysis · Mathematics 2025-10-14 Wanrong Hao , Yunqing Huang

In this paper we describe a new model for solidification with heat flux using the phase field crystal (PFC) framework. The equations are thermodynamically consistent, in the sense that the time rate of change of the entropy density is…

Materials Science · Physics 2021-07-13 C. Wang , S. M. Wise

For an arbitrary unbounded domain $\Omega\subset\R^3$ and for $\eps>0$, we consider the damped hyperbolic equations \leqno{(H_\eps)} \eps u_{tt}+ u_t+\beta(x)u- \sum_{ij}(a_{ij}(x) u_{x_j})_{x_i}&=f(x,u),\quad x\in \Omega,…

Analysis of PDEs · Mathematics 2007-05-23 M. Prizzi , K. P. Rybakowski

We discuss an active phase field crystal (PFC) model that describes a mixture of active and passive particles. First, a microscopic derivation from dynamical density functional theory (DDFT) is presented that includes a systematic treatment…

Soft Condensed Matter · Physics 2022-10-26 Michael te Vrugt , Max Philipp Holl , Aron Koch , Raphael Wittkowski , Uwe Thiele

We investigate the equilibrium properties of bcc-liquid interfaces modeled with a continuum phase-field crystal (PFC) approach [K. R. Elder and M. Grant, Phys. Rev. E 70, 051605 (2004)]. A multiscale analysis of the PFC model is carried out…

Materials Science · Physics 2009-11-13 Kuo-An Wu , Alain Karma

A new isotropic magneto-elastic phase field crystal (PFC) model to study the relation between morphological structure and magnetic properties of pure ferromagnetic solids is introduced. Analytic calculations were used to determine the phase…

Materials Science · Physics 2015-06-16 Niloufar Faghihi , Nikolas Provatas , K. R. Elder , Martin Grant , Mikko Karttunen

Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC…

The paper is concerned with the exponential attractors for the viscoelastic wave model in $\Omega\subset \mathbb R^3$: $$u_{tt}-h_t(0)\Delta u-\int_0^\infty\partial_sh_t(s)\Delta u(t-s)\mathrm ds+f(u)=h,$$ with time-dependent memory kernel…

Analysis of PDEs · Mathematics 2021-04-29 Yanan Li , Zhijian Yang

A new phase field crystal (PFC) type theory is presented, which accounts for the full spectrum of solid-liquid-vapor phase transitions within the framework of a single density order parameter. Its equilibrium properties show the most…

Materials Science · Physics 2015-06-23 Gabriel Kocher , Nikolas Provatas

We present a computer simulation study on the crystalline phases of hard ellipsoids of revolution. For aspect ratios greater than or equal to 3 the previously suggested stretched-fcc phase [D. Frenkel and B. M. Mulder, Mol. Phys. 55, 1171…

Soft Condensed Matter · Physics 2007-05-23 Patrick Pfleiderer , Tanja Schilling

In light of recent study on the dark energy models that manifest an equation of state $w<-1$, we investigate the cosmological evolution of phantom field in a specific potential, exponential potential in this paper. The phase plane analysis…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Jian-gang Hao , Xin-zhou Li

The anisotropic phase-field crystal model recently proposed and used by Prieler et al. [J. Phys.: Condens. Matter 21, 464110 (2009)] is derived from microscopic density functional theory for anisotropic particles with fixed orientation.…

Materials Science · Physics 2015-05-27 Muhammad Ajmal Choudhary , Daming Li , Heike Emmerich , Hartmut Löwen

We introduce a dislocation density tensor and derive its kinematic evolution law from a phase field description of crystal deformations in three dimensions. The phase field crystal (PFC) model is used to define the lattice distortion,…

Materials Science · Physics 2022-06-06 Vidar Skogvoll , Luiza Angheluta , Audun Skaugen , Marco Salvalaglio , Jorge Viñals

We present and discuss the development of an unconditionally stable algorithm used to solve the evolution equations of the Phase Field Crystal (PFC) model. This algorithm allows for an arbitrarily large algorithmic time step. As the basis…

Computational Physics · Physics 2009-11-13 Mowei Cheng , James A. Warren

The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be…

Soft Condensed Matter · Physics 2009-05-28 Sven van Teeffelen , Rainer Backofen , Axel Voigt , Hartmut Löwen

A nonlocal phase-field crystal (NPFC) model is presented as a nonlocal counterpart of the local phase-field crystal (LPFC) model and a special case of the structural PFC (XPFC) derived from classical field theory for crystal growth and…

Numerical Analysis · Mathematics 2026-05-20 Qiang Du , Kai Wang , Jiang Yang

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…

Materials Science · Physics 2015-05-13 P. F. Tupper , Martin Grant

We study a two-phase modified Stefan problem modeling solid combustion and nonequilibrium phase transition. The problem is known to exhibit a variety of non-trivial dynamical scenarios. We develop a priori estimates and establish…

Analysis of PDEs · Mathematics 2007-05-23 M. L. Frankel , V. Roytburd