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Phase field crystal (PFC) models constitute central tools for a microscopic understanding of the dynamics of complex systems in soft matter physics. They have found widespread application in the modeling of the uniaxial orientational…

Soft Condensed Matter · Physics 2026-01-22 Anouar El Moumane , René Wittmann , Hartmut Löwen , Michael te Vrugt

The phase-field crystal model (PFC) describes crystal structures at diffusive timescales through a periodic order parameter representing the atomic density. One of its main features is that it naturally incorporates elastic and plastic…

Materials Science · Physics 2023-07-07 Maik Punke , Vidar Skogvoll , Marco Salvalaglio

We present a phase field theory for binary crystal nucleation. In the one-component limit, quantitative agreement is achieved with computer simulations (Lennard-Jones system) and experiments (ice-water system) using model parameters…

Soft Condensed Matter · Physics 2009-11-07 Laszlo Granasy , Tamas Borzsonyi , Tamas Pusztai

We determine the speed of a crystallisation (or more generally, a solidification) front as it advances into the uniform liquid phase after the system has been quenched into the crystalline region of the phase diagram. We calculate the front…

Soft Condensed Matter · Physics 2013-03-25 A. J. Archer , M. J. Robbins , U. Thiele , E. Knobloch

The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. This is because the phase-field…

Mathematical Physics · Physics 2015-07-29 Philippe Vignal , Lisandro Dalcin , Donald L. Brown , Nathan Collier , Victor M. Calo

While biological crystallization processes have been studied on the microscale extensively, models addressing the mesoscale aspects of such phenomena are rare. In this work, we investigate whether the phase-field theory developed in…

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…

We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems. In particular, this involves the determination of lines of phase coexistence related to first…

Soft Condensed Matter · Physics 2021-01-22 Max Philipp Holl , Andrew J. Archer , Uwe Thiele

We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma-plot with rounded cusps that can approach arbitrarily closely the true gamma-plot with sharp cusps that…

Materials Science · Physics 2009-11-10 Jean-Marc Debierre , Alain Karma , Franck Celestini , Rahma Guerin

Crystallization of supersaturated liquids usually starts by heterogeneous nucleation. Mounting evidence shows that even homogeneous nucleation in simple liquids takes place in two steps; first a dense amorphous precursor forms, and the…

Materials Science · Physics 2014-07-15 László Gránásy , Frigyes Podmaniczky , Gyula I. Tóth , György Tegze , Tamás Pusztai

Even though our theoretical understanding of dendritic solidification is relatively well developed, our current ability to model this process quantitatively remains extremely limited. This is due to the fact that the morphological…

Materials Science · Physics 2007-05-23 Jean Bragard , Alain Karma , Youngyih H. Lee , Mathis Plapp

Particle-stabilised emulsions are a cornerstone of soft matter science due to their broad application and fundamental relevance. Computer simulations provide key insights into the formation and behaviour of these emulsions, yet current…

Soft Condensed Matter · Physics 2026-02-19 Elisabeth C. Eij , Joost de Graaf , Martin F. Haase , Jesse M. Steenhoff

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 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…

Materials Science · Physics 2015-05-18 Michael Greenwood , Nikolas Provatas , Jörg Rottler

In this work, a phase-field model is developed for the dendritic growth with gas bubbles in the solidification of binary alloys. In this model, a total free energy for the complex gas-liquid-dendrite system is proposed through considering…

Fluid Dynamics · Physics 2024-07-03 Chengjie Zhan , Zhenhua Chai , Dongke Sun , Baochang Shi , Shaoning Geng , Ping Jiang

In the literature, two quite different phase-field formulations for the problem of alloy solidification can be found. In the first, the material in the diffuse interfaces is assumed to be in an intermediate state between solid and liquid,…

Materials Science · Physics 2011-11-23 Mathis Plapp

The inherent inconsistency in identifying the phase field in the phase field crystal Theory with the material mass and, simultaneously, with material distortion is discussed. In its current implementation, elastic relaxation in the phase…

Materials Science · Physics 2025-02-25 Amit Acharya , Luiza Angheluta , Jorge Vinals

Colloidal model systems allow studying crystallization kinetics under fairly ideal conditions with rather well characterized pair interactions and minimized external influences. In complementary approaches therefore experiment, analytic…

Soft Condensed Matter · Physics 2015-06-19 Thomas Palberg

The active phase-field-crystal (active PFC) model provides a simple microscopic mean field description of crystallization in active systems. It combines the PFC model (or conserved Swift-Hohenberg equation) of colloidal crystallization and…

Soft Condensed Matter · Physics 2021-03-10 Lukas Ophaus , Edgar Knobloch , Svetlana V. Gurevich , Uwe Thiele

Planar solidification from an undercooled melt has been considered using the phase-field model. The solute and the phase fields have been found in the limit of small impurity concentration. These solutions in the limit of vanishing velocity…

Materials Science · Physics 2007-05-23 Denis Danilov