Latest publications

Crystallization: Colloidal suspense

László Gránásy1,2, Gyula Tóth3

1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
2BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom
3Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, U.K.

Topics: Phase field crystal

Nonlinear hydrodynamic theory of crystallization

Gyula Tóth1, László Gránásy2,3, György Tegze2

1Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, U.K.
2Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
3BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

We present an isothermal fluctuating nonlinear hydrodynamic theory of crystallization in molecular liquids. A dynamic coarse-graining technique is used to derive the velocity field, a phenomenology which allows a direct coupling between the free energy functional of the classical density functional theory and the Navier–Stokes equation. In contrast to the Ginzburg–Landau type amplitude theories, the dynamic response to elastic deformations is described by parameter-free kinetic equations. Employing our approach to the free energy functional of the phase-field crystal model, we recover the classical spectrum for the phonons and the steady-state growth fronts. The capillary wave spectrum of the equilibrium crystal–liquid interface is in good qualitative agreement with the molecular dynamics simulations.

Phase-Field Modeling of Polycrystalline Solidification: From Needle Crystals to Spherulites-A Review

László Gránásy1,2, László Rátkai1, Attila Szállás1, Bálint Korbuly1, Gyula Tóth3, László Környei4, Tamás Pusztai1

1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
2BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom
3Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, U.K.
4Department of Mathematics and Computational Sciences, Széchenyi István University, Győr 9026, Hungary

Advances in the orientation-field-based phase-field (PF) models made in the past are reviewed. The models applied incorporate homogeneous and heterogeneous nucleation of growth centers and several mechanisms to form new grains at the perimeter of growing crystals, a phenomenon termed growth front nucleation. Examples for PF modeling of such complex polycrystalline structures are shown as impinging symmetric dendrites, polycrystalline growth forms (ranging from disordered dendrites to spherulitic patterns), and various eutectic structures, including spiraling two-phase dendrites. Simulations exploring possible control of solidification patterns in thin films via external fields, confined geometry, particle additives, scratching/piercing the films, etc. are also displayed. Advantages, problems, and possible solutions associated with quantitative PF simulations are discussed briefly.

Topics: Polycrystalline solidification, Spiral eutectic dendrites

Free energy of the bcc-liquid interface and the Wulff shape as predicted by the phase-field crystal model

Frigyes Podmaniczky1, Gyula Tóth2, Tamás Pusztai1, László Gránásy1,3

1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
2Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, U.K.
3BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

The Euler-Lagrange equation of the phase-field crystal (PFC) model has been solved under appropriate boundary conditions to obtain the equilibrium free energy of the body centered cubic crystal-liquid interface for 18 orientations at various reduced temperatures in the range ε∈[0,0.5]. While the maximum free energy corresponds to the {100} orientation for all ε values, the minimum is realized by the {111} direction for smaller ε(<0.13), and by the {211} orientation for higher ε. The predicted dependence on the reduced temperature is consistent with the respective mean field critical exponent. The results are fitted with an eight-term Kubic harmonic series, and are used to create stereographic plots displaying the anisotropy of the interface free energy. We have also derived the corresponding Wulff shapes that vary with increasing ε from sphere to a polyhedral form that differs from the rhombo-dodecahedron obtained previously by growing a bcc seed until reaching equilibrium with the remaining liquid.

Spiraling eutectic dendrites

Tamás Pusztai1, László Rátkai1, Attila Szállás1, László Gránásy1,2

1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
2BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

Eutectic dendrites forming in a model ternary system have been studied using the phase-field theory. The eutectic and one-phase dendrites have similar forms, and the tip radius scales with the interface free energy as for one-phase dendrites. The steady-state eutectic patterns, appearing on these two-phase dendrites, include concentric rings and single- to multiarm spirals from which the fluctuations choose; a stochastic phenomenon characterized by a peaked probability distribution. The number of spiral arms correlates with the tip radius and the kinetic anisotropy.

Topics: Spiral eutectic dendrites

Heterogeneous Crystal Nucleation: The Effect of Lattice Mismatch

Gyula Tóth1, György Tegze2, Tamás Pusztai2, László Gránásy2,3

1Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, U.K.
2Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
3BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

A simple dynamical density functional theory is used to investigate freezing of an undercooled liquid in the presence of a crystalline substrate. We find that the adsorption of the crystalline phase on the substrate, the contact angle, and the height of the nucleation barrier are nonmonotonic functions of the lattice constant of the substrate. We show that the free-growth-limited model of particle-induced freezing by Greer et al. [Acta Mater. 48, 2823 (2000)] is valid for larger nanoparticles and a small anisotropy of the interface free energy. Faceting due to the small size of the foreign particle or a high anisotropy decouples free growth from the critical size of homogeneous nuclei.

Topics: Heterogeneous nucleation, Phase field crystal

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Heike Emmerich1, Hartmut Löwen2, Raphael Wittkowski2, Thomas Gruhn1, Gyula Tóth3, György Tegze4, László Gránásy4,5

1Lehrstuhl für Material- und Prozesssimulation, Universität Bayreuth, D-95440 Bayreuth, Germany
2Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
3Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, U.K.
4Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
5BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

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 method operates on atomic length and diffusive time scales, and thus constitutes a computationally efficient alternative to molecular simulation methods. Its intense development in materials science started fairly recently fol- lowing the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial studies, dynamical density functional theory and thermodynamic concepts have been linked to the PFC approach to serve as further theoretical fundamentals for the latter. In this review, we summarize these methodological development steps as well as the most important applications of the PFC method with a special focus on the interaction of development steps taken in hard and soft matter physics, respectively. Doing so, we hope to present today's state of the art in PFC modelling as well as the potential, which might still arise from this method in physics and materials science in the nearby future.

Topics: Phase field crystal

Selected issues of phase-field crystal simulations

Heike Emmerich1, László Gránásy2,3, Hartmut Löwen4

1Lehrstuhl für Material- und Prozesssimulation, Universität Bayreuth, D-95440 Bayreuth, Germany
2Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
3BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom
4Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany

In this contribution our focus is on the phase-field crystal method, which can be viewed as the youngest methodology in the field of interface computation based on recent work by Elder et al. (Phys. Rev. Lett. 88, 245701 (2002)). It bridges the gap between the molecular simulation approaches and the phase-field approach by operating on diffusive time scales yet atomic length scales. Here we review the fundaments of the phase-field crystal method as well as different models established so far with the aim to capture the main features of the wide range of phase diagrams found in materials science more and more comprehensively.

Amorphous Nucleation Precursor in Highly Nonequilibrium Fluids

Gyula Tóth1, Tamás Pusztai2, György Tegze2, Gergely Tóth3, László Gránásy2,4

1Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, U.K.
2Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
3Institute of Chemistry, Eötvös University, P.O. Box 32, H-1518 Budapest, Hungary
4BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

Dynamical density-functional simulations reveal structural aspects of crystal nucleation in undercooled liquids: The first appearing solid is amorphous, which promotes the nucleation of bcc crystals but suppresses the appearance of the fcc and hcp phases. These findings are associated with features of the effective interaction potential deduced from the amorphous structure.

Topics: Phase field crystal

Faceting and Branching in 2D Crystal Growth

György Tegze1, Gyula Tóth2, László Gránásy1,3

1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
2Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, U.K.
3BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

Using atomic scale time-dependent density functional calculations we confirm that both diffusion-controlled and diffusionless crystallization modes exist in simple 2D systems. We provide theoretical evidence that a faceted to nonfaceted transition is coupled to these crystallization modes, and faceting is governed by the local supersaturation at the fluid-crystalline interface. We also show that competing modes of crystallization have a major influence on mesopattern formation. Irregularly branched and porous structures are emerging at the crossover of the crystallization modes. The proposed branching mechanism differs essentially from dendritic fingering driven by diffusive instability.

Topics: Phase field crystal

Pages