Phase-field approach to polycrystalline solidification including heterogeneous and homogeneous nucleation

Advanced phase-field techniques have been applied to address various aspects of polycrystalline solidification including different modes of crystal nucleation. The height of the nucleation barrier has been determined by solving the appropriate Euler-Lagrange equations. The examples shown include the comparison of various models of homogeneous crystal nucleation with atomistic simulations for the single component hard-sphere fluid. Extending previous work for pure systems (Gránásy L, Pusztai T, Saylor D and Warren J A 2007 Phys. Rev. Lett. 98 art no 035703), heterogeneous nucleation in unary and binary systems is described via introducing boundary conditions that realize the desired contact angle. A quaternion representation of crystallographic orientation of the individual particles (outlined in Pusztai T, Bortel G and Gránásy L 2005 Europhys. Lett. 71 131) has been applied for modeling a broad variety of polycrystalline structures including crystal sheaves, spherulites and those built of crystals with dendritic, cubic, rhombododecahedral, truncated octahedral growth morphologies. Finally, we present illustrative results for dendritic polycrystalline solidification obtained using an atomistic phase-field model

Nonequilibrium steady states in fluids of platelike colloidal particles

Nonequilibrium steady states in an open system connecting two reservoirs of platelike colloidal particles are investigated by means of a recently proposed phenomenological dynamic density functional theory [M. Bier and R. van Roij, Phys. Rev. E 76, 021405 (2007)]. The platelike colloidal particles are approximated within the Zwanzig model of restricted orientations, which exhibits an isotropic-nematic bulk phase transition. Inhomogeneities of the local chemical potential generate a diffusion current which relaxes to a nonvanishing value if the two reservoirs coupled to the system sustain different chemical potentials. The relaxation process of initial states towards the steady state turns out to comprise two regimes: a smoothening of initial steplike structures followed by an ultimate relaxation of the slowest diffusive mode. The position of a nonequilibrium interface and the particle current of steady states depend nontrivially on the structure of the reservoirs due to the coupling between translational and orientational degrees of freedom of the fluid

Relaxation dynamics in fluids of platelike colloidal particles

The relaxation dynamics of a model fluid of platelike colloidal particles is investigated by means of a phenomenological dynamic density functional theory. The model fluid approximates the particles within the Zwanzig model of restricted orientations. The driving force for time-dependence is expressed completely by gradients of the local chemical potential which in turn is derived from a density functional -- hydrodynamic interactions are not taken into account. These approximations are expected to lead to qualitatively reliable results for low densities as those within the isotropic-nematic two-phase region. The formalism is applied to model an initially spatially homogeneous stable or metastable isotropic fluid which is perturbed by switching a two-dimensional array of Gaussian laser beams. Switching on the laser beams leads to an accumulation of colloidal particles in the beam centers. If the initial chemical potential and the laser power are large enough a preferred orientation of particles occurs breaking the symmetry of the laser potential. After switching off the laser beams again the system can follow different relaxation paths: It either relaxes back to the homogeneous isotropic state or it forms an approximately elliptical high-density core which is elongated perpendicular to the dominating orientation in order to minimize the surface free energy. For large supersaturations of the initial isotropic fluid the high-density cores of neighboring laser beams of the two-dimensional array merge into complex superstructures.Comment: low-resolution figures due to file size restrictions, revised versio

On the growth and form of spherulites

Many structural materials (metal alloys, polymers, minerals, etc.) are formed by quenching liquids into crystalline solids. This highly non-equilibrium process often leads to polycrystalline growth patterns that are broadly termed "spherulites" because of their large-scale average spherical shape. Despite the prevalence and practical importance of spherulite formation, only rather qualitative concepts of this phenomenon exist. The present work explains the growth and form of these fundamental condensed matter structures on the basis of a unified field theoretic approach. Our phase field model is the first to incorporate the essential ingredients for this type crystal growth: anisotropies in both the surface energy and interface mobilities that are responsible for needle-like growth, trapping of local orientational order due to either static heterogeneities (impurities) or dynamic heterogeneities in highly supercooled liquids, and a preferred relative grain orientation induced by a misorientation-dependent grain boundary energy. Our calculations indicate that the diversity of spherulite growth forms arises from a competition between the ordering effect of discrete local crystallographic symmetries and the randomization of the local crystallographic orientation that accompanies crystal grain nucleation at the growth front (growth front nucleation or GFN). The large-scale isotropy of spherulitic growth arises from the predominance of GFN.Comment: 14 pages, 11 figure

Nucleation and Bulk Crystallization in Binary Phase Field Theory

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 evaluated from the free energy and thickness of the interface. The critical undercoolings predicted for Cu-Ni alloys accord with the measurements, and indicate homogeneous nucleation. The Kolmogorov exponents deduced for dendritic solidification and for "soft-impingement" of particles via diffusion fields are consistent with experiment.Comment: 4 pages, 4 figures, accepted to PR

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

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 following 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 fundaments 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.Comment: 95 pages, 48 figure

Regular dendritic patterns induced by non-local time-periodic forcing

The dynamic response of dendritic solidification to spatially homogeneous time-periodic forcing has been studied. Phase-field calculations performed in two dimensions (2D) and experiments on thin (quasi 2D) liquid crystal layers show that the frequency of dendritic side-branching can be tuned by oscillatory pressure or heating. The sensitivity of this phenomenon to the relevant parameters, the frequency and amplitude of the modulation, the initial undercooling and the anisotropies of the interfacial free energy and molecule attachment kinetics, has been explored. It has been demonstrated that besides the side-branching mode synchronous with external forcing as emerging from the linear Wentzel-Kramers-Brillouin analysis, modes that oscillate with higher harmonic frequencies are also present with perceptible amplitudes.Comment: 15 pages, 23 figures, Submitted to Phys. Rev.