Nonlinear hydrodynamic theory of crystallization

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. Contrary 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 a good qualitative agreement with the molecular dynamics simulations

Faceting and branching in 2D crystal growth

The official published version of the Article can be accessed from the link below - Copyright @ 2011 APSUsing 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.This work has been supported by the EU FP7 Collaborative Project ENSEMBLE under Grant Agreement NMP4-SL-2008-213669 and by the Hungarian Academy of Sciences under Contract No. OTKA-K-62588

Komplex rendszerek dinamikája = Dynamics of complex systems

Térelméleti módszerekkel vizsgáltuk a túlhűtött folyadékból a kristályos fázisba átvezető kritikus fluktuációk tulajdonságait. Megmutattuk, hogy a Ginzburg-Landau sorfejtésen alapuló modellek kielégítő pontossággal adják meg a nukleációs gát magasságát. A polikristályos megszilárdulás 3D leírására a kristálytani orientáció kvaternió-reprezentációján alapuló fázismező elméletet dolgoztunk ki, mellyel olyan komplex alakzatok képződését modelleztünk, mint az egymással kölcsönható dendritek, a szferolitok széles skálája, ill. a shish-kebab morfológia. Egyszerű dinamikus sűrűség funkcionál elmélet keretében a kristályos megszilárdulás mikroszkopikus vonatkozásait vizsgáltuk a kristály nukleációt megelőző amorf prekurzor megjelenésétől, a diffúziós instabilitásokon át, a versengő diffúzió kontrollált és diffúzió mentes modusok mintázatképződésben játszott szerepéig. Klasszikus és kvantum rendszerek nem-egyensúlyi relaxációját vizsgáltuk gyorshűtési folyamatok során ahol a rendszer kezdő állapotát különböző feltételekkel szabályoztuk. Tanulmányoztuk a dinamikai folyamat során kialakuló fürtök és a fázisokat elválasztó határrétegek tulajdonságait és vizsgáltuk a mintába befagyott rendezetlenség szerepét is. | We have used field theoretic models to characterize the heterophase fluctuations that drive the system from un-dercooled liquid to the crystalline state. We have shown that models relying on Ginzburg-Landau expanded free energy predict the nucleation barrier fairly accurately. We have developed a phase-field theory relying on the qua-ternion representation when describing crystallographic orientation in 3D. Using this approach, formation of complex solidification patterns such as interacting dendrites, a variety of spherulites, and the shish-kebab mor-phology has been modeled. Using a simple dynamical density functional theory, we have explored the micro-scopic aspects of crystallization, including the formation of amorphous nucleation precursors, the diffusional in-stabilities, and the role competing diffusionless and diffusion controlled growth modes play in pattern formation. We have studied non-equilibrium relaxation of classical and quantum systems following a quench in which the initial state of the system is prepared in different forms. We have investigated the properties of the clusters, as well as the behavior of the interface which separates the evolving phases. We have also studied the role of quenched disorder in such processes

Heterogeneous nucleation of/on nanoparticles: a density functional study using the phase-field crystal model

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 crystalline phase appears via heterogeneous nucleation in/on the precursor cluster. Herein, we review recent results by a simple dynamical density functional theory, the phase-field crystal model, for (precursor-mediated) homogeneous and heterogeneous nucleation of nanocrystals. It will be shown that the mismatch between the lattice constants of the nucleating crystal and the substrate plays a decisive role in determining the contact angle and nucleation barrier, which were found to be non-monotonic functions of the lattice mismatch. Time dependent studies are essential as investigations based on equilibrium properties often cannot identify the preferred nucleation pathways. Modeling of these phenomena is essential for designing materials on the basis of controlled nucleation and/or nano-patterning

Phase-field crystal modeling of heteroepitaxy and exotic modes of crystal nucleation

We review recent advances made in modeling heteroepitaxy, two-step nucleation, and nucleation at the growth front within the framework of a simple dynamical density functional theory, the Phase-Field Crystal (PFC) model. The crystalline substrate is represented by spatially confined periodic potentials. We investigate the misfit dependence of the critical thickness in the Stranski–Krastanov growth mode in isothermal studies. Apparently, the simulation results for stress release via the misfit dislocations fit better to the People–Bean model than to the one by Matthews and Blakeslee. Next, we investigate structural aspects of two-step crystal nucleation at high undercoolings, where an amorphous precursor forms in the first stage. Finally, we present results for the formation of new grains at the solid-liquid interface at high supersaturations / supercoolings, a phenomenon termed Growth Front Nucleation (GFN). Results obtained with diffusive dynamics (applicable to colloids) and with a hydrodynamic extension of the PFC theory (HPFC, developed for simple liquids) will be compared. The HPFC simulations indicate two possible mechanisms for GFN