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

Phase field theory of interfaces and crystal nucleation in a eutectic system of fcc structure: II. Nucleation in the metastable liquid immiscibility region

The official version of this Article can be accessed from the link below - Copyright @ 2007 American Institute of PhysicsIn the second part of our paper, we address crystal nucleation in the metastable liquid miscibility region of eutectic systems that is always present, though experimentally often inaccessible. While this situation resembles the one seen in single component crystal nucleation in the presence of a metastable vapor-liquid critical point addressed in previous works, it is more complex because of the fact that here two crystal phases of significantly different compositions may nucleate. Accordingly, at a fixed temperature below the critical point, six different types of nuclei may form: two liquid-liquid nuclei: two solid-liquid nuclei; and two types of composite nuclei, in which the crystalline core has a liquid "skirt," whose composition falls in between the compositions of the solid and the initial liquid phases, in addition to nuclei with concentric alternating composition shells of prohibitively high free energy. We discuss crystalline phase selection via exploring/identifying the possible pathways for crystal nucleation.This work has been supported by the Hungarian Academy of Sciences under contract No. OTKA-K-62588 and by the ESA PECS Nos. 98021 and 98043

Free energy of the bcc-liquid interface and the Wulff shape as predicted by the Phase-Field Crystal model

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 $\epsilon\in\left[0,0.5\right]$. While the maximum free energy corresponds to the $\left\{ 100\right\}$ orientation for all $\epsilon$ values, the minimum is realized by the $\left\{ 111\right\}$ direction for small $\epsilon\,(<0.13)$, and by the $\left\{ 211\right\}$ orientation for higher $\epsilon$. 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 $\epsilon$ 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

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

Jahn-Teller distortion in Cs4C60 studied by vibrational spectroscopy

We have measured the infrared spectra of Cs(4)C(60) in the temperature range 220 - 450 K. Two anomalies in the low-frequency modes at 270 K and 400 K point to changes in molecular or crystal structure. The most probable explanation is a rotator phase above 400 K and a fully ordered phase below 220 K; the intermediate structure is one where molecular Jahn-Teller distortions compete with crystal field effects

Nem-egyensúlyi morfológiák dinamikája = Dynamics of non-equilibrium morphologies

Elméleti módszereket és számítógépes szimulációkat használtunk az elsőrendű fázisátalakulásokhoz kapcsolódó morfológiák képződési dinamikájának vizsgálatára. Ennek keretében sűrűség funkcionál- és fázismező modelleket dolgoztunk ki a túlhűtött egy- és többkomponensű folyadékokban, ill. oxidüvegekben történő homogén nukleáció leírására. A modellparaméterek rögzítése atomisztikus szimulációkból ill. kísérletekből származó felületi jellemzők segítségével történt. A nukleációs gát magasságára vonatkozó paraméter-mentes jóslataink jól egyeznek az atomisztikus szimulációkból ill. kísérletekből származó eredményekkel. Fázismező elméletet dolgoztunk ki az egyensúlytól távoli, binér polikristályos megszilárdulás modellezésére két- és három dimenzióban. Ennek segítségével olyan komplex, a csíraképződés és növekedés kölcsönhatásával kialakuló morfológiák képződését írtunk le elsőként, mint a rendezetlen dendrites, szferolitos, és kristálykéve alakzatoké. Alacsony dimenziós, különböző kémiai összetevőket tartalmazó rendszereket vizsgáltunk, ahol a részecskék diffúziós mozgást végeznek és közöttük kémiai reakciók jöhetnek létre (reakció-diffúzió modellek). A rendszerben lezajló nem-egyensúlyi fázisátalakulást a mintába befagyott rendezetlenség jelenlétében tanulmányoztuk renormálási csoport módszerrel és numerikus szimulációval. Megállapítottuk, hogy kellően erős rendezetlenség mellett az átalakulás egy ún. végtelenül rendezetlen fix-ponttal írható le. | We applied theoretical methods and computer simulations to investigate morphologies forming during first order transformations and their dynamics. Along these lines, density functional and phase field models have been developed for describing homogeneous crystal nucleation in undercooled one- and two component liquids, and oxide glasses. The model parameters have been fixed using interfacial properties from atomistic simulations or experiment. Our parameter free predictions for the height of the nucleation barrier are in a good agreement with results from atomistic simulations or experiment. We have worked out a phase field theory for modeling polycrystalline solidification in binary alloys far-from-equilibrium in two and three dimensions. Using this approach, we were able to describe the formation of complex morphologies appearing via interacting nucleation and growth, such as the disordered dendritic, spherulitic, and crystal sheaf structures. We have studied multi-component low dimensional systems in which the particles show diffusive motion and chemical reactions take place between them (reaction-diffusion problems). In the presence of quenched disorder we have investigated the properties of non-equilibrium phase transitions by renormalization group method and by numerical simulations. We have shown that for strong enough disorder the transition is controlled by a so called infinite disorder fixed point

Phase field theory of crystal nucleation in hard sphere liquid

The phase field theory of crystal nucleation described in [L. Granasy, T. Borzsonyi, T. Pusztai, Phys. Rev. Lett. 88, 206105 (2002)] is applied for nucleation in hard--sphere liquids. The exact thermodynamics from molecular dynamics is used. The interface thickness for phase field is evaluated from the cross--interfacial variation of the height of the singlet density peaks. The model parameters are fixed in equilibrium so that the free energy and thickness of the (111), (110), and (100) interfaces from molecular dynamics are recovered. The density profiles predicted without adjustable parameters are in a good agreement with the filtered densities from the simulations. Assuming spherical symmetry, we evaluate the height of the nucleation barrier and the Tolman length without adjustable parameters. The barrier heights calculated with the properties of the (111) and (110) interfaces envelope the Monte Carlo results, while those obtained with the average interface properties fall very close to the exact values. In contrast, the classical sharp interface model considerably underestimates the height of the nucleation barrier. We find that the Tolman length is positive for small clusters and decreases with increasing size, a trend consistent with computer simulations.Comment: 7 pages, 7 figure

Phase Field Theory of Heterogeneous Crystal Nucleation

A phase eld approach is developed to model wetting and heterogeneous crystal nucleation of an undercooled pure liquid in contact with a sharp wall. We discuss various choices for the boundary condition at the wall and determine the properties of critical nuclei, including their free energy of formation and the contact angle as a function of undercooling. We nd for particular choices of boundary conditions, we may realize either an analog of the classical spherical cap model or decidedly non-classical behavior, where the contact angle decreases from its value taken at the melting point towards complete wetting at a critical undercooling.Comment: 4 figure

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