Computational Materials Science Group

Tegze György, Frigyes Podmaniczky¹

¹Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary

In turbulent Rayleigh-Bénard convection, it is generally acknowledged that the thermal boundary layer (BL) governs heat transfer, although its scaling with the Rayleigh number is still debated. Various methods have been developed to measure the characteristic thickness of the BL, which are mostly employed in a time-averaged manner. Among them, only the slope method can be applied in an instant of time, being therefore capable of time-resolved analysis; however, it provides no further insight when the Nusselt number is known. Accordingly, the average properties of the BL are thoroughly studied, mainly in the context of heat transfer; its time-dependent structural dynamics and roughness remain largely unexplored. Here, we propose a Lagrangian method to characterize both the time-averaged and the spatio-temporal evolution of the BL, that marks the edge of the BL where convective and diffusive transports overlap. The characteristic thickness of the BL, that is defined by this method, is not a trivial function of the Nusselt number and can be considered a potential tool to analyze the BL structure while varying the Nusselt number. It is also demonstrated using 3D direct numerical simulations, that the injection of heat is extremely inhomogeneous in space and time; the vast majority of heat accumulates in narrow domains, that is governed by the local plume dynamics.

Frigyes Podmaniczky¹, László Gránásy^1,2

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

We present recent advances in phase-field crystal (PFC) modeling of crystal nucleation in simple undercooled liquids, where dynamics is based on hydrodynamic density relaxation, as opposed to the diffusive dynamics in colloid systems. Herein, we address two-step nucleation, the nucleation of new grains at the growth front, and crystal nucleation on the surface of foreign particles in flow. Owing to the different numerical complexity of these problems, we consider three different realizations of the hydrodynamic approach that are optimized to deal with the individual tasks. We show that during two-step nucleation taking place at high supersaturations, amorphous and layered two-dimensional quasicrystalline domains form simultaneously in the first stage, which is then followed by bcc nucleation/transformation of the existing solid into the stable body-centered structure. Next, the formation of satellite crystals at the solid-liquid interface, observed in molecular dynamics simulations are studied. We find that the interference of density waves ahead of the rough growth front may assist the formation of such satellite crystals. Finally, we show that, under appropriate conditions, fluid flow may tear off heterogeneously nucleated crystal particles from the surface of a curved substrate, as envisaged for colloidal systems.

Tamás Pusztai¹, László Rátkai¹, Levente Horváth, László Gránásy^1,2

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

The melting of 2D lamellar and 3D rod eutectic structures was studied by multi-phase-field simulations. A binary model eutectic system was investigated in a standard directional solidification setup. Switching from solidification to melting was realised by inverting the pulling speed of the sample. Steady state melting profiles were obtained as the long-time solutions of the evolution equations solved in the minimal representative domains of the periodic structures. Series of simulations were performed using different volume fractions of the initial solid phases, different values of the temperature gradient, and different widths of the simulation domain. It was found that melting occurs with a nearly flat interface if the average composition of the initial solid structure is equal to the eutectic composition. If the volume fraction of the solid phases is changed and the average composition becomes off-eutectic, then the melting positions of the phases decouple: the phase of sub-eutectic amount will melt near the eutectic temperature, while the phase of super-eutectic amount will melt near its liquidus temperature corresponding to the off-eutectic mean composition. The lamellar/rod spacing imposed by the width of the simulation domain has only minor effect on the interface temperature. Besides the steady states, we could observe two kinds of instabilities in the regime of non-planar melting both in 2D and 3D. By increasing the lamellar spacing, oscillations may appear around the trijunction and along the phase boundaries. By decreasing the lamellar spacing and increasing the pulling speed, the lamellae/rods of the phase that protrude deeper in the melt become thinner and may eventually break up to a series of small spherical particles before melting completely.

László Gránásy^1,2, László Rátkai¹, Gyula Tóth³, Pupa Gilbert, Igor Zlotnikov⁴, 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.
⁴B CUBE - Center for Molecular Bioengineering, Technische Universität Dresden, Germany

While biological crystallization processes have been studied on the microscale extensively, there is a general lack of models addressing the mesoscale aspects of such phenomena. In this work, we investigate whether the phase-field theory developed in materials’ science for describing complex polycrystalline structures on the mesoscale can be meaningfully adapted to model crystallization in biological systems. We demonstrate the abilities of the phase-field technique by modeling a range of microstructures observed in mollusk shells and coral skeletons, including granular, prismatic, sheet/columnar nacre, and sprinkled spherulitic structures. We also compare two possible micromechanisms of calcification: the classical route, via ion-by-ion addition from a fluid state, and a nonclassical route, crystallization of an amorphous precursor deposited at the solidification front. We show that with an appropriate choice of the model parameters, microstructures similar to those found in biomineralized systems can be obtained along both routes, though the time-scale of the nonclassical route appears to be more realistic. The resemblance of the simulated and natural biominerals suggests that, underneath the immense biological complexity observed in living organisms, the underlying design principles for biological structures may be understood with simple math and simulated by phase-field theory.