Computational Materials Science Group

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.

Chang-Yu Sun, László Gránásy^1,2, Cayla Stifler, Tal Zaquin, Rajesh Chopdekar, Nobumichi Tamura, James Weaver, Jun Zhang, Stefano Goffredo, Giuseppe Falini, Matthew Marcus, Tamás Pusztai¹, Vanessa Schoeppler³, Tali Mass, Pupa Gilbert

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
³B CUBE - Center for Molecular Bioengineering, Technische Universität Dresden, Germany

Spherulites are radial distributions of acicular crystals, common in biogenic, geologic, and synthetic systems, yet exactly how spherulitic crystals nucleate and grow is still poorly understood. To investigate these processes in more detail, we chose scleractinian corals as a model system, because they are well known to form their skeletons from aragonite (CaCO3) spherulites, and because a comparative study of crystal structures across coral species has not been performed previously. We observed that all 12 diverse coral species analyzed here exhibit plumose spherulites in their skeletons, with well-defined centers of calcification (CoCs), and crystalline fibers radiating from them. In 7 of the 12 species, we observed a skeletal structural motif not observed previously: randomly oriented, equant crystals, which we termed “sprinkles”. In Acropora pharaonis, these sprinkles are localized at the CoCs, while in 6 other species, sprinkles are either layered at the growth front (GF) of the spherulites, or randomly distributed. At the nano- and micro-scale, coral skeletons fill space as much as single crystals of aragonite. Based on these observations, we tentatively propose a spherulite formation mechanism in which growth front nucleation (GFN) of randomly oriented sprinkles, competition for space, and coarsening produce spherulites, rather than the previously assumed slightly misoriented nucleations termed “non-crystallographic branching”. Phase-field simulations support this mechanism, and, using a minimal set of thermodynamic parameters, are able to reproduce all of the microstructural variation observed experimentally in all of the investigated coral skeletons. Beyond coral skeletons, other spherulitic systems, from aspirin to semicrystalline polymers and chocolate, may also form according to the mechanism for spherulite formation proposed here.