Phase-field lattice Boltzmann model for dendrites growing and moving in melt flow

László Rátkai1, Tamás Pusztai1, László Gránásy1,2

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 phase-field and lattice Boltzmann methods have been combined to simulate the growth of solid particles moving in melt flow. To handle mobile particles, an overlapping multigrid scheme was developed, in which each individual particle has its own moving grid, with local fields attached to it. Using this approach we were able to simulate simultaneous binary solidification, solute diffusion, melt flow, solid motion, the effect of gravity, and collision of the particles. The method has been applied for describing two possible modes of columnar to equiaxed transition in the Al–Ti system.

Crystal growth kinetics as an architectural constraint on the evolution of molluscan shells

Vanessa Schoeppler1, Robert Lemanis, Elke Reich1, Tamás Pusztai2, László Gránásy2,3, Igor Zlotnikov1

1B CUBE - Center for Molecular Bioengineering, Technische Universität Dresden, Germany
2Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
3BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

Molluscan shells are a classic model system to study formation–structure–function relationships in biological materials and the process of biomineralized tissue morphogenesis. Typically, each shell consists of a number of highly mineralized ultrastructures, each characterized by a specific 3D mineral–organic architecture. Surprisingly, in some cases, despite the lack of a mutual biochemical toolkit for biomineralization or evidence of homology, shells from different independently evolved species contain similar ultrastructural motifs. In the present study, using a recently developed physical framework, which is based on an analogy to the process of directional solidification and simulated by phase-field modeling, we compare the process of ultrastructural morphogenesis of shells from 3 major molluscan classes: A bivalve Unio pictorum, a cephalopod Nautilus pompilius, and a gastropod Haliotis asinina. We demonstrate that the fabrication of these tissues is guided by the organisms by regulating the chemical and physical boundary conditions that control the growth kinetics of the mineral phase. This biomineralization concept is postulated to act as an architectural constraint on the evolution of molluscan shells by defining a morphospace of possible shell ultrastructures that is bounded by the thermodynamics and kinetics of crystal growth.

Kinetics of coarsening have dramatic effects on the microstructure: Self-similarity breakdown induced by viscosity contrast

Hervé Henry1, György Tegze2

1Laboratoire Physique de la Matière Condensée, École Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau Cedex, France
2Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary

The viscous coarsening of a phase separated mixture is studied and the effects of the viscosity contrast between the phases are investigated. From an analysis of the microstructure, it appears that for moderate departure from the perfectly symmetric regime the self-similar bicontinuous regime is robust. However, the connectivity of one phase decreases when its volume fraction decreases or when it is becoming less viscous than the complementary phase. Eventually self-similarity breakdown is observed and characterized.

Phase-field modeling of crystal nucleation in undercooled liquids - A review

László Gránásy1,2, Gyula Tóth3, James A. Warren4, Frigyes Podmaniczky1, György Tegze1, László Rátkai1, 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.
4Metallurgy Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA

We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the conventional phase-field approaches that rely on spatially averaged (coarse grained) order parameters in capturing freezing, and by the recently developed phase-field crystal models that work on the molecular scale, while employing time averaged particle densities, and are regarded as simple dynamical density functional theories of classical particles. Besides simpler cases of homogeneous and heterogeneous nucleation, phenomena addressed by these techniques include precursor assisted nucleation, nucleation in eutectic and phase separating systems, phase selection via competing nucleation processes, growth front nucleation (a process, in which grains of new orientations form at the solidification front) yielding crystal sheaves and spherulites, and transition between the growth controlled cellular and the nucleation dominated equiaxial solidification morphologies.

Biomineralization as a Paradigm of Directional Solidification: A Physical Model for Molluscan Shell Ultrastructural Morphogenesis

Vanessa Schoeppler1, László Gránásy2,3, Elke Reich1, Nicole Poulsen1, René de Kloe4, Phil Cook5, Alexander Rack, Tamás Pusztai2, Igor Zlotnikov1

1B CUBE - Center for Molecular Bioengineering, Technische Universität Dresden, Germany
2Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
3BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom
4EDAX, Tilburg, The Netherlands
5ESRF – The European Synchrotron, Grenoble, France

Molluscan shells are a model system to understand the fundamental principles of mineral formation by living organisms. The diversity of unconventional mineral morphologies and 3D mineral-organic architectures that comprise these tissues, in combination with their exceptional mechanical efficiency, offers a unique platform to study the formation-structure-function relationship in a biomineralized system. However, so far, morphogenesis of these ultrastructures is poorly understood. Here, a comprehensive physical model, based on the concept of directional solidification, is developed to describe molluscan shell biomineralization. The capacity of the model to define the forces and thermodynamic constraints that guide the morphogenesis of the entire shell construct-the prismatic and nacreous ultrastructures and their transitions-and govern the evolution of the constituent mineralized assemblies on the ultrastructural and nanostructural levels is demonstrated using the shell of the bivalve Unio pictorum. Thereby, explicit tools for novel bioinspired and biomimetic bottom-up materials design are provided.

Topics: Polycrystalline solidification

Self-similarity and coarsening rate of a convecting bicontinuous phase separating mixture: Effect of the viscosity contrast

Hervé Henry1, Tegze György

1Laboratoire Physique de la Matière Condensée, École Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau Cedex, France

We present a computational study of the hydrodynamic coarsening in three dimensions of a critical mixture using the Cahn-Hilliard/Navier-Stokes model. The topology of the resulting intricate bicontinuous microstructure is analyzed through the principal curvatures to prove self-similar morphological evolution. We find that the self-similarity exists for both systems: isoviscous and with variable viscosity. However, the two systems have a distinct topological character. Moreover, an effective viscosity that accurately predicts the coarsening rate is proposed.

Topological defects in two-dimensional orientation-field models for grain growth

Bálint Korbuly1, Mathis Plapp2, Hervé Henry2, James A. Warren3, László Gránásy1,4, Tamás Pusztai1

1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
2Laboratoire Physique de la Matière Condensée, École Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau Cedex, France
3Metallurgy Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
4BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

Standard two-dimensional orientation-field-based phase-field models rely on a continuous scalar field to represent crystallographic orientation. The corresponding order parameter space is the unit circle, which is not simply connected. This topological property has important consequences for the resulting multigrain structures: (i) trijunctions may be singular; (ii) for each pair of grains there exist two different grain boundary solutions that cannot continuously transform to one another; (iii) if both solutions appear along a grain boundary, a topologically stable, singular point defect must exist between them. While (i) can be interpreted in the classical picture of grain boundaries, (ii) and therefore (iii) cannot. In addition, singularities cause difficulties, such as lattice pinning in numerical simulations. To overcome these problems, we propose two formulations of the model. The first is based on a three-component unit vector field, while in the second we utilize a two-component vector field with an additional potential. In both cases, the additional degree of freedom introduced makes the order parameter space simply connected, which removes the topological stability of these defects.

Topics: Orientation field models, Polycrystalline solidification

Hydrodynamic theory of freezing: Nucleation and polycrystalline growth

Frigyes Podmaniczky1, Gyula Tóth2, György Tegze1, László Gránásy1,3

1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
2Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, U.K.
3BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

Structural aspects of crystal nucleation in undercooled liquids are explored using a nonlinear hydrodynamic theory of crystallization proposed recently [G. I. Tóth et al., J. Phys.: Condens. Matter 26, 055001 (2014)], which is based on combining fluctuating hydrodynamics with the phase- field crystal theory. We show that in this hydrodynamic approach not only homogeneous and heterogeneous nucleation processes are accessible, but also growth front nucleation, which leads to the formation of new (differently oriented) grains at the solid-liquid front in highly undercooled systems. Formation of dislocations at the solid-liquid interface and interference of density waves ahead of the crystallization front are responsible for the appearance of the new orientations at the growth front that lead to spherulite-like nanostructures.

Videos of growth front nucleation

Topics: Polycrystalline solidification

Grain coarsening in two-dimensional phase-field models with an orientation field

Bálint Korbuly1, Tamás Pusztai1, Hervé Henry2, Mathis Plapp2, Markus Apel3, László Gránásy1,4

1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
2Laboratoire Physique de la Matière Condensée, École Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau Cedex, France
3Access e.V., Intzestr. 5, 52072 Aachen, Germany
4BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

In the literature, contradictory results have been published regarding the form of the limiting (long-time) grain size distribution (LGSD) that characterizes the late stage grain coarsening in two-dimensional and quasi-two-dimensional polycrystalline systems. While experiments and the phase-field crystal (PFC) model (a simple dynamical density functional theory) indicate a lognormal distribution, other works including theoretical studies based on conventional phase-field simulations that rely on coarse grained fields, like the multi-phase-field (MPF) and orientation field (OF) models, yield significantly different distributions. In a recent work, we have shown that the coarse grained phase-field models (whether MPF or OF) yield very similar limiting size distributions that seem to differ from the theoretical predictions. Herein, we revisit this problem, and demonstrate in the case of OF models [by R. Kobayashi et al., Physica D 140, 141 (2000) and H. Henry et al. Phys. Rev. B 86, 054117 (2012)] that an insufficient resolution of the small angle grain boundaries leads to a lognormal distribution close to those seen in the experiments and the molecular scale PFC simulations. Our work indicates, furthermore, that the LGSD is critically sensitive to the details of the evaluation process, and raises the possibility that the differences among the LGSD results from different sources may originate from differences in the detection of small angle grain boundaries.

Topics: Orientation field models, Polycrystalline solidification

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