Latest publications

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

Gyula Tóth1,2, László Gránásy2,3

1Institute of Physics and Technology, University of Bergen, Allégaten 55, N-5007 Bergen, Norway
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

In 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.

Phase field theory of heterogeneous crystal nucleation

László Gránásy1,2, Tamás Pusztai1, D Saylor, James A. Warren3

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
3Metallurgy Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA

The phase field approach is used to model heterogeneous crystal nucleation in an undercooled pure liquid in contact with a foreign 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. For particular choices of boundary conditions, we may realize either an analog of the classical spherical cap model or decidedly nonclassical behavior, where the contact angle decreases from its value taken at the melting point towards complete wetting at a critical undercooling, an analogue of the surface spinodal of liquid-wall interfaces.

Komplex kristálymorfológiák modellezése három dimenzióban

Tamás Pusztai1, G Bortel, Gyula Tóth2,1, László Gránásy1,3

1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
2Institute of Physics and Technology, University of Bergen, Allégaten 55, N-5007 Bergen, Norway
3BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

Phase field theory of nucleation and polycrystalline pattern formation

László Gránásy1,2, Tamás Pusztai1, T Börzsönyi

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 review our recent modeling of crystal nucleation and polycrystalline growth using a phase field theory. First, we consider the applicability of phase field theory for describing crystal nucleation in a model hard sphere fluid. It is shown that the phase field theory accurately predicts the nucleation barrier height for this liquid when the model parameters are fixed by independent molecular dynamics calculations. We then address various aspects of polycrystalline solidification and associated crystal pattern formation at relatively long timescales. This late stage growth regime, which is not accessible by molecular dynamics, involves nucleation at the growth front to create new crystal grains in addition to the effects of primary nucleation. Finally, we consider the limit of extreme polycrystalline growth, where the disordering effect due to prolific grain formation leads to isotropic growth patterns at long times, i.e., spherulite formation. Our model of spherulite growth exhibits branching at fixed grain misorientations, induced by the inclusion of a metastable minimum in the orientational free energy. It is demonstrated that a broad variety of spherulitic patterns can be recovered by changing only a few model parameters.

Polycrystalline patterns in far-from-equilibrium freezing: a phase field study

László Gránásy1,2, Tamás Pusztai1, T Börzsönyi, Gyula Tóth3,1, György Tegze1, James A. Warren4, Jack F. Douglas5

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
3Institute of Physics and Technology, University of Bergen, Allégaten 55, N-5007 Bergen, Norway
4Metallurgy Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
5Polymers Division, National Institute of Standards and Technology,Gaithersburg, MD, 20899, USA

We discuss the formation of polycrystalline microstructures within the framework of phase field theory. First, the model is tested for crystal nucleation in a hard sphere system. It is shown that, when evaluating the model parameters from molecular dynamics simulations, the phase field theory predicts the nucleation barrier for hard spheres accurately. The formation of spherulites is described by an extension of the model that incorporates branching with a definite orientational mismatch. This effect is induced by a metastable minimum in the orientational free energy. Spherulites are an extreme example of polycrystalline growth, a phenomenon that results from the quenching of orientational defects (grain boundaries) into the solid as the ratio of the rotational to the translational diffusion coefficient is reduced, as is found at high undercoolings. It is demonstrated that a broad variety of spherulitic patterns can be recovered by changing only a few model parameters.

Topics: Polycrystalline solidification

Phase field theory of liquid phase separation and solidification with melt flow

György Tegze1, 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

A phase-field theory of binary liquid phase separation and solidification coupled to fluid flow is presented. The respective equations of motion and Navier-Stokes equations are solved numerically. We incorporate composition and temperature dependent capillary forces. The free energies of the bulk liquid phases are taken from the regular solution model. In the simulations, we observe Marangoni motion of the droplets, and direct and indirect hydrodynamic interactions between the droplets. We observe that capillary effects dramatically accelerate droplet coagulation and that solidification interacts with liquid phase separation.

Phase field theory of polycrystalline freezing in three dimensions

Tamás Pusztai1, G Bortel, 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

A phase field theory, we proposed recently to describe nucleation and growth in three dimensions (3D), has been used to study the formation of polycrystalline patterns in the alloy systems Al-Ti and Cu-Ni. In our model, the free energy of grain boundaries is assumed proportional to the angular difference between the adjacent crystals expressed in terms of the differences of the four symmetric Euler parameters called quaternions. The equations of motion for these fields have been obtained from variational principles. In the simulations cubic crystal symmetries are considered. We investigate the evolution of polydendritic morphology, present simulated analogies of the metallographic images, and explore the possibility of modeling solidification in thin layers. Transformation kinetics in the bulk and in thin films is discussed in terms of the Johnson-Mehl-Avrami-Kolmogorov approach.

Multi-scale approach to CO2-hydrate formation in aqueous solution: Phase field theory and molecular dynamics. Nucleation and growth

György Tegze1, Tamás Pusztai1, Gyula Tóth2,1, László Gránásy1,3, A Svandal, T Buanes, T Kuznetsova, Bjørn Kvamme2

1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
2Institute of Physics and Technology, University of Bergen, Allégaten 55, N-5007 Bergen, Norway
3BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

A phase field theory with model parameters evaluated from atomistic simulations/experiments is applied to predict the nucleation and growth rates of solid CO2 hydrate in aqueous solutions under conditions typical to underwater natural gas hydrate reservoirs. It is shown that under practical conditions a homogeneous nucleation of the hydrate phase can be ruled out. The growth rate of CO2 hydrate dendrites has been determined from phase field simulations as a function of composition while using a physical interface thickness 0.85±0.07 nm evaluated from molecular dynamics simulations. The growth rate extrapolated to realistic supersaturations is about three orders of magnitude larger than the respective experimental observation. A possible origin of the discrepancy is discussed. It is suggested that a kinetic barrier reflecting the difficulties in building the complex crystal structure is the most probable source of the deviations.

Phase field theory of crystal nucleation and polyerystalline growth: A review

László Gránásy1,2, Tamás Pusztai1, T Börzsönyi, Gyula Tóth3,1, György Tegze1, James A. Warren4, Jack F. Douglas5

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
3Institute of Physics and Technology, University of Bergen, Allégaten 55, N-5007 Bergen, Norway
4Metallurgy Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
5Polymers Division, National Institute of Standards and Technology,Gaithersburg, MD, 20899, USA

We briefly review Our recent modeling of crystal nucleation and polycrystalline growth using a phase field theory. First, we consider the applicability of phase field theory for describing crystal nucleation in a model hard sphere Fluid. It is shown that the phase field theory accurately predicts the nucleation barrier height for this liquid when the model parameters are fixed by independent Molecular dynamics calculations. We then address various aspects of polycrystalline solidification and associated crystal pattern formation at relatively long timescales. This late stage growth regime, which is not accessible by Molecular dynamics, involves nucleation at the growth front to create new crystal grains in addition to the effects of primary nucleation. Finally, we consider the limit of extreme polycrystalline growth, where the disordering effect due to prolific grain formation leads to isotropic growth patterns at long times, i.e., spherulite formation. Our model of spherulite growth exhibits branching at fixed grain misorientations, induced by the inclusion of a metastable minimum in the orientational free energy. It is demonstrated that a broad variety of spherulitic patterns can be recovered by changing only a few model parameters.

Topics: Polycrystalline solidification

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