Phase-Field Modeling of Polycrystalline Solidification: From Needle Crystals to Spherulites-A Review

László Gránásy1,2, László Rátkai1, Attila Szállás1, Bálint Korbuly1, Gyula Tóth3,1, László Környei4, 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
3Institute of Physics and Technology, University of Bergen, Allégaten 55, N-5007 Bergen, Norway
4Department of Mathematics and Computational Sciences, Széchenyi István University, Győr 9026, Hungary

Advances in the orientation-field-based phase-field (PF) models made in the past are reviewed. The models applied incorporate homogeneous and heterogeneous nucleation of growth centers and several mechanisms to form new grains at the perimeter of growing crystals, a phenomenon termed growth front nucleation. Examples for PF modeling of such complex polycrystalline structures are shown as impinging symmetric dendrites, polycrystalline growth forms (ranging from disordered dendrites to spherulitic patterns), and various eutectic structures, including spiraling two-phase dendrites. Simulations exploring possible control of solidification patterns in thin films via external fields, confined geometry, particle additives, scratching/piercing the films, etc. are also displayed. Advantages, problems, and possible solutions associated with quantitative PF simulations are discussed briefly.

Topics: Polycrystalline solidification, Spiral eutectic dendrites

Free energy of the bcc-liquid interface and the Wulff shape as predicted by the phase-field crystal model

Frigyes Podmaniczky1, Gyula Tóth2,1, Tamás Pusztai1, 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

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 ε∈[0,0.5]. While the maximum free energy corresponds to the {100} orientation for all ε values, the minimum is realized by the {111} direction for smaller ε(<0.13), and by the {211} orientation for higher ε. 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 ε 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.

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