LÁ SZLÓ GRÁ NÁ SY, LÁ SZLÓ RÁ TKAI, ATTILA SZÁ LLÁ S, BÁ LINT KORBULY, GYULA I. TÓ TH, LÁ SZLÓ KÖ RNYEI, and TAMÁ S PUSZTAI 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.

We extend the phase field model of heterogeneous crystal nucleation developed recently [L. Gránásy, T.Pusztai, D. Saylor, and J. A. Warren, Phys. Rev. Lett. 98, 035703 (2007)] to binary alloys. Three approaches are considered to incorporate foreign walls of tunable wetting properties into phase field simulations: a continuum realization of the classical spherical cap model (called Model A herein), a non-classical approach (Model B) that leads to ordering of the liquid at the wall, and to the appearance of a surface spinodal, and a non-classical model (Model C) that allows for the appearance of local states at the wall that are accessible in the bulk phases only via thermal fluctuations. We illustrate the potential of the presented phase field methods for describing complex polycrystalline solidification morphologies including the shish-kebab structure, columnar to equiaxed transition, and front-particle interaction in binary alloys. PACS number(s): 64.60. Qb, 64.70.Dv, 82.60.Nh

Abstract. Advanced phase-field techniques have been applied to address various aspects of polycrystalline solidification including different modes of crystal nucleation. The height of the nucleation barrier has been determined by solving the appropriate Euler-Lagrange equations. The examples shown include the comparison of various models of homogeneous crystal nucleation with atomistic simulations for the single component hard-sphere fluid. Extending previous work for pure systems (Gránásy L, Pusztai T, Saylor D and Warren J A 2007 Phys. Rev. Lett. 98 art no 035703), heterogeneous nucleation in unary and binary systems is described via introducing boundary conditions that realize the desired contact angle. A quaternion representation of crystallographic orientation of the individual particles (outlined in Pusztai T, Bortel G and Gránásy L 2005 Europhys. Lett. 71 131) has been applied for modeling a broad variety of polycrystalline structures including crystal sheaves, spherulites and those built of crystals with dendritic, cubic, rhombododecahedral, truncated octahedral growth morphologies. Finally, we present illustrative results for dendritic polycrystalline solidification obtained using an atomistic phase-field model.

Eutectic solidification front formed in the presence of a highly anisotropic solid-liquid interfacial free energy. It has been demonstrated that the eutectic pattern is sensitive to the morphology of the solid-liquid interface. ABSTRACTA simple phase-field model is used to address anisotropic eutectic freezing on the nanoscale in two (2D) and three dimensions (3D). Comparing parameter-free simulations with experiments, it is demonstrated that the employed model can be made quantitative for Ag-Cu. Next, we explore the effect of material properties, and the conditions of freezing on the eutectic pattern. We find that the anisotropies of kinetic coefficient and the interfacial free energies (solid-liquid and solid-solid), the crystal misorientation relative to pulling, the lateral temperature gradient, play essential roles in determining the eutectic pattern. Finally, we explore eutectic morphologies, which form when one of the solid phases are faceted, and investigate cases, in which the kinetic anisotropy for the two solid phases are drastically different.

We consider geometrical or Ising clusters (i.e., domains of parallel spins) in the square lattice random-field Ising model by varying the strength of the Gaussian random field Delta . In agreement with the conclusion of a previous investigation [Phys. Rev. E 63, 066109 (2001)], the geometrical correlation length, i.e., the average size of the clusters xi is finite for Delta>Delta_{c} approximately 1.65 and divergent for DeltaDelta_{c} . The scaling function of the distribution of the mass of the clusters as well as the geometrical correlation function are found to involve the scaling exponents of critical percolation. On the other hand, the divergence of the correlation length, xi(Delta) approximately (Delta-Delta_{c});{-nu} , with nu approximately 2 , is related to that of tricritical percolation. It is verified numerically that critical geometrical correlations transform conformally.