Ginzburg-landau-type multiphase field model for competing fcc and bcc nucleation

The official published version of the Article can be accesed from the link below - Copyright @ 2011 APSWe address crystal nucleation and fcc-bcc phase selection in alloys using a multiphase field model that relies on Ginzburg-Landau free energies of the liquid-fcc, liquid-bcc, and fcc-bcc subsystems, and determine the properties of the nuclei as a function of composition, temperature, and structure. With a realistic choice for the free energy of the fcc-bcc interface, the model predicts well the fcc-bcc phase-selection boundary in the Fe-Ni system.This work has been supported by the Hungarian Academy of Sciences under contract OTKA-K-62588, and by the ESA under PECS Contract No. 98059. Work by JRM has been sponsored by the Materials Sciences and Engineering Division, Office of Basic Energy Sci- ences, U.S. Department of Energy

Phase field approach to heterogeneous crystal nucleation in alloys

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

Consistent multiphase-field theory for interface driven multidomain dynamics

We present a new multiphase-field theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical and physical consistency. We first analyze previous multiphase-field theories, and identify their advantageous and disadvantageous features. On the basis of this analysis, we introduce a new way of constructing the free energy surface, and derive a generalized multiphase description for arbitrary number of phases (or domains). The presented approach retains the variational formalism; reduces (or extends) naturally to lower (or higher) number of fields on the level of both the free energy functional and the dynamic equations; enables the use of arbitrary pairwise equilibrium interfacial properties; penalizes multiple junctions increasingly with the number of phases; ensures non-negative entropy production, and the convergence of the dynamic solutions to the equilibrium solutions; and avoids the appearance of spurious phases on binary interfaces. The new approach is tested for multi-component phase separation and grain coarsening

Hydrodynamic theory of freezing: Nucleation and polycrystalline growth

Structural aspects of crystal nucleation in undercooled liquids are explored using a nonlinear hydrodynamic theory of crystallization proposed recently [G. I. Toth 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

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

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

Advanced operator-splitting-based semi-implicit spectral method to solve the binary phase-field crystal equations with variable coefficients

We present an efficient method to solve numerically the equations of dissipative dynamics of the binary phase-field crystal model proposed by Elder et al. [Phys. Rev. B 75, 064107 (2007)] characterized by variable coefficients. Using the operator splitting method, the problem has been decomposed into sub-problems that can be solved more efficiently. A combination of non-trivial splitting with spectral semi-implicit solution leads to sets of algebraic equations of diagonal matrix form. Extensive testing of the method has been carried out to find the optimum balance among errors associated with time integration, spatial discretization, and splitting. We show that our method speeds up the computations by orders of magnitude relative to the conventional explicit finite difference scheme, while the costs of the pointwise implicit solution per timestep remains low. Also we show that due to its numerical dissipation, finite differencing can not compete with spectral differencing in terms of accuracy. In addition, we demonstrate that our method can efficiently be parallelized for distributed memory systems, where an excellent scalability with the number of CPUs is observed

Crystallization: colloidal suspense

According to classical nucleation theory, a crystal grows from a small nucleus that already bears the symmetry of its end phase—but experiments with colloids now reveal that, from an amorphous precursor, crystallites with different structures can develop

Diffusion-controlled anisotropic growth of stable and metastable crystal polymorphs in the phase-field crystal model

The official published version of the article can be accessed from the link below - Copyright @ 2009 APSWe use a simple density functional approach on a diffusional time scale, to address freezing to the body-centered cubic (bcc), hexagonal close-packed (hcp), and face-centered cubic (fcc) structures. We observe faceted equilibrium shapes and diffusion-controlled layerwise crystal growth consistent with two-dimensional nucleation. The predicted growth anisotropies are discussed in relation with results from experiment and atomistic simulations. We also demonstrate that varying the lattice constant of a simple cubic substrate, one can tune the epitaxially growing body-centered tetragonal structure between bcc and fcc, and observe a Mullins-Sekerka-Asaro-Tiller-Grinfeld-type instability.This work has been supported by the EU FP7 Collaborative Project ENSEMBLE under Grant Agreement NMP4-SL-2008-213669, the Hungarian Academy of Sciences under contract OTKA-K-62588, the Academy of Finland via its COMP CoE grant, and by Tekes via its MASIT33 project. A. J. acknowledges financial support from the Finnish Academy of Science and Letters. T. P. acknowledges support from the Bolyai Ja´nos Grant

Shear enhanced heterogeneous nucleation in some Mg- and Al- alloys

Intensive shearing was applied to alloy melts at temperatures above their liquidus by using a twinscrew mechanism. The sheared melt was then cast into a TP1 mould for microstructural examination. Alloy melts with or without shearing were also filtered using the Prefil technique developed by N-Tech Ltd in order to analyse oxides and other second phase particles. The experimental results showed a significant grain refinement through enhancement of heterogeneous nucleation. The intensive melt shearing converted oxide films and agglomerates into well dispersed fine particles with a narrow size distribution. It was confirmed that the fine oxide particles can act as potent sites for nucleation during the solidification of the sheared melt. This paper presents the experimental results and theoretical analysis of shear enhanced heterogeneous nucleation during solidification of Mg- and Al-alloys. A multi-step heterogeneous nucleation mechanism has been proposed and discussed