Phase-field approach to heterogeneous nucleation (original) (raw)
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Phase field approach to heterogeneous crystal nucleation in alloys
Physical Review B, 2009
We extend the phase field model of heterogeneous crystal nucleation developed recently [L. Gránásy, T. 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.
PHASE-FIELD ANALYSIS OF NUCLEATION PHENOMENA Ph. D. thesis
Crystalline materials play an essential role in our everyday life. Most of them are polycrystalline, ie, composed of a large number of crystallites, whose size, shape and composition distributions determine their properties and failure characteristics. The size scale of the constituent crystal grains varies between a few nanometers (nanocrystalline alloys) and centimeters in different classes of materials.
Phase field theory of crystal nucleation and polycrystalline growth: A review
Journal of Materials Research, 2006
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.
Classical nucleation theory in the phase-field crystal model
Physical review, 2018
A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phasefield methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations. In this work, we numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times in the simplest version of the PFC model, for various parameter choices. We show that the model naturally exhibits qualitative agreement with the predictions of classical nucleation theory (CNT) despite a lack of some explicit atomistic features presumed in CNT. We also examine the early appearance of lattice structure in nucleating grains, finding disagreement with some basic assumptions of CNT. We then argue that a quantitatively correct nucleation theory for the PFC model would require extending CNT to a multi-variable theory.
Investigating Nucleation Using the Phase-Field Method
Journal of the Indian Institute of Science, 2016
The first order phase transitions, like freezing of liquids, melting of solids, phase separation in alloys, vapor condensation, etc., start with nucleation, a process in which internal fluctuations of the parent phase lead to formation of small seeds of the new phase. Owing to different size dependence of (negative) volumetric and (positive) interfacial contributions to work of formation of such seeds, there is a critical size, at which the work of formation shows a maximum. Seeds that are smaller than the critical one decay with a high probability, while the larger ones have a good chance to grow further and reach a macroscopic size. Putting it in another way, to form the bulk new phase, the system needs to pass a thermodynamic barrier via thermal fluctuations. When the fluctuations of the parent phase alone lead to transition, the process is called homogeneous nucleation. Such a homogeneous process is, however, scarcely seen and requires very specific conditions in nature or in th...
Nucleation and polycrystalline solidification in binary phase field theory
2004
We present a phase field theory for the nucleation and growth of one and two phase crystals solidifying with different crystallographic orientations in binary alloys. The accuracy of the model is tested for crystal nucleation in single component systems. It is shown that without adjustable parameters the height of the nucleation barrier is predicted with reasonable accuracy. The kinetics of primary solidification is investigated as a function of model parameters under equiaxial conditions. Finally, we study the formation of polycrystalline growth morphologies (disordered dendrites, spherulites and fractal-like aggregates).
Phase-field Theory of Nucleation and Growth in Binary Alloys
Lecture Notes in Computational Science and Engineering, 2003
We present a phase field theory for binary crystal nucleation. Using the physical interface thickness, we achieve quantitative agreement with computer simulations and experiments for unary and binary substances. Large-scale numerical simulations are performed for multi-particle freezing in alloys. We deduce the Kolmogorov exponents for dendritic solidification and for the "soft-impingement" of crystallites interacting via diffusion fields.
Physical Review B, 2007
A simple numerical model which calculates the kinetics of crystallization involving randomly distributed nucleation and isotropic growth is presented. The model can be applied to different thermal histories and no restrictions are imposed on the time and the temperature dependencies of the nucleation and growth rates. We also develop an algorithm which evaluates the corresponding emerging grain size distribution. The algorithm is easy to implement and particularly flexible making it possible to simulate several experimental conditions. Its simplicity and minimal computer requirements allow high accuracy for two-and three-dimensional growth simulations. The algorithm is applied to explore the grain morphology development during isothermal treatments for several nucleation regimes. In particular, thermal nucleation, pre-existing nuclei and the combination of both nucleation mechanisms are analyzed. For the first two cases, the universal grain size distribution is obtained. The high accuracy of the model is stated from its comparison to analytical predictions. Finally, the validity of the Kolmogorov-Johnson-Mehl-Avrami model is verified for all the cases studied.