Simulation study of nucleation in a phase-field model with nonlocal interactions

Abstract

We examine the phenomenon of nucleation in a two-dimensional phase-field model in order to calculate quantities associated with a field-theoretic model and to determine the impact of spatially nonlocal interactions on both droplet morphology and nucleation rate. We use an approximate numerical technique, together with model A Langevin dynamics, in order to characterize the saddle surface that separates stable and metastable states in function space. We thus obtain the free energy of formation of a critical droplet as well as the statistical prefactor, which, except for a dynamical prefactor, determine the nucleation rate. The standard Ginzburg-Landau energy is employed and, in addition, we consider the role of a short-range, spatially nonlocal interaction on nucleation. ͓S1063-651X͑98͒04003-3͔

Multiphase solidification in multicomponent alloys

“…Besides simulating the nucleation process, the phase field theory can be used to calculate the height of the nucleation barrier as reported by Roy et al [238] and Gránásy et al [235]. Fixing the model parameters such that the free energy and thickness of the equilibrium planar interface is recovered, good quantitative agreement has been achieved with computer simulations for the Lennard-Jones system, and with experiments on ice nucleation in undercooled water [235].…”

Approaching equilibrium and the distribution of clusters

“…noiseless dynamics [19,26]. For fixed ∆h these two criteria agree in the R → ∞ limit, but can give different results for finite R [27].…”

Phase-field approach to heterogeneous nucleation

“…The main objection of their approach is the fact that the critical clusters are created ad hoc so, on the one hand, the model explains the KJMA equation just by construction and, on the other hand, it cannot explain the existence of an incubation time observed in the experiments. A similar approach was used by Roy et al [12] to study nucleation in a phase field model with nonlocal interactions. Recently, more complex phase field models have been proposed for similar systems: The so-called multiphase-field models [27,28], in which every cluster appearing embedded in the metastable phase is described by its own field and, on the other hand, those models in which the phase field is coupled with another field representing the orientation of crystalline planes [29,30].…”