A Stochastic Phase-Field Model Computed From Coarse-Grained Molecular Dynamics

TL;DR

This paper develops a stochastic phase-field model for phase transformations between solid and liquid by coarse-graining molecular dynamics simulations, capturing nucleation, growth, and interface effects at the microscale.

Contribution

It introduces a method to derive Allen-Cahn model functions directly from microscopic stochastic molecular dynamics simulations.

Findings

Computed a double-well reaction term from molecular dynamics.

Derived a diffusion matrix describing noise in the phase-field.

Demonstrated coarse-graining of microscale dynamics to continuum models.

Abstract

Results are presented from numerical experiments aiming at the computation of stochastic phase-field models for phase transformations by coarse-graining molecular dynamics. The studied phase transformations occur between a solid crystal and a liquid. Nucleation and growth, sometimes dendritic, of crystal grains in a sub-cooled liquid is determined by diffusion and convection of heat, on the macroscopic level, and by interface effects, where the width of the solid-liquid interface is on an atomic length-scale. Phase-field methods are widely used in the study of the continuum level time evolution of the phase transformations; they introduce an order parameter to distinguish between the phases. The dynamics of the order parameter is modelled by an Allen--Cahn equation and coupled to an energy equation, where the latent heat at the phase transition enters as a source term. Stochastic fluctuations are sometimes added in the coupled system of partial differential equations to introduce nucleation and to get qualitatively correct behaviour of dendritic side-branching. In this report the possibility of computing some of the Allen-Cahn model functions from a microscale model is investigated. The microscopic model description of the material by stochastic, Smoluchowski, dynamics is considered given. A local average of contributions to the potential energy in the micro model is used to determine the local phase, and a stochastic phase-field model is computed by coarse-graining the molecular dynamics. Molecular dynamics simulations on a two phase system at the melting point are used to compute a double-well reaction term in the Allen--Cahn equation and a diffusion matrix describing the noise in the coarse-grained phase-field.