2009/08/10 by Erik von Schwerin, von Schwerin, Erik
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #65C20 #65C35 #65Z05 #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena #Theoretical and Computational Physics #nanoparticles nucleation surface interactions
paper · pdf · doi:10.48550/arxiv.0908.1367
openalex publication_date 2009/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.