A microscopic model for solidification

TL;DR

This paper introduces a microscopic lattice-based model for non-isothermal solidification, incorporating stochastic fluctuations and thermal effects, providing detailed insights into nucleation and growth regimes at a molecular level.

Contribution

It presents a novel microscopic Potts spin model that includes latent heat and thermal conduction, advancing understanding of solidification mechanisms beyond coarse-grained approaches.

Findings

Model agrees with continuum treatments

Captures stochastic fluctuations in nucleation

Characterizes growth regimes with scaling exponents

Abstract

We present a novel picture of a non isothermal solidification process starting from a molecular level, where the microscopic origin of the basic mechanisms and of the instabilities characterizing the approach to equilibrium is rendered more apparent than in existing approaches based on coarse grained free energy functionals \`a la Landau. The system is composed by a lattice of Potts spins, which change their state according to the stochastic dynamics proposed some time ago by Creutz. Such a method is extended to include the presence of latent heat and thermal conduction. Not only the model agrees with previous continuum treatments, but it allows to introduce in a consistent fashion the microscopic stochastic fluctuations. These play an important role in nucleating the growing solid phase in the melt. The approach is also very satisfactory from the quantitative point of view since the relevant growth regimes are fully characterized in terms of scaling exponents.