Kramers-like Picture for Crystal Nucleation

TL;DR

This paper presents a novel kinetic framework for analyzing homogeneous crystal nucleation using a Kramers-like equation based on a global order parameter, bridging theoretical models and simulations.

Contribution

It introduces a new scheme applying the internal degrees of freedom formalism to derive a Kramers-type kinetic equation for nucleation, linking different theoretical and simulation approaches.

Findings

Provides explicit expressions for kinetic coefficients.

Recovers transition rates from reactive flux in quasi-stationary case.

Offers a theoretical framework for interpreting simulation results.

Abstract

We introduce a new scheme to analyze the kinetics of homogeneous nucleation in terms of a global order parameter. Our approach is based on the application of the internal degrees of freedom formalism to derive a kinetic equation of the Kramers type formulated for a global reaction coordinate. We provide explicit expressions for the quantities and coefficients involved in the process, suitable for simulation. In addition, our picture recovers in the quasi-stationary case the transition rate obtained from the method of reactive flux. The equation we present may provide a link between theoretical approaches to homogeneous nucleation (generally formulated in terms of a kinetic equation of the Fokker-Planck type) and simulations (which mostly employ linear response theory). In this context, our scheme provides a theoretical framework to interpret and extend the results obtained in recent simulations.