Gibbs free energies of Fe clusters can be approximated by Tolman correction to accurately model cluster nucleation and growth

TL;DR

This paper introduces a method to accurately calculate Gibbs free energies of Fe clusters using molecular dynamics data, improving cluster nucleation modeling by incorporating a size-dependent Tolman correction to surface tension.

Contribution

The study presents a new approach to determine free energies of Fe clusters with 2-100 atoms, including a size-dependent surface tension correction, enhancing predictive modeling of cluster growth.

Findings

The free energies differ significantly from the spherical approximation.

The Tolman correction improves modeling accuracy of cluster formation.

Updated nucleation rate expression accounts for size-dependent surface tension.

Abstract

Accurate Gibbs free energies of Fe clusters are required for predictive modeling of Fe cluster growth during condensation of a cooling vapor. We present a straightforward method of calculating free energies of cluster formation using the data provided by molecular dynamics (MD) simulations. We apply this method to calculate free energies of Fe clusters having from 2 to 100 atoms. The free energies are verified by comparing to an MD-simulated equilibrium cluster size distribution in a sub-saturated vapor. We show that these free energies differ significantly from those obtained with a commonly used spherical cluster approximation - which relies on a surface tension coefficient of a flat surface. The spherical cluster approximation can be improved by using a cluster size-dependent Tolman correction for the surface tension. The values for the Tolman length and effective surface tension were derived, which differ from the commonly used experimentally measured surface tension based on the potential energy. This improved approximation does not account for geometric magic number effects responsible for spikes and troughs in densities of neighbor cluster sizes. Nonetheless, it allows to model cluster formation from a cooling vapor and accurately reproduce the condensation timeline, overall shape of the cluster size distribution, average cluster size, and the distribution width. Using a constant surface tension coefficient resulted in distorted condensation dynamics and inaccurate cluster size distributions. The analytical expression for cluster nucleation rate from classical nucleation theory (CNT) was updated to account for the size-dependence of cluster surface tension.