The Gibbs-Thomson formula at small island sizes - corrections for high vapour densities

TL;DR

This study investigates the deviations of the Gibbs-Thomson formula at small island sizes and high vapour densities, using simulations and theoretical corrections based on the Ising model to improve understanding of equilibrium island behavior.

Contribution

The paper introduces correction methods to the Gibbs-Thomson formula at high vapour densities by leveraging the Ising model and high field series expansions, addressing limitations of the ideal gas approximation.

Findings

Corrections to the Gibbs-Thomson formula are necessary at high vapour densities.

Finite size effects influence island stability and are characterized both theoretically and via simulations.

Microscopic origins of the Gibbs-Thomson effect are linked to geometric constraints on island edges.

Abstract

In this paper we report simulation studies of equilibrium features, namely circular islands on model surfaces, using Monte-Carlo methods. In particular, we are interested in studying the relationship between the density of vapour around a curved island and its curvature-the Gibbs-Thomson formula. Numerical simulations of a lattice gas model, performed for various sizes of islands, don't fit very well to the Gibbs-Thomson formula. We show how corrections to this form arise at high vapour densities, wherein a knowledge of the exact equation of state (as opposed to the ideal gas approximation) is necessary to predict this relationship. Exploiting a mapping of the lattice gas to the Ising model one can compute the corrections to the Gibbs-Thomson formula using high field series expansions. We also investigate finite size effects on the stability of the islands both theoretically and through simulations. Finally the simulations are used to study the microscopic origins of the Gibbs-Thomson formula. A heuristic argument is suggested in which it is partially attributed to geometric constraints on the island edge.