Relaxation kinetics in two-dimensional structures

TL;DR

This paper investigates how islands and pores in two-dimensional structures approach equilibrium, revealing two distinct relaxation regimes and deriving scaling laws confirmed by simulations.

Contribution

It generalizes the two-regime relaxation scenario to a broad class of kinetic models and structures, providing analytical and simulation validation.

Findings

Identified two relaxation regimes: stepwise at low temperature and smooth at high temperature.

Derived analytical scaling laws for equilibration times.

Confirmed scaling laws through kinetic Monte Carlo simulations.

Abstract

We have studied the approach to equilibrium of islands and pores in two dimensions. The two-regime scenario observed when islands evolve according to a set of particular rules, namely relaxation by steps at low temperature and smooth at high temperature, is generalized to a wide class of kinetic models and the two kinds of structures. Scaling laws for equilibration times are analytically derived and confirmed by kinetic Monte Carlo simulations.