Kinetic Monte Carlo simulations of electrodeposition: Crossover from continuous to instantaneous homogeneous nucleation within Avrami's law

TL;DR

This paper uses kinetic Monte Carlo simulations to study how lateral diffusion influences phase transition dynamics in a 2D lattice gas, revealing a crossover from continuous to instantaneous nucleation described by an extended Avrami's law.

Contribution

It extends Avrami's law to include exponentially decaying nucleation rates and demonstrates the crossover from continuous to instantaneous nucleation in electrodeposition.

Findings

Decaying nucleation rate causes a gradual crossover from continuous to instantaneous nucleation.

Instantaneous nucleation can be homogeneous, leading to negative minima in correlation functions.

The extended KJMA theory accurately estimates the order of magnitude for nucleation rate and interface velocity.

Abstract

The influence of lateral adsorbate diffusion on the dynamics of the first-order phase transition in a two-dimensional Ising lattice gas with attractive nearest-neighbor interactions is investigated by means of kinetic Monte Carlo simulations. For example, electrochemical underpotential deposition proceeds by this mechanism. One major difference from adsorption in vacuum surface science is that under control of the electrode potential and in the absence of mass-transport limitations, local adsorption equilibrium is approximately established. We analyze our results using the theory of Kolmogorov, Johnson and Mehl, and Avrami (KJMA), which we extend to an exponentially decaying nucleation rate. Such a decay may occur due to a suppression of nucleation around existing clusters in the presence of lateral adsorbate diffusion. Correlation functions prove the existence of such exclusion zones. By comparison with microscopic results for the nucleation rate I and the interface velocity of the growing clusters v, we can show that the KJMA theory yields the correct order of magnitude for Iv^2. This is true even though the spatial correlations mediated by diffusion are neglected. The decaying nucleation rate causes a gradual crossover from continuous to instantaneous nucleation, which is complete when the decay of the nucleation rate is very fast on the time scale of the phase transformation. Hence, instantaneous nucleation can be homogeneous, producing negative minima in the two-point correlation functions. We also present in this paper an n-fold way Monte Carlo algorithm for a square lattice gas with adsorption/desorption and lateral diffusion.