On the validity of the Arrhenius picture in two-dimensional submonolayer growth

TL;DR

This paper challenges the traditional interpretation of the Arrhenius diagram in surface processes, showing that a constant apparent activation energy can mask shifts in the controlling elementary reaction due to configurational effects.

Contribution

It demonstrates that the apparent activation energy is a weighted average influenced by multiple reactions and configurations, not just a single rate-limiting step.

Findings

Constant apparent activation energy can occur despite shifts in controlling reactions.

Configurational contributions significantly affect the apparent activation energy.

Simulation results reveal complex diffusion behaviors in heteroepitaxial systems.

Abstract

For surface-mediated processes, such as on-surface synthesis, epitaxial growth and heterogeneous catalysis, a constant slope in the Arrhenius diagram of the corresponding rate of interest against inverse temperature, $\log R$ {\it vs} $1/k_B T$, is traditionally interpreted as the existence of a bottleneck elementary reaction (or rate-determining step), whereby the constant slope (or apparent activation energy, $E_{app}^{R}$) reflects the value of the energy barrier for that reaction. Here, we show that a constant value of $E_{app}^{R}$ can be obtained even if control shifts from one elementary reaction to another. In fact, we show that $E_{app}^{R}$ is a weighted average and the leading elementary reaction will change with temperature while the actual energy contribution for every elementary reaction will contain, in addition to the traditional energy barrier, a configurational term directly related to the number of local configurations where that reaction can be performed. For this purpose, we consider kinetic Monte Carlo simulations of two-dimensional submonolayer growth at constant deposition flux, where the rate of interest is the tracer diffusivity. In particular, we focus on the study of the morphology, island density and diffusivity by including a large variety of single-atom, multi-atom and complete-island diffusion events for two specific metallic heteroepitaxial systems, namely, Cu on Ni(111) and Ni on Cu(111), as a function of coverage and temperature.