  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.
