  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.
