Surface diffusion capture in nucleation theory

The diffusion of adatoms over a substrate, their capture by isolated clusters of atoms and their release from such clusters is examined, in order to calculate nucleation rates. Two approaches are used: the first considers the fluxes of distinct atoms between the clusters and the vapour, while the second considers the total transfer rates between the clusters and adsorbed monomer. While the two approaches lead to similar results, the first is simpler to apply. It is shown that the monomer density in the neighbourhood of clusters is uniform only when captured atoms are replenished by cluster decay, i.e. when the net growth rate is zero, and is depleted below the mean value near growing clusters, including those growing through the critical size. It is further shown that the net capture rate of monomer by critical nuclei, i.e. the net rate at which they become supercritical, cannot exceed the steady-state surface diffusion limited flux of distinct atoms, and that nucleation rate relations derived with the assumption of a uniform monomer density are wrong. The correct relations are given.