Sintering of two-dimensional nanoclusters in metal(100) homoepitaxial systems: Deviations from predictions of Mullins continuum theory

We present a comparison of the predictions of atomistic and continuum models for the sintering of pairs of near-square two-dimensional nanoclusters adsorbed on the (100) surface in fcc metal homoepitaxial systems. Mass transport underlying these processes is dominated by periphery diffusion (PD) of adatoms along the edge of the clusters. A Mullins-type continuum model for cluster evolution incorporates anisotropy in the step edge stiffness (reflecting the energetics and adsorption site lattice structure in the atomistic model), and can also account for anisotropy in the step edge mobility (reflecting details of the kinetics). In such continuum treatments, the characteristic time τ_eq for relaxation of clusters with linear size of order L satisfies τ_eq∼L⁴. Deviations may generally be expected for small sizes L or low temperatures T. However, for the relaxation of dumbbell-shaped clusters (formed by corner-to-corner coalescence of square clusters), atomistic simulations for PD with no kink rounding barrier (δ=0) reveal that τ_eq∼L⁴ always applies. In contrast, atomistic simulations with a large kink rounding barrier (δ>0) reveal distinct scaling with τ_eq∼L³, for low T or small L, thus providing an effective way to test for δ>0. For the relaxation of faceted rectangular clusters (formed by side-to-side coalescence of square clusters), atomistic simulations for PD with δ=0 reveal that τ_eq∼L², for low T or small L. This is consistent with a recent proposal by Combe and Larralde. For large δ>0, τ_eq has an even weaker dependence on L. We elucidate scaling behavior and the effective activation barrier for relaxation in terms of the individual atomistic PD processes and their barriers.