Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes

Abstract

For diffusion of two-dimensional homoepitaxial clusters of $N$ atoms on metal (100) surfaces mediated by edge atom hopping, macroscale continuum theory suggests that the diffusion coefficient scales like ${D}_{N}\ensuremath{\sim}{N}^{\ensuremath{-}\ensuremath{\beta}}$ with $\ensuremath{\beta}=3/2$. However, we find quite different and diverse behavior in multiple size regimes. These include: (i) facile diffusion for small sizes $N<9$; (ii) slow nucleation-mediated diffusion with small $\ensuremath{\beta}<1$ for ``perfect'' sizes $N={N}_{p}={L}^{2}$ or $L(L+1)$, for $L=3,4, ...$ having unique ground-state shapes, for moderate sizes $9\ensuremath{\le}N\ensuremath{\le}\mathrm{O}({10}^{2})$; the same also applies for $N={N}_{p}+3, {N}_{p}+4, ...$ (iii) facile diffusion but with large $\ensuremath{\beta}>2$ for $N={N}_{p}+1$ and ${N}_{p}+2$ also for moderate sizes $9\ensuremath{\le}N\ensuremath{\le}\mathrm{O}({10}^{2})$; (iv) merging of the above distinct branches and subsequent anomalous scaling with $1\ensuremath{\lesssim}\ensuremath{\beta}<3/2$, reflecting the quasifacetted structure of clusters, for larger $N=\mathrm{O}({10}^{2})$ to $N=\mathrm{O}({10}^{3})$; (v) classic scaling with $\ensuremath{\beta}=3/2$ for very large $N=\mathrm{O}({10}^{3})$ and above. The specified size ranges apply for typical model parameters. We focus on the moderate size regime where we show that diffusivity cycles quasiperiodically from the slowest branch for ${N}_{p}+3$ (not ${N}_{p}$) to the fastest branch for ${N}_{p}+1$. Behavior is quantified by kinetic Monte Carlo simulation of an appropriate stochastic lattice-gas model. However, precise analysis must account for a strong enhancement of diffusivity for short time increments due to back correlation in the cluster motion. Further understanding of this enhancement, of anomalous size scaling behavior, and of the merging of various branches, is facilitated by combinatorial analysis of the number of the ground-state and low-lying excited state cluster configurations, and also of kink populations.