Communication: Diverse nanoscale cluster dynamics: Diffusion of 2D epitaxial clusters

The dynamics of nanoscale clusters can be distinct from macroscale behavior described by continuum formalisms. For diffusion of 2D clusters of N atoms in homoepitaxial systems mediated by edge atom hopping, macroscale theory predicts simple monotonic size scaling of the diffusion coefficient, D ∼ N, with β = 3/2. However, modeling for nanoclusters on metal(100) surfaces reveals that slow nucleation-mediated diffusion displaying weak size scaling β < 1 occurs for "perfect" sizes N = L and L(L+1) for integer L = 3,4,… (with unique square or near-square ground state shapes), and also for N+3, N+4,…. In contrast, fast facile nucleation-free diffusion displaying strong size scaling β ≈ 2.5 occurs for sizes N+1 and N+2. D versus N oscillates strongly between the slowest branch (for N+3) and the fastest branch (for N+1). All branches merge for N = O(10), but macroscale behavior is only achieved for much larger N = O(10). This analysis reveals the unprecedented diversity of behavior on the nanoscale.