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 ∼ N^-β, 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_p = L² and L(L+1) for integer L = 3,4,… (with unique square or near-square ground state shapes), and also for N_p+3, N_p+4,…. In contrast, fast facile nucleation-free diffusion displaying strong size scaling β ≈ 2.5 occurs for sizes N_p+1 and N_p+2. D_N versus N oscillates strongly between the slowest branch (for N_p+3) and the fastest branch (for N_p+1). All branches merge for N = O(10²), but macroscale behavior is only achieved for much larger N = O(10³). This analysis reveals the unprecedented diversity of behavior on the nanoscale.