Island shape controls magic-size effect for heteroepitaxial diffusion

Lattice mismatch of Cu on Ag(111) produces fast diffusion for "magic sizes" of islands. A size- and shape-dependent reptation mechanism is responsible for low diffusion barriers. Initiating the reptation mechanism requires a suitable island shape, not just magic sizes. Shape determines the dominant diffusion mechanism and leads to multiple clearly identifiable magic-size trends for diffusion depending on the number of atoms whose bonds are shortened during diffusion, which ultimately affects the self-assembly of islands.