A free energy landscape perspective on the nature of collective diffusion in amorphous solids

The nature of collective diffusion in amorphous solids is in strong contrast with diffusion in crystals. However, the atomic-scale mechanism and kinetics of such collective diffusion remains elusive. Here the free energy landscape of collective diffusion triggered by single atom hopping in a prototypical Cu₅₀Zr₅₀ metallic glass is explored with well-tempered metadynamics which significantly expands the observation timescale of diffusion at atomic-scale. We clarify an experimentally suggested collective atomic diffusion mechanism in the deep glassy state. The collective nature is strongly temperature-dependent. It evolves from string-like motion with only several atoms to be large size collective diffusion at high temperature, which can promote the atomic transport upon glass transition temperature. We also clarify the apparent diffusivity is dominated by the highest free energy barrier of atomic diffusion among widely distributed free energy barriers due to the dynamic heterogeneity of metallic glass, which suggests the sequential nature of diffusion is a proper assumption to the metallic glasses with dynamic heterogeneity. The temperature and pressure dependence of diffusion free energy landscape are further quantified with activation entropy, (19.6 ± 2.5)k_B, and activation volume, (7.9 ± 3.4) ų, which agree quantitatively with experiments. Laboratory timescale simulations of atomic diffusion brings physical insights into the unique atomic motion mechanism in non-crystalline materials.