Amorphous materials are classified as strong or fragile based on the temperature dependence of the diffusion constant near the glass transition temperature, T_g. In the strong limit, the diffusion displays Arrhenius temperature dependence, while in fragile liquids, there is a crossover from Arrhenius to a super-exponential (exp[-(T₀/T)² ]), power law ((T-T_c )^ß ), or Vogel-Fulcher-Tamman (exp[-B/(T-T₀ )]) temperature dependence just above T_g.

This change in diffusive behavior is attributable to the relative size of the diffusive barriers compared to the average barrier height that separates adjacent local minima on the potential energy surface. In the strong limit, the potential energy surface is thought to be uniformly rough - all of the barriers are barriers to diffusion - while atoms in fragile liquids have to become activated to cross the small barriers in addition to the larger diffusive barriers. At temperatures well in excess of T_g, these barriers are crossed easily, and the barriers between basins are manifest in simple Arrhenius-like temperature dependence. As the temperature falls, atoms must diffuse over the small barriers to reach the diffusive barriers, so the diffusion constant can display non-Arrhenius temperature dependence. To date, however, there is no comprehensive microscopic theory that connects the topology of the potential energy surface to the diffusive behavior near T_g. We are working to understand this crossover behavior in glassy materials and to study the detailed dynamics of diffusive hopping in amorphous materials.