Comparing models for diffusion in supercooled liquids: The eutectic composition of the Ag-Cu alloy

We present a comparison between the Continuous Time Random Walk (CTRW) model for dispersive transport and Zwanzig's model of self-diffusion in liquids using the cage correlation function as a means for obtaining the characteristic hopping times. This comparison was done using a realistic model for the interactions between metal atoms in a system that is known to form metallic glasses; We find that although the CTRW model uses a pathological model for the distribution of waiting times, the predictions of this theory are much closer to the actual diffusion constants than those obtained via Zwanzig's model. We also find that there is a simple linear relationship between the stretching parameter (beta) for Kohlrausch-Williams-Watts decay of the cage correlation function and the dispersion parameter (gamma) that characterizes the "fractal" distribution of waiting times in the CTRW model.