The Arrhenius Law versus the Vogel Law

In the study of relaxation phenomena in glassy materials, we derive a relaxation law based on a defect diffusion model. Either exponential or stretched exponential relaxation can occur depending on the defect transport properties. Within our model, the manner in which the defect concentration changes with temperature determines the manner in which a characteristic time scale diverges. Either Arrhenius or Vogel-like behavior can be obtained. In the former case the time scale is infinite only at zero temperature, while for a Vogel type law the time scale will diverge at a finite temperature.