Non-exponential relaxation in disordered materials:: Phenomenological correlations and spectrally selective experiments

In most glass-forming materials external perturbations are relaxed in a non-exponential fashion. It is shown that the degree of non-exponentiality is phenomenologically correlated with the departure from simple thermally activated behavior as measured by the fragility index m. In model glass formers such as the Ge-As-Se ternary alloy, and to some degree for amorphous materials in general, the correlations with these properties are observed also for other characteristic features. These include the specific heat step and the aging kinetics in the glass transformation range. While phenomenological correlations have proven very useful for rationalizing the properties of many glass formers, they have provided little direct insight into the nature of the non-exponential relaxation itself. In this respect the invention of spectrally selective techniques, allowing to manipulate the observable primary response, has yielded evidence for its heterogeneous character, As an example of these developments the implications of some recent reduced 4D deuteron magnetic resonance experiments on a supercooled liquid are discussed.