Soft phonons in glasses

The dynamics of glasses differs strongly from the one of crystals. Coexisting with the long wavelength phonons one finds additional low energy excitations: tunneling, soft localized variations and relaxations. The soft potential model postulates a common origin of these additional excitations. In its low temperature limit (typically T < 1 K) it is equivalent to the well-known tunneling model. From general properties of the distribution functions describing the soft potentials one derives the temperature dependencies of quantities such as the specific heat or the thermal conductivity. These universal relations hold to about T = 10 K. Fitting the parameters of the model to the experimental data one finds 20–100 atoms to participate in the excitation modes. Extensions to higher temperatures are possible by introducing material dependent distribution functions. Computer simulations are used to test the assumptions of the model and to provide some insight into the microscopic origin of the modes. One finds soft vibrational modes concentrated on 10 or more atoms. These modes are centered at structural irregularities.