Heat conductivity of amorphous solids: Simulation results on model structures

Through numerical simulation and consideration of phonon scattering by two-level states, the heat conductivity κ(T), where T is temperature, has been calculated on model structures. The values obtained are in good quantitative agreement with measured data on polymethylmethacrylate, epoxy, amorphous selenium, and amorphous silicon dioxide over the temperature range 0.1 to 100 K. The calculated results reproduce the plateau feature, in the range of 5 to 20 K, that is generic to the heat conductivity of amorphous solids. Two model parameters, one characterizing the degree of structural disorder and the other related to the relaxational absorption of two-level states, are identified as being responsible for the behavior of κ(T) at T ≳ 5 K. The simulation results indicate the existence of a frequency-independent phonon diffusion regime that is consistent with the minimum phonon mean-free-path hypothesis. The magnitude of the phonon diffusion constant in this regime is shown to give a reasonable quantitative account of high-temperature κ(T) in amorphous systems.