Low-temperature thermal conductivity of amorphous silica

Abstract

In order to understand the importance and limitations of the role of low-temperature thermal-conductivity data in understanding amorphous glasses, we have used the two-level tunneling-state model to generate fits to such data. A variety of densities of states have been utilized, including the forms previously suggested to explain specific-heat, ultrasonic-attenuation, and thermal-conductivity data. We find that the low-temperature (3.5 K) fits to the data can be generated with all of the different forms of the density of states considered. In the intermediate temperature region (3.5-15 K) where there is a plateau, a variation in the strengths of the two different scattering processes, resonant and relaxation scattering processes, generates the various shapes seen in the thermal-conductivity data of different amorphous materials. With the strengths used for the best fit, we calculate the value of the coupling constant $\ensuremath{\gamma}$ to be in accord with ultrasonic-phonon-echo experiments. The high-temperature thermal conductivity, above the plateau, requires a gentle tailing off in the density of states. Finally, an equally good fit to the complete thermal-conductivity curve can be generated with both a nearly constant density of states and a density of states which has a quadratic energy dependence.