Theory of the Thermal Conductivity of Amorphous Solids

Abstract

Thermal conduction by means of lattice waves in glasses will be discussed. Random arrangements of molecular units can be treated as point defects which scatter phonons, with possible enhancement of the scattering due to correlations over longer distances. However, such a model does not result in sufficient scattering at low frequencies and accounts neither for the thermal resistivity at ordinary temperatures nor at low temperatures, unless correlations over unlikely long distances are assumed. An additional interaction mechanism is provided by phonon-assisted transitions between the states of two-level systems, with a wide distribution of level spacings. These systems, whose presence in amorphous systems are postulated, also give rise to an excess specific heat at low temperatures, linear in temperature. This model also accounts for saturation effects in the absorption of high-frequency ultrasonic waves. Unfortunately we know too little about the basic structure of amorphous solids to derive the density, the level-spacing distribution and the phonon interaction strength of these centers. In a simpler case of crystalline Ti-V alloys, where such centers have also been observed, it is possible to derive the first two of these parameters, and hence the excess specific heat, from the known size difference of the two ions.