Thermal conductivity of amorphous materials above the plateau

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Abstract
We calculate the contribution to the thermal conductivity, κ, in amorphous solids of the hopping of localized vibrational modes coupled to phonons via the anharmonic interaction. This contribution is generally important for temperatures above the plateau region in κ. The temperature-dependent thermal conductivity is expressed in terms of the temperature-dependent phonon mean free path, both quantities being calculated perturbatively in the anharmonic coupling. Experimental data available for the latter quantity give us estimates of the temperature-dependent thermal conductivity for vitreous silica in excellent agreement with measured values. The averaged anharmonic couplings obtained from comparison with data are found to be (roughly) 2 orders of magnitude larger than in a regular crystalline solid with comparable sound velocity. We attribute this enhancement to the more ‘‘open’’ network character of amorphous solids. It is shown that this large value of the coupling constant does not invalidate the perturbative calculation, provided that a temperature-dependent condition on the hopping lifetimes is satisfied. At sufficiently high temperatures, this condition will eventually be violated, leading to deviations from the predicted temperature dependence for the hopping contribution to the thermal conductivity. We estimate the deviation, again in a perturbation expansion, and speculate that this effect accounts for the observed nonuniversality of κ(T) above the plateau region.