Lattice Thermal Conductivity in High-Concentration Mixed Crystals

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Abstract
The lattice thermal conductivity in high-concentration harmonic isotopically disordered mixed crystals is calculated within the coherent-potential approximation from the appropriate Kubo formula using the energy current operators of Hardy. The infrared divergence in harmonic systems is eliminated by restriction to finite systems and, in a three-dimensional case, by adding an anharmonic phonon-phonon scattering term. Numerical calculations are performed in one, two, and three dimensions with nearest-neighbor forces for a linear chain, a simple square lattice, and a simple cubic lattice, respectively. In one and two dimensions, comparisons with the computer experiments of Payton et al. show qualitative agreement with the concentration dependence of the thermal conductivity at all concentrations although the overall magnitude is larger by factors of about 10.8 and 5.4, respectively. It is observed that low-frequency resonant modes considerably decrease the thermal conductivity.