Peak intrinsic thermal conductivity in non-metallic solids and new interpretation of experimental data for argon

Abstract

The inelastic nature of 3-phonon processes is investigated within the framework of perturbation theory and linearized Boltzmann transport equation (BTE). By considering the energy conservation rule governing this type of interaction in a statistical average sense, the impact of different forms of the regularized energy-conserving Dirac delta function on 3-phonon scattering rates was evaluated. Strikingly, adopting Lorentz distribution, in accordance with the shape of eigenenergy broadening of phonon normal modes due to the leading term of crystal anharmonicity, was found to play a critical role in activating umklapp processes at low temperature, leading to intrinsic lattice thermal conductivity peak at finite temperature for perfect crystal. This characteristic behavior, unique to the Lorentzian, lays foundation for developing adjustable-parameter-free computational models for reliable prediction of the finite lattice conductivity at low temperature, even in the absence of extrinsic scattering processes (e.g., by crystal imperfections and boundary). An iterative solution scheme for BTE was used to compute the intrinsic thermal conductivity of solid argon over the entire temperature range (2-80 K). For the first time, the experimentally observed T 2 behavior in the low temperature, T, limit and the peak temperature (∼8 K) were successfully recovered, in addition to the classical high temperature T −1 behavior above 20 K by the sole use of 3-phonon processes. The good agreement with experiment indicates that phonon-phonon interactions dominate over the entire temperature range in argon, contrary to previous hypotheses that the subpeak regime is dominated by phonondefect scattering. Anisotropy in thermal conductivity of single crystal at low temperature due to phonon focusing was observed. In addition, argon conductivity is underestimated by an order of magnitude in single mode relaxation time approximation, where the collective nature of phonon mode relaxation is ignored.

A combined theoretical-experimental investigation of thermal transport in low-dose irradiated thorium dioxide

“…Brillouin zone summations for phonon-phonon scattering rates, lattice specific heat, and thermal conductivity are performed over the irreducible Brillouin zone [54,55] of the face-centered cubic lattice structure of ThO2. Here, a uniform cubic mesh of 1299 representative q-points is used to sample the irreducible Brillouin zone.…”