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

TL;DR

This study reveals that considering Lorentzian energy conservation in 3-phonon interactions explains the intrinsic thermal conductivity peak in non-metallic solids like argon, matching experimental data across all temperatures.

Contribution

It introduces a new approach using Lorentz distribution for energy conservation in phonon interactions, enabling accurate prediction of low-temperature thermal conductivity without extrinsic scattering.

Findings

Successfully modeled the $T^2$ behavior at low temperatures.

Predicted the thermal conductivity peak at around 8 K.

Found phonon-phonon interactions dominate over defect scattering in argon.

Abstract

The inelastic nature of 3-phonon processes is investigated within the framework of perturbation theory and linearized Boltzmann Transport Equation. By considering the energy conservation rule governing this type of interactions 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. An iterative solution scheme for Boltzmann Transport Equation 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 phonon-defect scattering dominates the sub-peak regime. 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.