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The inelastic nature of 3-phonon processes is investigated within theframework of perturbation theory and linearized Boltzmann Transport Equation.By considering the energy conservation rule governing this type of interactionsin a statistical average sense, the impact of different forms of theregularized energy-conserving Dirac delta function on 3-phonon scattering rateswas evaluated. Strikingly, adopting Lorentz distribution, in accordance withthe shape of eigenenergy broadening of phonon normal modes due to the leadingterm of crystal anharmonicity, was found to play a critical role in activatingumklapp processes at low temperature, leading to intrinsic lattice thermalconductivity peak at finite temperature for perfect crystal. Thischaracteristic behavior, unique to the Lorentzian, lays foundation fordeveloping adjustable-parameter-free computational models for reliableprediction of the finite lattice conductivity at low temperature, even in theabsence of extrinsic scattering processes. An iterative solution scheme forBoltzmann Transport Equation was used to compute the intrinsic thermalconductivity of solid argon over the entire temperature range (2-80 K). For thefirst time, the experimentally observed $T^2$ behavior in the low temperature,$T$, limit and the peak temperature (~ 8 K) were successfully recovered, inaddition to the classical high temperature $T^{-1}$ behavior above 20 K by thesole use of 3-phonon processes. The good agreement with experiment indicatesthat phonon-phonon interactions dominate over the entire temperature range inargon, contrary to previous hypotheses that phonon-defect scattering dominatesthe sub-peak regime. Anisotropy in thermal conductivity of single crystal atlow temperature due to phonon focusing was observed. In addition, argonconductivity is underestimated by an order of magnitude in Single ModeRelaxation Time approximation.

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