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Solid-solution alloy scattering of phonons is a demonstrated mechanism to reduce the lattice thermal conductivity. The analytical model of Klemens works well both as a predictive tool for engineering materials, particularly in the field of thermoelectrics, and as a benchmark for the rapidly advancing theory of thermal transport in complex and defective materials. This comment/review outlines the simple algorithm used to predict the thermal conductivity reduction due to alloy scattering, as to avoid common misinterpretations, which have led to a large overestimation of mass fluctuation scattering. The Klemens model for vacancy scattering predicts a nearly 10× larger scattering parameter than is typically assumed, yet this large effect has often gone undetected due to a cancellation of errors. The Klemens description is generalizable for use in ab initio calculations on complex materials with imperfections. The closeness of the analytic approximation to both experiment and theory reveals the simple phenomena that emerges from the complexity and unexplored opportunities to reduce thermal conductivity. 

A model for the thermal conductivity of bulk solids is proposed in the limit of diffusive transport mediated by diffusons as opposed to phonons. This diffusive thermal conductivity, κ diff , is determined by the average energy of the vibrational density of states, ℏ ω avg , and the number density of atoms, n . Furthermore, κ diff is suggested as an appropriate estimate of the minimum thermal conductivity for complex materials, such that (at high temperatures): . A heuristic finding of this study is that the experimental ω avg is highly correlated with the Debye temperature, allowing κ diff to be estimated from the longitudinal and transverse speeds of sound: . Using this equation to estimate κ min gives values 37% lower than the widely-used Cahill result and 18% lower than the Clarke model for κ min , on average. This model of diffuson-mediated thermal conductivity may thus help explain experimental results of ultralow thermal conductivity.