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  1. Semiconductor engineering relies heavily on doping efficiency and dopability. Low doping efficiency may cause low mobility and failure to reach target carrier concentrations or even the desired carrier type. Semiconducting thermoelectric materials perform best with degenerate carrier concentrations, meaning high performance in new materials might not be realized experimentally without a route to optimal doping. Doping in the classic PbTe thermoelectric system has been largely successful but reported doping efficiencies can vary, raising concerns about reproducibility. Here, we stress the importance of phase equilibria considerations during synthesis to avoid undesired intrinsic defects leading to sub-optimal doping. By saturation annealing at 973 K, we decidedly fix the composition in single crystal iodine-doped PbTe samples to be Pb-rich or Te-rich without introducing impurity phases. We show that, regardless of iodine concentration, degenerate n-type carrier concentrations with ideal doping efficiency require Pb-rich compositions. Electrons in Te-rich samples are heavily compensated by charged intrinsic Pb vacancy defects. From Hall effect measurements and a simple defect model supported by modern defect calculations, we map out the 973 K ternary Pb–Te–I phase diagram to explicitly link carrier concentration and composition. Furthermore, we discuss unintentional composition changes due to loss of volatile Te during synthesis and measurements. The methods and concepts applied here may guide doping studies on other lead chalcogenide systems as well as any doped, complex semiconductor. 
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  2. 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. 
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