PbTe, one of the most promising thermoelectric materials, has recently demonstrated thermoelectric figure of merit (ZT ) of above 2.0 when alloyed with group II elements.The improvements are due mainly to significant reduction of lattice thermal conductivity (κ l ), which was in turn attributed to nanoparticle precipitates. However, a fundamental understanding of various phonon scattering mechanisms within the bulk alloy is still lacking. In this work, we apply the newly-developed density-functionaltheory (DFT)-based compressive sensing lattice dynamics (CSLD) approach to model lattice heat transport in PbTe, MTe, and Pb 0.94 M 0.06 Te (M=Mg, Ca, Sr and Ba), compare our results with experimental measurements, with focus on strain effect and mass disorder scattering. We find that (1) CaTe, SrTe and BaTe in the rock-salt structure exhibit much higher κ l than PbTe, while MgTe in the same structure shows anomalously low κ l ; (2) lattice heat transport of PbTe is extremely sensitive to static strain induced by alloying atoms in solid solution form; (3) mass disorder scattering plays a major role in reducing κ l for Mg/Ca/Sr-alloyed PbTe through strongly suppressing the lifetimes of intermediate-and high-frequency phonons, while for Baalloyed PbTe, precipitated nanoparticles are also important. a) Electronic mail: yxia@anl.gov b) Electronic mail: mchan@anl.gov 1 arXiv:1712.01926v1 [cond-mat.mtrl-sci] 5 Dec 2017 Thermoelectric (TE) devices, which are capable of converting waste heat into electricity, are ideal alternative renewable energy technologies to overcome limited fossil fuel resources and environmental challenges. 1 Thermoelectric energy conversion efficiency is characterized by the dimensionless figure of merit ZT = S 2 σT /(κ e +κ l ), where S, σ and T are the Seebeck coefficient, the electrical conductivity, and temperature, and κ e and κ l are the electronic and lattice thermal conductivities, respectively. ZT is generally optimized by maximizing the thermoelectric power factor S 2 σ and minimizing κ l . 2,3PbTe-based TE materials are among the highest performing, partly because of strong inherent phonon anharmonicity, leading to low κ l . 4 To further enhance ZT , simultaneously reducing κ l and improving the power factor can be achieved by introducing anionic and cationic dopants. Recent experiments show that p-type PbTe alloyed with group II elements (Mg, Ca, Sr and Ba) achieved ZT well above 1.5. 5-11 It is found in experiments and theoretical calculations that, with group II dopants, electronic properties are improved owing to convergence of multiple valence bands and band gap widening. 8,9 With respect to lattice heat transport, significant reduction of κ l is observed, which was attributed to the all-scale hierarchical architectures-induced phonon scattering due to the presence of solid-solution point defects, nanoscale precipitates, and grain boundaries. 4,7 However, fundamental understanding of the roles of various phonon scattering mechanisms in reducing κ l is still lacking. Previous first-princ...