Enhanced Thermoelectric\nProperties in Na-Doped PbTe\nvia Pb Vacancies and Trace Eu Doping

Enhancing the thermoelectric performance of Na-doped\nPbTe is challenging\ndue to the low solubility of Na, a problem that remains insufficiently\nexplored from a theoretical perspective, particularly regarding the\nrole of Pb vacancies. In this study, we utilize crystal orbital Hamilton\npopulation and electron localization function analyses to investigate\nthe impact of Pb vacancies on Na solubility in PbTe. Our findings\nindicate that Pb vacancies strengthen Na–Te bonding and improve\nelectron localization around Te atoms, which reduces the formation\nof Te vacancies and facilitates a higher dissolution of Na. Furthermore,\nwe examine the effects of trace Eu doping in Pb<sub>0.95</sub>Na<sub>0.04</sub>Te, which optimizes band convergence, leading to a power\nfactor of ∼27 μW cm<sup>–1</sup> K<sup>–2</sup> at 823 K and a significant reduction in lattice thermal conductivity\nto ∼0.42 W m<sup>–1</sup> K<sup>–1</sup>. The\nsynergistic effects of these modifications result in a peak <i>zT</i> of ∼2.3 at 823 K and an average <i>zT</i> of ∼1.2 across the temperature range of 323 to 823 K. These\ninsights highlight Pb vacancies and trace Eu doping as promising strategies\nfor advancing high-performance thermoelectric materials, thus contributing\nto the broader field of thermoelectric research and material development.