Lattice thermal conductivity controls thermoelectric performance in bulk sulfides: a comparative FP-LAPW and quasi-harmonic Debye study of PbS, MoS₂ and WS₂

Metal sulfides are earth-abundant and far less toxic than the tellurides that dominate thermoelectric devices, yet which performs best has never been settled on a common computational footing. We compare cubic PbS and the layered dichalcogenides MoS₂ and WS₂ using the FP-LAPW method with the Tran–Blaha modified Becke–Johnson potential, semi-classical Boltzmann transport theory and the quasi-harmonic Debye model. Because plain PBE overestimates the interlayer separation of the dichalcogenides, their full property chain was recomputed with the DFT-D3 dispersion correction; PbS, whose rock-salt lattice has no van der Waals gap, was treated with PBE throughout. The correction reduces the c-axis error to 1.25% for MoS₂ and 0.04% for WS₂ and removes the unphysical PBE result C₃₃ > C₁₁ for MoS₂, raising C₁₁/C₃₃ from 0.78 to 5.72 (experiment: 4.58). It also lowers the lattice thermal conductivity roughly two-fold for MoS₂ and four-fold for WS₂, narrowing the advantage of PbS from about seventeen-fold to between four and nine. This margin still reverses the electronic ranking: at 500 K the dichalcogenides reach power factors of 3.1–3.8 mW m−¹ K−², three times that of PbS (1.35 mW m−¹ K−²), yet PbS attains ZT = 0.91 against 0.62 for WS₂ and 0.34 for MoS₂. Absolute κ_L and ZT values are model-based estimates within the Debye–Slack and constant-relaxation-time approximations, but the ordering PbS > WS₂ > MoS₂ survives both the dispersion correction and a fifty-fold variation of the relaxation time. Superior electronic transport does not guarantee superior thermoelectric performance.