High ZT and low lattice thermal conductivity in defective half-Heusler Zr 0.75 PtSb 1 − x Bi x alloys: promising for mid- and high-temperature thermoelectric applications

Abstract In this study, employing first-principles DFT calculation, we explore defective half-Heusler (HH) compounds to achieve a superior figure of merit ( ZT ). The defective HH compound Zr 0.75 PtSb is engineered by introducing vacancies into the non-18 valence electron count (VEC) HH compound, ZrPtSb. Our analysis encompasses the crystalline and electronic structure, Seebeck coefficient, electrical and thermal conductivity, power factor ( PF ), and ZT . The findings reveal p-type semiconducting behavior in the defective HH Zr 0.75 PtSb compound, while ZrPtSb compound exhibits metallic characteristics. Further alloying the Sb site with Bi atoms effectively tunes the band gap, resulting from significant changes in the electronic structure. This work highlights low lattice thermal conductivity ( κ L ∼ 9.5 W mK −1 ) in the defective HH Zr 0.75 PtSb compound, which is further reduced by alloying the Sb site with Bi atoms. The resultant κ L for Zr 0.75 PtSb is three to four times lower than the prototype XYZ HH compounds. The TE properties—including Seebeck coefficient ( S ), electrical conductivity ( σ ), electronic thermal conductivity ( κ e ), ZT of the defective HH Zr 0.75 PtSb 1 − x Bi x system are systematically investigated. For the parent compound Zr 0.75 PtSb, a peak ZT of approximately 0.97 is predicted at 1000 K within a carrier concentration range of 10 20 to 10 22 cm −3 . Bi substitution at the Sb site notably tune the TE performance, primarily owing to modifications in the transport properties. In particular, Zr 0.75 PtSb 0.75 Bi 0.25 exhibits a significantly enhanced ZT ≈ 1.41 at 1000 K, marking a 43% increase over the undoped system. These results highlight the potential of defective HH compounds for mid- to high-temperature TE applications and offer guidance for experimental efforts toward optimizing ZT .