High ZT and low lattice thermal conductivity in defective half-Heusler Zr _0.75 PtSb <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi/> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mtext>x</mm

In this study, employing first-principles DFT calculation, we explore<i>defective half-Heusler (HH)</i>compounds to achieve a superior figure of merit (<i>ZT</i>). The<i>defective HH</i>compound Zr_0.75PtSb 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 (<i>PF</i>), and<i>ZT</i>. The findings reveal<i>p-type</i>semiconducting behavior in the<i>defective HH</i>Zr_0.75PtSb 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 (κL∼9.5W mK^-1) in the<i>defective HH</i>Zr_0.75PtSb compound, which is further reduced by alloying the Sb site with Bi atoms. The resultant<i>κ</i>_<i>L</i>for Zr_0.75PtSb is three to four times lower than the prototype XYZ HH compounds. The TE properties-including Seebeck coefficient (<i>S</i>), electrical conductivity (<i>σ</i>), electronic thermal conductivity (<i>κ</i>_<i>e</i>),<i>ZT</i>of the<i>defective HH</i>Zr_0.75PtSb1-xBi_<i>x</i>system are systematically investigated. For the parent compound Zr_0.75PtSb, a peak<i>ZT</i>of approximately 0.97 is predicted at 1000 K within a carrier concentration range of 10²⁰to 10²²cm^-3. Bi substitution at the Sb site notably tune the TE performance, primarily owing to modifications in the transport properties. In particular, Zr_0.75PtSb_0.75Bi_0.25exhibits a significantly enhanced<i>ZT</i> ≈ 1.41 at 1000 K, marking a 43% increase over the undoped system. These results highlight the potential of<i>defective HH</i>compounds for mid- to high-temperature TE applications and offer guidance for experimental efforts toward optimizing<i>ZT</i>.