Using the 18-Electron Rule To Understand the Nominal 19-Electron Half-Heusler NbCoSb with Nb Vacancies

The 18-electron rule is a widely used criterion in the search for new half-Heusler thermoelectric materials. However, several 19-electron compounds such as NbCoSb have been found to be stable and exhibit thermoelectric properties rivaling state-of-the art materials. Using synchrotron X-ray diffraction and density functional theory calculations, we show that samples with nominal (19-electron) composition NbCoSb actually contain a half-Heusler phase with composition Nb_0.84CoSb. The large amount of stable Nb vacancies reduces the overall electron count, which brings the stoichiometry of the compound close to an 18-electron count, and stabilizes the material. Excess electrons beyond 18 electrons provide heavy doping needed to make these good thermoelectric materials. This work demonstrates that considering possible defect chemistry and allowing small variation of electron counting leads to extra degrees of freedom for tailoring thermoelectric properties and exploring new compounds. Here we discuss the 18-electron rule as a guide to find defect-free half-Heusler semiconductors. Other electron counts such as 19-electron NbCoSb can also be expected to be stable as n-type metals, perhaps with cation vacancy defects to reduce the electron count.