Using first-principles DFT we systematically investigate the thermodynamic stability and off-stoichiometry in 108 nominal 19-electron half-Heusler (hH) compounds. We demonstrate unambiguously that considering a cation deficiency towards the off-stoichiometric valence balanced, VEC = 18 composition is necessary for explaining the stability of all previously reported nominal VEC = 19 compounds. This is understandable in terms of an energy benefit from valence balance considering the valence of each atom using Zintl chemistry that offsets the energy penalty of forming defects in nearly all cases. Thus, we propose a valence balanced rule to understand the ground state stability of half-Heuslers irrespective of stoichiometry and nominal electron count (8, 18 or 19). Using this generalized rule we (a) predict 16 previously unreported nominal 19-electron XYZ half-Heuslers and (b) rationalize the reports of giant off-stoichiometries in compounds such as Ti(1−x)NiSb which has been known for over 50 years. Of the 16 new compounds predicted here, Ti(1−x)PtSb was synthesized and the half-Heusler phase confirmed through X-ray studies. The flexibility in stoichiometry of the half-Heusler systems to attain a stable valence balanced composition by accommodating large defect concentrations opens up multiple dimensions for discovery of multi-component defective half-Heuslers based on intrinsic and extrinsic defects which compensate for the nominally non-18-electron count of the structure.
