The theoretical analysis of the effect of multi-site substitution based on the 18 valence electron count (VEC) rule on the electrical, thermal and thermoelectric properties of two well known half Heusler (HH) alloys, TiNiSn and TiCoSb, are reported.

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In order to improve the thermoelectric performance of TiCoSb we have substituted 50% of Ti equally with Zr and Hf at Ti site and Sb with Sn and Se equally at Sb site. The electronic structure of Ti0.5Zr0.25Hf0.25CoSn0.5Se0.5 is investigated using the full potential linearized augmented plane wave method and the thermoelectric transport properties are calculated on the basis of semi-classical Boltzmann transport theory. Our band structure calculations show that Ti0.5Zr0.25Hf0.25CoSn0.5Se0.5 has semiconducting behavior with indirect band gap value of 0.98 eV which follow the empirical rule of 18 valence-electron content to bring semiconductivity in half Heusler compounds, indicating that one can have semiconducting behavior in multinary phase of half Heusler compounds if they full fill the 18 VEC rule and this open-up the possibility of designing thermoelectrics with high figure of merit in half Heusler compounds. We show that at high temperature of around 700K Ti0.5Zr0.25Hf0.25CoSn0.5Se0.5 has high thermoelectric figure of merit of ZT = 1.05 which is higher than that of TiCoSb (~ 0.95) suggesting that by going from ternary to multinary phase system one can enhance the thermoelectric figure of merit at higher temperatures.