  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.
