  The electronic structures of TixZrx/2CoPbxTex, TixZrx/2Hfx/2CoPbxTex (x =
0.5), and the parent compound TiCoSb were investigated using the full potential
linearized augmented plane wave method. The thermoelectric transport properties
of these alloys are calculated on the basis of semi-classical Boltzmann
transport theory. From the band structure calculations we show that the
substitution of Zr,Hf in the Ti site and Pb and Te in the Sb site lower the
band gap value and also change the indirect band (IB) gap of TiCoSb to the
direct band (DB) gap. The calculated band gap of TiCoSb, TixZrx/2CoPbxTex, and
TixZrx/2Hfx/2CoPbxTex are 1.04 eV (IB), 0.92 eV (DB), and 0.93 eV (DB),
respectively. All these alloys follow the empirical rule of 18 valence-electron
content which is essential for bringing semiconductivity in half Heusler
alloys. It is shown that the substitution of Hf at the Ti site improve the ZT
value (~1.05) at room temperature, whereas there is no significant difference
in ZT is found at higher temperature. Based on the calculated thermoelectric
transport properties, we conclude that the appropriate concentration of Hf
substitution can further improve the thermoelectric performance of
TixZrx/2Hfx/2CoPbxTex.
