First-principles calculations to investigate structural, mechanical, electronic, transport and thermoelectric properties of XTiPd(X=Si, Ge, Sn, Pb) Half Heusler alloys

The half heusler alloys PdTiX(X= Si Ge, Sn, Pb) focused on their structural, electronic, thermal and thermoelectric properties are investigated by employing first-principles DFT calculations and Boltzmann transport theory. All the concerned materials are observed to be stabilized in its $\alpha$-structural phase(XTiPd) with indirect band-gap. The interplay of partially filled 3d valence electrons of Ti in their localized and hybridized state for determining their stable structural phase and electronic properties is studied in detail. It is found that as X in XTiPd gets substituted in the increasing order of their atomic mass, the band-gap, formation energy, and overall thermal conductivity are reduced considerably. In comparison with other half heusler alloys these materials are obtained with high Seebeck coefficient and moderate electrical and thermal conductivities leading to high figure of merit. Out of all the materials investigated in the present work, SiTiPd is observed with more widened band gap of 0.78 eV and high lattice thermal conductivity of ${\kappa }_L$= 27.68 W/m.K whereas PbTiPd has a lowest band gap of 0.38 eV and lowest ${\kappa }_L$= 7.64 W/m.K at 300 K. The relaxation time($\tau$) is calculated in the range of $10^{-13}-$ $10^{-14}$ s for all XTiPd using Bardeen and Shockley’s deformation potential approximation method. High throughput DFT calculations are performed to extract the accurate thermoelectric efficiency of chosen alloys in terms of figure of merit($zT$). An enhanced thermoelectric efficiency of $zT$=1.4 for SnTiPd at 1200 K, $zT$= 1.25 for PbTiPd at 1000 K and $zT=1$ for XTiPd(X= Si, Ge) at 1200 K are obtained using these throughput calculations. The present study affirms that all the half heusler materials XTiPd(X = Si, Ge, Sn,Pb) can be harnessed as the potential candidates for thermoelectric applications.