Comprehensive theoretical analysis of XPtSi (X = Ti, Zr, Hf) half-Heusler alloys: bridging the Slack equation and BTE for accurate thermoelectric predictions

Abstract

In this study, we present a comprehensive theoretical investigation of the structural, electronic, and thermoelectric properties of half-Heusler alloys XPtSi (X = Ti, Zr, Hf) using density functional theory (DFT), deformation potential theory, and phonon transport calculations. Alloys exhibit indirect semiconducting behavior with band gaps of 0.94 eV, 1.57 eV, and 1.50 eV for TiPtSi, ZrPtSi, and HfPtSi, respectively, evaluated using the modified Becke–Johnson potential. Spin–orbit coupling was found to have minimal influence on the electronic structure. Mechanical stability, negative formation energies, and ductile characteristics indicate the structural robustness of these materials. Thermoelectric transport coefficients were calculated using semi-classical Boltzmann transport theory, with carrier relaxation times estimated via deformation potential theory. Lattice thermal conductivity was computed using both the Slack equation and the Boltzmann transport equation (BTE) via Phono3py. The BTE approach revealed reductions of 13.7%, 23.4%, and 29.1% compared to Slack's model for TiPtSi, ZrPtSi, and HfPtSi, respectively, due to phonon–phonon scattering. At 1200 K, the maximum figure of merit (ZT) values reached 0.63, 0.62, and 0.63 for p-type, and 0.39, 0.74, and 0.68 for n-type TiPtSi, ZrPtSi, and HfPtSi, respectively. These results highlight the promise of XPtSi alloys as efficient thermoelectric materials for high-temperature waste heat recovery applications.