Comprehensive Theoretical Analysis of XPtSi (X = Ti, Zr, Hf) Half-Heusler Alloys: Bridging Slack Equation and BTE for Accurate Thermoelectric Predictions

Abstract

We have undertaken a comprehensive investigation into the electronic and thermoelectric properties of the half-Heusler alloys XPtSi (where X = Ti, Zr, Hf) through first-principles calculations employed in VASP code. These alloys demonstrate semiconductor behavior, characterized by an indirect band gap with corresponding energies of 0.94 eV, 1.57 eV, and 1.50 eV for XPtSi (X = Ti, Zr, Hf), as determined using the modified Becke-Johnson potential. Additionally, we assessed the influence of spin-orbit coupling on the band structures. However, its impact on the systems studied was found to be negligibly small. Demonstrating negative formation energy and ductile behavior, these alloys display flexibility against structural and mechanical distortions. The analysis of thermoelectric heat transport properties entailed the utilization of semi-classical Boltzmann theory, whereas the Slack equation was employed to predict lattice thermal conductivity for both p-type and n-type alloys. Compared to the Slack model, the values derived from the BTE exhibit a reduction of 13.7%, 23.4%, and 29.1%, respectively for XPtSi (X = Ti, Zr, Hf), as a result of phonon-phonon interactions. Notably, the p-type TiPtSi, ZrPtSi, and HfPtSi half-Heulser alloys exhibit maximum figure of merit values of 0.63, 0.62, and 0.63 at 1200K, respectively. Similarly, the n-type alloys demonstrate peak figure of merit values of 0.39, 0.74, and 0.68 respectively at same temperature. Our conducted studies and results strongly suggest for the potential deployment of XPtSi materials (where X = Ti, Zr, Hf) in thermoelectric applications accelerated towards the reclamation of waste energy.