First-principles identification of PtTiGe and PtTiPb as high-efficiency thermoelectric half-Heuslers

Abstract This study presents a comprehensive first-principles investigation of the structural, mechanical, electronic, optical, thermoelectric, and thermodynamic properties of half-Heusler PtTiZ (Z = Ge, Pb) compounds using the full-potential linearized augmented plane-wave (FP-LAPW) method combined with semiclassical Boltzmann transport theory. Exchange–correlation effects were treated within the LDA, PBE-GGA, and Tran–Blaha modified Becke–Johnson (TB-mBJ) schemes to achieve accurate electronic descriptions. Both alloys crystallize in a stable cubic F-43 m structure and exhibit indirect semiconducting behavior with band gaps of 0.66 eV (PtTiGe) and 0.387 eV (PtTiPb). The density-of-states analysis indicates that the valence region is dominated by Ti-3d and Z-p hybridized states, confirming strong p–d interactions. Mechanical stability criteria and positive elastic constants verify that both compounds are mechanically robust, with PtTiGe being stiffer and harder than PtTiPb. Optical results reveal pronounced absorption and high optical conductivity in the ultraviolet region, suggesting potential for optoelectronic applications. Thermoelectric analysis demonstrates p-type character with Seebeck coefficients of 229.21 µV K⁻¹ (PtTiGe) and 236.21 µV K⁻¹ (PtTiPb) at 300 K, and 235.05 µV K⁻¹ and 237.31 µV K⁻¹ at 1200 K, respectively. The corresponding lattice thermal conductivities decrease to 0.45 W m⁻¹ K⁻¹ and 0.32 W m⁻¹ K⁻¹, yielding maximum dimensionless figures of merit (ZT) of 0.68 and 0.70 at 1200 K. Thermodynamic results confirm that the Debye temperature increases with pressure while heat capacity decreases, ensuring stability at elevated conditions. Overall, the synergistic combination of electronic tunability, optical responsiveness, and favorable thermoelectric performance highlights PtTiZ (Z = Ge, Pb) as promising candidates for high-temperature thermoelectric and ultraviolet-optoelectronic applications.