Predicted low Lattice Thermal Conductivity, high Thermoelectric Figure of Merit, and Mechanical and Dynamical Stability of HfPdSn half-Heusler compound

As part of this theoretical investigation, the structural, electronic, elastic, thermodynamic, and thermoelectric aspects of the HfPdSn half-Heusler compound were explored using density functional theory (DFT). To refine the description of these electronic properties, two treatments were applied: the GGA-PBE approximation and the modified Becke-Johnson potential (TB-mBJ), known for improving the accuracy of band gaps in semiconductors. The results obtained show that the compound is mechanically and dynamically stable, as proven by elastic and phononic calculations, suggesting its experimental feasibility. The electronic analysis reveals an indirect band gap semiconductor character, whose value varies depending on the method used: approximately 0.396 eV with GGA-PBE and 0.383 eV with TB-mBJ. The thermodynamic properties show an evolution consistent with statistical theory: the vibrational energy increases with temperature, while the free energy becomes more negative due to increasing entropy. Entropy saturates at high temperatures, and the heat capacity follows Debye’s law before reaching the Dulong-Petit limit. These trends indicate the predicted vibrational stability of the material and its potential thermoelectric performance, based on our computational analysis. In addition, the thermoelectric properties were studied within the framework of Boltzmann’s semi-classical transport theory, applying the constant relaxation time approximation. Key parameters such as the Seebeck coefficient, normalized electrical conductivity, electronic thermal conductivity and ZT figure of merit were calculated. At 300 K, the lattice thermal conductivity remains low (≈2.214 W·m −1 ·K −1 ), in good agreement with several values in the literature, confirming its thermal stability. This agreement also extends to the ultra-low range between 0.4 and 1.8 Wm −1 K −1 , confirming the consistency and reliability of the result obtained. At temperatures above 500 K, analysis of the ZT figure of merit reveals an almost exponential increase up to approximately 800 K, where ZT reaches a maximum of 0.68, reflecting a joint improvement in electrical conductivity and Seebeck coefficient, as well as a possible relative decrease in thermal conductivity. Overall, the results suggest that the HfPdSn compound could have significant thermoelectric potential, particularly for intermediate to high temperature heat recovery applications, with model-predicted performance comparable to some well-known reference materials such as Bi 2 Te 3 .