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Summary In the present work, we have used the first principles approach combined with semi classical Boltzmann Transport equations to calculate the structural, mechanical, electronic, and thermoelectric properties of LiTiCoX (X = Si, Ge). These materials are indirect band gap semiconductors with band gap 1.22 eV for LiTiCoSi and 1.09 eV for LiTiCoGe, respectively. Both materials are mechanically and dynamically stable. At room temperature, the value of Seebeck coefficient is 2016 μV/K (1799 μV/K) for LiTiCoSi (LiTiCoGe) and the electrical conductivity is in the order of 106 S/m for both materials. The highest value of figure of merit recorded is 0.14 (LiTiCoGe) and 0.10 (LiTiCoSi) for p‐type doping at 700 K temperature in both the materials. Hence, the theoretical results can be the compelling evidences to investigate the present materials experimentally in future.

The electronic, structural and thermoelectric properties of TiPdSn half Heusler material have been studied using density functional theory and semi classical Boltzmann transport theory. It has been found that TiPdSn is an indirect band gap semiconductor with band gap 0.48 eV. TiPdSn exhibits large power factor for p-type composition which is equal to 14.88 × 10 11 W/msK 2 at 700 K. The lattice thermal conductivity and relaxation time decrease with an increase in temperature. To analyze the stability of this compound, phonon properties like phonon dispersion, phonon density of states and heat capacity have been calculated. The maximum value of ZT , which is equal to 0.74, is attained at 500 K.

In the last few decades, the varieties of semiconductors have been explored for electronic and thermoelectric applications. As per such motivations, in present research work, the investigation of two quaternary Heuslers (QHs) i.e. LiHfCoGe and LiHfCoSn (having semiconducting nature) have been carried out for structural, electronic, vibrational, elastic, mechanical, thermodynamical and thermoelectric properties within the computational approach of Density Functional Theory (DFT) and Boltzmann transport equations. Both the alloys are enriched with p-type semiconducting nature along with the dynamical stability that crystallizes in FCC cubic structure of F-43m space group. The high Seebeck coefficient values are like of excellent fundamental thermoelectric character. The high melting points expose their scope in the high-temperature regions. Even the figure of merit (ZT) is of average range but better than many of the compounds of the same kind for the constant relaxation time approximations however all the thermoelectric properties are also measured and presented at the calculated relaxation time by deformation potential theory. The effect of spin orbit coupling is also studied on the thermoelectric properties. The practical utilization of the materials can be evaluated from the elastic and mechanical properties that are favorable to manufacturing efficient and reliable Thermoelectric Modules in high-temperature range. A sufficient discussion of thermodynamic properties is carried out to give an image of the internal lattice thermal vibrations. It is worth mentioning that the present research work has the standards to be discussed in experimental research areas of energy conversion techniques.

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