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.

Crystal structure in conventional unit cell for Fe2TaZ (Z = Al, Ga, In) in Fm3̄m configuration.

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We study the dynamics of one-dimensional uniform lattice with the interatomic Born-Mayer potential. The travelling wave solutions such as solitons are analytically described. The wave propagation in the one-dimensional lattice where nearest neighbour atoms interact via the Born-Mayer potential is considered. The Born-Mayer lattice admits travelling wave type solutions represented by Jacobian elliptic functions and limiting form of such a wave solution is the localized pulse-like form called the solitary wave. This solitary wave has further remarkable properties under collision, leading to the concept of solitons in nonlinear discrete lattices which has been studied.