We have performed a comprehensive demonstration of electrical, structural, dynamical, mechanical, thermodynamical and transport properties of Li based LiNbRhZ (Z= Al, Ga, and In) quaternary Heusler (QH) alloys utilising Density Functional Theory (DFT). Calculation of electronic properties via generalized gradient approximation (GGA) and Heyd-Scuseria-Ernzerhof (HSE06) hybrid method, disclose the semiconductor nature with indirect band gap. We found the bandgap calculated by HSE06 is close to experimental value as compared to GGA. Density of states (DOS) analysis shows that 4d states of Nb and Rh atoms contributed significantly to the valance and conduction band near Fermi energy. Absence of negative frequency in phonon dispersion curve shows the dynamical stability and the negative value of formation energy suggested the thermodynamic stability of these alloys. To confirm practical reliability, elastic and mechanical properties are calculated. The value of Pugh's ratio and Cauchy pressure ensures the ductile nature of studied alloys. We have calculated all thermoelectric (TE) parameters via Boltzmann Transport theory. The computed melting point of LiNbRhZ (Z = Al, Ga, and In) alloys are found to be 1911.69 ± 300 K, 1790.97 ± 300 K and 1788.42 ± 300 K respectively, which anticipate potential in high temperature thermoelectric devices. The role of lattice vibrations in total thermal conductivity is prominent only up to 300 K in all discussed alloys. The amazing thermoelectric characteristics of LiNbRhZ alloys render these quaternary Heusler alloys as possible thermoelectric materials in high temperatures.
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