We hereby discuss the structural stability of Fe$_2$CrSb via energetic considerations, phonon dynamics and mechanical aspects. Later, the electronic, magnetic and thermoelectric properties are discussed in order to reach out the possible explanations of the observed half-metallic bandgap and other physical properties. Phonon dispersion of Fe$_2$CrSb with positive-only frequencies accompanied by the observed elastic parameters indicate the dynamic stability and mechaneablity of this alloy. The relaxed and optimized structural calculations predict the ferromagnetic Cu$_2$MnAl-type L$_{21}$ phase as the stable one. This compound has a half-metallic ferromagnetic character with an integer magnetic moment of 3 ${\mu}$B, which is in good agreement with the Slater–Pauling (SP) rule. Finally, we have pronounced the thermoelectric performance against the temperature range of 50–800 K using Boltzman transport theory. The room temperature Figure of merit (0.54) reaches to maximum of 0.67 at 800 K, indicating that Fe$_2$CrSb can work at low as well as high temperature thermoelectric devices operations.

Researchers have looked into quaternary Heusler (QH) compounds for their potential use in futuristic gadgets like photovoltaic cells, optical fibres, thermoelectric modules and spintronic sensors. As per such motivations and research interests, here we are presenting two recently reported Li-based QH compounds LiNbCoAl and LiNbCoGa which are stabilized into face-centred cubic structure of space group F-43m with semiconducting nature. These compounds exhibit high melting temperatures, showing the p-type semiconducting nature and are found to have advantageous thermoelectric capabilities in the high-temperature range. Additionally, the dynamical stability and appropriate elastic and mechanical characteristics for the foundation of effective thermoelectric modules in the temperature range of 1600 K enhance their scientific and technical scope. The electronic band structure is discussed along with the density of states for the betterunderstanding of the electrical properties. The thermodynamic response up to a temperature of 1600 K is also examined for understanding in terms of free energy, specific heat at constant volume and entropy. The special dependences in thetwo and three dimensions are applied and investigated to characterize the anisotropic nature. However all the required thermoelectric properties are calculated and presented, and the highest figure of merit value at 1600 K for both materials is 0.47 for LiNbCoAl and 0.56 for LiNbCoGa, respectively. As per their excellent practical properties, the current study asserts that both QH compounds should really be considered for energy conversion techniques in high-temperature environments. For the complete study prospectus, these materials are being disclosed for the first time here.