Exploring the possibility of enhancing the high figure-of-merit ( $>$ 2) of Na$_{0.74}$CoO$_{2}$ by using combined experimental and theoretical studies.

Search of new thermoelectric (TE) materials with high figure-of-merit (ZT) is always inspired the researcher in TE field. Here, we present a combined experimental and theoretical study of TE properties of Na$_{0.74}$CoO$_{2}$ compound in high temperature region. The experimental Seebeck coefficient is found to vary from 64 to 118 $\mu$V/K in the temperature range 300 - 620 K. The positive values of S are indicating the dominating p-type behaviour of the compound. The observed values of thermal conductivity ($\kappa$) are found to be 2.2 to 2.6 W/m-K. To understand the experimental transport properties, we have carried out the calculations using DFT and DFT+U. The best matching between experimental and calculated values are observed when the calculation is done by chosen U = 4 eV in DFT+U. Calculations predict the half-metallic ferromagnetic ground state of the compound. By taking calculated S and electrical conductivity along with experimental $\kappa$, we have optimized the ZT values up to 1200 K and the maximum value is found to be ~ 0.67 at 1200 K. Computational study suggests that the possibility of n-type behaviour of the compound which can lead to a large value of ZT at higher temperature region. Electron doping of 5.1$\times$10$^{20}$ cm$^{-3}$ is expected to give rise the high ZT value of ~ 2.7 at 1200 K. Using these temperature dependent ZT values, we have calculated the maximum possible values of efficiency of thermoelectric generator (TEG) made by p and n-type Na$_{0.74}$CoO$_{2}$. Present study suggests that one can get the efficiency of a TE cell as high as ~ 11% when the cold and hot end temperature are fixed at 300 K and 1200 K, respectively. Such high values of ZT and efficiency suggest that Na$_{0.74}$CoO$_{2}$ can be used as a potential candidate for high temperature TE applications.