Exploring the possibility of enhancing the figure-of-merit ( $>$ 2) of Na$_{0.74}$CoO$_{2}$: A combined experimental and theoretical study

Search of new thermoelectric (TE) materials with high \textit{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 (S) 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 value of thermal conductivity ($\kappa$) is $\sim$ 2.2 W/m-K at 300 K. In the temperature region $300-430$ K, the value of $\kappa$ increases up to $\sim$ 2.6 W/m-K and then decreases slowly till 620 K with the corresponding value of $\sim$ 2.4 W/m-K. We have also carried out the theoretical calculations and the best matching between experimental and calculated values of transport properties are observed in spin-polarized calculation within DFT+\textit{U} by chosen \textit{U} = 4 eV. The maximum calculated value of ZT is found to be $\sim$ 0.67 at 1200 K for p-type conduction. Our 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 $\sim$ 5.1$\times$10$^{20}$ cm$^{-3}$ is expected to give rise the high ZT value of $\sim$ 2.7 at 1200 K. Using these temperature-dependent ZT values, we have calculated the maximum possible values of efficiency ($\eta$) of thermoelectric generator (TEG) made by p and n-type Na$_{0.74}$CoO$_{2}$. The present study suggests that one can get the efficiency of a TE cell as high as $\sim$ 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.