Mn-activated ZrO$_2$ nanocrystal was successfully synthesized using the chemical co-precipitation technique. Nanocrystals have been widely studied in terms of their structural and optical aspects. X-ray diffraction (XRD) analysis confirmed the formation of monoclinic and tetragonal phases in pure and Mn-doped ZrO$_2$ nanocrystals. The unit cell structure of m-ZrO$_2$ and t-ZrO$_2$ has been modelled using the Rietveld refinement crystallographic data. A photoluminescence (PL) study revealed emission intensity peaks at 378 nm for pure ZrO$_2$ and 380 nm for Mn-doped ZrO$_2$ nanocrystal under 280 nm excitation. A significant red shift was observed in Mn-doped ZrO$_2$ nanocrystal due to the oxygen vacancy. The incorporation of Mn to ZrO$_2$ nanocrystals reduced the optical band gap from 5.07 to 2.02 eV. The morphological analysis revealed that the typical particle sizes were in the nanoscale range, with 38 nm for pure ZrO$_2$ and 70 nm for Mn-doped ZrO$_2$ nanocrystals.

Herein, we employed the sol–gel technique to synthesize Cu$_2$O-based nanocrystals with Co and Na doping and co-doping, respectively. A correlation was established among several characterizations of cuprous oxide-based nanocrystals to observe their feasibility in the field of energy materials. Raman spectra typically show the formation of Cu$_2$O, whereas, in the case of Na co-doping, it exhibits the partial presence of CuO. This form of the results prompts the conductivity of nanocrystal samples to be enhanced. According to the current–voltage measurement, the current response slightly increases as doping and co-doping concentrations rise, in which Na5% co-doped Cu$_2$O:Co shows the optimum. Photoluminescence (PL) lifetime measurement shows increases in relative PL lifetime intensity caused by Na doping, which may be attributed to oxygen vacancies. Moreover, it is observed from the cyclic voltammetry (CV) profile that the Na and Co-doped concentration significantly enhances energy storage capability. The electrode using Na5%Cu$_2$O:Co has shown capacitive retention of 69% after 500 GCD cycles @ 10 A g$^{–1}$. This indicates the practical applicability of these developed cuprous oxide-based nanocrystals as electrode materials for improved electrochemical property. Eventually, the charge–discharge was performed at different current densities, in which specific capacitance was consistent with the CV result.