## 3 Results and Discussion
### Morphological and Structural Properties
Furthermore, the calculated lattice constants match the reported values: for JCPDF 00-036-1451, \(a\) = 3.24972a = 3.24972 A and \(c\) = 5.2161c = 5.2161 A, while for JCPDF 00-037-1413, \(a\) = 5.04310a = 5.04310 A, \(b\) = 5.2020b = 5.2020 A, and \(c\) = 5.2640c = 5.2640 A, with axial ratios \(a/b\) = 0.9694a/b = 0.9694 and \(c/b\) = 1.0119c/b = 1.0119. The doped samples show well-defined crystallization diffractions, which agree ZnZrO\({}_{3}\) (cubic)-nanocomposites. The Mn-doped sample's 3% XRD measurement showed that the structure is a pure crystalline phase of cubic ZnZrO\({}_{3}\) nanocomposites. The annealed samples' patterns showed no peaks from impurities or residues, suggesting that the nanocomposites are purely crystalline. High crystallinity also promotes efficient energy transfer and minimizes scattering losses during the excitation and emission processes. The Mn dopant can substitute for Zn or Zr in the ZnZrO\({}_{3}\) lattice, modifying the electronic structure and creating suitable energy states for luminescence with average crystalline sizes of 28 nm and 24 nm in ZnZrO\({}_{3}\) and Mn (3%)-doped ZnZrO\({}_{3}\), respectively. Manganese ions can exist in multiple oxidation states depending on the doping concentration (e.g., Mn\({}^{2+}\) or Mn\({}^{4+}\)), each contributing differently to the emission properties. Mn\({}^{2+}\) ions are known for their strong green/red emissions due to the \({}^{4}\)T\({}_{1}\rightarrow{}^{6}\)A\({}_{1}\) transitions. In contrast, Mn\({}^{4+}\) ions exhibit deep-red emissions via \({}^{2}\)E \(\rightarrow{}^{4}\)A\({}_{2}\) transitions. Figure 3: XRD graphs for ZnZrO\({}_{3}\) at different levels of Mn doping. The average crystalline sizes predicated by the Debye-Sherrer equation for Mn-doped samples (3%) were found to be 28 and 24 nm, respectively (Equation (1)). XRD analyses of the samples (3% Mn-doped ZnZrO\({}_{3}\)) [33] were also conducted. \[D=\frac{k\lambda}{\beta\text{cos}\theta} \tag{1}\]  
\[\frac{1}{d^{2}}=\left[\frac{h^{2}+k^{2}+l^{2}}{a^{2}}\right] \tag{2}\]  
where \(k\) is the crystal width constant at (0.94), (_hkl_) are the Miller indices from the JCPDS reference files, \(\theta\) is the Bragg angle, \(\lambda\) is the X-ray wavelength, and \(\beta\) is the full width at half-maximum (FWHM). The photoluminescence (PL) spectra of (Figure 4) Mn-doped ZnZrO\({}_{3}\) nanoparticle nanocomposites, which extend from 350 to 900 nm, reveal key insights into their electronic and defect structures. The emission bands at approximately 500, 502, 604, and 612 nm correspond to green and red luminescence. The green emission at around 500-502 nm suggests the presence of defect-induced radiative transitions, which can be attributed to oxygen vacancies acting as electron-trapping sites that facilitate radiative recombination, producing green emissions. These vacancies generate defect states within the bandgap, enabling electron-hole pair recombination through mid-gap energy levels. Zinc and zirconium vacancies or interstitials also contribute to defect-related emissions. Defect states caused by Zn\({}^{2+}\) or Zr\({}^{4+}\) vacancies in the ZnZrO\({}_{3}\) lattice can introduce additional energy levels that participate in visible emissions. When ZnZrO\({}_{3}\) is doped with Mn ions, an emissions-band shift appears in the red region (604-612 nm). This red emission arises from the Mn\({}^{2+}\) ion substitution at either Zn\({}^{2+}\) or Zr\({}^{4+}\) sites. The introduction of Mn ions alters the electronic structure, leading to new radiative transitions.