## 3 Results
\begin{tabular}{c} (Ce\({}_{0.4}\)Zr\({}_{0.6}\))O\({}_{2}\) \\ (Zr\({}_{0.88}\)Ce\({}_{0.12}\))O\({}_{2}\) \\ \end{tabular}  & \ \begin{tabular}{c} Fm-3m (225) cubic-P42/nmc \\ (137) tetragonal \\ \end{tabular}  & \begin{tabular}{c} a\({}_{\text{c}}\) = 5.31842 \\ c\({}_{\text{t}}\) = 5.32258 \\ \end{tabular}  \\ \hline
0.85 & \begin{tabular}{c} Ce\({}_{0.69}\)Zr\({}_{0.31}\)O\({}_{2}\) \\ \end{tabular}  & \ \begin{tabular}{c} Fm-3m (225) cubic \\ \end{tabular}  & \begin{tabular}{c} a\({}_{\text{c}}\) = 5.34311 \\ \end{tabular}  \\ \hlineTo justify the interpretation of the XRD pattern analysis, Raman spectroscopy was carried out for all samples. In Figure 4, the Raman spectra of the obtained ceramics are shown. For the undoped CeO\({}_{2}\), the most pronounced peak at 470 cm\({}^{-1}\) corresponds to the triply degenerate optical phonon mode F\({}_{2\text{g}}\). This mode is characteristic of cubic fluorite structures with the space group Fm3m [20]. With a decrease in x from 1.0 to 0.9, a wide peak at 600 cm\({}^{-1}\) occurred, showing the D\({}_{2}\) band which is indicates defects [21]. The D1 band is associated with defect species like an oxygen vacancy, which disrupts the Oh symmetry, while the D2 band corresponds to MO\({}_{8}\)-type defect species with Oh symmetry, including a dopant cation without any oxygen vacancy. There was another decreasing peak at 130 cm\({}^{-1}\), which was also connected with crystal defects in the CeO\({}_{2}\)-ZrO\({}_{2}\) system [12]. The Raman spectra of samples with x = 0.6 showed tetragonal zirconia peaks, which is in good agreement with the XRD data. In the range of concentration x from 0.4 to 0.15, pronounced peaks of the tetragonal phase can be clearly observed. Two peaks at 140 and 315 cm\({}^{-1}\) and three peaks at 244, 455, and 631 cm\({}^{-1}\) related to the B\({}_{\text{lg}}\) mode and E\({}_{\text{g}}\) mode, respectively, were considered the main evidence of tetragonal phase formation in the sintered ceramics [22]. For the samples with x = 0.15, 0.10, 0.05, and 0.00, their Raman spectra showed 13 active modes including 7 A\({}_{\text{g}}\) (peaks positions 177, 189, 304, 346, 474, 558, 634 cm\({}^{-1}\)) and 6 B\({}_{\text{g}}\) (peak positions 220, 332, 381, 505, 534, 614 cm\({}^{-1}\)). All these modes belong to the monoclinic phase of ZrO\({}_{2}\)[23]. Figure 4: The Raman spectra of the obtained CeO\({}_{2}\)-ZrO\({}_{2}\) ceramic samples, sintered at 1500 °C with concentrations of CeO\({}_{2}\) of (**a**) x = 0.5–1.0; (**b**) x = 0.0–0.5. Red reference line refers to CeO\({}_{2}\) vibration mode, while gray reference lines refer to ZrO\({}_{2}\) modes. Figure 3: The dependence of porosity (**a**) and phase composition (**b**) on content of CeO\({}_{2}\). SEM images of the cross-section of the most representative sample are showed in Figure 5. In Figure 5a, a cross-section of the pure zirconia ceramics is shown. Crack formation is associated with the transition t \(\rightarrow\) m during cooling after the sintering process is over [7]. These features greatly reduce the density and mechanical properties of ceramics and increase porosity (Figures 1a and 3a). FSZ ceramics were obtained at concentrations of x = 0.20 and 0.25 with a fine grain size distribution (Figure 5b). The coexistence of two types of grains (feather-like and polygonal grains) in mixed-phase ceramics is illustrated in Figure 5c,d. The EDX spectra collected from all the samples showed that the fracture surface only consisted of Ce, Zr, and O atoms, and the concentrations of zirconium and cerium were generally proportional to the composition of the initial oxide mixture. To demonstrate this, the EDX spectra of some compositions are shown in Figure 6. The elemental composition of the synthesized ceramics is shown in Table 2. From Figure 6 and Table 2, it can be seen that in Ce-rich ceramics, the atomic concentration of Ce was higher than the atomic concentration of Zr, and vice versa.