## 3 Results  
It is known that ceria and zirconia have a high melting temperature (2400 \({}^{\circ}\)C and \(\sim\)2700 \({}^{\circ}\)C, respectively), so a sintering temperature of 1500 \({}^{\circ}\)C is not sufficient to achieve full theoretical density [7]. For this reason, to increase the density of the final ceramics, sintering was performed for 5 h. The dependence of the measured apparent density and volumetric shrinkage on the weight fraction of ceria is shown in Figure 1. The calculated values of apparent density were between the theoretical density of monoclinic zirconia and ceria for x > 0.15 (Figure 1a). When x < 0.15, the apparent density was lower than both theoretical densities. It was also found out that values of volumetric shrinkage had a decreasing trend with increasing x (Figure 1b). To clarify these results and investigate the phase composition of the sintered ceramics, the XRD method was used. The comparison of the diffraction patterns for all the samples under investigation is shown in Figure 2a. It can be seen that the set of peaks varied significantly at low concentrations of ceria and high concentrations of zirconia. This is due to the m-phase formation in pure zirconia and c-phase formation in low-doped ceria. After analyzing the peaks, it can be concluded that there are only three possible phases in sintered ceramics. A cubic phase (space group Fm3m), tetragonal phase (space group P42/nmc), and monoclinic phase (space group P21/c) were the observed phases from the XRD patterns of the samples under investigation. For a more detailed demonstration of the observed phases, the XRD patterns of samples with x = 0.0, 0.2, 0.5, and 1.0 are shown in Figure 2b. The XRD quantitative and qualitative analyses were conducted using DiracEva 2.1 software (Bruker, Germany) with the help of a PDF crystallographic database, and the results of these analyses are shown in Table 1. The calculation of the lattice parameters was performed using DiracEva 2.1 and the most suitable PDF card and manually fitting the Bragg peaks positions to the experimental ones. The lattice parameter calculated for the cubic phase of the doped ceria oxide decreased with a decrease in the CeO\({}_{2}\) concentration in the initial charge. When the concentration of x reached 0.6, a significant amount of tetragonal zirconia oxide was formed. Another interesting observation that can be pointed out is the dependence of the sample porosity and tetragonal phase concentration on the x value. The phase composition was obtained by the corundum number method using DifracEva 2.1 and corundum numbers from the PDF cards. The porosity can be estimated with the formula \(\mathrm{P}=(1-\rho_{\mathrm{app}}/\rho_{\mathrm{XRD}})\)-100%, where \(\rho_{\mathrm{app}}\) is the apparent density and \(\rho_{\mathrm{XRD}}\) is the X-ray density. The XRD densities were calculated as a weighted mean value between all constituted phases according to the formula \(\rho_{\mathrm{XRD}}=\rho_{1}\cdot c_{1}+\rho_{2}\cdot c_{2}+\ldots\rho_{n} \cdot c_{n}\). As can be seen from Figure 3, with an increasing amount of tetragonal phase, the was porosity reduced from \(\sim\)20% to 2.5%. Despite the obtained results, further investigation of the ceramics' microstructure and grain morphology should be conducted to clarify the mechanisms of densification in the obtained samples. Figure 1: The dependence of apparent density (**a**) and volumetric shrinkage of sintered samples (**b**). Figure 2: The comparison of XRD patterns of all samples (**a**) and detailed demonstration of observed phases on the XRD patterns of some characteristic samples (**b**). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**x** & **Phase** & **Structure** & **Lattice Parameters** \\ \hline
0.00 & ZrO\({}_{2}\) & P21/c (14) monoclinic & \begin{tabular}{c} a\({}_{\text{m}}\) = 5.14082 \\ b\({}_{\text{m}}\) = 5.21282 \\ c\({}_{\text{m}}\) = 5.31783 \\ \end{tabular}  \\ \hline
0.05 & (Zr\({}_{0.98}\)Ce\({}_{0.02}\))O\({}_{2}\) & P21/c (14) monoclinic &