## 4 Discussion  
The pronounced dependence of shrinkage on ceria content can be explained with phase transitions which occur in the ceramics during sintering. For samples with x = 0-0.15 (Figure 1), long cracks on the surface of tablets were observed, which indicated the high porosity of these ceramics. The possible reasons for the increasing volumetric shrinkage in high-content ZrO\({}_{2}\) ceramics are significant volume changes during the m \(\rightarrow\) t transition and low porosity [26]. As it was shown in Results section phase, transitions from monoclinic zirconia and cubic ceria were analyzed by XRD and Raman spectroscopy (Figures 2 and 4). Both the XRD technique and Raman spectroscopy indicated the formation of FSZ ceramics with a tetragonal structure at x = 0.2 and 0.25. The range of PSZ zirconia formation also was observed. The main feature of the measured XRD patterns was the shift of peaks in the cubic phase to higher 20 angles with decreasing x values. This feature indicates a decreasing interplanar distance in the cubic crystal lattice and, consequently, a decreasing lattice parameter. The decreasing of the lattice parameter occurs due to the difference between the Ce\({}^{4+}\) and Zr\({}^{4+}\) ionic radii (0.97 A vs. 0.84 A, respectively). When smaller Zr\({}^{4+}\) cations substitute for Ce\({}^{4+}\), the cubic lattice retains its structure but the interplanar distances are reduced, forming a substitutional solid solution. The occurrence of tetragonal phases in the sintered ceramics indicates the limit of substitution and the formation of two-phased c + t ceramics. The completion of a solid-phase chemical reaction depends on mixture homogeneity, particle size, and the sintering conditions. From a technological point of view, it is very important to achieve certain parameters after sintering which sometimes do not require ideal homogeneity or completion of solid-phase reactions between components. The relatively low temperature of sintering could be the reason for incomplete chemical reactions. This feature can be seen from the phase analysis which was conducted on the XRD patterns. The chemical compositions of the ceria-zirconia ceramics were significantly different from experimental ones. Nevertheless, considering the conditions used in this work, some interesting observations can be pointed out. According to the chemical formulas of phases in the PDF database, the solubility limit of Zr\({}^{4+}\) in the CeO\({}_{2}\) cubic lattice is 0.4-0.5. This limit occurred at a mass concentration of CeO\({}_{2}\) of 0.6. With further decreases in x, tetragonal phases (Zr\({}_{0.88}\)Ce\({}_{0.12}\))O\({}_{2}\) and (Zr\({}_{0.85}\)Ce\({}_{0.15}\))O\({}_{2}\) were formed, and for x = 0.25 and 0.2, pure tetragonal zirconia phases were observed. Another thing that can be pointed out from Table 1 is that for tetragonal phases in mixed-phase ceramics, no significant change in lattice parameters was found. It can be concluded that with a decline in the value of x, different processes and mechanisms of phase formation can be distinguished. The first one was the substitution in cubic ceria of Ce\({}^{4+}\) with Zr\({}^{4+}\), which stopped after reaching the solubility limit when x reached 0.6. Then, the formation of mixed two-phased ceramics (c + t) with increasing concentrations of tetragonal phase can be observed. In this case, the mechanisms of phase substitution of CeO\({}_{2}\) with zirconium and substitution of ZrO\({}_{2}\) with cerium come into play. Increasing the amount of zirconia did not lead to further substitution in the tetragonal lattice, but to an increase in the t-phase amount. Another explanation is, as was mentioned before, pure tetragonal zirconia formation at x = 0.25 and 0.20 (Figure 3b). In the final process, substituted monoclinic zirconia was formed. All these processes have been well studied, but some explanation needs to be given.