## 5 Conclusions  
A complex study was performed to investigate the phase composition, and structural, mechanical, and dielectric characteristics of (1\(-\)x)-ZrO2-x-CeO2 ceramics derived from micron-sized powders via solid-state synthesis. For the first time, significant changes in the dielectric properties with variations in the composition of the zirconia-ceria system were observed. The analysis of the phase composition of the sintered samples using the XRD and Raman spectroscopy methods made it possible to clarify the known phase diagrams of the ZrO2-CeO2 system, namely, to determine the areas of formation of the pure tetragonal ZrO2-t phase and the ZrO2-t+ ZrO2-c mixture (predominance of the t-phase), as well as the region of formation of substitutional solid solutions with a fluorite crystal structure. Densitymeasurements and porosity evaluations of the resulting ceramics showed that porosity decreased with decreasing x values above x = 0.25, while density varied non-monotonically within the range of 5.6-6.2 g/cm\({}^{3}\). Below this concentration, a significant decrease in density, shrinkage, and an increase in porosity was observed due to the formation of cracks due to the martensitic transition t\(\rightarrow\)m upon cooling. During the study of scanning electron microscopy images, it was observed that the main feature of the morphology in the sintered ceramics with c + t phases was the presence of polygonal grains (t-phase) of a wide range of sizes and feathery grains (c-phase). Through microhardness measurements and analyses of the microstructure and phase composition, it was found that a significant increase in microhardness HV0.2 (from 600 to 1500) occurred in ceramics with a high t-phase content and an average grain size of \(\sim\)2-3 \(\upmu\)m. The dielectric measurements showed that the value of high frequency permittivity \(\epsilon^{*}\) increased with decreasing x from 17 to 36 due to the decrease in porosity and the formation of the tetragonal ZrO\({}_{2}\)-t phase. The dramatic decrease in the tangent loss values in doped ceria ceramics is explained by the complete solid-phase reactions and the presence of Ce\({}^{4+}\)/Ce\({}^{3+}\) cations. It was also found that ceramics with a predominance of the t-phase are high-quality dielectrics, while ceramics with a fluorite lattice exhibit high dielectric losses. The obtained results can be of great use in the field of design of advanced ceramics, especially in applications like refractories, dispersed nuclear fuels, or solid oxide fuel cells.  
Conceptualization, S.G.G., R.I.S., A.L.K., D.I.S. and D.B.B.; methodology, R.I.S., A.L.K., N.O.V., D.I.S. and S.G.G.; formal analysis, S.G.G., R.I.S., N.O.V., A.L.K., D.I.S. and D.B.B.; investigation, S.G.G., R.I.S., N.O.V., A.L.K., Y.A.G. and N.A.S.; resources, writing--original draft preparation, and writing--review and editing, S.G.G., R.I.S., N.O.V. and Y.A.G.; visualization, R.I.S., Y.A.G., N.O.V. and N.A.S.; supervision, A.L.K. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (AP19679979).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.