## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**C\({}_{\mathbf{w}}\)** & **O Concentration, at.\%** & **Zr Concentration, at.\%** & **Ca Concentration, at.\%** \\ \hline
0.00 & 54.39 & 45.61 & - \\
0.05 & 54.85 & 43.97 & 1.17 \\
0.10 & 55.02 & 40.24 & 4.74 \\
0.15 & 58.78 & 34.83 & 6.39 \\
0.20 & 60.40 & 31.17 & 8.43 \\
0.25 & 58.46 & 28.07 & 13.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of surface chemical composition analysis using the EDX method. Figure 6: Elemental mapping of cross-sections of fabricated specimens. processes in the ceramics, unlike, for example, in ferrite ceramics like NiFe\({}_{2}\)O\({}_{4}\)[37; 38; 39; 40]. Generally, the dielectric properties of ceramics depend on electronic polarization, ionic polarization, relaxation, and resonance. Low-frequency relaxation in oxide ceramics with transition elements or ions of different valences can occur in accordance with [PERSON]'s theory, which considers ceramic to be a nonhomogeneous medium with intergranular boundaries and crystalline grains with different dielectric properties [17; 41]. In such a medium, there is a possibility of the Maxwell-Wagner polarization mechanism occurring between poorly conducting intergranular interfaces and well-conducting crystalline grains. This was not observed in the obtained samples, which suggests a small difference in the dielectric properties of the structural units of the synthesized zirconium ceramics (intergranular boundaries, grains, and pores). As will be shown later, the variation in the dielectric permittivity is related to the porosity of the samples and phase composition of the ceramics. Figure 7b illustrates the frequency dependence of the dielectric loss tan \(\delta\), which demonstrates how much of the energy of an electric sinusoidal wave is transferred to heat during the repolarization processes. Zirconia ceramics are considered to be high-Q dielectric materials for microwave application [42]. The low losses can be attributed to the presence of only losses associated with phonon vibrations in the crystal structure of high-density homogeneous ceramics, and these losses can reach values of 5\(\cdot\)10\({}^{-3}\) or even 6\(\cdot\)10\({}^{-4}\)[43]. If dielectric monocrystal or polycrystal (ceramics) is free from structural defects, impurities, porosity, and microcracks, only intrinsic loss mechanisms contribute to the value of tan \(\delta\). The measurement results show that the lowest losses in the larger region of the frequency spectrum were characterized by the sample without doping (0.0025-0.005). When C\({}_{\rm w}\) was increased to 0.05, the value of tan \(\delta\) increased by a factor of \(\sim\)3 in the low-frequency region and decreased rapidly with increasing frequency. This behavior can be attributed to the pronounced polydispersed grain size distribution in ceramics and the presence of a large percentage of small-sized grains. In this case, the surface fraction of atoms increases, which increases the number of unsaturated chemical bonds. These unsaturated bonds can be considered defects in the crystal lattice that can anchor electrical dipoles and interfere with the polarization process. For the other samples, the dielectric losses were 0.005-0.0075 in the investigated frequency range. It can be concluded that the main mechanisms of dielectric losses in the obtained ceramics are electronic polarization and ionic polarization. To determine the reasons for the change in the dielectric constant when the dopant concentration is increased, the following factors should be considered: the porosity of the ceramics, the phase composition, and the influence of the dopant element on polarizability. Figure 7: Frequency dependences of dielectric permittivity (**a**) and loss tangent (**b**) for the obtained ceramics. Determining the porosity of ceramics without using techniques that utilize gases or liquids requires knowledge of the density of the material.