## 3 Results and Discussion
According to the effective medium theory, the dielectric constant of a heterogeneous medium is a function of the dielectric constant of the components and their concentrations [48]. Assuming that the dielectric constant of calcium zirconate is sufficiently high, an increase in its fraction can cause an increase in the dielectric constant despite the higher porosity of the synthesized ceramics. The dielectric permittivity of CaZrO\({}_{3}\) is estimated to be 23-32 in a number of studies [49; 50; 51], which is greater than that of highly doped Ca-substituted zirconia ceramics [52]. Figure 8b shows the results of the Vickers microhardness measurements. The sample with a concentration of C\({}_{\rm w}\) = 0.15 is characterized by high microhardness HV0.2 = 11.2 GPa, which is comparable to other data in the literature on zirconia ceramics [53; 54; 55]. The microhardness and dielectric constant of ceramics depend on the phase composition and porosity. The grain size can also be emphasized as an additional factor that can affect the microhardness. In large grains, the propagation of mechanical stresses through dislocations occurs over long distances. In the case of small grains, dislocations stop at intergranular boundaries, making defect formation more difficult [56]. In other words, when the proportion of intergranular boundaries is large, the probability of crossing already formed dislocations of different orientations and crystal lattice types, which are contained in neighboring grains, increases. In this case, anchor points are created to prevent the atomic planes from sliding relative to each other. The low microhardness of the undoped sample can be explained by the presence of tensile stresses and microcracks in the structure after annealing. With increasing dopant concentration, the microhardness increased owing to the decrease in porosity at C\({}_{\rm w}\) = 0.05 and the change in average grain size. For the samples with C\({}_{\rm w}\) = 0.10 and C\({}_{\rm w}\) = 0.15, a significant decrease in density and an increase in grain size were observed compared to the sample with the lowest dopant fraction. It is also worth noting that in the case of these samples, the highest concentration of the cubic phase (more than 90%) was observed. Specifically, for the sample with a dopant concentration of 0.10, the highest values of average grain size and the percentage of grains with a size greater than 12 um (8%) were observed. For the sample with C\({}_{\rm w}\) = 0.15, the distribution histograms show that the percentage of grains with sizes larger than 12 um decreased to \(\sim\)1%. It can be concluded that the increase in microhardness in the obtained ceramics in the range of weight concentrations of 0.05-0.15 CaCO\({}_{3}\) is associated with the stabilization of the cubic phase and a narrower distribution of grain sizes. As the dopant concentration increased, the microhardness decreased, which was directly related to the decrease in the apparent density and the presence of a large number of pores in the microstructure. The formation of the CaZrO\({}_{3}\) phase did not have a significant impact on the effective microhardness of the obtained samples because the microhardness values for ZrO\({}_{2}\) and calcium zirconate were approximately the same.