## 3 Results and Discussion  
The physical properties and structural characteristics of oxide ceramics are strongly dependent on their phase composition [25]. For this reason, the identification of the phase composition of the obtained samples via powder X-ray diffraction and Raman spectroscopy was conducted. The X-ray powder diffractograms for the synthesized ceramics are shown in Figure 1. Phase analysis showed the presence of three phases in the samples: ZrO\({}_{2}\)-m (zirconium oxide monoclinic cell, space group P21/c, COD 04-004-4339), ZrO\({}_{2}\)-c (zirconium oxide cubic cell, space group Fm-3m, COD 04-002-8314), and CaZrO\({}_{3}\) (calcium zirconate orthorhombic cell, space group Pcmn, PDF 00-035-0790). Quantitative analysis of the diffractograms was conducted via the Rietveld method using Profex 5.0.2 software [26]. The phase analysis revealed that the undoped ceramics had only the monoclinic ZrO\({}_{2}\)-m phase. With increasing dopant concentrations up to C\({}_{\rm w}\) = 0.05-0.15, two zirconium oxide phases were present in the ceramics: monoclinic ZrO\({}_{2}\)-m and cubic ZrO\({}_{2}\)-c. With a further increasein CaCO\({}_{3}\) concentration, no monoclinic phase was found and the phase composition was represented by the ZrO\({}_{2}\)-c phase together with the perovskite CaZrO\({}_{3}\) phase. The sintering of the ZrO\({}_{2}\)-m charge with a small amount of dopant containing Ca\({}^{2+}\) ions leads to the replacement of Zr\({}^{4+}\) ions by calcium and the formation of oxygen vacancies [27]. This substitution is the driving force for stabilizing the ZrO\({}_{2}\)-c phase and  
Figure 1: Powder diffractograms of the obtained samples. (**a**) pristine; (**b**) C\({}_{\rm w}\) = 0.05; (**c**) C\({}_{\rm w}\) = 0.10; (**d**) C\({}_{\rm w}\) = 0.15; (**e**) C\({}_{\rm w}\) = 0.20; (**f**) C\({}_{\rm w}\) = 0.25.  
suppressing the martensitic transition upon cooling to room temperature [28]. When the dopant concentration was increased to 0.20, the CaZrO\({}_{3}\) phase was formed. It can be argued that at a concentration of 0.20, the limit at which Ca\({}^{2+}\) ions can enter the crystal lattice of the ZrO\({}_{2}\)-c phase was reached. The formation of cubic-phase ZrO\({}_{2}\)-c with CaZrO\({}_{3}\) at concentrations of 0.20 and 0.25 agrees with the obtained phase diagrams for the CaO-ZrO\({}_{2}\) system [29; 30]. Despite using calcium carbonate as the initial reagent, the annealing process is presumed to cause the decomposition of CaCO\({}_{3}\)\(\rightarrow\) CaO + CO\({}_{2}\) (decomposition temperature ~1000 \({}^{\circ}\)C), followed by the reaction CaO + ZrO\({}_{2}\)\(\rightarrow\) CaZrO\({}_{3}\). As a result, the experimental data align well with the phase diagrams. The results of the calculated values of the lattice parameters for the measured diffractograms are given in Tables 1 and 2. The observed increase in the lattice parameter and volume in the cubic phase suggests that the incorporation of Ca\({}^{2+}\) ions, which have a larger ionic radius, into the ZrO\({}_{2}\)-m structure leads to two significant outcomes. Firstly, it induces the transition of the monoclinic phase into the cubic phase. Secondly, it causes the expansion of the cubic unit cell. In the case of the ZrO\({}_{2}\)-m phase, the unit cell volume decreases with increasing dopant concentration owing to the decrease in parameters a and b. The highest values of the unit cell volume and parameters a and b for the undoped sample can be attributed to the tensile stresses developed after cooling. To confirm this hypothesis, the Williamson-Hall method was applied to an undoped sample to determine the type of stress (compressive or tensile) from an analysis of the diffractogram peaks. [31]. The FWHM (Full Width at Half Maximum) and the peak center of the most prominent reflections were determined using Profex 5.0.2 software. Figure 2a shows that the approximation line has a positive slope, indicating tensile stresses.