## 3 Results and Discussion
### Strength and Analysis of Fracture Surface  
A change in phase balance is obviously related to the material strength (Figure 7). The main regularities of a change in phase balance in relation to the material strength (Figures 6 and 7) were found as follows:  
* For the 3 YSZ ceramic, the strength is almost linearly related to the t-ZrO\({}_{2}\) phase fraction;
* For the 6 YSZ ceramic, there is no linear relationship between the strength of the material and phase fractions, as the fractions of both the cubic and monoclinic ZrO\({}_{2}\) phases are quite high. All the above results confirm a synergistic effect of yttria content, pore size distributions and their fractions, grain size distributions and corresponding area fractions, and phase balance on flexural strength. Therefore, a thorough analysis of these microstructural features allows to propose an appropriate fracture micromechanism. This, in turn, allowed improving the mechanical properties of the ceramics via the processing technology optimization. Based on SEM images of fracture surfaces for the 3 YSZ and 6 YSZ ceramics (Figure 8), the void size and cleavage facet size distributions have been analyzed. It was found that the patterns of the void size distributions vary with the yttria content. The 3 YSZ ceramic exhibited a decrease in fractions of voids in the 0.3-0.5 \(\upmu\)m, 0.7-0.9 \(\upmu\)m, and \(>\)0.9 \(\upmu\)m size ranges, with a simultaneous increase in the \(<\)0.3 \(\upmu\)m and 0.5-0.7 \(\upmu\)m size ranges (Figure 9a), with decreasing the sintering temperature. In contrast, the 6 YSZ ceramic showed a significant decrease in the fraction of voids in the \(<\)0.3 \(\upmu\)m range with a gradual  
Figure 6: Phase balance for 3 YSZ and 6 YSZ ceramics sintered at three temperatures. Notation: m is monoclinic, c is cubic, and t is tetragonal ZrO\({}_{2}\). increase in fractions of voids in all the other ranges (Figure 9b). Moreover, for this material, the most distinct difference in the fraction of voids, namely a decrease in the fraction of voids in the \(<\)0.3 \(\upmu\)m range by 2.8 times, was found with a decrease in sintering temperature from 1550 to 1500 \({}^{\circ}\)C. Such a distinct increase in the fraction of small voids at the sintering temperature of 1550 \({}^{\circ}\)C may be related, to a great extent, to plenty of small pores occurring under such conditions. The fracture void formation is believed to depend on the presence of pre-existing pores. In particular, both the Figure 2b and Table 1 confirm this assumption for the 6 YSZ ceramic sintered at 1550 \({}^{\circ}\)C. For such sintering conditions, the fraction of the smallest pores is maximal (i.e., 76%, see Figure 2b), the average pore size is minimal (i.e., 0.5 \(\upmu\)m, see Table 1), and the area fraction of pores is minimal (i.e., 0.5%, see Table 1). In contrast, the fractions of pores in the size range of 0.6-1.5 \(\upmu\)m and larger ones are minimal for these conditions. Figure 8: SEM-BSE fractography for (**a–c**) 3 YSZ and (**d–f**) 6 YSZ ceramics sintered at (**a,d**) 1550, (**b,e**) 1500, and (**c,f**) 1450 \({}^{\circ}\)C.  
Figure 7: Flexural strength of 3 YSZ and 6 YSZ ceramics sintered at three temperatures. In short summary, with a decrease in sintering temperature from 1550 through 1500 to 1450 \({}^{\circ}\)C:  
* The average size of fracture voids decreased by 67% in the 3 YSZ ceramic; however, it increased by 33% in the 6 YSZ material (Table 1);
* The void size distributions showed a decrease in the fraction of larger >0.7 \(\upmu\)m voids with decreasing sintering temperature in the 3 YSZ ceramic (Figure 9a); however, this fraction increased in 6 YSZ material (Figure 9b);
* The observed variations in fracture void size distributions does not fully align with the trend for the average void size. Therefore, the size distributions should always be used for the characterization of microstructure evolution in YSZ ceramics, instead of the average void size parameter.