## 3 Results and Discussion
### Analysis of the Impact of the Firing Conditions and Pr Content  
The results of the firing experiments designed using Taguchi planning to assess the impact of Pr additions and firing conditions on the density \(\rho_{\text{exp}}\), structural features (pyrochlore-to-fluorite peak area ratio A\({}_{(222)\text{P}}\)/A\({}_{(111)\text{F}}\), lattice parameter of the main fluorite phase \(a_{\text{F}}\)), and electrical properties (electrical conductivity at 700 \({}^{\circ}\)C and corresponding activation energy E\({}_{\text{A}}\)) of the 5 YSZ ceramics are summarized in Table 3.  
A preliminary examination of the changes in the density of the fired ceramics (Table 3) suggests a prevailing effect of Pr contents, and this is confirmed by the correlation matrix calculated with standard Microsoft Excel formulae (Table 5). This negative dependence on Pr contents is counterintuitive, taking into account the higher atomic mass of Pr relative to Zr and Y, and indicates a negative impact on sintering, which cannot be reversed by increasing the firing temperature. Note also the negative correlation between density and lattice parameter. In fact, the lattice parameter of the main fluorite phase increases with nominal Pr contents and also with firing conditions, as revealed by the correlation matrix (Table 5) and as expected for the incorporation of larger Pr\({}^{3+}\) cations into the fluorite YSZ lattice. The dependence of density on individual parameters is also demonstrated by averaging the results for every level, as shown in Figure 9A. This confirms the prevailing dependence on Pr contents, and that a poor signal-to-noise ratio prevents statistical relevance for dependence on other parameters. The relative contents of the pyrochlore phase also increase mainly with nominal Pr contents, as indicated by the area peak ratio A\({}_{(222)\text{P}}\)/A\({}_{(111)\text{F}}\) (Figure 9B). The opposite effects of firing temperature are probably due to kinetic limitations by the direct firing of precursor powder mixtures. As already mentioned, the actual contents of Pr are lower than expected for the onset of the pyrochlore phase in either binary ZrO\({}_{2}\)-Pr\({}_{2}\)O\({}_{3}\)[19; 20; 21; 22] or ternary ZrO\({}_{2}\)-Y\({}_{2}\)O\({}_{3}\)-Ln\({}_{2}\)O\({}_{3}\) (Ln = La, Nd, Sm) systems [36; 37; 38; 39; 40; 41; 42] under equilibrium conditions at elevated temperatures. The impact on the conductivity is mainly ascribed to the contents of Pr (Figure 9C), and this may be attributed to a combination of microstructural and structural changes, as revealed also by a positive correlation between conductivity and density (and therefore an inverse correlation between conductivity and porosity), and negative correlation with the lattice parameter of the main conducting phase (Table 5). The effects of activation energy are also consistent with structural changes, which combine the effects of nominal Pr contents and also the effects of firing temperature and firing time (Table 5), which contribute to an increase in the effective content of the  
Figure 9: Averaged results for the dependence of (**A**) density, (**B**) pyrochlore-to-fluorite peak area ratio and (**C**) electrical conductivity at 700 \({}^{\circ}\)C on the individual factors, with corresponding errors bars to emphasize the signal-to-noise ratio; (**D**–**F**) multivariate fitting vs. experimental results for the corresponding parameters using Equations (8) and (9). The fitting parameters are given in Table 6.  
Further confirmation for the dependence of density, structural features and properties on the nominal composition and the firing conditions were obtained by multivariate fitting. However, one performed the following transformation of these variables, as expected for the thermal activation of the sluggish microstructural or structural changes after direct firing.