## 3 Results and Discussion
### Praseodymium Oxidation State  
Figure 6A illustrates the variations of the average oxidation state of praseodymium cations in selected Pr-substituted 5 YSZ samples on temperature cycling in air estimated from the thermogravimetric data. As praseodymium is the only variable-valence cation in the prepared materials, the absolute values of oxygen content in the samples and Pr oxidation state were calculated from the thermogravimetric data on reduction in 10%H\({}_{2}\)-N\({}_{2}\) flow (Figure 6B) assuming the nominal overall cation composition and that all praseodymium cations in the reduced samples are in 3+ state:  
\[\text{Zr}_{1-x-y}\text{Y}_{x}\text{Pr}_{y-z}^{3+}\text{Pr}_{z}^{4+}\text{O}_{ 2-0.5(x+y)+0.5z}+0.5z\text{H}_{2}\to\text{Zr}_{1-x-y}\text{Y}_{x}\text{Pr}_{ y}^{3+}\text{O}_{2-0.5(x+y)}+0.5z\text{H}_{2}\text{O}\uparrow. \tag{6}\]  
Thus, the change of the mass on reduction was assigned to the oxygen release from the oxide sample associated with the Pr\({}^{4+}\rightarrow\) Pr\({}^{3+}\) reduction allowing the calculation of the average oxidation state of the praseodymium cations and the fraction of Pr\({}^{4+}\) in the oxidized samples.  
The results indicate that Pr\({}^{3+}\) prevails in the studied materials; the estimated fraction of Pr\({}^{4+}\) at 600-1000 \({}^{\circ}\)C is 1.3-2.1% with respect to the total praseodymium content. Furthermore, the average praseodymium valence shows a very weak temperature dependence in air. This differs from the binary praseodymium oxide where the average oxidation state of praseodymium in air varies between approximately 3.66+ below 300 \({}^{\circ}\)C and 3.42+  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Sample** & \(\mathbf{\rho_{\text{exp}}}\)**, **g/cm\({}^{3}\)** & \(\mathbf{\rho_{\text{exp}}}\)**/\(\mathbf{\rho_{\text{theor}}}\)**, \%** & \(\mathbf{a_{\text{F}}}\)**, Å** & **A**\({}_{\text{2222P}}\)**/A\({}_{(III)\text{F}}\)** & \(\mathbf{\sigma_{700}}\)**, **S/m** & **E\({}_{\text{A}}\)**, **eV** \\ \hline P05-1450-1 & 5.58 & & 5.1400 & 0.040 & 0.684 & 1.01 \\ P10-1450-4 & 5.37 & & 5.1505 & 0.059 & 0.483 & 1.07 \\ P15-1450-9 & 5.16 & & 5.1613 & 0.122 & 0.302 & 1.08 \\ P10-1500-1 & 5.34 & & 5.1512 & 0.058 & 0.469 & 1.06 \\ P15-1500-4 & 5.13 & & 5.1503 & 0.056 & 0.299 & 1.09 \\ P05-1500-9 & 5.52 & 91 & 5.1487 & 0.000 & 0.719 & 1.04 \\ P15-1550-1 & 5.05 & & 5.1593 & 0.083 & 0.276 & 1.07 \\ P05-1550-4 & 5.53 & 91 & 5.1460 & 0.000 & 0.426 & 1.07 \\ P10-1550-9 & 5.35 & 88 & 5.1623 & 0.000 & 0.473 & 1.13 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Density, lattice parameter of the main fluorite phase, pyrochlore-to-fluorite peak area ratio, conductivity at 700 \({}^{\circ}\)C, and activation energy for electrical conductivity.  
at 1000 \({}^{\circ}\)C [17; 18], and from Mn-substituted 5 YSZ where manganese valence changes reversibly from \(\sim\)2.9+ at T \(\leq\) 300 \({}^{\circ}\)C to (2.50-2.56)+ at 1000 \({}^{\circ}\)C in air [15]. On the other hand, the obtained results are in agreement with the literature reports suggesting the prevailing trivalent state of praseodymium cations in zirconia-rich (ZrO\({}_{2}\))\({}_{1\text{-}x}\)(PrO\({}_{y}\))\({}_{x}\) ceramics [24; 29] and Pr\({}_{2}\)Zr\({}_{2}\)O\({}_{7}\)-based pyrochlores [45] sintered at high temperatures.