## 3 Results and Discussion
### Electrical Conductivity in Air  
Electrical studies were done using bar-shaped ceramics samples. Impedance spectroscopy of these samples revealed only two contributions in the frequency range 20 Hz-1 MHz: high-frequency (HF) semicircle attributed to the bulk properties of the sample, and a low-frequency (LF) contribution assigned to the electrode process. The spectra were fitted using a simple (R\({}_{\text{HF}}\) \(\mid\) CPE\({}_{\text{HF}}\))(R\({}_{\text{LF}}\) \(\mid\) CPE\({}_{\text{LF}}\)) equivalent circuit (where R is the resistance and CPE is the constant phase element [46]) to extract the total ohmic resistance R\({}_{\text{HF}}\) of the sample. The calculated specific capacitance for the HF and LF contributions was on the order of \(\sim\)10\({}^{-10}\) F/cm and \(\sim\)10\({}^{-4}\) F/cm, respectively. No grain boundary or secondary phase contributions could be detected and extracted from the impedance spectroscopy data for this sample geometry even at temperatures around 500 \({}^{\circ}\)C (Figure 7). The data on the electrical conductivity of Pr-substituted 5 YSZ are summarized in Figure 8 and Table 3. The conductivity exhibit nearly linear behavior in Arrhenius coordinates, _ln\(\sigma\)T-1/T_, similar to yttria-stabilized zirconia electrolytes. The conductivity of prepared  
Figure 6: (**A**) Temperature dependence of average oxidation state of praseodymium cations in air estimated from the thermogravimetric data; (**B**) relative weight change of powdered P10-1550-9 sample in one ox \(\rightarrow\) red \(\rightarrow\) ox cycle at 900 \({}^{\circ}\)C. Shadowed areas in (**B**) correspond to the flushing of the system with inert gas between oxidizing and reducing atmospheres. Figure 7: Examples of impedance spectra of Pr-substituted 5 YSZ ceramics at 500 \({}^{\circ}\)C in air. cearamics varies in the range 2.0-4.1 S/m at 900 \({}^{\circ}\)C and 0.28-0.68 S/m at 700 \({}^{\circ}\)C and is lower compared to dense 8 YSZ ceramics. The activation energy for electrical conductivity at 500-1050 \({}^{\circ}\)C for all the samples varies in a narrow range of 1.0-1.1 eV (Table 3). The measurements of oxygen ion transference numbers of selected samples by the modified EMF technique demonstrated that these materials are predominantly oxygen ionic conductors under oxidizing conditions close to atmospheric oxygen pressure (Table 4). The contribution of electronic conductivity, estimated as \(\sigma_{\rm e}=\sigma(1-\overline{\rm{t_{O}}})\), to the total conductivity at 700-900 \({}^{\circ}\)C increases with increasing praseodymium content from 0.3-0.4% for P05-1500-9 to 0.9-1.9% for P15-1500-4 at p(O\({}_{2}\)) = 0.21-1.00 atm. A minor increase in the electronic contribution can be attributed to the introduction of \(p\)-type electronic transport with an increasing concentration of Pr cations in the zirconia lattice [23,24] and/or to the presence of a non-negligible fraction of the pyrochlore-type phase in the latter sample. Stoichiometric Pr\({}_{2}\)Zr\({}_{2}\)O\({}_{7}\) is known to be a mixed ionic-electronic conductor with prevailing \(p\)-type electronic conductivity under oxidizing conditions [45,47]. The total conductivity of Pr\({}_{2}\)Zr\({}_{2}\)O\({}_{7}\) at 700-1000 \({}^{\circ}\)C is 0.5-1.5 orders of magnitude lower compared to 8 YSZ and the studied Pr-substituted 5 YSZ ceramics (Figure 8A). Thus, the segregation of the pyrochlore-type phase has a negative impact on the total electrical conductivity of ceramic samples.