## 3 Results and Discussion
### Behavior on Redox Cycling  
The exposure to reducing conditions is expected to induce the complete reduction in the fraction of Pr\({}^{4+}\) to Pr\({}^{3+}\) and, therefore, a lattice expansion caused by the difference in ionic radii of tetravalent and trivalent praseodymium. However, as discussed above, the fraction of Pr\({}^{4+}\) in the studied samples is low, \(\leq\)2% of the total praseodymium content. As a result, the transformation of the residual Pr\({}^{4+}\) to Pr\({}^{3+}\) on heating in a 10%H\({}_{2}\)-N\({}_{2}\) atmosphere has a negligible effect on the thermochemical expansion of Pr-substituted 5 YSZ ceramics (Figure 10B). This behavior is different from, for instance, Mn-substituted 5 YSZ ceramics where Mn\({}^{3+}\leftrightarrow\) Mn\({}^{2+}\) redox changes cause substantial dimensional variations on thermal cycling between reducing and oxidizing atmospheres [15].  
One should also note that the stabilization of the prevailing 3+ oxidation state of praseodymium cations under oxidizing conditions results in a low oxygen storage capacity. The estimations from the thermogravimetric data (Figure 6B) showed that the oxygen storage capacity of the samples P05-1500-9 and P10-1550-9 at 900 \({}^{\circ}\)C is limited to 2.0-2.5 umol/g on cycling between oxidizing and highly reducing conditions.  
The exposure to a reducing atmosphere results, however, in irreversible changes in electrical conductivity. Figure 11 illustrates the variations in the electrical conductivity of selected samples in a relatively short reduction-oxidation cycle at 900 \({}^{\circ}\)C. Switching from oxidizing to reducing conditions induces a slow decrease in the conductivity with time which cannot be attributed to a drop in partial \(p\)-type electronic conductivity. On returning back to atmospheric oxygen pressure, the level of conductivity is not recovered to the initial level, but remains stable with time.  
The changes in electrical conductivity in ox-red-ox cycles coincide with the thermogravimetric data for powdered samples in a similar cycle showing that the weight changes and, therefore, the Pr oxidation state was not fully reversible after re-oxidation at 900 \({}^{\circ}\)C (Figure 6B). In particular, the average oxidation state of Pr cations after one redox cycle  
Figure 11: Variations of electrical conductivity of selected Pr-substituted 5 YSZ samples in one ox \(\rightarrow\) red \(\rightarrow\) ox cycle at 900 \({}^{\circ}\)C.  
at 900 \({}^{\circ}\)C dropped irreversibly from 3.021+ to 3.016+ for P05-1500-9 and from 3.013+ to 3.008+ for P10-1550-9. Thus, the changes in electrical conductivity are interrelated with the changes in the oxidation state of praseodymium. At the same time, no structural alterations could be detected by XDR after short-term redox cycles at 900 \({}^{\circ}\)C. The variations in the calculated fluorite lattice parameters of P05-1500-9 and P10-1550-9 samples after either thermogravimetric or electrical studies were \(\leq\)0.015%.  
Note that the aging of conductivity (a slow decrease in ionic conductivity) with time at elevated temperatures, around 1000 \({}^{\circ}\)C, is known for yttria-stabilized zirconia [30; 50]. The proposed mechanisms responsible for aging include a continuous transformation to a lower conducting phase (i.e., cubic to tetragonal) and oxygen vacancy ordering processes. Most likely, similar phenomena are responsible for the conductivity changes in Pr-substituted 5 YSZ ceramics. In particular, according to the available phase diagrams [19; 20; 21], the thermodynamically equilibrium phase composition of the (ZrO2)1-x(PrOy)\({}_{x}\) system for \(x\) = 0.02-0.42 at 900 \({}^{\circ}\)C corresponds to a mixture of monoclinic ZrO2- and cubic Pr2 Zr2O7-based phases. Apparently, exposure to reducing conditions may facilitate the processes that cause a reduction in conductivity with time.