## 3 Results and Discussions
However, for the correct comparison, the total conductivity values must be divided into ionic and electronic contributions. To establish the nature of electrical transport in BaLa\({}_{2}\)In\({}_{2}\)O\({}_{7}\), the conductivity measurements vs. \(p\)O\({}_{2}\) were performed (Figure 5). As can be seen (Figure 5a), in the electrolytic area (\(p\)O\({}_{2}=10^{-16}\)-\(10^{-5}\) atm), the independence of conductivity values from \(p\)O\({}_{2}\) was observed. Thus, the oxygen-ionic conductivity dominates in this region. For layered structures, oxygen-ionic transport is usually described in terms of anti-Frenkel disordering:  
\[\mathrm{O}_{\mathrm{O}}^{\mathrm{V}}\Leftrightarrow\mathrm{V}_{\mathrm{o}}^{ \bullet\bullet}+\mathrm{O}_{\mathrm{i}}^{\prime\prime} \tag{1}\]  
where O\({}_{\mathrm{i}}^{\prime\prime}\) is the oxygen atom in the interstitial position; \(\mathrm{V}_{\mathrm{O}}^{\bullet\bullet}\) is the oxygen vacancy. The possibility of the formation of interstitial oxygen is provided by the existence of a rock-salt block and the possibility of increasing the coordination number of the cation that is located there. Accordingly, the formation of oxygen vacancies occurs in the perovskite block; the cation, octahedrally surrounded by oxygen, lowers the coordination number. That is, the presence of oxygen-deficient perovskite blocks plays an important role in the formation of oxygen-ion transport. Therefore, for such structures, it is possible to expect a significant oxygen-ionic conductivity without doping. Moreover, the measurements of the conductivity versus \(p\)O2 showed that the phases of BaLa2 In2O7 are stable over a wide range of \(p\)O2. The conductivity dependencies obtained in the dry oxidizing conditions (\(p\)O\({}_{2}=10^{-5}\)-0.21 atm) have a positive slope, which indicates the mixed ionic-electronic (hole) nature of conductivity:  
\[\frac{1}{2}\mathrm{O}_{2}\Leftrightarrow\mathrm{O}_{\mathrm{i}}^{\prime\prime} +2h^{\bullet} \tag{2}\]  
\[\mathrm{V}_{\mathrm{o}}^{\bullet\bullet}+\frac{1}{2}\mathrm{O}_{2} \Leftrightarrow\mathrm{O}_{\mathrm{O}}^{\mathrm{K}}+h^{\bullet} \tag{3}\]  
where O\({}_{\mathrm{i}}^{\prime\prime}\) is the oxygen atom in the interstitial position; \(\mathrm{V}_{\mathrm{O}}^{\bullet\bullet}\) is the oxygen vacancy; \(h^{\bullet}\) is the hole. Obviously, both of these processes can be realized in the structure. However, it is impossible to say which process prevails. For the layered composition based on BaNdInO\({}_{4}\), the calculations of formation energies of point defects were made [41]. The energy of processes described by Equation (3) is about 1.2 eV. However, the data for Equation (2) are missing. It should be noted that the conductivity values obtained in the dry Ar (blue symbols in the Figure 5) are the same as the conductivity values from the electrolytic area (black symbols in the Figure 5a). Therefore, in an _argon_ atmosphere, it is relatively easy to measure the temperature dependence of _oxygen-ionic_ conductivity in a wide temperature range. It was shown earlier, for the compositions based on BaLaInO\({}_{4}\), the conductivity values obtained under dry Ar corresponded to the oxygen-ionic conductivity values [45]. Based on this, the oxygen-ionic transport number \(t_{Q^{2}}\) can be calculated as: \begin{table}
\begin{tabular}{c c c c} \hline
**Element** & **Value (700 \({}^{\circ}\)C)** & **Value (600 \({}^{\circ}\)C)** & **Value (500 \({}^{\circ}\)C)** \\ \hline CPE1 & \(2.1\times 10^{-12}\) & \(2.4\times 10^{-12}\) & \(3.2\times 10^{-12}\) \\ R1 & 13 & 36 & 158 \\ CPE2 & \(4.1\times 10^{-10}\) & \(3.7\times 10^{-10}\) & \(2.1\times 10^{-10}\) \\ R2 & 2 & 8 & 33 \\ CPE3 & \(6.0\times 10^{-7}\) & \(5.6\times 10^{-7}\) & \(7.0\times 10^{-7}\) \\ R3 & 3 & 7 & 39 \\ \hline \end{tabular}
\end{table} 
Table 2: Results of Nyquist-plots fitting, where CPE is the constant phase element (F), and R is the resistance (k\(\Omega\)-cm).