## 3 Results and Discussions
The temperature dependencies of the conductivity obtained under dry (\(p\)H\({}_{2}\)O = 3.5\(\cdot\)10\({}^{-5}\) atm) and wet (\(p\)H\({}_{2}\)O = 2\(\cdot\)10\({}^{-2}\)) air (\(p\)O\({}_{2}\) = 0.21 atm) and Ar (\(p\)O\({}_{2}\) \(\sim\)10\({}^{-5}\) atm) are shown in Figure 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multirow{2}{*}{**a, b (Å)**} & \multirow{2}{*}{**c (Å)**} & \multirow{2}{*}{**Vcell (Å\({}^{3}\))**} & \multirow{2}{*}{**Water Uptake**} \\  & & & & \\ \hline
0 & 5.914(9) & 20.846(5) & 729.3365 & 0.17 \\
0.05 & 5.918(5) & 20.848(9) & 730.3086 & 0.16 \\
0.10 & 5.919(2) & 20.853(6) & 730.6461 & 0.17 \\
0.15 & 5.920(3) & 20.861(0) & 731.1770 & 0.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Lattice parameters, unit cell volume and water uptake for the solid solution BaLa\({}_{1.9-x}\)Sr\({}_{x}\)Gd\({}_{0.1}\)In\({}_{2}\)O\({}_{7-0.5x}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Composition**} & \multicolumn{4}{c}{**Content of Element, Atomic \%**} \\ \cline{2-5}  & **Ba** & **La** & **In** & **Sr** & **Gd** \\ \hline
1 & 20.2 (20.0) & 40.1 (40.0) & 39.7 (40.0) & - & - \\
2 & 20.1 (20.0) & 37.3 (37.0) & 39.8 (40.0) & 0.9 (1.0) & 1.9 (2.0) \\
3 & 20.3 (20.0) & 36.0 (36.0) & 39.8 (40.0) & 1.9 (2.0) & 2.0 (2.0) \\
4 & 20.2 (20.0) & 35.3 (35.0) & 39.7 (40.0) & 2.8 (3.0) & 2.0 (2.0) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The average element ratios determined by EDS analysis for the samples BaLa\({}_{2}\)In\({}_{2}\)O\({}_{7}\) (1), BaLa\({}_{1.85}\)Sr\({}_{0.05}\)Gd\({}_{0.1}\)In\({}_{2}\)O\({}_{6.975}\) (2), BaLa\({}_{1.8}\)Sr\({}_{0.1}\)Gd\({}_{0.1}\)In\({}_{2}\)O\({}_{6.95}\) (3), BaLa\({}_{1.75}\)Sr\({}_{0.15}\)Gd\({}_{0.1}\)In\({}_{2}\)O\({}_{6.925}\) (4) (theoretical values are given in the brackets). Figure 2: SEM (**a**) and EDX (**b**) results for the composition BaLa\({}_{1.8}\)Sr\({}_{0.1}\)Gd\({}_{0.1}\)In\({}_{2}\)O\({}_{6.95}\). Figure 3: The EIS plots for the composition BaLa\({}_{1.75}\)Sr\({}_{0.15}\)Gd\({}_{0.1}\)In\({}_{2}\)O\({}_{6.925}\) obtained at 390 \({}^{\circ}\)C, 410 \({}^{\circ}\)C and 430 \({}^{\circ}\)C in dry air (**a**) and at 410 \({}^{\circ}\)C in dry and wet air (**b**). As can be seen, the changes in atmospheric humidity (\(p\)H\({}_{2}\)O variation) and oxygen partial pressure do not affect the general shape and regularities of the conductivity values changes. The increase in the dopant concentration leads to the increase of the electrical conductivity values (Figure 5a). Figure 5b shows the concentration dependence of the conductivity in dry Ar, i.e., at lower oxygen partial pressure, where the conductivity nature is predominantly oxygen-ionic. The conductivity increases with increasing strontium content, which is explained by an increase in the concentration of oxygen vacancies:  
\[2\text{SrO}\xrightarrow{\text{La}_{2}\text{O}_{3}}2\text{Sr}^{\prime}_{\text{ La}}+2\text{O}^{\times}_{\text{o}}+\text{V}^{\bullet\bullet}_{\text{o}} \tag{1}\]  
where \(\text{Sr}^{\prime}_{\text{La}}\) is strontium ion in lanthanum sites; \(\text{V}^{\bullet\bullet}_{\text{o}}\) is the oxygen vacancy; \(\text{O}^{\times}_{\text{o}}\) is the oxygen atom in the regular position. The comparison of the oxygen-ionic conductivity of the solid solutions BaLa\({}_{1.9-x}\)Sr\({}_{x}\)Gd\({}_{0.1}\)In\({}_{2}\)O\({}_{7-0.5x}\), BaLa\({}_{2-x}\)Sr\({}_{x}\)In\({}_{2}\)O\({}_{7-0.5x}\) and BaLa\({}_{2-x}\)Gd\({}_{x}\)In\({}_{2}\)O\({}_{7}\) at 500 \({}^{\circ}\)C is shown in Figure 5c. As can be seen, the conductivity value for the co-doped composition BaLa\({}_{1.8}\)Sr\({}_{0.1}\)Gd\({}_{0.1}\)In\({}_{2}\)O\({}_{6.95}\) is higher than for the isovalent-doped composition BaLa\({}_{1.9}\)Gd\({}_{0.1}\)In\({}_{2}\)O\({}_{7}\) with the same gadolinium concentration. The reason for this is the higher concentration of ionic charge carriers (oxygen ions) due to the formation of oxygen vacancies during acceptor doping.