## 3 Results and Discussions  
The phase characterization of composition BaLa\({}_{0.9}\)Pr\({}_{0.1}\)InO\({}_{4}\) was made using XRD analysis. Figure 1a represents the Le Bail refinement of the X-ray obtained data. The composition is single phase and it has orthorhombic symmetry (_Pbca_ space group). The image of the crystal structure of the monolayer perovskite is presented in the inset of Figure 1a. The introduction of Pr\({}^{3+}\) ions into the La\({}^{3+}\) sublattice (isovalent doping) leads to the expansion of the crystal lattice (Table 1). An increase in the size of the unit cell is observed during doping despite the close ionic radii of trivalent metals Pr\({}^{3+}\) and La\({}^{3+}\) (\(r_{\text{La}^{3+}}\) = 1.216 A, \(r_{\text{Pr}^{3+}}\) = 1.179 A [64]). The presence of ions with different electronegativity (\(\chi_{\text{La}}\) = 1.10, \(\chi_{\text{Pr}}\) = 1.13 [65]) could be the cause of the changes in the local structure and in the interatomic distances due to the additional repulsion effects. A similar effect was observed for another doped composition based on BaLaInO\({}_{4}\)[59; 60], and the presence of ions with different electronegativity in the same sublattice can be considered as the reason of the changes in the crystal lattice size. The morphology of the obtained sample was checked using scanning electron microscopy. Composition BaLa\({}_{0.9}\)Pr\({}_{0.1}\)InO\({}_{4}\) consists of grains (\(\sim\)3-5 \(\upmu\)m) agglomerated in the particles with the size \(\sim\)10 \(\upmu\)m (Figure 1b,c). The elemental composition was proved via EDS analysis. The average element ratios for BaLa\({}_{0.9}\)Pr\({}_{0.1}\)InO\({}_{4}\) composition are presented in Table 2. The good agreement between theoretical and experimental values was confirmed. The amount of water uptake was measured via thermogravimetry (TG) coupled with the differential scanning calorimetry (DSC) method. The results are presented in Figure 2. As we can see, the initially hydrated composition loses mass due to water release that was confirmed by MS-results. No other volatile components were detected. The main mass loss happens at \(\sim\) 200-400 \({}^{\circ}\)C, which is confirmed by the signal on the DSC-curve (green line in Figure 2). The dissociative water intercalation into the crystal structure of layered \begin{table}
\begin{tabular}{c c c c c} \hline
**Model** & **Barium** & **Lanthanum** & **Prasedymium** & **Indium** \\ \hline \multirow{2}{*}{Content} & 33.4 & 29.9 & 3.2 & 33.5 \\ \cline{2-5}  & (33.3) & (30.0) & (3.3) & (33.4) \\ \hline \end{tabular}
\end{table} 
Table 2: The results of the energy-dispersive analysis for the composition BaLa\({}_{0.9}\)Pr\({}_{0.1}\)InO\({}_{4}\) (theoretical values in atomic % are provided in the brackets). Figure 1: The results of the XRD—(**a**) (R\({}_{\rm p}\) = 2.11, R\({}_{\rm wp}\) = 2.25, \(\chi^{2}\) = 1.32) and SEM-investigations (**b**,**c**) for the composition BaLa\({}_{0.9}\)Pr\({}_{0.1}\)InO\({}_{4}\). perovskites is possible due to the placement of hydroxyl groups in the rock salt space of the layered framework [62]:  
\[\mathrm{H_{2}O+O_{o}^{x}\Leftrightarrow(OH)_{o}^{\bullet}+(OH)_{i}^{{}^{\prime}}} \tag{1}\]  
Consequently, the increasing of the crystal lattice size should lead to the increasing of the water uptake [62]. As we can see, the water uptake for the Pr-doped composition is about 1 mol water per formula unit (Figure 2), which is bigger than 0.62 mol registered for undoped BaLaInO4 composition [62]. In other words, a good correlation between the changes of the geometric characteristics of the unit cell and water uptake is observed. The electrotransport properties of the Pr-doped composition were investigated via the impedance spectroscopy method. Nyquist plots under dry and wet air at 400 \({}^{\circ}\)C are presented in Figure 3a as an example of collected data. The calculation of conductivity values was made using the resistance value obtained by extrapolating the high-frequency semicircle to the abscissa axis (capacitance \(\sim\)10\({}^{-12}\) F/cm).