## 3 Results and Discussion
### Transport Properties
The activation energies will be discussed below in the analysis of partial conductivities. The difference in conductivity values in dry and wet temperatures is higher for Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\). At 350 \({}^{\circ}\)C, the difference in values of electric conductivity in dry and wet air for Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) is more than an order, whereas for Ba\(\gamma\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\), the difference is about 0.7 orders. This is connected to the higher values of proton concentration in Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\), which was shown by thermogravimetric measurements. For the determination of the partial conductivities and the type of dominant carriers, the conductivity was measured as a function of oxygen partial pressure. Figure 7 shows the oxygen partial pressure dependencies of electric conductivity in dry and wet atmospheres for Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) (Figure 7a) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) (Figure 7b). It is seen that in both cases the conductivity values decrease with decreasing oxygen partial pressure from 0.21 to 10\({}^{-4.5}\) atm. This shows the presence of some p-type conductivity contribution (\(\sigma_{h}\)). The behavior of the conductivity of the investigated compounds at this oxygen partial pressure range can be expressed as an oxygen incorporation process and the filling of structural vacancies:  
\[\mathbf{V}_{\mathbf{O}}^{\times}+\frac{1}{2}\mathrm{O}_{2}\rightleftharpoons 2h^{\bullet}+ \mathrm{O}_{V_{\mathbf{O}}^{\prime}}^{\prime}, \tag{2}\]  
where \(\mathbf{V}_{\mathbf{O}}^{\times}\) is a structural oxygen vacancy, \(h^{\bullet}\) is hole, and \(\mathrm{O}_{V_{\mathbf{O}}^{\prime}}^{\prime}\) is the oxygen atom in the structural oxygen vacancy position. With temperature decrease, the slope of the dependencies reduces, which means that the p-type conductivity contribution decreases. Therefore, Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) can be characterized as mixed hole-oxygen-ion conductors in dry air (0.21 atm). For the oxygen partial pressure range of 10\({}^{-18}\)-10\({}^{-4.5}\) atm, a plateau can be seen in the conductivity--\(p\)O\({}_{2}\) dependencies. Ionic defects dominate in this \(p\)O\({}_{2}\)- range, and the concentration of electron defects is negligible. Figure 7: Oxygen partial pressure dependence of total conductivity for Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) (**a**) [56] and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) (**b**) in dry (\(p\)H\({}_{2}\)O = 3.5 \(\times\) 10\({}^{-5}\) atm) and wet (\(p\)H\({}_{2}\)O = 1.92 \(\times\) 10\({}^{-2}\) atm) atmospheres; filled symbols are attributed to dry atmosphere, empty symbols are attributed to wet atmosphere. This plateau is characteristic of oxygen-ionic conductivity attributed with the intrinsic oxygen vacancies \(\mathbf{V}_{\mathbf{O}}^{\times}\) in the structure. The slopes of the log\(\sigma\)-log\(\
u\)O\({}_{2}\) dependencies in the wet atmosphere at \(p\)O\({}_{2}\)\(>\) 10\({}^{-4.5}\) atm are flatter than in comparison to the dry atmosphere, which indicates a decrease in the contribution of hole conductivity; at 500 \({}^{\circ}\)C, the conductivity is independent of \(p\)O\({}_{2}\), which confirms the dominant ionic nature of the conductivity over the whole investigated range of \(p\)O\({}_{2}\). It is seen that over the whole of oxygen partial pressure range for all of the investigated temperatures, the values of conductivity in the wet atmosphere are higher than in the dry atmosphere. The higher values of conductivity in the wet atmosphere can be explained by the contribution of proton conductivity. The difference in the conductivity values in dry and wet atmospheres increase with the reducing temperatures caused by the hydration process and the increase in proton concentration.