## 3 Results and Discussion
### Transport Properties
At 800 \({}^{\circ}\)C, the difference in the conductivity values is about 0.1 and 0.05 orders in air, and at the plateau region, the difference rises to 0.3 and 0.2 orders of magnitude for Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\), respectively. At 500 \({}^{\circ}\)C, the difference in the conductivity values for dry and wet atmospheres is about 0.3 and 0.2 orders, while at the plateau region, the difference is about 0.75 and 0.60 orders of magnitude for Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\), respectively. It can be said that in wet air (\(p\)O\({}_{2}\) = 0.21 atm), the investigated compounds demonstrate mixed proton-hole conductivity; with decreasing temperature, the contribution of proton conductivity rises, and at the temperatures below 500 \({}^{\circ}\)C, Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) exhibit dominant proton conductivity. The comparison of the dependencies of conductivity as a function of \(p\)O\({}_{2}\) for Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) in dry and wet atmospheres is shown in Figure 8. In general, the view of the dependencies for these compounds is similar. As mentioned above, Ba\({}_{5}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) at high temperatures exhibits higher values of conductivity than Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\). Thus at 500 \({}^{\circ}\)C, the conductivity values of Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) are higher for the whole investigated oxygen partial pressure range. In wet air, the difference in conductivity values for Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) are insignificant due to the lower proton concentration in hydrated Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\), and, therefore, the lower contribution of proton conductivity. In addition, Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) exhibits a higher positive slope of conductivity dependence in both dry and wet atmospheres at the oxygen partial pressure range of 10\({}^{-4.5}\)-0.21 atm than Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\), which indicates the higher contribution of hole conductivity to the total conductivity value. According to the data on oxygen partial pressure conductivity dependence, the partial conductivities \(\sigma_{i}\) were calculated in air (\(p\)O\({}_{2}\) = 0.21 atm). Oxygen-ion conductivity \(\sigma_{\rm O^{2}}\) was  
Figure 8: The comparison of oxygen partial pressure dependencies of total conductivity for Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\)[56] and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) 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 at 500 \({}^{\circ}\)C.  
determined as conductivity at the plateau of the dry atmosphere (\(\sigma_{\rm O^{2}}\)= \(\sigma_{\rm plateau}^{\rm dry}\)); the hole conductivity \(\sigma_{h}\) values were obtained by subtracting the oxygen-ion conductivity from the total conductivity in air (\(\sigma_{\rm h}^{\rm dry}\) = \(\sigma_{\rm 0.21 atm}^{\rm dry}\)-\(\sigma_{\rm O^{2}}\)). The values of proton conductivity \(\sigma_{\rm H^{+}}\) were defined by the subtraction of ion conductivity in dry atmosphere (plateau region) from ion conductivity in wet atmosphere (plateau region) (\(\sigma_{\rm H^{+}}=\sigma_{\rm plateau}^{\rm wet}\)-\(\sigma_{\rm plateau}^{\rm dry}\)) with the assumption that the oxygen-ion conductivity is independent of the concentration of protons. The hole conductivity values \(\sigma_{h}\) in the wet atmosphere were defined as the difference of the total conductivity value at oxygen pressure 0.21 atm and of the value of oxygen-ion and proton conductivities (\(\sigma_{\rm h}^{\rm wet}\) = \(\sigma_{\rm 0.21 atm}^{\rm wet}\)-\(\sigma_{\rm O^{2}}\)-\(\sigma_{\rm H^{+}}\)).