## 3 Results and Discussion
### Conductivity
#### 3.3.2 Temperature Dependencies of Conductivity
showed that the protonic conductivities were lower for CaZrO\({}_{3}\)-doped ceramics than those for SrZrO\({}_{3}\) and BaZrO\({}_{3}\)-based materials; furthermore, the proton conductivity increased with an increasing ionic radius of the B-site cation dopant Ga-In-Y in BaZr\({}_{0.95}\)M\({}_{0.05}\)O\({}_{3-5}\)[61]. [PERSON] et al. [62] explained the decrease in protonic conductivity for Ca-doped rare-earth niobates Re\({}_{1-x}\)Ca\({}_{x}\)NbO\({}_{4}\) (Re = La, Nd, Gd, Tb, Er, Y) with a decreasing radius of the rare-earth cations (La >Nd > Tb > Er) by the decrease in polarizability of the oxide sublattice. In other words, if the distance between the oxygen ions is greater, then the lattice becomes more flexible and proton transport becomes faster; as a result, the proton conductivity increases. It should be noted that the enhancements of the bulk conductivity in wet air in comparison with dry air at temperatures below 400 \({}^{\circ}\)C reached ~0.5 orders of magnitude for the composition La\({}_{2}\)Sc\({}_{0.9}\)Ca\({}_{0.1}\)ZnO\({}_{5.45}\). For the undoped phase and for the sample La\({}_{2}\)Sc\({}_{0.9}\)Mg\({}_{0.1}\)ZnO\({}_{5.45}\), these differences in conductivities in wet and dry air were not significant, although the phases are characterized by the presence of proton current carriers. Such behavior can be explained by the presence of holes in dry air. If the atmosphere is oxidizing (air), a formation of electronic holes will follow in order to compensate for the oxygen vacancies according to the equation:  
\[V_{o}^{\bullet\bullet}+\frac{1}{2}O_{2}\Leftrightarrow O_{o}^{\times}+2h^{ \bullet}, \tag{10}\]  
where \(V_{o}^{\bullet\bullet}\) is oxygen vacancy, \(O_{o}^{\times}\) are regular oxygen sites, \(h^{\bullet}\) is a hole. In wet air, the concentration of holes decreases as a result of interacting with water vapor according to the equation:  
\[H_{2}O+2h^{\bullet}+2O_{o}^{\times}\Leftrightarrow\frac{1}{2}O_{2}+2(\text{ OH})_{o}^{\bullet}, \tag{11}\]  
where \(O_{o}^{\times}\) are regular oxygen sites, \(h^{\bullet}\) is a hole, and \((\text{OH})_{o}^{\bullet}\) are defects that appear when protons are localized at regular oxygen sites. Thus, the conductivity behavior of La\({}_{2}\)ScZnO\({}_{5.5}\) and La\({}_{2}\)Sc\({}_{0.9}\)Mg\({}_{0.1}\)ZnO\({}_{5.45}\) samples in a wet atmosphere indicates a complex combination of proton and hole conductivities. A decrease in the concentration of most mobile hole carriers leads to a decrease in conductivity; however, with a decrease in temperature, a gradual increase in the concentration of proton carriers can compensate for this effect and even increase the total conductivity. Nevertheless, to confirm this assumption, it is necessary to carry out additional studies on the differentiation of the conductivity into ion and electrical contributions. A comparison of the conductivity La\({}_{2}\)ScZnO\({}_{5.5}\) with the Ca\({}^{2+}\)-doped sample based on LaScO\({}_{3}\) with the composition La\({}_{0.9}\)Ca\({}_{0.1}\)ScO\({}_{3-8}\)[33], is also shown in Figure 7. As can be seen, in wet air, the doped sample La\({}_{0.9}\)Ca\({}_{0.1}\)ScO\({}_{3-5}\) exhibited high conductivity, which exceeded by 0.5 orders of magnitude that of Ca\({}^{2+}\)-doped La\({}_{2}\)ScZnO\({}_{5.5}\). Since the concentrations of protons in the doped compound La\({}_{0.9}\)Ca\({}_{0.1}\)ScO\({}_{3-8}\) were small [33], the high conductivity in wet air was due to the high mobility of protons in comparison with the investigated doped phases based on La\({}_{2}\)ScZnO\({}_{5.5}\). It can be assumed that the protons in the Ca\({}^{2+}\)-doped La\({}_{2}\)ScZnO\({}_{5.5}\) compounds are more trapped than in doped LaScO\({}_{3}\) and are less mobile. Although the obtained phases are inferior in terms of conductivity, the introduction of Zn\({}^{2+}\) makes it possible to significantly reduce the sintering temperature of the material.