## 3 Results and Discussion
### Oxygen-Hydrogen Groups State  
The IR spectra of Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) are shown in Figure 3. It can be seen that the spectra for Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\), in general, have a similar shape. A broad band can be seen in the range of 2500-3500 cm\({}^{-1}\) for both compounds that confirms the presence of oxygen-hydrogen groups in the hydrated samples of the investigated materials. This range of frequencies is attributed to oxygen-hydrogen stretching vibrations (\(\
u\)OH). Analysis of the bending vibrations (8M-OH) range can be used for identification of the states of the oxygen-hydrogen groups. The region below 1500 cm\({}^{-1}\) is attributed to the bending vibrations of the hydroxide group OH\({}^{-}\). The presence of the band with the frequency \(\sim\)1430 cm\({}^{-1}\) confirms the presence of M-OH groups in the hydrated samples of Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\). The absence of bands with frequencies of \(\sim\)1600 cm\({}^{-1}\) and \(\sim\)1700 cm\({}^{-1}\) indicates the absence of water molecules and H\({}_{3}\)O\({}^{+}\) ions in the hydrated  
Figure 1: Rietveld profile fitting of powder X-ray diffraction pattern for Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) (**a**) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) (**b**). Observed (dots), calculated (line), and difference (bottom) data, and angular positions of reflections (bars) are shown.  
Figure 2: Crystal structures of Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) (**a**) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) (**b**).  
forms of the investigated compounds. IR spectra also contain a wide band in the range of 1700-2100 cm\({}^{-1}\), which is more intense in the case of Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\). This band is attributed to the mixed vibrations and it cannot be used for oxygen-hydrogen group identification. Therefore, the main form of oxygen-hydrogen groups existing in the hydrated forms of Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) is the hydroxide group OH\({}^{-}\); thus, the changing in structural blocks from BaZrO\({}_{3}\) to Ba\({}_{3}\)In\({}_{4}\)O\({}_{9}\) does not lead to any changes in the forms of the oxygen-hydrogen groups.  
The broad band of stretching vibrations in the range of 2500-3500 cm\({}^{-1}\) had a complex structure as a result of the superposition of several contributions, and consequently, this indicates the presence of different energetically nonequivalent OH\({}^{-}\)-groups in the hydrated compounds. The main maximum of this band is located at the frequency \(\sim\)3350 cm\({}^{-1}\) for both compounds. The second maximum is located at the frequency \(\sim\)2830 cm\({}^{-1}\) for Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) and for Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\), indicating OH\({}^{-}\)-groups are involved in forming stronger hydrogen bonds. So, the shape and position of the IR bands for both compounds are identical.  
Thus, according to the IR-data analysis, it can be concluded that the protons in the hydrated compounds Ba\({}_{5}\)In\({}_{2}\)Al\({}_{2}\)ZrO\({}_{13}\) and Ba\({}_{7}\)In\({}_{6}\)Al\({}_{2}\)O\({}_{19}\) are presented in the form of OH\({}^{-}\)-groups.