## 3 Results (A Comparison of the Theoretical and Experimental Results)
), as in the case of laminated silicates, indicate the dominant role of tunneling dielectric relaxation protons in the low-temperature area, since the maximum density of TSDC (measured at 94 K (graph 1 in Figure 4) with an activation energy of 0.07 \(\pm\) 0.01 eV) is characterized. Taking into account the quantum effects, the theoretical calculated energy of activation is equal to 0.08 eV and, excluding tunneling, 0.16 eV. At high temperatures, in the field of non-linear volumetric charge polarization (290 K (graph 1 in Figure 4; Table 4)),  
Figure 1:8 Scheme of H\({}_{3}\)O\({}^{+}\) ion movement due to the gradual transfer of the proton in a chalcanthite crystal CuSO\({}_{4}\cdot\)5H\({}_{2}\)O. The arrows show the movement of the proton; the numbers indicate the stages of its movement. a comparison of the numerical values of activation energy calculated from the experiment (0.34 \(\pm\) 0.04 eV) and phenomenological theory (based on Equation (24)), respectively, is presented, considering tunneling (0.35 eV) and thermal activation only (0.41 eV). This points to the significant influence of quantum kinetic phenomena on proton-relaxation polarization in crystalline hydrates. The mechanism of migration of defects in H\({}_{3}\)O\({}^{+}\) due to the gradual transfer of the proton described in Figure 5 can be used write the refined chemical formula of a chalcanthite crystal, from the perspective of the geometrical location of the main structural elements in the tetrahedral elementary cell of the complex compound \(\left[\text{Cu}^{2+}\cdot\text{4H}_{2}\text{O}\right]\cdot\left[\text{SO} _{4}{}^{2-}\right]\cdot\text{H}_{2}\text{O}\). Due to the commonality of the chemical structure and the geometry of the crystalline structures, an H\({}_{3}\)O\({}^{+}\) ion transfer mechanism is implemented in materials such as crystalline hydrates by analogous hydrogen ion migration schemes, according to the detailed ion formulas of the class:  
Figure 1:9 Figure 4:0 Figure 4:1  
The mineral moresonite NiSO\({}_{4}\cdot\)7H\({}_{2}\)O is characterized by emerald green or greenish white with glassy gloss, crystallized in an orthorombic system. It occurs as small crystals, stalactites or crusts. Natural crystals are needle-shaped, and synthetic-prismatic. Moresonite is soluble in water and dehydrates in open air, turning into NiSO\({}_{4}\cdot\)6H\({}_{2}\)O [70]. Magnesium sulfate, magnesium sulfate MgSO\({}_{4}\) (salt, colorless crystals, density 2.66 g/cm\({}^{3}\). At 1100-1200 \({}^{\circ}\)C, it decomposes into MgO, SO\({}_{2}\), and O\({}_{2}\)) [71]. The solubility of MgSO\({}_{4}\) in water at 20 \({}^{\circ}\)C, 25.2% by mass MgSO\({}_{4}\) forms crystalline hydrates with 1, 2, 3, 4, 5, 6, 7, and 12 water molecules [71]. At room temperature, it crystallizes from aqueous solutions into epsomite MgSO\({}_{4}\cdot\)7H\({}_{2}\)O (Epson salt). It is also found in nature as a mineral of kizerite MgSO\({}_{4}\cdot\)H\({}_{2}\)O. Alkaline salts with MgSO\({}_{4}\) form double salts, including naturally occurring langbeinite K\({}_{2}\)SO\({}_{4}\cdot\)2 MgSO\({}_{4}\), astrakhanite Na\({}_{2}\)SO\({}_{4}\cdot\)MgSO\({}_{4}\cdot\)4H\({}_{2}\)O, polygalite Na\({}_{2}\)SO\({}_{4}\cdot\)MgSO\({}_{4}\cdot\)2 Ca\({}_{2}\)SO\({}_{4}\cdot\)2H\({}_{2}\)O and cainite KCl\(\cdot\)MgSO\({}_{4}\cdot\)3H\({}_{2}\)O [72; 73]. We also note the appearance of aqueous sodium sulfate Na\({}_{2}\)SO\({}_{4}\cdot\)10H\({}_{2}\)O mineral mirabilite (Glauber's salt) [72; 73]. Regardless of whether there is an even or odd number of water molecules in the sulfate-based expression, the H\({}_{3}\)O\({}^{+}\) ion transfer mechanism in the electric field remains similar to the one described above (Figure 5). Let us return to the question of the theoretical spectra of thermally stimulated currents in the HBC.