## 3 Results (A Comparison of the Theoretical and Experimental Results)
The results of the quantum mechanical calculation of the relaxer parameters (Tables 1 and 2) in the natural phlogopite \(\mathrm{KMg_{3}(AlSi_{3}O_{10})(OH)}_{2}\) and onot talc \(\mathrm{Mg_{3}(Si_{4}O_{10})(OH)}_{2}\) confirm the following Bjerrum defect migration scheme for \(\mathrm{H_{3}O^{+}}\):  
Defect formation in \(\mathrm{H_{3}O^{+}}\) in the water layer or due to the introduction of proton-donor impurities is as follows:  
\[\mathrm{H_{2}O+H^{+}\to H_{3}O^{+}}.\]  
The transition from ion \(\mathrm{H_{3}O^{+}}\) to anion \(\mathrm{SO_{4}^{2-}}\), for the formation of a protonated \(\mathrm{HSiO_{4}^{2-}}\) anion, is as follows:  
\[\mathrm{H_{3}O^{+}+SiO_{4}^{4-}\to H_{2}O+HSiO_{4}^{3-}}.\]  
3. The reorientation of a protonated anion due to the transition of protons inside it:  
\[\mathrm{HSiO_{4}^{3-}\to SiO_{4}H^{3-}}.\]  
4. The transition of a proton between cells of the anionic sublattice, where the newly formed protonated anion acquires the opposite orientation:  
\[\mathrm{SiO_{4}H^{3-}\to HSiO_{4}^{3-}}.\]  
5. Reorientation of the second protonated anion:  
\[\mathrm{HSiO_{4}^{3-}\to SiO_{4}H^{3-}}.\]  
6. The transition of a proton to a water molecule and the formation of a defect in \(\mathrm{H_{3}O^{+}}\):  
\[\mathrm{SiO_{4}H^{3-}+H_{2}O\to\ SiO_{4}^{4-}+H_{3}O^{+}}.\]  
For natural muscovite \(\mathrm{KAl_{2}(AlSi_{3}O_{10})(OH)}_{2}\), TSDC maxima were observed at temperatures of 105 K, 153 K, 190 K, 206 K, 230 K, 246 K, 295 K (Figure 3) [1,4]. According to Table 3, the similarity of the chemical structure of muscovite to crystals of phlogopite and onot talc determines the commonality of the physical mechanism of the migration of ionization defects in \(\mathrm{H_{3}O^{+}}\), which are responsible for the monorelaxation maximum of the TSDC density at the temperature of 153 K (Table 3), associated with proton tunneling between layers of silicate anions \(\mathrm{SiO_{4}^{4-}}\) and layers of water molecules. Note that the experimental values of the energy activation of protons in the area of low-temperature maxima (in natural phlogopite: 0.05 \(\pm\) 0.01 eV at 100 K; in onot talc: 0.06 \(\pm\) 0.01 eV at 86 K; in muscovite: 0.04 \(\pm\) 0.01 eV at 105 K) fall within the range of small values of this parameter for HBC (from 0.01 to 0.1 eV) [1]. At the same time, the theoretical activation energy values computed for the data maxima by analytic Equation (27), taking into account the tunneling of protons, as is to be expected, are much closer to experimental values (computed by semi-empirical methods [1,4]) than those computed using only the thermal activation of protons on hydrogen bonds (Tables 1-3). Theoretical equilibrium concentrations of protons, calculated by tunneling, are also closer to the experimental ones (Tables 1-3). This circumstance makes it possible to reassert the commonality of the physical nature of data on thermally stimulated current maximums, connected in laminated silicates at temperatures T = 50-100 K, with the tunnel movement of protons inside and between silicate anions SiO\({}_{4}^{4-}\)[1,2,69]. It is not difficult to see that the influence of tunneling on dielectric relaxation in laminated silicates also appears for the high-temperature (290-450 K) maximum of TSDC density associated with volumetric charge polarization (nonlinear bulk charge relaxation) caused by a relaxation movement of mixed type (due to the movement of structural defects H\({}_{3}\)O\({}^{+}\), OH\({}^{-}\), H\({}^{+}\)) [1]. Here, according to Tables 1-3, the experimental values of the energy activation of protons (in natural phlogopite: 0.35 \(\pm\) 0.05 eV at 405 K; in onot alc: 0.40 \(\pm\) 0.06 eV at 305 K; in muscovite: 0.38 \(\pm\) 0.06 eV at 295 K) fall within a range of values from 0.3 to 0.45 eV. At the same time, the values of theoretical activation energies computed considering quantum effects, as well as at low temperatures, are closer to the experimental values than those computed with only classical proton transitions (Tables 1-3).