## 1 Introduction
### Basic Principles of Quasi-Classical Model of Ion Relaxation Polarization
), at electric field strengths of \(\left|\overset{\rightarrow}{\text{E}}\right|\approx 10^{5}\)-\(10^{6}\)\(\frac{\text{V}}{\text{M}}\) in the temperature range of T = 50-550 K, migration polarization is caused by the diffusive movement of hydrogen ions (protons) along hydrogen bonds with activation energy U\({}_{0}\approx 0.05\div 0.7\) eV in the direction of field lines (parallel to the crystal axis \(\overset{\rightarrow}{\text{E}}\parallel\overset{\rightarrow}{\text{C}}\)) [1, 4, 8]. This phenomenon can be called proton conduction, and the set of relaxation processes associated with proton diffusion in the electric field is called proton relaxation. In terms of electrophysical properties, the HBCs are classified as proton semiconductors and dielectrics (PSD) [1, 4, 8]. This approach allows, from the point of view of the unified theory of proton conduction, the consideration of various polarization effects in HBCs (in particular, the electret effect) and the revelation of the influence of lattice parameters and the molecular parameters of relaxants (e.g., activation energy, the natural frequency of oscillations in potential pits, and the equilibrium concentration) on dielectric permittivity and specific bulk electrical conductivity [1, 4, 8]. In [3], a detailed analysis of defect migration mechanisms in hydrogen-bonded crystals (HBC) is presented, accompanied by experimental and theoretical graphs of thermally stimulated depolarization current (TSDC) densities. Examples include phlogo-pite KMg\({}_{3}\)(AlSi\({}_{3}\)O\({}_{10}\))(OH)\({}_{2}\) (Figure 1 in [3]), mica oneta talc Mg\({}_{3}\)(Si\({}_{4}\)O\({}_{10}\))(OH)\({}_{2}\) (Figure 2 in [3]), muscovite KAl\({}_{2}\)(AlSi\({}_{3}\)O\({}_{10}\))(OH)\({}_{2}\) (Figure 3 in [3]), and chemically pure chalcan-thite CuSO\({}_{4}\).5H\({}_{2}\)O (Figure 4 in [3]). Experimental and theoretical molecular parameter values for each type of relaxor in these crystals are provided in Tables 1-4 of [3]. The study establishes the dominant role of proton tunneling (within and between ions of the anionic sublattice) in the low-temperature TSDC density maximum (50-100 K) in HBC. The influence of quantum proton transitions on thermally stimulated depolarization in the high-temperature region (150-550 K) is also identified. Theoretical studies of thermally stimulated depolarization kinetics in [3] are based on the phenomenological kinetic theory for a double symmetric potential well model. Comparisons of theoretical and experimental results in [3] substantiate the significant role of quantum proton tunneling in the crystal structure of HBC across a wide temperature range (50-550 K). Ultimately, ref. [3] proposes experimentally and theoretically substantiated migration schemes for H\({}_{3}\)O\({}^{+}\). Ultimately, ref. [3] proposes experimentally and theoretically substantiated migration schemes for H\({}_{3}\)O\({}^{+}\) ions. These schemes involve stepwise proton movement within the layered dielectric structure, between adjacent water molecule layers, or between a water molecule layer and an anion layer. Proton migration occurs under the influence of external electric field forces along hydrogen bond lines oriented along the crystal's \(\mathbf{C}\)-axis. Figure 1 illustrates the migration scheme of H\({}_{3}\)O\({}^{+}\) ions through stepwise proton H\({}^{+}\) movement, demonstrated using chemically pure chalcanthite (Figure 5 in [3]; Figure 1 in this work). The results of the quantum mechanical calculation of the relaxers parameters (Table 4 in [3]) confirm the following Bjerrum defect migration scheme H\({}_{3}\)O\({}^{+}\) (Figure 1):  
1. Defect formation H\({}_{3}\)O\({}^{+}\) in the water layer or due to the introduction of proton-donor impurities sH\({}_{2}\)O + H\({}^{+}\) \(\rightarrow\) H\({}_{3}\)O\({}^{+}\). 2. Transition from ion H\({}_{3}\)O\({}^{+}\) to anion SO\({}_{4}^{2-}\), the formation of a protonated anion HSO\({}_{4}^{-}\): H\({}_{3}\)O\({}^{+}\) + SO\({}_{4}^{2-}\)\(\rightarrow\) H\({}_{2}\)O + HSO\({}_{4}^{-}\). 3.