## 1 Introduction
### Basic Principles of Quasi-Classical Model of Ion Relaxation Polarization
Methods Used in the Generalized Quasi-Classical Physical-Mathematical Model of Ion-Relaxation Polarization  
Since crystals of the HBC class--in which the main hydrogen ions are the (most mobile) charge carriers in the region of fields and temperatures far from the breakdown (for protons)--are the most effective variant of crystals with ion-molecular chemical bonds in terms of the effects of the quantum tunneling of relaxers on polarization, the construction of a generalized quasi-classical model of relaxation polarization and prolongation for materials of the class of ion dielectrics (a special case of which is the HBCs) must be carried out based on a kinetic equation with coefficients recorded while taking into account the quantum transitions of relaxers (for which, in this model, we take arbitrary ions capable of moving along chemical bonds, both due to thermal activation and tunneling). If an ion of this kind is a cation, then the crystalline potential pattern of such an ion, when an external electric field is applied to the dielectric, acquires asymmetry in the direction of the field lines. If the simulated charged particle is an anion, then, accordingly, the asymmetry of the crystalline potential pattern of such a particle is established against the directed field lines. Obviously, the rate of cation transition across the field is higher than that against the field, and vice versa for anions. As noted above, under conditions of relaxation polarization in the dielectric under the influence of an external (polarizing) electric field (which is constant and alternating), diffusion transfer of the main (most mobile) charges (relaxers) occurs, i.e., migration polarization. The main contribution to the polarization of this type is made by ions called conduction ions, moving with low activation energies (0.01-1 eV) at the fixation points (equilibrium positions) in the field of the crystal lattice perturbed by the electric field. The number of states (equilibrium positions) for ions is taken to be of the order of \(10^{6}\div 10^{7}\) --a multi-pit undisturbed potential pattern [1; 4; 8]. As a result of the relaxation polarization of the dielectric, a spatially inhomogeneous volume-charge distribution is formed in the space between the electrodes. One of the conditions for the occurrence of a volumetric charge is the blocking or partial blocking of the electrodes [1; 8]. Transfer processes are considered for an ideal lattice--neglecting both the existence of traps and recombination processes--dissociation of charge carriers [1; 8]. The distance between equilibrium positions for ions is taken to be equal to the value of the lattice constant \(a\). The crystalline potential relief, due to the redistribution of charge carriers between states (potential wells), is modeled by a function not only of the x coordinate but also of time t [1]. In many cases, in semiconductors and dielectrics, one type of charge carrier (relaxers) is the most mobile compared with the others [2; 4; 8]. Ions and polar groups act as mobile relaxers in dielectrics with a complex crystal structure (e.g., layered minerals, ceramics), particularly in crystals with hydrogen bond defects (HBCs), including Bjerrum defects (relating to ionization, e.g., H\({}_{3}\)O\({}^{+}\) and OH\({}^{-}\), and orientation defects, like L and D), orientation defects associated with ion vacancies (VL and VL D defects), and hydrogen ions (protons) localized on hydrogen bonds [1]. So, for example, in crystals of Ib-ice, defects of H\({}_{3}\)O\({}^{+}\)[2, 4, 8] have the greatest mobility. In HBCs (layered silicates, crystalline hydrates, etc.