## 5 Scientific Novelty and Scientific and Practical Significance of the Research Results
### Development of Concepts of the Properties of Crystals with Ion-Molecular Chemical Bonds (CIMB)  
The methods of nonlinear quasi-classical kinetic theory constructed in this scientific article are, as noted above, universal and applicable in the mathematical description of dielectric relaxation for almost all crystals of the CIMB class and perfectly consistent with experimental data. Under such conditions, based on comparisons of this mathematical model in combination with numerical optimization methods in calculating the quantities measured in experiments (currents; dielectric losses), the constructed theory is effective in calculating the molecular parameters of relaxators (activation energy and frequency of natural oscillations of ions in a potential well; equilibrium concentration of ions in the space of the crystal structure; width of the potential barrier (for protons in PSD); lattice constant) in the previously indicated wide range of temperatures. This methodology is applicable not only to research but also to forecast the behavior of the parameters of structural defects using a computer program package and, on this basis, the electrophysical properties of CIMB class crystals depending on the temperature range, geometric characteristics of the crystal, its dimensions (in this model, the thickness of the sample) and the range of polarizing field strengths. From this point of view to a first approximation, it can be argued that the methods of the developed theory have an effective influence on the design of the materials under study, their shape, type of symmetry, and 3D modeling parameters. The analytical and numerical methods of the quasi-classical kinetic theory of polarization developed in this scientific article, adapted by us in comparison with the experiment for HBC (layered silicates (natural minerals such as phlogopite, muscovite, talc, pyrophyllite, vermiculite, etc. ); crystal hydrates), can be transferred to the study of polarization effects and conductivity in other materials similar in type of crystal lattice with high-quality ionic conductivity (perovskites; various types of ceramics, in particular, corundum-zirconium ceramics, characterized by ultra-high ionic conductivity in the high-temperature region (1250 K) at a frequency of 1 kHz) [5]. Comparative Analysis of the Quasi-Classical and Quantum Mechanical Methods for Describing Dielectric Relaxation in CIMB  
This scientific article offers a review, with elements of clarifications and additions, of the issues of mathematical description of the kinetics of nonlinear dielectric relaxation in crystals belonging to the CIMB class. At the same time, the methodology of the work is based on a quasi-classical approach based on the solution of a generalized nonlinear kinetic equation, modeled as a balanced equation for the number of particles (in this case, relaxers (ions)) moving between potential wells separated by potential barriers perturbed by a polarizing field. This picture of the process fits well into the methodology of the quasi-classical approach to studying the kinetics of non-equilibrium systems in disturbing force fields, and according to the results of numerical estimates of the dielectric loss tangent angle and the density of thermally stimulated polarization (and depolarization) currents, the quasi-classical method is quite effective in describing dielectric relaxation in IMCBC, covering a wide range of field parameters (0.1-1000 MV/m; 1 kHz-300 GHz) and temperatures (1-1550 K). Thus, the quasi-classical model is applicable in almost all ranges of temperature field parameters characteristic of the processes of this kind in these materials. The existing discrepancies for the low-temperature region (50-100 K) [135] are the application of elements of quantum mechanical theory at the level of theoretical estimates of the statistically averaged quantum transparency of the potential barrier, moreover, at the level of the quantum Boltzmann distribution (in the range of the quantum canonical Gibbs distribution) and the WKB method.