## 5 Scientific Novelty and Scientific and Practical Significance of the Research Results
### Influence of High-Order Polarization Harmonics on Dielectric Relaxation
#### 5.9.2 Ionic Conductivity of Corundum-Zirconium Ceramics  
In [5], the unique electrophysical properties of corundum-zirconium ceramics, which exhibit ultra-high electrical (ionic) conductivity and abnormally high dielectric constant in the region of ultra-high temperatures (1200-1500 K), were investigated. Thus, at an alternating field frequency of 1 kHz and at a temperature T = 1250 K, this material exhibits an abnormally high real component of the dielectric constant (CDP) equal to approximately (2.0-2.5) million.  
The effect of ultra-high ionic conductivity, experimentally discovered in CZC, according to the authors [5], is due to the quasi-ferroelectric effect associated with the rearrangement of the structure of the oxygen sublattice near the critical temperature.  
The methods developed within the framework of the nonlinear kinetic theory of dielectric relaxation and conductivity of ionic dielectrics, from our point of view, will allow us to deepen and strengthen the level of research on the electrophysical properties of CZC at the analytical level in the direction of developing theoretical schemes for analyzing the effects of the chemical composition of a given composite and the properties of its structure on the mechanism of oxygen ion transfer between layers of a composite sample and the value of its ionic conductivity and permittivity.  
The application of the formulas of the quasi-classical model (156), together with (119a), (119b), will allow us to construct and analyze the frequency and temperature spectra of the real and imaginary components of the complex dielectric permittivity (CDP) in a wide temperature range (1-1550 K) at different frequencies of the alternating field (1 kHz-500 GHz) and establish the chemical composition characteristic of a given composite, calculate its geometric parameters and optimize the numerical values of the activation energy and the concentration of conductivity ions near the phase transition point.  
In relation to HBC, we have carried out this kind of theoretical research, confirming, using Formulas (157)-(159), the specific behavior of the dielectric loss tangent and the presence of its maximum, as well as the maximum of the real component CDP in nano-sized layers (1-10 nm) of phlogoptite mica in the region of Maxwellian relaxation in the temperature range T = 550-1550 K (high-temperature quasi-ferroelectric effect). An abnormally high CDP maximum in a phlogoptite sample appears at T = 1090 K and has an amplitude of 6.5 million. Moreover, the quantum transparency of the potential barrier for protons, calculated by the quasi-classical method, at a sufficiently high CDP activation energy of protons (0.5-0.7 eV) was 0.2-0.5. Thus, all factors indicate the quantum nature of the high-temperature quasi-ferroelectric effect in nanosized HBC layers.  
Evidently, in ceramics, this effect is observed at micrometer layer thicknesses. The reason for this difference is due to the diversity of the chemical composition of the samples and the distinctive molecular parameters of the main charge carriers.