Mathematical Description of Non-Linear Relaxating Polarization in Dielectrics With Hydrogen Bonds

Kalytka, V. A.

doi:10.18287/2541-7525-2017-23-3-71-83

Cited by 3 publications

(38 citation statements)

References 4 publications

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“…The purpose of this paper, in the continuation of [1][2][3], is to develop generalized (for any approximation of the perturbation theory) methods for the analytical study of the influence of the nonlinearities of the kinetic equations of the original phenomenological model ( [3], p. 13) on the mechanism for the formation of the volume-charge distribution in the dielectrics type of hydrogen-bonded crystals (HBC). The results of these studies can be used in the mathematical description and modeling of the ionic conductivity and relaxation polarization processes in crystals with ionic-molecular chemical bonds, a special case of which are hydrogen-bonded crystals (characterized by proton conductivity).…”

Section: Mathematical and Physical Model Of The Nonlinear Relaxation ...mentioning

confidence: 99%

“…In ( 2)-( 6), the following designations are adopted: ρ(ξ;τ) = 𝑛(x;t) − n is an ion excess concentration over its steady-state concentration n ; 𝑧(ξ;τ) = We also introduce an additional dimensionless small parameter Ξ = <1. It is important from the point of view of the further expansion of solutions to Equation (2) in series in the powers of the parameter Λ = ∑ sin πs ( ) ([3], p. 16), which, in turn, determined the interaction parameter of relaxation modes, at the base frequency ω [3].…”

Section: Studies Of the Nonlinear Kinetic Equationmentioning

confidence: 99%

“…In the last twenty years in the industry, hydrogen-bonded crystals (HBC)-based materials (and their composites) have been widely used in insulating and cable technology, capacitor technology (electrically controlled nonlinear capacitors), physicochemical technologies (solid state electrolytes), laser technology (regulators of laser radiation parameters and electric shutters), radio electronics, radio engineering (elements of radiation generators and microwave control systems), etc. [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the imposition of an electric field on the crystal (directed along the crystal axis) leads to the diffusion motion of protons in the direction of field lines (proton conductivity). Thus, according to electrophysical properties, HBC are classified as proton semiconductors and dielectrics (PSCD) [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

“…The area of abnormally high nonlinearities is of special interest. It manifests in PSCD in the range of ultra-low (helium) temperatures (1-10 K) in the region of weak fields (100 kV/m-1000 kV/m) and the range of ultra-high temperatures (550-1500 K) in the region of strong fields (10 MV/m-1000 MV/m) ( [1], p. 43; [2], p. 74). Conditions of this type can be defined as extreme for the operation of the heterogeneous functional elements of process circuits of electrical (instrumentation, computer, etc.)…”

Section: Introductionmentioning

confidence: 99%

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Theoretical Studies of Nonlinear Relaxation Electrophysical Phenomena in Dielectrics with Ionic–Molecular Chemical Bonds in a Wide Range of Fields and Temperatures

et al. 2022

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This paper is devoted to the development of generalized (for a wide range of fields (100 kV/m–1000 MV/m) and temperatures (0–1500 K) in the radio frequency range (1 kHz–500 MHz)) methods for the theoretical investigation of the physical mechanism of nonlinear kinetic phenomena during the establishment of the relaxation polarization, due to the diffusion motion of the main charge carriers in dielectrics with ionic–molecular chemical bonds (hydrogen-bonded crystals (HBC), including layered silicates, crystalline hydrates and corundum–zirconium ceramics (CZC), etc.) in an electric field. The influence of the nonlinearities equations of the initial phenomenological model of dielectric relaxation (in HBC-proton relaxation) on the mechanism for the formation of volume–charge polarization in solid dielectrics is analyzed. The solutions for the nonlinear kinetic Fokker–Planck equation, together with the Poisson equation, for the model of blocked electrodes are built in an infinite approximation (including all orders k of smallness without dimensional parameters) of perturbation theory for an arbitrary order r of the frequency harmonic of an alternating external polarizing field. It has been established that the polarization nonlinearities in ion-molecular dielectrics, already detected at the fundamental frequency, are interpreted in the mathematical model (for the first time in this work) as interactions of the relaxation modes of the volume charge density calculated on different orders of spatial Fourier harmonics. At the fundamental frequency of the field, an analytical generalized expression is written for complex dielectric permittivity (CDP), which is expressed analytically in terms of special relaxation parameters, which are quite complex real functions in the fields of frequency and temperature. The theoretical CDP and the dielectric loss tangent spectra studied depend on the nature of the relaxation processes in the selected temperature range (Maxwell and diffusion relaxation; thermally activated and tunneling relaxation), which is relevant from the point of view of choosing exact calculation formulas when analyzing the optimal operating modes of functional elements (based on dielectrics and their composites) for circuits of instrumentation, radio engineering and power equipment in real industrial production.

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Section: Mathematical and Physical Model Of The Nonlinear Relaxation ...mentioning

confidence: 99%

Section: Studies Of the Nonlinear Kinetic Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Theoretical Studies of Nonlinear Relaxation Electrophysical Phenomena in Dielectrics with Ionic–Molecular Chemical Bonds in a Wide Range of Fields and Temperatures

et al. 2022

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Nonlinear Electrophysical Phenomena in Ionic Dielectrics with a Complicated Crystal Structure

et al. 2020

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Physical and Mathematical Models of Quantum Dielectric Relaxation in Electrical and Optoelectric Elements Based on Hydrogen-Bonded Crystals

Kalytka,

Mekhtiyev,

Neshina

et al. 2023

Crystals

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The quantum statistical properties of the proton subsystem in hydrogen-bonded crystals (HBC) are investigated. Based on the non-stationary Liouville operator equation (taking into account a number of assumptions established in the experiment), a quantum kinetic equation is constructed for the ensemble of non-interacting protons (an ideal proton gas) moving in the crystal potential image perturbed by the external electric field. The balanced density matrix for the unperturbed proton subsystem is constructed using the quantum canonical Gibbs distribution, and the non-balanced density matrix is calculated from the solutions of the nonlinear quantum kinetic equation by methods in linear approximation of perturbation theory for the blocking electrode model. Full quantum mechanical averaging of the polarization operator makes it possible to study the theoretical frequency-temperature spectra of the complex dielectric permittivity (CDP) calculated using quantum relaxation parameters that differ significantly from their semiclassical counterparts. A scheme is presented for an analytical study of the dielectric loss tangent in the region of quantum nonlinear relaxation in HBC. The results obtained in the given paper are of scientific interest in developing the theoretical foundations of proton conduction processes in energy-independent memory elements (with anomalously high residual polarization) based on thin films of ferroelectric materials in the ultralow temperature range (1–10 K). The theoretical results obtained have a direct application to the study of the tunneling mechanisms of spontaneous polarization in ferroelectric HBC with a rectangular hysteresis loop, in particular in crystals of potassium dideutrophosphate (KDP), widely used in nonlinear optics and laser technology. The quantum properties of proton relaxation in HBC can be applied in the future to the study of solid-state electrolytes with high proton conductivity for hydrogen energy, capacitor technology (superionics, varicodes), and elements of MIS and MSM structures in the development of resonant tunnel diodes for microelectronics and computer technology.

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Mathematical Description of Non-Linear Relaxating Polarization in Dielectrics With Hydrogen Bonds

Cited by 3 publications

References 4 publications

Theoretical Studies of Nonlinear Relaxation Electrophysical Phenomena in Dielectrics with Ionic–Molecular Chemical Bonds in a Wide Range of Fields and Temperatures

Theoretical Studies of Nonlinear Relaxation Electrophysical Phenomena in Dielectrics with Ionic–Molecular Chemical Bonds in a Wide Range of Fields and Temperatures

Nonlinear Electrophysical Phenomena in Ionic Dielectrics with a Complicated Crystal Structure

Physical and Mathematical Models of Quantum Dielectric Relaxation in Electrical and Optoelectric Elements Based on Hydrogen-Bonded Crystals

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