Dispersion Relations for Proton Relaxation in Solid Dielectrics

Kalytka, V. A.; Korovkin, Nikolay

doi:10.1007/s11182-017-1027-5

Cited by 9 publications

(33 citation statements)

References 2 publications

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“…Since for HBC the condition ς = The effect of the temperature on the mechanism of the relaxation movement of the protons is reflected in kinetic coefficients W ( ) U ,δ ,ν ;T calculated in the lapproximation of the perturbation theory, taking into account both thermally activated (classical) and tunnel (quantum) transitions of ions (in HBC -protons) ( [4], p. 154)…”

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

confidence: 99%

“…Comparing the formula 4], p. 151) with the expression ( 26), let us write the complex dielectric susceptibility (CDS) in the form of…”

Section: The Complex Dielectric Permittivitymentioning

confidence: 99%

“…Within the framework of this scientific paper, we do not investigate the temperature relationships of the statistically averaged quantum transparency coefficient of a potential barrier for various configurations of the energy spectrum (discrete degenerate or non-degenerate; quasi-continuous) tunneling protons depending on the parameters of the undisturbed potential crystal lattice field (hydrogen bond field). Detailed studies of this issue carried out in the works [1,2,4,14,15] showed that the nature and properties of the quantum transparency coefficient for protons in the hydrogenbonded crystals (HBC) are most qualitatively disclosed for the discrete degenerate model (split into sublevels within individual energy zones, as a result of the effect of neighboring potential pits on a proton localized in the region of a given potential pit). The numerical values of the statistically averaged quantum transparency coefficient are significantly dependent on the parameters of the potential barrier (especially from its height, which makes sense of the activation energy), crystal thickness and temperature range.…”

Section: Effect Of Temperature On Theoretical Spectra Of Complex Diel...mentioning

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 practical use and scientific practical significance of the non-linear elements based on PSCD are detailed more in ( [1], pp. [41][42] and pertain to space technologies, nanotechnologies and high-voltage technology [3,4].…”

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%

“…Comparing the formula 4], p. 151) with the expression ( 26), let us write the complex dielectric susceptibility (CDS) in the form of…”

Section: The Complex Dielectric Permittivitymentioning

confidence: 99%

Section: Effect Of Temperature On Theoretical Spectra Of Complex Diel...mentioning

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

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Nonlinear Electrophysical Phenomena in Ionic Dielectrics with a Complicated Crystal Structure

et al. 2020

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Development of a model fiber-optic sensor of the external action on the basis of diffraction gratings with variable parameters of the system

Madi

Kalytka

Аlkina

et al. 2019

J. Phys.: Conf. Ser.

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Physical and mathematical model of the control system parameters of the optical signal using the sensor of the external action on the basis of a diffraction grating with variable characteristics (the lattice period; the width of the transparent strip (zone); width of the absorbing strip (zone)) are developing. A mathematical model of the diffraction grating is constructed on the basis of equations to calculate the resulting intensity and amplitude of the interference light passing through the grating. For the model of a lattice with a round hole, equations containing special functions of the Bessel function type, calculated numerically by calculating convergent infinite power series and integrals which are not calculated analytically, are proposed. The degree of accuracy of the developed model is determined by the severity of the underlying fundamental equations of theoretical and mathematical physics.

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Dispersion Relations for Proton Relaxation in Solid Dielectrics

Cited by 9 publications

References 2 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

Development of a model fiber-optic sensor of the external action on the basis of diffraction gratings with variable parameters of the system

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