Nonlinear Polarization Effects in Dielectrics with Hydrogen Bonds

Kalytka, V. A.; Коровкин, Михаил Владимирович; Mekhtiyev, A. D.; Yurchenko, A. V.

doi:10.1007/s11182-018-1457-8

Cited by 13 publications

(14 citation statements)

References 9 publications

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“…The authors of [3] have built their solutions to the equation systems ( 2)-( 6) by methods of the perturbation theory using power series ([3], p. 12) ρ(ξ;τ) = ∑ γ ρ (ξ;τ), z(ξ;τ) = ∑ γ z (ξ;τ) (7) in the third approximation by parameter γ. In [3], based on the functions ρ (ξ;τ), ρ (ξ;τ), ρ (ξ;τ), by the method of mathematical induction the recurrence formulas have been devised for calculating relaxation modes ρ ( ) (ξ, τ), ρ ( ) (ξ, τ)-volume density of charge ρ(ξ;τ), calculated in the k-th approximation of the perturbation theory, at the frequencies ω,2ω of the variable field, respectively, (expressions ( 18), ( 19) from [3], p. 15).…”

Section: Studies Of the Nonlinear Kinetic Equationmentioning

confidence: 99%

“…Further, representing (7) in the form of ρ(ξ, τ) = ∑ ∑ γ ρ ( ) (𝜉, 𝜏) , ρ(ξ, τ) = ∑ ρ ( ) (ξ, τ) , we will write the expansion of the frequency harmonic number r for the function 𝜌(𝜉, 𝜏) in power series by the powers of the parameter γ ρ…”

Section: Studies Of the Nonlinear Kinetic Equationmentioning

confidence: 99%

“…Here 𝜆 = 0,1,2,3,... . The frequency harmonic of the polarization, of order 𝑟 = 2𝜆 + 1, according to (7), P ( ) (t) = ∑ xρ ( ) (ξ,τ) dx , taking into account (20), becomes…”

Section: The Complex Dielectric Permittivitymentioning

confidence: 99%

“…In (38), the relaxation coefficients (33a) are a converging infinite functional series, obtained as a result of solutions of the Fokker-Planck Equation (2) together with the Poisson Equation (3) in an infinite approximation of the perturbation theory by a small dimensionless parameter γ = ( ) ( ) < 1 according to Equation (7), at the fundamental frequency of the alternating electric field and thereby are the consequences of sufficiently stringent solutions to the generalized nonlinear kinetic Equation (2). They allow us to calculate the spatially inhomogeneous bulk density of the excess electric charge in arbitrary approximation (multiplicity r) on frequency harmonics (21).…”

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

confidence: 99%

“…This allows us, with a certain degree of accuracy, to judge the significant influence of the temperature range on the mechanism of the nonlinear relaxation processes when generating polarization of the dielectric in the wide range of field parameters. It is obvious that in the region of weak fields (0.1-1 MV/m) the non-linearities will appear due to low-temperature (10-50 K) polarization effects (quantum diffusion polarization), and in the region of strong fields (10-1000 MV/m) the non-linearities will appear due to high-temperature (550-1500 K) polarization effects (nonlinear bulk-charge polarization of the mixed type) [7,[12][13][14][15][16].…”

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

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: Studies Of the Nonlinear Kinetic Equationmentioning

confidence: 99%

Section: Studies Of the Nonlinear Kinetic Equationmentioning

confidence: 99%

“…Here 𝜆 = 0,1,2,3,... . The frequency harmonic of the polarization, of order 𝑟 = 2𝜆 + 1, according to (7), P ( ) (t) = ∑ xρ ( ) (ξ,τ) dx , taking into account (20), becomes…”

Section: The Complex Dielectric Permittivitymentioning

confidence: 99%

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

confidence: 99%

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

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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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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Nonlinear Polarization Effects in Dielectrics with Hydrogen Bonds

Cited by 13 publications

References 9 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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