Quantum-mechanical model of dielectric losses in nanometer layers of solid dielectrics with hydrogen bonds at ultra-low temperatures

Abstract

Upon based the finite difference methods construct the solutions for Liouville quantum kinetic equation linearized by the external field, in complex with the stationary Schrodinger equation and the Poisson operator equation, for an ensemble of non-interacting hydrogen ions (protons) migrating in the field of a crystal lattice perturbed by a variable polarizing field. The influence of the phonon subsystem is not taken into account. The equilibrium (non-balanced) proton density matrix is calculated using quantum Boltzmann statistics. The temperature spectra of dielectric losses tangent angle for hydrogen bonded crystals (HBC) in a wide temperature range (50–550 K) are calculated. At the theoretical level detected the effects of nano-crystalline states (1–10 nm) during the polarization of HBC in the region of ultra-low temperatures (4–25 K).

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

“…Theoretical developments aimed at applying quantum kinetic theory of proton conductivity and polarization [7,[12][13][14][15][16]29,30] to questions and quantum theory of hightemperature superconductivity [43] are relevant.…”

“…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].…”

“…Another criterion of validity of formulae ( 8) and ( 25) of the nonlinear approximation of the perturbation theory investigated above is their ultimate transition to results of the linear kinetic theory of the relaxation polarization [7,[12][13][14][15][16]. To this end, we simplify the expression for the polarization (8).…”

“…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.…”

“…The advantages of expressions (38), compared to the particular linear equations (46) are that formulae (39) are constructed, as noted above, at the base frequency of the alternating polarizing field, everything up to infinite is taken into account, approximation, by a small dimensionless parameter of the perturbation theory when solving the Fokker-Planck Equation ( 2) and, as a consequence, the results of the effects of the spatially inhomogeneous polarization-induced electric field in the dielectric. This is very important in studies of the effects of the volume-charge distribution of relaxers in the mixed-type relaxation region, manifested in the region of sufficiently high temperatures (250-450 K), when, against the background of the dominant mechanism of thermally activated proton transitions [1,2,15,16], proton tunneling continues to make a significant contribution to the kinetics of nonlinear thermally activated depolarization [1,2]. As noted in [3,4], the polarization nonlinearities associated with the formation of charge-volume polarization in dielectrics with the ion-molecular type of chemical bond and manifesting in the region of ultra-high temperatures (550-1500 K) and strong electric fields (10-100 MV/m) [7,14], result from a mixed type of relaxer movements (protons) activated both by classical (due to thermal motion and the interaction of protons with the crystal lattice) transitions and quantum tunnel transitions.…”