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Dimensional effects in nanosized layers under establishing polarization in hydrogen-bonded crystals

“…The method [10,13,14] can be effectively applied to evaluation of the empirical parameters of the complex permittivity diagrams in nanosized layers at low temperatures, where the proton tunneling should be taken into account. Unfortunately, no experimental studies of polarization of hydrogen-bonded crystals are available in scientific literature.…”

“…The calculation by formula (44) using the method adopted in [10,13] reveals anomalies in the kinetics of relaxation processes in nanosized layers manifesting in the shifts of the thermostimulated depolarization-current maxima to low temperatures with decrease in the crystal-layer thickness. Table 3 shows the calculated temperatures of the thermostimulated depolarization-current maxima for chalcanthite crystals.…”

Quantum Properties of Dielectric Losses Spectra in Lamellar Crystals at Extra-low Temperatures

“…At low temperatures (70-100 ), due to significant transparency of potentional barrier, distance between neighboring energy levels is increased, energy spectrum of relaxed protons becomes quasidiscreet, which leads them to quantum distribution 10,11 .…”

“…Calculation of theoretical spectra of the thermostimulated currents of depolarization (TCDP) in quadratic approximation 10 , as in works [3,9], is based upon the solving of equation of Focker -Planck, at blocking electrodes. In 10 , exactness of quantum-mechanical approach at tunneling calculation is in the use of density matrix apparatus for the calculation of TCDP density.…”

“…Authors of 12,13 apply the results of nonlinear quantum theory of thermostimulated depolarization to the study of dimensional effects in nanometric layers (3 -30 nm) of crystallohydrates (chalcanthite) and layered silicates (phlogopite). Upon the base of quantummechanical formula for TCDP density by varying the thickness of crystal layer, it was defined, that low-temperature theoretical maximum of TCDP density is moved from the sphere of low temperatures (94 K -chalcanthite 100 Kphlogopite) at 30 mkm to extra-low temperatures (25 K -chalcanthite, 29K -phlogopite) at 3 nm, which is conditioned by abnormal structural changes of energy spectra of protons at temperatures of liquid helium (4 -25K ).…”