Debye Relaxation Theory Research Articles

Multi-interfacial magnetic carbon nanotubes encapsulated hydrangea-like NiMo/MoC/N-doped carbon composites for efficient microwave absorption

Developing high-performance microwave absorbing materials is still a challenge to address the electromagnetic pollution. Interfacial engineering to heighten interfacial polarization plays a key role in microwave absorption. In this work, Multiple interfacial magnetic carbon nanotubes encapsulated hydrangea-like NiMo/MoC/N-doped carbon were prepared via carbothermic reduction. The phase structure and electromagnetic properties can be regulated by thermal treatment temperature. Dielectric loss mechanisms were analyzed deeply by Debye relaxation theory. The results indicated the composites exhibit excellent microwave absorption properties. Reflection loss (RL) less than −20 dB can be achieved in the frequency range of 3.76–17.52 GHz with the absorber thickness varied from 1.3 mm to 5.0 mm when the thermal treatment temperature was 700 °C. The strongest RL value reach to −70.1 dB at 14.2 GHz with the absorber thickness of only 1.52 mm when the thermal treatment temperature is 800 °C. The radar cross section (RCS) reduction calculated through computer simulation technology is used to analyze the microwave absorption capability in the actual far field. The RCS reduction is 17.05 dBm2 when the scattering angle is 0°. This work provided a novel approach for realizing the multi-interface absorbers for high-performance microwave absorption.

Interpretation of the giant dielectric constant in the single crystal of the CH3NH3PbBr3 perovskite

The dielectric studies of the CH3NH3PbBr3 single crystal were conducted in wide frequency and temperature ranges. The giant dielectric constant (up to 106) which was obtained at low frequencies based on these measurements was considered according to the induced polarization of the electrodes caused by the migration of ions and also the intrinsic polarization included in the hybrid network. Various temperature and frequency evolution regimes were shown and considered for the electrical conductivity (σ′(ω,T),σ″(ω,T)) and the dielectric functions (ε′(ω,T),ε″(ω,T)). In accordance with the Cole-Cole relaxation model and the Debye relaxation theory, pertinent phenomenological approaches were used in order to examine the included dielectric properties as well as the conductivity behavior. Hence, at high temperatures, the migration of the CH3NH3+ ions augments electrode polarization in the low-frequency range. At intermediate frequencies, however, ion hopping results in a modified Cole-Cole relaxation model at high temperatures and in a Debye-type relaxation at low temperatures. This study indicates the correlation between the giant dielectric constant whose activation energy depends on the polar CH3NH3+ ions and the alternating current conductivity enforced by ion migration.

Modifying of the dielectric properties of adsorbed water in the force field of a solid surface

The results of thermodynamic and acoustoelectric studies of changes in the dielectric properties of adsorbed water under the influence of a solid surface force field are presented. It is noted that the dielectric properties of adsorbed water depend not only on the characteristic size of the system, but also on the interaction energy with the solid surface. Near the hydrophilic solid surface, the density of adsorbed water is increased and the mobility of molecules is reduced. The opposite effect occurs for hydrophobic surfaces. The frequency dependences of the dielectric properties of adsorbed water, as in the case of water in the solid and liquid phase, can be characterized using Debye relaxation theory. It is shown that a significant increase in the orientational dielectric relaxation time in adsorbed water can be explained by taking into account the energy of interfacial boundaries.

Debye-like relaxation behavior and electric field induced dipole re-orientation of the 0.6BaTiO3-0.4Bi(Mg1/2Ti1/2)O3 ceramic

Mechanisms of the dielectric relaxation and electric field induced dipole re-orientation process in the 0.6BaTiO3-0.4Bi(Mg1/2Ti1/2)O3 ceramic have been investigated by a combination of experiments and simulations. Using the modified Debye relaxation theory, the observed strong relaxation is related to the evolution of the distribution of relaxation times with increasing temperatures. The increased freezing temperature under dc bias electric fields indicates that the nonlinear dielectric behavior has positive contributions to the total polarization. In relaxor state, the dielectric response of the 0.6BaTiO3-0.4Bi(Mg1/2Ti1/2)O3 ceramic shows a maximum value with the increasing external fields, which is attributed to two main polarization mechanisms, lattice phonon polarization and re-orientation of polar clusters. The contribution of these two polarization mechanisms is separated by the multi-polarization model, indicating that the re-orientation of polar clusters is responsible for the increase of the dielectric constant. At last, Monte Carlo method is performed to simulate the dipole re-orientation process, and the simulated results are consistent with experimental findings. This study provides a different perspective to investigate the relaxor materials with isolated polar clusters.

Colossal permittivity and dielectric relaxation of (Li, In) Co-doped ZnO ceramics

In this study, a colossal permittivity up to 3800 and a low dielectric loss of 0.11 at 1 kHz have been obtained from the (Li, In) co-doped ZnO ceramic [Zn(1−2x)(Li, In)xO] when x was 0.5%. Electric modulus spectroscopy and impedance analysis were used to investigate the origin of its high permittivity. Two relaxation peaks and a dielectric anomaly were observed in the temperature range of 293–363 K. According to the Debye relaxation theory, the low- and high-temperature relaxation peaks with activation energies of 0.09 eV and 0.29 eV, have been attributed to the hopping of singly and doubly charged oxygen vacancies, which are created by lithium and indium ions doping and oxygen deficiency during sintering process. After thermal treatment in an oxidizing atmosphere, the peaks related to the singly and doubly charged oxygen vacancies disappear and the permittivity reduces to ∼460 at room-temperature. From the X-ray photoelectron spectra (XPS), the concentrations of oxygen vacancies decrease after the O2-annealing process. The results reveal that the oxygen defects would be the main origin of the colossal permittivity of co-doped ZnO at room-temperature range.

Study of the Dielectric Behaviour of Cr-Doped Zinc Nano Ferrites Synthesized by Sol-Gel Method

The series of Cr-Zn nano ferrites having the general composition CrxZnFe2-xO4 (0 ≤ x ≤ 0.5) have been synthesized successfully in the nanocrystalline form using the sol-gel method. The samples were sintered at 900°C for 3 hours. The effect of chromium substitution on dielectric properties of Zn-ferrites is reported in this paper. The analysis of XRD patterns revealed the formation of single phase cubic spinel structure for all the Cr-Zn ferrite samples. The FTIR spectra show two strong absorption bands in the range of 400 - 600 cm-1, which corroborate the spinel structure of the samples. The average grain size was found to be in the nanometer range and of the order of 43 - 63 nm obtained using TEM images. The lattice parameter and crystallite size decrease with increase in Cr concentration (x). The investigation on dielectric constant (e'), dissipation factor (D) and ac conductivity (σac) was carried out at a fixed frequency 1 kHz and in the frequency range of 100 Hz to 1 MHz at room temperature using LCR meter. The plots of dielectric constant (e') versus frequency show the normal dielectric behavior of spinel ferrites. The value of ac conductivity (σac) increases with increase in frequency for all the compositions. The appearance of the peak for each composition in the dissipation factor versus frequency curve suggests the presence of relaxing dipoles in the Cr-Zn nano ferrite samples. It is also found that the shifting of the relaxation peak towards lower frequency side with an increase in chromium content (x) is due to the strengthening of dipole-dipole interactions. The composition and frequency dependence of the dielectric constant, dielectric loss and ac-conductivity are explained based on the Koop’s two-layer model, Maxwell-Wagner polarization process, and Debye relaxation theory.

Interfacial synthesis of polypyrrole microparticles for effective dissipation of electromagnetic waves

A strategy has been adopted to regulate the dielectric properties of polypyrrole microparticles for good electromagnetic absorption performance through an interfacial synthesis process. Classical Debye relaxation theory and resistor-capacitor model have been employed to illustrate the electromagnetic dissipation mechanism of polypyrrole microparticles. The prepared polypyrrole microparticles exhibit an effective electromagnetic absorption bandwidth 5.48 GHz (deeper than −10 dB) from 12.52 to 18 GHz with a filler loading of 15 wt. % in paraffin. It was demonstrated that the morphologies of conducting polymers can significantly affect the dissipation of electromagnetic waves, supplying a strategy for the design of effective electromagnetic absorption materials.

Role of defects in determining the electrical properties of ZnO ceramics

A greatly enhanced breakdown electric field of ∼8 kV/cm was achieved in multi-doping ZnO ceramics, and the role of defects in determining the electrical properties were systematically investigated in this work. At low temperature of around 203 K, it is found that the dielectric loss is composed of dc conduction and two defect relaxation peaks with activation energy at 0.24 eV and 0.37 eV, which can be effectively described according to Debye relaxation theory. At high temperature of 473 K, anther two defect relaxation peaks with activation energy at 0.65 eV and 0.98 eV are found to obey Cole-Davidson function, which are greatly affected by additives and closely related to the electrical properties of ZnO ceramics. Additionally, impedance analysis shows that the grain boundary resistance of ZnO ceramics is increased from 0.56 MΩ to 15.7 MΩ at 473 K and the corresponding activation energy of grain boundary is elevated from 0.23 eV to 1.03 eV. The frequency dependence of the conductivity is interpreted with the Jonscher's law, which indicates that the contribution of dc conduction at low frequency can be evidently suppressed by additives. An equivalent circuit model is demonstrated for expounding the association between enhanced electrical properties and defect relaxation in ZnO ceramics.

Dielectric Properties of CaCu<sub>3</sub>Ti<sub>4</sub>O<sub>12</sub> Ceramics

CaCu3Ti4O12 ceramics were prepared by the traditional solid-state reaction method and the dielectric properties were investigated, the activation energy and relaxation time factor of the samples were calculated. Debye relaxation theory was attempted to analyze the experimental datum, the static and high-frequency dielectric constants were obtained according to Cole-Cole spectra. The temperature dependence of the dielectric constant of CaCu3Ti4O12 were fitted by computer and the theoretical results nearly agree with experimental results.

DIELECTRIC PROPERTIES OF POROUS Si3N4-SiO2-BN COMPOSITES

Porous Si 3 N 4- SiO 2- BN composites were prepared by adding starch as both pore former and consolidator. Bruggeman effective-medium model, Maxwell-Garnett model and logarithmic model were used to describe and predict the dielectric constant of porous Si 3 N 4- SiO 2- BN ceramics. Relative dielectric constant of porous Si 3 N 4- SiO 2- BN composites decreases with the increase of apparent porosity within limits, and these models can forecast the change of the dielectric constant of the porous ceramics quite well. The minimum relative dielectric constant is 2.5 at the apparent porosity of 0.555 at room-temperature. The relationship between dielectric constant and temperature were investigated. It was found dielectric constant varied a lot with the increase of temperature, and Debye relaxation theory was employed to explain the variation of the dielectric constant with temperature increment. But the Debye relaxation theory can not explain the reason of variation of dielectric constant at the temperature range from 300°C to 900°C. To ascertain the cause of changes of dielectric constant at this temperature region, differential scanning calorimentry (DSC) measurement was performed. In this temperature region, phase transition behavior occurs at nearly 300°C in the porous composites. The new phase probably has a tidy large dielectric constant, and the dielectric constant increases sharply.

Electromagnetic Property of MnZn Ferrite/SrTiO<sub>3</sub>/PTFE Composites

MnZn ferrite powder was modified by SrTiO3 sol and then filled into PTFE matrix to form MnZn ferrite/SrTiO3/PTFE composite. The effect of modification and heat-treatment on the electromagnetic property of the composite was investigated. The results revealed that the as-prepared composite possessed high permeability, high permittivity and low loss. The modification and heat-treatment could improve the electromagnetic property of the composites. The frequency dependence of the dielectric property of the composite is accorded with Debye relaxation theory.

Pyroelectric behavior and dielectric properties of linear copolysiloxane/eicosylamine superlattice

The pyroelectric behavior and dielectric properties of a superlattice containing a Langmuir-Blodgett (LB) film of alternately monomeric eicosylamine and linear copolysiloxane substituted with aromatic acid side chains have been investigated in the temperature range of \(13 - 29~^\circ\)C. The pyroelectric coefficient of the superlattice increases with temperature, exhibiting the highest coefficient of 6.2 ± 0.2\(~\mu\,\)cm\(^{-2}~\)K-1 at 29 °C. The dielectric behavior of the superlattice is investigated by examining the dielectric loss and capacitance in the frequency range of 102 to 105 Hz. The maximum loss values for all temperatures in the range occur at a frequency ∼5000 Hz which correspond to a relaxation time of 3.18 × 10-5 s. The Cole-Cole plots obtained experimentally are found to be broad and fall inside the semicircle derived from the Debye relaxation theory. However, they agree fit with the semi-empirical Cole-Cole relaxation model. The parameter α obtained from the Cole-Cole relaxation model decreases with temperature indicating the rise in the internal degrees of freedom of the dipole in the superlattice.

A new method of calculating the activation energy of relaxor ferroelectrics

Based on the Debye relaxation theory, the temperature dependence of relaxation time can be obtained from the temperature dependence of dielectric loss. Then the relaxation activation energy Q and the pre-exponential factor τ0 can be calculated. The values of Q of four typical relaxor ferroelectrics: disordered (degree of order S= 0.35) Pb(Sc0.5Ta0.5)O3 single crystal, disordered (S = 0.40) Pb(Sc0.5Ta0. 5)O3 ceramic, 0.85Pb(Zn1/3Nb2/3)O3-0.15BaTiO3 ceramic, and 0.93Pb(Mg1/3Nb2/3)O3-0.07PbTiO3 ceramic, are 0.50ev, 0.38ev, 0.43ev, 0.73ev, respectively. The activation energies are independent of frequency. On the other hand, τ0 depend on the frequency. So the relaxation characteristics of relaxor ferroelectrics come from the distribution in τ0. The distribution in τ0 maybe results from the distribution in the size of micro polar regions.

Dielectric dispersion of biological matter: model combining Debye-type and "universal" responses.

The remarkably broad dielectric dispersions exhibited by solid dielectrics are well-known examples of the failure of Debye's relaxation theory; such dispersions are much better represented by a "fractional power law" described by Jonscher [A. K. Jonscher, Nature 267, 673 (1977)] as the "universal dielectric response." As it happens, however, recent experimental advances in this field suggest that neither of the two approaches is general enough to cope with the dielectric response of biological tissues, which combines striking features from both types of behavior. A phenomenological function is therefore proposed, which not only reproduces observations on biological tissues but also includes all of Jonscher's "universal response," the Debye, Cole-Cole, and Davidson-Cole functions, as its special cases.

Investigation of NMR Relaxation Data Using Dipole Correlation Function

In this work, the theories of the relaxation mechanism leading to the dipole-correlation function, playing an important role in the analysis of the spin-lattice and spin-spin relaxation times in magnetic rezonance, are investigated. An evaluation of these theories is made in the light of the experimental data. It is found that the spin-lattice relaxation data of the glassy medium, particularly, do not obey much the single dipole correlation function of the form exp(-t/τ), obtained from the classical Debye relaxation theory of the polar molecules. On the other hand, it is observed that the data can be represented by the non-exponential correlation function driven from the cooperative relaxation models based on the spin-defect interactions. Furthermore, it is shown that the spin-spin relaxation time, obtained from the dipole-correlation function representing the relaxation of the one-dimensional Ising spins with nearest neighbor interactions, is in complete agreement with the experimental observations.

Far-infrared properties of dilute phenols and halobenzenes in a polyethylene matrix

The far-infrared absorption coefficient of phenol, thiophenol and the analogous halobenzenes in a polyethylene matrix have been investigated using a far-infrared laser. The absorptions are interpreted in terms of an asymmetric double well, for which the theory is derived, and Debye relaxation theory. Phenol is found to be more strongly coupled to the matrix than is thiophenol. For both molecules the matrix modification of the barrier to internal rotation is far greater than any asymmetry introduced.

Dielectric Properties of Semiconductors at Low Temperatures

The dielectric constant κ′ and the dielectric loss κ″ of p-type, n-type, and compensated Si have been studied at frequencies from 103 to 109 Hz and temperatures from 4.2 to 300 °K. At frequencies above 107 Hz, the κ′ decreases with temperature from 12.1 at 4.2 °K to 11.94 at 300 °K. In this frequency region, electronic polarizability of Si only is observed. At frequencies below 107 Hz the atomic polarizability of dopants (or impurities) is predominant. In this frequency range the κ′ and κ″ show strong variation with temperature and depend on the matrix material, the dopants, and frequency. At lowest temperatures the dopants are inactive and the κ′ corresponds to that at high frequency. By increasing the temperature, dipoles are activated and correspondingly, κ′ and κ″ are changed. Within about 10 °K, the κ′ reaches a maximum value and then remains constant, while the κ″ shows a relatively sharp maximum at the temperature where the κ′ curve goes through inflection. The temperature of κ″ maxima are for Sb, 18.0, 19.5, 21.5, and 23.5 °K; for B, 22, 24, 27, and 29 °K; for P, 25, 29, 33, and 38 °K; for B + P (compensated), 27, 31, 36, and 42 °K. The °K numbers correspond to the frequencies 103, 104, 105, and 106 Hz. The variation of κ′ and κ″ with frequency and temperature is explained by the Debye relaxation theory. From the relation of frequency and temperature of κ″ maxima, the following activation energies have been obtained: for Sb, 0.0431 eV; for B, 0.0410 eV; for P, 0.0427 eV; for B + P, 0.0431 eV. Our activation energy data correspond quite closely to the published data obtained by optical activation for the same dopants. In a very pure sample, 30 000 Ω cm, three κ″ maxima have been observed which may correspond to three excited levels. Some preliminary results for Ge, GaAs, and CdS are also given. Our results indicate that dielectric measurements are very suited for the study of semiconductors.

Transient Behavior of Domains in Liquid Crystals

Using an optical technique the formation and decay of domains in high applied electric fields has been studied for two nematic liquid crystals, p-azoxyanisole and p-butoxybenzoic acid. The decay time was found to be independent of the applied field but proportional to the sample thickness over the range studied. The rise time exhibited a d2/V type dependence on sample thickness (d) and applied voltage (V). This behavior is also found in solid ferroelectrics at high fields where domain propagation is the limiting switching factor. A phenomenological theory of domain kinetics was structed in the spirit of the Debye relaxation theory which accounts for the essential features of the experimental data. A justification for this approach was also found in its ability to account for the very low-frequency (<500 cps), large signal-dispersion data for these materials which featured a thickness dependence of the relaxation time.