Frequency Dependence Of Complex Permittivity Research Articles

Selective microwave absorption of SiC–Si3N4 porous ceramics prepared by sacrificial template method

Porous SiC–Si3N4 ceramics with various pore structures were prepared by adding different amounts and sizes of pore-forming agents (Polymethyl methacrylate, PMMA). The dielectric and wave absorption properties of porous ceramics were investigated over a wide temperature and frequency range. Increasing the porosity reduced the frequency dependence of complex permittivity. When the porosity increased from 50.97% to 54.59%, the loss tangent was slightly enhanced due to pore-induced polarization. An optimal pore size range enhanced the dielectric properties, beyond which a lower loss tangent was exhibited. Increasing the porosity reduced the temperature dependence of the loss tangent, and the peak of the change rate of the loss tangent moved to a higher temperature. The minimum reflection loss at room temperature can reach - 49.61 dB at 11.91 GHz for a 1.9 mm-thick sample. The minimum reflection loss at 9.72 GHz for 25 vol% PMMA-added porous ceramic with a 2.1 mm-thick material can be as low as - 65.92 dB at 300 °C. The porosity can be changed to achieve selective electromagnetic wave absorption at different temperatures.

Epoxy Casting Systems with Harmless Hardeners for Outdoor Applications

Presented thesis is focused on studying of electro-insulating casting systems based on epoxy resin. The aim of the article is to acquaint the reader with the development of this systems – epoxy resin with hardeners that comply with REACH authorization. The temperature and frequency dependence of complex permittivity, complex electric modulus, loss factor and inner and surface resistivity of the given samples are investigated.

Electrophysical properties of ferrite-containing filaments for additive technology at EHF range

The technology of producing ferrite-containing filament for 3D printer was described. The electrophysical properties of ferrite-containing filament sample at 115-258 GHz frequency range was investigated. The article presents the frequency dependence of complex permittivity and conductivity of sample obtained by fused deposition method (FDM) from filament based on acrylonitrile butadiene styrene (ABS) plastic with the addition of 20% ferrite.

Effects of particle size on electromagnetic properties of spherical carbonyl iron

Classification experiments using the spherical carbonyl iron (SCI) with particle size ranged from 1 to 7 µm were conducted by an air classifier. The electromagnetic properties of the SCI with different particle size were investigated in the frequency range of 2–18 GHz. The effects of particle size on the microwave absorption properties of the SCI were discussed on the results of scanning electronic microscopy, vibrating sample magnetometer, and frequency dependence of complex permittivity and permeability. The results show that the larger particle size leads to higher permittivity and lower permeability. The dielectric loss is attributed to the Debye dipolar polarization, while the magnetic loss arises from natural resonance and blocking resonance between superparamagnetism and ferromagnetism. The SCI with average particle size of 1.49 µm exhibits the optimal microwave absorption performance. A minimum reflection loss (RL) of − 50.8 dB is achieved at 15.6 GHz with a thickness of 1.27 mm, along with the corresponding bandwidth of RL less than − 10 dB (90% absorption) covering 7.04 GHz. Notably, the SCI with smaller particle size (about 1–3 µm) show superior microwave absorption properties at higher frequency range and thinner thickness than the corresponding larger ones (about 5 µm), which is mainly attributed to the improved impedance matching.

Dielectric properties of films of Ag-ED20 epoxy nanocomposite synthesized in situ. Temperature dependence of direct current conductivity

The influence of silver myristate used as a precursor of silver nanoparticles on the direct current conductivity σ dc of epoxy polymer within the concentration range of ≤0.8 wt % was investigated. The value of direct current conductivity was determined on the basis of analysis of the frequency dependence of complex permittivity within the frequency range of 10−2–105 Hz. The temperature dependence of σ dc is composed of two regions. The dependence corresponds to the Vogel-Fulcher-Tammann empirical law σ dc = σ dc0exp{‒DT 0/(T-T 0)} (where T 0 is the Vogel temperature and D is the strength parameter) at temperatures higher than the glass transition temperature T g. At the same time, T 0 does not depend on the concentration of nanoparticles. The Arrhenius temperature dependence characterized by activation energy about 1.2 eV is observed at temperatures lower than T g. The observed shape of the temperature dependence is related to the change in the mechanism of conductivity after “freezing” of ionic mobility at temperatures lower than T g. The value of σ dc is increased as the concentration of nanoparticles is raised within the temperature range of T > T g. The obtained dependence of σ dc on silver myristate concentration is similar to the root one, indicating the absence of percolation within the studied range of concentrations.

A Comparable Study on the Microwave Absorption Properties of Al/Fe/Co Doped OMC/Paraffin Wax Composites

Al/Fe/Co doped ordered mesoporous carbon (OMC) composites have been synthesized by a facile method, and the influence of dopant on the electromagnetic (EM) and microwave absorption properties was investigated in the frequency range of 2–18[Formula: see text]GHz. Compared with Fe/Co–OMC composites, the Al–OMC nanocomposite played a great role in adjusting values and frequency dependence of complex permittivity, which gives rise to significant improved microwave absorption and reduced thickness of the corresponding paraffin wax composites. Reflection loss (RL) values less than [Formula: see text]5[Formula: see text]dB and [Formula: see text]10[Formula: see text]dB were obtained in the frequency range of 9.2–18[Formula: see text]GHz and 10.7–14.7[Formula: see text]GHz with a single thickness of 2.00[Formula: see text]mm, respectively. Such enhanced EM wave absorption property of the Al–OMC/paraffin wax composite was ascribed to its superior impedance matching characteristic. Thin thickness, broadband absorption microwave absorbers with Al doped OMC nanocomposites were obtained.

MgCuZnFe2O4 + PbZrTiO3 Nanocomposites for EMI Applications

Mg0.48Cu0.12Zn0.4Fe2O4 and Pb(Zr0.52Ti0.48)O3nanopowders were prepared using high energy mechanical milling and sintering method. The phase formation and microstructure of the milled powders were characterized using Fourier Transform Infrared Spectrometer (FTIR), X-Ray diffractometer (XRD) and Scanning Electron Microscope (SEM). The xPb (Zr0.52Ti0.48)O3 + (1-x)Mg0.48Cu0.12Zn0.4Fe2O4 (x =0 – 1) nanocomposites were prepared by mechanical milling method. The perovskite phase (PZT) and spinel phase (MCZ) of composites were confirmed by XRD and SEM. The average grain size of the composites was in the range 120-162 nm. The density of composites increases on increase of PZT phase. From the studies of magnetic and ferroelectric hysteresis loops, it was confirmed that the composites exhibit magnetic and ferroelectric properties. The frequency dependence of complex permittivity and permeability were measured in the frequency range 1 MHz – 1.8 GHz. The microwave absorbing properties of the present composites were studied in the frequency range 8 GHz- 12 GHZ. The minimum reflection loss of the composites decreases with increase of PZT phase. The composite with 20% PZT phase has shown a minimum reflection loss of -34.3 dB near 10.45 GHz. From these studies, prepared composites can be used as good absorbing materials for suppressing electromagnetic interference.

Electromagnetic and absorption properties of nano-sized and micro-sized Fe4N particles

Single-phase Fe4N has been synthesized by gaseous nitriding micro-sized and nano-sized Fe particles at 793 K under ammonia atmosphere. The electromagnetic properties of their wax composite with 75 wt.% magnetic particles have been investigated within the frequency range of 1–18 GHz. Both size and phase effects on the microwave absorption properties were discussed on the results of scanning electronic microscopy, X-ray diffraction, hysteresis loop, and the frequency dependence of complex permittivity and permeability. The results show that nano-sized particles have superior absorbing performance at lower frequency band than the corresponding micro-sized ones, which is mainly attributed to the higher dielectric constant caused by interfacial polarization. The Fe4N composites exhibit much stronger absorption in 2–8 GHz than Fe composites. The reflection loss (RL) values of less than −10 dB are observed in a wide frequency bandwidth from 1.8 to 11 GHz for nano-sized Fe4N composite with absorber thickness of 1.2–5.0 mm. Its minimum RL value (RLmin = −33 dB) appears at 3.5 GHz with a thickness of 3.0 mm. This study demonstrates the possible application of producing thin and light absorbers from nano-sized Fe4N particles for microwave absorption at S and C bands (2–8 GHz).

Nanocrystalline gadolinium iron garnet for circulator applications

Due to high resistivity and low microwave losses, gadolinium iron garnets (GdIG) are useful materials for non-reciprocal devices such as circulators or isolators. Keeping the miniaturization and cost reduction in mind, the trend is to modify the conventional methods of preparation of samples. In this connection we have synthesized nanocystalline GdIG by using the Microwave Hydrothermal method at 160°C/45min. As synthesized powders were characterized by using X-ray diffraction (XRD), transmission electron microscopy and Fourier Transform Infrared Spectroscopy. XRD patterns show the formation of a garnet phase with crystallite size varying between 19nm and 40nm. Differential Thermal Analysis studies were also carried out on the nanopowders. The powders were densified at a lower sintering temperature of 1100°C/45min using a microwave sintering method. The sintered samples were characterized by XRD and atomic force microscopy. The frequency dependence of complex permittivity and ferromagnetic resonance were measured in the Ka band frequency (27–40GHz). Magnetic properties were also measured at room temperature.

Nonpolar Solvothermal Fabrication and Electromagnetic Properties of Magnetic Fe3O4 Encapsulated Semimetal Bi Nanocomposites

Magnetic Fe3O4 nanoparticles (NPs) encapsulated semimetal Bi nanocomposites were fabricated by a solvothermal method based on the nonpolar 1-octadecene. Bi and Fe ions were introduced into the oil phase by the complex with sodium oleate in the as-prepared solution. The nanocomposites were oil soluble and dispersed well in any nonpolar solution with the surface modification of oleic acid. It is argued that hydroxyl groups as the reductant induce the formation of Bi microspheres and prevent Fe3O4 NPs from oxidation. The frequency dependence of complex permittivity and permeability indicates that Bi and interface polarization of Bi/Fe3O4 nanocomposites are responsible for the dielectric resonances, and superparamagnetic Fe3O4 NPs weaken the natural resonance.

AC CONDUCTIVITY AND DIELECTRIC PROPERTIES OF PMMA/FULLERENE COMPOSITES

Dielectric properties and electrical conductivity of different concentrations of Poly methylmethacrylate (PMMA)/fullerene C60 composites have been reported at room temperature in the frequency range from 1 kHz to 5 MHz. The frequency dependence of complex permittivity, ε*, and complex electrical modulus, M*, have been measured. Frequency dependence of dielectric constant, follows Cole–Cole dielectric relaxation equations, was investigated diagrammatically. Moreover, equations of Tsangaris et al. have been tested for our case to describe the dielectric behavior of particulate polymeric composite containing fillers which give a satisfactory agreement taking into account the variation of the aspect ratio with the volume fraction of fullerene C60 doped in the PMMA matrix.

Frequency Dependence Measurements of Complex Permittivity of Dielectric Plates Using TE0m1 Modes in a Circular Cavity

A circular cavity resonance method is improved to measure the frequency dependence of complex permittivity of a dielectric plate by using multimode TE0m1 with integer m. The measurement principle is based on a rigorous analysis by the Ritz-Galerkin method. A new circular cavity with lowered height is designed from a mode chart of a cavity to decrease the number of unwanted modes near the TE0m1 modes. A copper cavity having 20GHz for the TE011 mode was constructed based on this design. For glass cloth PTFE, RT/duroid 6010 and FR-4 dielectric plates, the frequency dependences are measured from resonant frequencies for the TE0m1 (m =1, 2, 3 . . .) modes. These measured results agree well with ones measured by using the conventional four different size cavities with TE011 mode. It is verified that the designed cavity structure is useful to measure the frequency dependence of low loss dielectric plates.

Complex Magnetic Permeability and Dielectric Permittivity of Ferrites in Millimeter Waves

We report a first-time study of complex magnetic permeability and dielectric permittivity of 99% pure powdered barium cobalt ferrite (Ba <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">22</sub> ) and pure solid barium hexaferrite ceramics (BaFe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">19</sub> ) in a broadband millimeter-wave frequency range. We performed transmittance measurements using a free-space quasi-optical millimeter-wave spectrometer, equipped with a set of high-power backward-wave oscillators as sources of tunable coherent radiation at each Q-, V-, and W-frequency band. We calculated frequency dependences of complex permittivity for both types of ferrites using analysis of recorded high-precision transmittance spectra and obtained frequency dependences of the magnetic permeability from Schlomann's equation for partially magnetized ferrites.

Properties of highly (100) oriented Pb(Mg1∕3,Nb2∕3)O3–PbTiO3 films on LaNiO3 bottom electrodes

The 70%Pb(Mg1∕3,Nb2∕3)O3–30%PbTiO3 (PMNT) films have been fabricated on LaNiO3 (LNO) coated silicon substrate. The conductive LNO films act as a seed layer for the growth of PMNT films, which depresses the formation of pyrochlore phase and induces the high (100) preferred orientation of perovskite PMNT films. Compared with the PMNT films grown on platinum bottom electrode, the ferroelectric properties of PMNT films grown on LNO are enhanced. The frequency dependence of complex permittivity from PMNT films on LNO is the conjunct result of polarization relaxation and movement of oxygen vacancy, which can be fitted by the function containing Debye and universal dielectric response models, respectively.

Dielectric modelling of cell division for budding and fission yeast

The frequency dependence of complex permittivity or the dielectric spectrum of a system including a cell in cell division has been simulated by a numerical technique based on the three-dimensional finite difference method. Two different types of cell division characteristic of budding and fission yeast were examined. The yeast cells are both regarded as a body of rotation, and thus have anisotropic polarization, i.e. the effective permittivity of the cell depends on the orientation of the cell to the direction of an applied electric field. In the perpendicular orientation, where the rotational axis of the cell is perpendicular to the electric field direction, the dielectric spectra for both yeast cells included one dielectric relaxation and its intensity depended on the cell volume. In the parallel orientation, on the other hand, two dielectric relaxations appeared with bud growth for budding yeast and with septum formation for fission yeast. The low-frequency relaxation was shifted to a lower frequency region by narrowing the neck between the bud and the mother cell for budding yeast and by increasing the degree of septum formation for fission yeast. After cell separation, the low-frequency relaxation disappeared. The simulations well interpreted the oscillation of the relative permittivity of culture broth found for synchronous cell growth of budding yeast.

Dielectric relaxation in gigahertz region and phase transition of BaTiO3-based ceramics

Ba ( Zr 0.25 Ti 0.75 ) O 3 (BZT) and (Ba0.6Sr0.4)TiO3 (BST) ceramics were prepared as typical samples of lead-free relaxors and ferroelectrics with the diffuse phase transition, respectively. A suitable measurement technique using microplanar electrode and electromagnetic field analysis was developed to measure the microwave dielectric properties for materials with high permittivity and high dielectric loss. Frequency dependence of complex permittivity of the two ceramics was measured up to 3GHz as a function of temperature. The dielectric dispersion of both ceramics was well explained by the stretched exponential model of the decay function in dielectric relaxation. In BST, a phase transition was observed at the permittivity peak temperature in the results of x-ray diffraction analysis, specific heat measurement, and the analysis of dielectric relaxation. The relaxation frequency of dipole fluctuation in BST was much higher than that of BZT. This high relaxation frequency enables us to use BST for dielectrics with high permittivity and low loss factors in microwave region. The continuous change from normal ferroelectrics to relaxors in BaTiO3-based ceramics was discussed.

Ferroelectric and dielectric properties of [Pb(Ni 1/3Nb 2/3)O 3–PbTiO 3]/[(Ni 0.2Cu 0.2Zn 0.6)Fe 2O 4] composites

A group of ferroelectric–ferromagnetic composites were developed from 0.8Pb(Ni 1/3Nb 2/3)O 3–0.2PbTiO 3 (PNNT) and (Ni 0.2Cu 0.2Zn 0.6)Fe 2O 4 (NiCuZn) by a solid-state reaction. X-ray diffraction (XRD) and scanning electron microscope (SEM) studies showed that the composites were composed of PNNT phase and NiCuZn phase. The sintered composites exhibit typical ferroelectric hysteresis loops at room temperature. With an increase of PNNT content, the remnant polarization of composites decreases. Meanwhile, the remnant polarization and the coercive field show little asymmetric characterization. Frequency dependence of complex permittivity was also measured. With an increase in the PNNT content, the permittivity increases while the resonant frequency tends to decrease. Musal's effective medium theory was used to model the dielectric properties of composites. It was found that Musal's expression worked well over a wide range of composition.

The skewed arc representation for the frequency dependence of complex permittivity

When a variable-frequency sinusoidal voltage is applied to a polar liquid dielectric, and the imaginary part of the complex permittivity plotted against the real part, Robert Cole and Kenneth Cole showed that, using the results of the analysis of Debye, a semicircle would result. This represents relaxational behaviour with a single relaxation time. Debye had ignored dipolar inertia, and also dipole–dipole interaction; he therefore expected his analysis to hold only for frequencies below the central frequency of the dispersion, and then only for dilute solutions of polar molecules in a non-polar solvent. In practice, even when these restrictions are not satisfied, in many cases Debye's analysis gives quite good predictions of experimental observations. However, for some liquids experiments do not yield a Cole–Cole semicircle but a skewed arc, i.e. a curve which tends to a semicircle at low frequencies, and to a straight line at high frequencies. Over 50 years ago such a curve was reported by Davidson and Cole for glycerol; it is represented by their empirical equation which is a simple modification of the equation given by Debye's original analysis. The Davidson–Cole equation can be analysed to yield a distribution of relaxation times. It is reasonable to interpret this to mean that some physical characteristic of the material must be such as to cause the distribution of relaxation times implicitly present in the Cole–Davidson equation. A satisfactory explanation of this causal relationship has yet to be put forward. In this paper such an explanation is suggested.

Determination of the Frequency Dependence of Complex Permittivity in the Pseudo-Microwave Range by an Advanced Perturbation Method

The authors proposed a suitable technique for the evaluation of complex permittivity in the pseudo-microwave range. Considerable improvements have been made in the accuracy of Q evaluation by the cavity perturbation method. The advanced method employed was five times as accurate as the conventional cursor function method, installed in network analyzers. The frequency dependence of complex permittivity for microwave dielectrics and low-temperature-fireable materials was also discussed. The results of frequency dependence measurements demonstrated that some characteristics of microwave dielectrics could not simply be determined by the Qf-constant rule. Therefore, development of an evaluation technique within the confines of the pseudo-microwave range was significant.

Analysis of dielectric relaxations of w/o emulsions in the light of theories of interfacial polarization

An attempt is made to apply dielectric theories of interfacial polarization to observations of dielectric relaxations for W/O emulsions. Approximate formulas for disperse systems in a W/O type were derived from the two theories: one proposed by Maxwell and Wagner for dilute disperse systems of spherical particles, and the other developed by Hanai for concentrated disperse systems. Dielectric measurements were carried out on concentrated W/O emulsions prepared from kerosene and distilled water or KCl aqueous solutions by minimal use of emulsifiers. Marked dielectric relaxations were observed with the emulsions, the dielectric parameters having been determined to characterize the relaxation data. Phase parameters such as relative permittivity, electric conductivity and volume fraction of the disperse phase were evaluated from the dielectric parameters by use of the approximate formulas of the respective theories. The phase parameters evaluated and the frequency dependence of complex permittivity of the W/O emulsions deduced from the theory for concentrated disperse systems are in excellent agreement with the observed data in comparison to that for dilute disperse systems. It is concluded that the dielectric relaxations due to the interfacial polarization of disperse systems of spheres are explained satisfactorily by the theory for concentrated disperse systems.