A comparative study of the effective dielectric constant of a medium containing randomly distributed dielectric spheres embedded in a homogeneous background medium

Abstract

The effective dielectric constant ∈_eff of a medium containing randomly distributed dielectric particles has been analysed by conventional methods: Foldy's approximation, the quasi-crystalline approximation (QCA) and the QCA with coherent potential. These conventional methods, however, have been indicated to become invalid for particles with a high dielectric constant; we have thus presented a new method that is valid for them. This paper compares ∈_eff of our method with those of the conventional methods by changing the volume fraction and the dielectric constant of spheres. As a result, our method is shown to be more powerful for the analysis of ∈_eff than the conventional methods.     

Temperature dependence of the dielectric properties of SBN in the frequency range of 10kHz–10MHz

The dielectric constant of Sr_0.75 Ba_0.25 Nb₂O₆ and its dielectric loss have been measured from -20°C to +90°C at various frequencies in the range of 10 KHz– 10 MHz. The result show, that despite the low half-wave field distance product (E·l)λ/2, the use for light modulation purposes is limited because of the high value of tan σ.     

Frequency and amplitude alterations of sound modes in a space-dependent random mass density field

We investigate the effect of a space-dependent random mass density field on small amplitude acoustic modes that are settled in a semi-infinite medium of a temperature growing linearly with depth. Using a perturbation method, the dispersion relation is derived in the form of Hill's determinant. Numerical solutions of this equation lead to the following conclusions: (a) a weak random field (with σ_eff = 0.05) essentially affects long waves which experience attenuation and a frequency reduction; (b) for a stronger random field (with σ_eff = 0.1), high-order sound modes behave as sound waves as they are attenuated and their frequencies are increased; (c) for a sufficiently strong random field (with σ_eff = 0.2), mode coupling occurs, as a result of which the dispersive curves cross each other, the sound modes loose their identities, and some modes are amplified. Here σ_eff denotes the effective strength of a random field.     

Thermodynamic and dielectric properties of polar lattices

Monte Carlo results are presented for the free energy and dielectric constant of systems of permanent dipoles disposed on the sites of simple cubic and face-centred cubic lattices as functions of the parameter ? = μ²ρ/kT. Alternative schemes are considered for taking account of the long-range character of the dipolar interaction, based on an Ewald-type sum or a reaction-field approximation; use of such a procedure is essential if the system is to have the correct dielectric properties. Different methods of calculating the dielectric constant are also compared. It is shown that the two methods of treating the long-range contribution to the energy lead to similar results for the dielectric constant, but use of the Ewald method apparently introduces a small but systematic error. The results on both free energy and dielectric constant are discussed in the light of predictions of a number of analytical approaches. In the case of the simple cubic lattice the general trend in the computed dielectric constant as a function of ? is in closer accord with the solution of the mean spherical approximation than with a simple Padé approximant to the Clausius-Mossotti function.     

Effect of the dielectric background on dispersion characteristics of metallo-dielectric photonic crystals

We theoretically study the effect of the dielectric background in two-dimensional metallo-dielectric photonic crystals. The metallo-dielectric photonic crystal consists of a square lattice of circular metallic rods embedded into a dielectric background. We calculate the photonic band structure by means of the plane wave method and the frequency-dependent finite-difference time-domain method. The transfer matrix method is used to obtain the reflectivity characteristics. Results show that the band structures shift toward lower frequencies and become flatter when the background dielectric constant increases. In addition, degeneracy can be broken and new gaps can be created in function of the dielectric background. We also found that the relative band gap width Δω/ω_g grows with increasing background dielectric constant and widths as large as 42.3% and 13.8% for the second and third band gaps can be achieved for ε_b = 9. We have investigated the origin of the new gap in these structures by studying the electric-field distribution at the band edges for the first five modes.     

Effect of Bi-substitution on the dielectric properties of polycrystalline yttrium iron garnet

The effect of Bi-substitution on the dielectric properties of yttrium iron garnet (YIG) was studied in this paper. The Bi-substituted YIG (YIG:Bi) polycrystalline samples, having composition of Y_3−xBi_xFe₅O₁₂, were prepared by the solid-state reaction method. x varied from 0 to 1.2. The phase formation and microstructure were performed by X-ray diffraction and scanning electron microscopy, respectively. Ions valency was identified by X-ray photoelectron spectroscopy. The impedance analyzers are used to measure the frequency dependence and the temperature dependence of relative dielectric constant (_r) and loss tangent (tan δ). The experimental results show that the Bi-substitution lowers the phase formation and sintering temperature. Electronic carrier concentration drops dramatically due to limitation of ferric valency variation. Hence, _r and tan δ decrease with addition of Bi. Dispersion characteristic indicates non-Debye-type dispersion. A maximum of _r appears as the temperature rises.     

Structure of some liquid alcohols, diols and triols: an analysis of dielectric data

This work is a continuation of our studies of the liquid structure of polyhydric alcohols and their solutions. Dielectric parameters (relaxation time, average cluster dipole moment μ¯_c, etc.) have been calculated for 1-hexanol in a wide temperature range in the framework of the cluster model proposed by Dissado and Hill; the values of apparent activation enthalpy ΔH_DHexp^≠ have been evaluated. These data were compared with the parameters previously determined by us for 2,5-hexanediol and 1,2,6-hexanetriol; the ratio μ¯_c/μ¯_v was used for an estimation of the number of molecules in clusters. It was found that at all temperatures in the range 303–393 K, the μ¯_c/μ¯_v values for 1-hexanol are significantly larger than the values of average degree of association p¯ calculated from equilibrium dielectric data; the ΔH_DHexp^≠ values for 1-hexanol are considerably lower than those for 2,5-hexanediol and 1,2,6-hexanetriol.     

Effect of an azo dye (DR1) on the dielectric parameters of a nematic liquid crystal system

 The dielectric parameters and relaxation properties of azo dye (DR1) doped E7 and pure E7 liquid crystal (LC) have been investigated in a wide frequency range of 10 k–10 MHz through the dielectric spectroscopy method at room temperature. Dielectric anisotropy (Δε) property of the LC changes from the positive type to negative type and dielectric anisotropy values decrease with doping of DR1. The relaxation frequency f_r of E7 and E7/DR1 LC was calculated by means of Cole–Cole plots. Influence of bias voltage on the dielectric parameters has also been investigated.     

Effective Ru moment in RuSr2Eu2−xCexCu2O10 from high-temperature magnetic susceptibility

We have made high-temperature (250 K<T<800 K) DC susceptibility measurements in the compounds RuSr₂Eu_2−xCe_xCu₂O₁₀ for x=0.6,0.8, and 1.0 in order to determine the Ru effective magnetic moment. After carefully subtracting all contributions to the magnetic susceptibility except that of the Ru ions, we have been able to fit the Ru susceptibility with a law χ_Ru=χ₀+C_Ru/(T−Θ_Ru). We have found that the Ru effective moment falls between the values expected for Ru⁵⁺ in spin states and . We have also found a dependence of μ_eff(Ru) and Θ_Ru with the Ce content x.     

具有各向异性的梯度颗粒复合材料的有效介电响应

本文研究了具有梯度壳层椭球颗粒复合体系的有效介电响应，在稀释条件下用准静态近似方法, 推导了颗粒壳层具有任意介电梯度形式的椭球颗粒复合体系的有效介电常数和部分共振条件的一般表达式。并以壳层的介电常数为主轴的幂函数形式为例，得出了通过调节壳层的介电梯度形式、颗粒的结构和形状,可以提高该体系的有效介电常数和实现部分共振的结论。     

On the electroweak and gluonic corrections to the hadronic width of the Z boson

The electroweak corrections to the Z-boson hadronic width are presented in a simple analytical form for the width itself, Λ_h, for its ratio to the leptonic width, R_l = Λ_h/Λ_l, for the Λ_b/Λ_h ratio, and for the total width Λ_Z. The rational parametrization, advocated in our recent papers on leptonic decays, simplifies the analysis of the hadronic decays too. There are two main results of this analysis: (1) All electroweak precision measurements agree within 1 σ with the electroweak Born approximation if the gluon coupling constant . Thus the electroweak radiative corrections have not been observed experimentally. The unexpected smallness of electroweak radiative corrections is caused by the mutual cancellation of the large positive contribution of a heavy top quark and the large negative contribution of all other virtual particles. (2) With electroweak radiative corrections being taken into account, the value of extracted from the experimental value of Λ_Z differs by 3σ from that obtained from R_l, if m_t 200 GeV; they agree within 1σ if m_t 150 GeV. Thus a low upper limit on m_t can be obtained from hadronic decays of the Z-boson alone, even without data on its leptonic decays.     

Wave beam tremble within an absorbing random medium with lens properties

The present paper investigates the joint influence of fluctuations of the complex dielectric constant, ε, of a medium and its lens properties on random displacements of a radiation beam. Based on a non-traditional approach, an expression is obtained for the variance of the beam energy centre tremble, σ²_ρ, taking into account the contribution of fluctuations of the real and imaginary parts of ε, as well as that of their correlations. It was shown that the influence of fluctuations of the imaginary part of ε is particularly pronounced in the initial section of the path, as well as in paths of great length. Due to regular refraction, a considerable enhancement of the dependence of σ²_ρ upon the path length occurs, with the greatest contribution being made by fluctuations of the imaginary part of the dielectric constant. A positive correlation of random changes of the real and imaginary parts of ε was shown to result in a partial compensation of the beam tremble.     

Dynamical Properties of Bidirectional Ring Laser with Both the Additive and Multiplicative Noises and Saturation Effect

The dynamical properties of a two-mode ring laser with both the additive and multiplicative noises are analyzed. Time-dependent probability density is obtained by the method of one-dimensional approximation. Some special behaviors of T_c and λ_eff are discussed when the multiplicative pump noise and saturation effect are included in the laser theory.     

Characterization of heterogeneous interaction in binary mixtures of ethylene glycol oligomer with water, ethyl alcohol and dioxane by dielectric analysis

The associating behaviour of the binary mixtures of ethylene glycol oligomer (EGO), i.e. ethylene glycol (EG), diethylene glycol (DEG) and poly(ethylene glycol)s (PEG200, PEG300, PEG400 and PEG600) with water (W), ethyl alcohol (EA) and 1,4-dioxane (DX) over the entire concentration range at 25 °C have been investigated through their accurately measured values of dielectric constant. The static dielectric constant ε_o, high frequency limiting dielectric constant ε_∞, dielectric relaxation strength Δε, excess dielectric parameters ε^E₀ and ε^E_∞, effective Kirkwood correlation factor g^eff and corrective correlation factor g_f of EGO–W, EGO–EA and EGO–DX mixtures were determined to obtain qualitative and quantitative information about the complex formation through H-bond in these systems. Most of the evaluated dielectric parameters of EG and DEG in different ‘cosolvents’ have different characteristics as compared to the PEG–cosolvent mixture. The observed linear and non-linear behaviour of Δε against EGO monomer unit mole fraction X confirms the variation in the homogeneous structures in their binary mixtures with concentration variation. Appearance of the maximum in ε^E₀ against X plots indicates that a complex stable adduct is formed in the EGO–W mixtures at stoichiometric ratio 1:1.7 for lower oligomers but this ratio seems to be 1.7:1 for higher EGO molecules, which confirms that the EGO size and chain flexibility affects the complex formation between EGO and W. In case of EG–EA mixture 1:1 stoichiometric ratio form stable adduct whereas for higher EGO–EA, it is 3:1, at EGO monomer unit level. The complex formation behaviour of DEG–EA has entirely different characteristics when compared to the other studied EGO–EA mixtures. Although, 1,4-dioxane has weak polar behaviour dielectric properties of EG–DX and DEG–DX confirm the formation of stable adducts at the stoichiometric ratio 2:1 of EGO monomer unit mole fraction to the DX. For the higher EGO–DX mixtures, stable adduct forms at the stoichiometric ratio 9:1. Except DEG–EA mixtures, the EGO–W and EGO–EA form the complex with reduction in the effective number of dipoles. In EG–DX mixtures, the heterogeneous species form with a large reduction in the effective number of dipoles, which changes as the effective number of dipoles increases with the increase in monomer repeat units of EGO. Further the net electronic polarization in these binary mixtures increases due to heterogeneous interaction over the entire mixing concentration range.     

Observation of enhanced dielectric permittivity in Bi doped BaFe12O19 ferrite

The dielectric properties of a 2.5 mol% Bi₂O₃ doped Ba-ferrite (BaFe₁₂O₁₉) have been investigated. The specimen shows a drastically enhanced (≈ 10⁵ times) permittivity (ε) through local polarization of Fe³⁺ electronic charges activated with nearby Bi³⁺ sites. The ε value also depends reasonably on thermal annealing (causes grain growth) of the samples. The specimens comprising large particle sizes (1–20 μ m) usually exhibit smaller ε values and low dielectric losses.     

Contribution of multiple scattering to the dielectric constant of a randomly inhomogeneous medium

Within the statistical theory of multiple scattering of light in random media, the dielectric constant of a suspension is represented as a diagram series in scattering orders and concentration of particles. The contributions of double and triple scattering events are determined. The extinction length and the transport mean free path in highly concentrated suspensions calculated with the use of the optical theorem are in good agreement with the available data. It is shown that the two-particle Born approximation, combined with the Mie form factor and the Percus-Yevick structure factor, is not adequate for systems with a high concentration of scatterers. A contribution to the optical parameters is found that is missing in the above approximation.     

Dynamical Properties of a Single-Mode Laser with Both Colored Noise and Injected Signal

The colored noise in a single-mode laser with injected signal is investigated by the method of two-dimensional unified colored noise approximation. The normalized correlation function λ₂(0), the intensity correlation time T_c and effective eigenvalue λ_eff are calculated. The effects of the injected signal I₀, colored noise strength P^ˊ and the noise correlation time τ on the dynamical properties of the single-mode laser are discussed.     

Synthesizing 0.9PZN–0.1BT by mechanically activating mixed oxides

0.9Pb(Zn_1/3Nb_2/3)–0.1BaTiO₃ (0.9PZN–0.1BT) of perovskite structure has been successfully prepared by mechanically activating mixed oxides of PbO, ZnO, Nb₂O₅, BaO and TiO₂. The novel mechanochemical technique skips the phase-forming calcination step at an intermediate temperature that is always required in both the conventional solid state reaction and chemistry-based precursor routes. Ultrafine 0.9PZN–0.1BT particles of perovskite structure were formed when the constituent oxides were mechanically activated for more than 10 h. The powder was sintered to a density of 96% theoretical density at 1100°C for 1 h. The sintered 0.9PZN–0.1BT exhibits perovskite structure and a peak dielectric constant of 8800 at the Curie temperature of 60°C when measured at a frequency of 100 Hz.     

高浓度纤维增强材料介电特性计算方法

针对复合材料的微观结构非均匀和各向异性特点带来的数值方法计算慢、内存消耗大的问题,利用均匀化方法计算纤维增强复合材料的等效电磁参数.采用了纤维低体积添加比至高体积添加比的迭代方法,同时提出了一个描述材料微观结构的修正的特征长度,将现有的均匀化方法推广至非准静态(微波频段)条件下高纤维浓度情况.提出的修正的均匀化模型可直接用于反射系数、屏蔽效能等计算,其屏蔽效能与实际微观结构复合材料的数值仿真结果进行了对比,验证了提出的等效电磁参数计算公式的有效性和频率适用范围.     

Dielectric behavior of hexaferrites BaCo2−xZnxFe16O27

The dielectric constant (′) and dielectric loss (tan δ) for hexaferrites BaCo_2−xZn_xFe₁₆O₂₇ have been studied as a function of frequency (f), temperature (T) and composition (x). The experimental results indicate that ′ and tan δ above the relaxation frequency only decrease as the frequency increases and as the temperature decreases. Tan δ shows the dielectric relaxation at certain critical frequencies which rise as temperature increases. The activation energy for the dielectric relaxation (E_D), ′, and tan δ are found to be minimum for x = 0.8.