Longitudinal Dielectric Constant Research Articles

Uniform quantized electron gas: Radiation correction

In this paper we analyze how radiation effects influence the correlation functions, the excess energy, and in turn the electron correlation energy of the quantized electron gas at temperature T=0. To that aim we resort to a statistical mechanical description of the quantum problem of electron correlations, based on the path integral formalism. In previous works we studied and found accurate results for the usual situation with the electrostatic Coulomb interaction. Here the additional problem with radiation is taken into account. This is facilitated by the equivalence to a dielectric fluid for which correlation functions for dipolar moments are established. From these functions follows the usual density–density (or charge–charge) correlation function needed for the longitudinal electrostatic problem, and in addition the one needed for the transverse radiation problem. While electrostatic excess energy is negative, the transverse one is positive. This quantity is small and decreases rapidly for decreasing densities. However, for high densities it approaches the electrostatic contribution, eventually becoming even larger. The part of the transverse energy from induced correlations turns out to be very small. Also, the non-local longitudinal and transverse dielectric constants of the electron gas are identified from the induced correlation functions.

The electroreduction of oxygen in aprotic solvents

The electrochemical reduction of oxygen in a range of six polar aprotic solvents is investigated via linear sweep voltammetry at platinum, gold, and carbon fibre microelectrodes. Values for the standard heterogeneous electron transfer rate constant (k0) are reported, and in all cases follow the trend with electrode material of k0(C) > k0(Pt) ~ k0(Au). The variation in k0 with solvent is discussed in terms of the Debye model and a dependence on the longitudinal dielectric relaxation constant (τL) is found of the form k0 ∝ τL−θ. Static solvent effects are accounted for via consideration of both spherical and connected-spheres models of solvation, and it is found that θ ≈ 0.65 indicating that the reduction of dioxygen in these solvents is a non-adiabatic outer-sphere electron transfer.

Tetragonal (K, Na)NbO3 based lead-free single crystal: Growth, full tensor properties, and their orientation dependence

A Li and Ta modified (K, Na)NbO3 lead-free single crystal with a large size (13 × 10 × 20 mm3) has been grown by using the top-seeded solution growth method. The large size allows us to carry out an extensive study on this tetragonal crystal. We have measured a complete set of elastic, dielectric, and piezoelectric constants for the [001]C poled crystal with the single domain state. The crystal exhibits high shear piezoelectricity with d15 = 518 pC/N and k15 = 0.733, showing excellent potential in shear electro-sonic energy transformation devices. It is found that the high shear piezoelectricity originates from the vicinity of orthorhombic-tetragonal phase transition, which favors polarization rotation greatly. The orientation dependence of longitudinal dielectric, piezoelectric, and elastic constants and electromechanical coupling factor in the 3-dimentional space were calculated based on the single domain dataset. We believe that this work is of great importance for both fundamental studies and device designs for lead-free materials.

Dielectric and piezoelectric properties of porous PZT–PCN ceramics sintered at different temperatures

Porous lead zirconate titanate–lead cobalt niobate 0.8Pb(Zr1/2Ti1/2)O3–0.2Pb(Co1/3Nb2/3)O3 (PZT–PCN) piezoelectric ceramics were fabricated by introducing pore-forming agent polymethyl methacrylate (PMMA), and the effect of sintering behavior on their microstructure, dielectric, and piezoelectric properties were investigated. The optimum sintering procedure was designed according to the thermogravimetric analysis of pore former. Finally the electrical properties were measured.The porosity of PZT–PCN ceramics decreased and the grain size increased with an increase in the sintering temperature at a fixed PMMA addition.“An increase in density with sintering temperature from 1050 to 1250°C results into an increase in longitudinal piezoelectric coefficient (d33) and relative dielectric constant (εr). This ‘in turn’ enhanced the hydrostatic figure of merit (dhgh) of the ceramics material”.The hydrostatic figure of merit (dhgh) of 24% porous PZT–PCN ceramics was eleven times more than that of dense ceramic. This kind of porous ceramic could be a promising candidate for medical diagnostic devices.

Monte carlo simulations of the pseudo-spin ising model for hydrogen-bonded ferroelectrics

Monte Carlo (MC) simulations are performed for hydrogen-bonded-type ferroelectrics by using a three dimensional pseudo-spin Ising model. The pseudo-spin interaction strengths V and U are related to the Slater-Takagi energy parameters ɛ0 and ɛ1 via U = (ɛ0 − ɛ1)/2 and V = (2ɛ1 − ɛ0)/4. The phase transition temperature and the longitudinal and transverse dielectric constants are calculated as functions of interaction ratio R = − U/V, in the range of R from 0 to 1. According to the MC simulations, the longitudinal dielectric constant exhibits a ferroelectric phase transition while the transverse constant exhibits behavior associated with an antiferroelectric transition. The transverse dipole moments obtained from a mean-field approximation and the domain motion in the microscopic structure are discussed in view of hydrogen-ion bombardment experiments on KH2PO4 crystals.

Molecular Density Functional Theory of Water

Three-dimensional implementations of liquid-state theories offer an efficient alternative to computer simulations for the atomic-level description of aqueous solutions in complex environments. In this context, we present a (classical) molecular density functional theory (MDFT) of water that is derived from first principles and is based on two classical density fields, a scalar one, the particle density, and a vectorial one, the multipolar polarization density. Its implementation requires as input the partial charge distribution of a water molecule and three measurable bulk properties, namely, the structure factor and the k-dependent longitudinal and transverse dielectric constants. It has to be complemented by a solute-solvent three-body term that reinforces tetrahedral order at short-range. The approach is shown to provide the correct 3-D microscopic solvation profile around various molecular solutes, possibly possessing H-bonding sites, at a computer cost two to three orders of magnitude lower than with explicit simulations.

Spontaneous radiation of a finite-size dipole emitter in hyperbolic media

We study the radiative decay rate and Purcell effect for a finite-size dipole emitter placed in a homogeneous uniaxial medium. We demonstrate that the radiative rate is strongly enhanced when the signs of the longitudinal and transverse dielectric constants of the medium are opposite, and the isofrequency contour has a hyperbolic shape. We reveal that the Purcell enhancement factor remains finite even in the absence of losses, and it depends on the emitter size.

Dispersion Relation of Longitudinal Oscillations in Relativistic Plasmas of Fast Electron Distribution

In the relativistic case, the dispersion equation of longitudinal oscillations in unmagnetized, collisionless and isotropic plasmas of fast electron distribution is derived from the longitudinal dielectric constant of plasma. The equation is analytically solved, and the long-wavelength and short-wavelength dispersion relations are obtained. Because of the discontinuity of the analytical dispersion curve, the dimensionless dispersion equation of longitudinal oscillations is numerically calculated to obtain the full dispersion curve of longitudinal oscillations in relativistic plasmas of fast electron distribution. Further more, by fitting the numerical solution, a simple functional expression of the dispersion curve is given in favor of applications. Finally, in the extremely relativistic case, the dispersion relation of fast electron distribution is compared with that of Maxwell distribution. It is shown that the two kinds of dispersion relations have similar properties in a certain range of wave numbers.

Theoretical exploration of factors affecting dielectric constants of masson pine

AbstractA theoretical model to calculate the dielectric constant of masson pine (Pinus massoniana) in the longitudinal direction was developed by considering the effect of wood moisture content, density, ratio of earlywood to latewood, and the volume fraction of ray cells. The calculated results were used to explore the relationship between dielectric constant and moisture content, density, and other factors. The results indicated that the dielectric constant of masson pine increased with the moisture content. From 0% to 30% moisture content, the longitudinal dielectric constant increased more than 5 times from 2.3 to 13.3. In the range of density from 0.450 to 0.650 (g cm−3at 15% moisture content, the longitudinal dielectric constant increased from 7.7 to 10.0. However, the longitudinal dielectric constant decreased as the volume fraction of ray cells increased.

Practical formulations of the electron capture rate in quantum wells by phonon emission at low carrier density

In this article the Green’s functions formalism is exploited to describe the coupled phonon-plasmon system in the plasmon pole approximation for the longitudinal dielectric constant, for two-dimensional quantum wells. Electron capture time in quantum wells is obtained in a closed form, separating contributions coming from different two-dimensional plasmon modes. Moreover, useful criteria are pointed out, in order to decide under which conditions a simpler description in the static limit of the plasmon pole approximation may be enough accurate. In the limit of low carrier density, an analytical expression for the capture rate by LO-phonon emission has been given, in the two-dimensional static limit of the longitudinal dielectric constant. By means of this analytic description, effects of screening, Fermi filling, and electrons momentum distribution at finite temperature on capture time may be separately investigated in detail.

Accurate measurements of the acoustical physical constants of synthetic /spl alpha/-quartz for SAW devices

Accurate measurements of the acoustical physical constants (elastic constants, piezoelectric constants, dielectric constants, and density) of commercially available and widely used surface acoustic wave (SAW)-grade synthetic a-quartz are reported. The propagation directions and modes of bulk waves optimal for accurately determining the constants were selected through numerical calculations, and three principal X-, Y-, and Z-cut specimens and several rotated Y-cut specimens were prepared from a single crystal ingot to determine the constants and to confirm their accuracy. All of the constants were determined through highly accurate measurements of the longitudinal velocities, shear velocities, dielectric constants, and density. The velocity values measured for the specimens that were not used to determine the constants agreed well with those calculated from the determined constants, within a difference of +/- 0.20 m/s (+/- 0.004%).

Dielectric relaxation of the electric field in poly(vinyl acetate): a time domain study in the range 10 −3–10 6 s

We have measured the polarization of poly(vinyl acetate) in terms of a real dielectric relaxation technique by studying the decay of the electric field E( t) for times 10 −3 s ≤ t ≤ 10 6 s under the condition of a constant dielectric displacement for t > 0. This represents a direct measurements of the dielectric modulus M( t), opposed to the conventional method of measuring the dielectric retardation ϵ( t), or its frequency domain analogue ϵ ∗(ω) . The advantages of accessing M( t) are a simple experimental set-up and for polar materials experimental times which are shorter by at least a factor of ϵ s/ ϵ ∞ relative to ϵ( t) decays. The latter effect is based on the well-known relation τ L = ϵ ∞/ ϵ s τ D between transversal and longitudinal dielectric time constants. For the polymer under study, we find that no significant change of the relaxation time distribution occurs within the experimental time window, i.e. from well above the glass transition at T g (if defined via τ g = τ( T g) = 100 s) to temperatures below T g where the average retardation times 〈τ〉 attain values of up to 10 7 s.

Effective longitudinal dielectric constant of a rectangular lattice of parallel conducting prolate spheroids

The effective longitudinal dielectric constant is calculated for an infinite, three-dimensional, rectangular lattice of identical, parallel, conducting prolate spheroids. The problem is formulated by means of a matrix equation. The matrix elements are explicitly worked out. The matrix equation embodies all the multipole interactions among the spheroids exactly, and is solved analytically by iteration. An exact solution is obtained formally as an infinite series. It is shown that the interaction effects can be quantified completely by a shift in value of the depolarization factor of the spheroids. In the spherical limit, the results reduce properly to those previously derived directly for a lattice of spheres. In the opposite, acicular limit, the interaction-shifted depolarization factor is obtained in closed form, and numerical results are presented. The calculation of the effective longitudinal magnetic permeability of a lattice of magnetic prolate spheroids is similar. The magnetic permeability is obtainable from the dielectric constant by simple variable substitutions.

Growth and ferroelectric properties of tungsten bronze Ba 2− xSr xK 1− yNa yNb 5O 15 (BSKNN) single crystals

The undoped and Ce-doped ferroelectric tungsten bronze crystals, specifically Ba 1.5Sr 0.5K 0.75Na 0.25Nb 5O 15 (BSKNN-1) and Ba 0.5Sr 1.5K 0.5Na 0.5Nb 5O 15 (BSKNN-2), have been grown in optical quality using the Czochralski technique. Although both of these crystals are tetragonal with point group 4mm, their growth habit along the [001] direction differs: BSKNN-1 crystals grow in a square shape with four well-defined facets, while BSKNN-2 crystals have an octahedral growth habit with eight well-defined facets. The longitudinal dielectric (ϵ 11) and linear electro-optic ( r 51) constants show strong enhancement when expanding from BSKNN-1 and BSKNN-2 crystals, indicating that the latter could be of major interest for electro-optic, photorefractive and pyroelectric applications.

Longitudinal and transverse dielectric constants of KDP-type ferro- and antiferroelectrics

Abstract A review is presented of the longitudinal and transverse dielectric properties of KDP-type crystals. An extended pseudo-spin model of Blinc-de Gennes tunneling model is studied. The model is solved within the molecular field approximation and the four-cluster expansion. A detailed quantitative comparison is presented between the theoretical predictions and the experimental data for KH2PO4, KD2PO4 and varioius antiferroelectric ADP-type crystals. For KD2PO4, very good quantitative fit is obtained to the measured temperature dependence of the spontaneous polarization Pc , and the longitudinal and transverse dielectric constants ϵ c and e a for both the paraelectric and the ferroelectric regime with a single set of parameters e0 ≃ 92K, e1,=907K, γ = 37K and γ = 0 K. For KH2PO4, quantitative agreement is obtained with the data for ϵc and e a in the paraelectric regime with a single set of parameters e0 = 92 K, e1, = 900 K, γ = 53 K and Γ = 300 K. The antiferroelectric version of the extended pseudo-s...

Complex permittivity measurement of optoelectronic substrates

We propose and analyse new techniques to measure both transverse and longitudinal dielectric constants and the loss tangent of anisotropic dielectric samples usually used in integrated optics such as LiNbO3

A note on Lindhard's representation for transverse and longitudinal dielectric constants

Lindhard's relation between the transverse and longitudinal permittivities and the magnetic susceptibility is shown to be incorrect. The tensorial nature of the wave-vector- and frequency-dependent dielectric permittivity is emphasized. A Vlasov plasma is used as an illustrative counter-example.

The coherent state approach to the Vlasov equation

The Vlasov equation is approached from the coherent state basis. This treatment has the virtue of keeping the classical correspondence explicit at various stages. As an illustration the classical expression for the longitudinal dielectric constant of a uniform magnetized plasma is obtained. While for gaseous plasmas quantum effects are negligible and classical physics is adequate, the present approach, constituting a quantal approach and passage to the classical limit, is motivated by advantages which accrue in more difficult problems involving non-linear interactions.

Classical electrodynamics of non-specular dielectric surfaces

The effect of spatial dispersion on the electrodynamics of surfaces is studied for a phenomenological model which describes the surface scattering of the elementary excitations in terms of a parameter p, the specular surface being the case p = 1. Surface impedance, reflectivity and surface mode dispersion relation are obtained for arbitrary p without resorting to additional boundary conditions. It is thus shown that the problem is sufficiently defined if the model, including the effect of the surface, is specified. Various forms of additional boundary conditions used in the literature are discussed and characterized as models corresponding to particular values of p. The different roles of the longitudinal and transverse dielectric constants are discussed in physical terms.

Negative-ion/molecule reactions in sulphur hexafluoride: J P McGeehan et al, J Phys D: Appl Phys, 8(2), 1975, 153–160

A quantum-statistical perturbation approach is used to calculate the absorptive part of the longitudinal dielectric constant of a magnetoplasma including correlation effects up to first order in the plasma parameter λ = k3D/n. The result is presented in terms of infinite sums over the Landau levels as well as in closed form. The classical limit is obtained and the long-wavelength expansion is carried out. In the limit k → 0 the two-particle collision-damping rate remains finite for all propagation directions in the case of an electron-ion plasma and is proportional to k2 for the electron gas.