Debye Equation Research Articles

Temperature changes of dielectric permittivity and relaxation in aqueous lithium iodide solutions

The complex permittivity of aqueous LiI solutions is studied over a wide range of concentrations at temperatures of 288–323 K in the water permittivity dispersion region at seven frequencies in the range of 7.5–25 GHz. One relaxation region describable by the Debye or Cole-Cole equation is observed in these solutions. Dielectric relaxation time τ and static permittivity ɛs are studied as dependent on temperature and concentration. The time and enthalpy of activation of dielectric relaxation decrease in going from water to solutions, which corresponds to the distortion of the initial water structure and the increasing mobility of water molecules in hydration shells of ions. In the initial concentration range, the water activity is a linear function of 1/ɛs. The negative temperature dependence of ɛs disappears in going to concentrated solutions. At high concentrations, the static dielectric constant increases in response to increasing temperature. The new trends in ɛs and τ at elevated temperatures of 313–323 K are due to the formation of ion pairs and other ion-water groups having high dipole moments.

Intermolecular interactions and molecular dynamics in bovine serum albumin solutions studied by small angle X-ray scattering and dielectric relaxation spectroscopy

We used small angle X-ray scattering (SAXS) and dielectric relaxation spectroscopy (DRS) to clarify static structure and molecular dynamics of bovine serum albumin (BSA) in solution. SAXS allowed us to access spatial correlations of the protein molecules in concentrated solutions at different ionic strength. Using a well-established Fourier inversion technique, called SQ-IFT, we deduced the effective pair correlation functions, g(r)eff, from the effective (or experimental) structure factors, S(q)eff, without assuming any potential models for protein–protein interactions. In terms of S(q)eff and g(r)eff, the mean nearest-neighbor distance, d⁎, the osmotic compressibility, κosm, and the coordination number, NC, were evaluated.The complex dielectric spectra of aqueous BSA solutions measured in the frequency range from 1MHz to 10GHz were able to be decomposed into three relaxation processes having different physical origins. The highest frequency process, whose relaxation time was ca. 8ps, was assigned to cooperative rearrangement of H-bond network of bulk-water. We evaluated the effective hydration number of a BSA molecule, Zhyd, using the bulk-water relaxation amplitude. This approach yielded ca. 1200 hydrated water molecules per a BSA molecule, corresponding to ca. 0.3g hydrated water per 1g protein. The lowest frequency process having a relaxation time of ca. 50ns was assigned to rotational diffusion of the BSA molecule. We confirmed that an effective molar volume of BSA calculated with Stokes–Einstein–Debye equation was identical to that predicted from its molecular weight and specific density. According to the Kirkwood relationship, the dipole–dipole orientational correlation factor decreased with an increase of protein concentration, which indicated the operation of BSA–BSA interaction and favored antiparallel dipolar correlation between the protein molecules.

Electromagnetic and microwave absorbing properties of SmCo coated single-wall carbon nanotubes/NiZn-ferrite nanocrystalline composite

The electromagnetism and microwave absorption properties of SmCo coated single-wall carbon nanotubes (SmCo@SWCNTs) and Ni0.5Zn0.5Fe2O4 ferrite (NiZn-ferrite) nanocrystalline composites with different ingredient weight ratios were investigated in the frequency range of 2–18 GHz. SmCo@SWCNTs were prepared by a direct current arc discharge method. NiZn-ferrite nanocrystalline was synthesized by a sol-gel method. The electromagnetic properties of the nanocomposites in the paraffin matrix were measured by a vector network analyzer. The Debye equation and Bruggeman symmetric medium equation were introduced to explain the dielectric properties of the nanocomposites, and the mechanisms for the dielectric and magnetic losses were discussed. The experiment results reveal that the absorbing properties of the nanocomposites could be improved by tuning for a suitable weight ratio between SmCo@SWCNTs and NiZn-ferrite nanocrystallines. The reflection loss simulation calculations demonstrated that the nanocomposite could be excellent materials for microwave absorption.

Dielectric behaviors of carbon nanotube/silicone elastomer composites

AbstractCarbon nanotubes (CNTs) with different aspect ratios were modified by a silane coupling agent. The modified CNTs were embedded into a silicone elastomer (SE) matrix to obtain the composites. The dielectric behaviors of the composites with different frequencies of outer electric field were investigated. The results showed that the CNTs were modified by a silane coupling agent to improve the interaction with the SE matrix. The dielectric loss and permittivity of the SE were enhanced by the addition of CNTs. The CNTs with larger aspect ratios had a more effective dielectric loss and permittivity-enhancing effect. There were three existent polarization mechanisms in the composites, and the response times of the three were different. When the field frequency increased, a polarization mechanism or two would not catch up with the increase, and the dielectric loss and permittivity would obviously be affected. The CNTs with larger aspect ratios had a more effective dielectric loss and permittivity-enhancing effect. According to the Debye equation, CNT/SE composites have a similar function as the parallel RLC circuit.

Atomic relaxation processes in an intermetallic Ti–43Al–4Nb–1Mo–0.1B alloy studied by mechanical spectroscopy

An advanced intermetallic γ-TiAl-based alloy containing Nb and Mo has been studied to understand the microscopic mechanisms taking place during thermal treatments carried out to adjust a fine, nearly lamellar microstructure. The evolution of the microstructure has been characterized by high-energy X-ray diffraction and electron microscopy, while the atomistic mechanisms of defect mobility have been studied through internal friction and dynamic modulus measurements. An internal friction relaxation peak has been observed at about 1050K (for 1Hz) in the initial oversaturated α2-Ti3Al phase, whose intensity strongly decreases after precipitation of the γ-TiAl laths. The activation parameters of this relaxation have been measured, Hact=3.1±0.05eV, τ0=8.3×10−17s and β=1.3, and the relaxation is attributed to a point defect mechanism taking place inside the supersaturated α2-Ti3Al phase. A new Zener-like atomistic model based on stress-induced reorientation of Al–VTi–Al dipoles has been developed to explain the observed relaxation, resolving the controversy concerning the relaxation peak at 1050K present in many γ-TiAl-based alloys. Precipitation of the γ-lamellae has also been considered as being responsible for the dynamic modulus hardening and, additionally, for another contribution to the internal friction at higher temperature than the described relaxation. Finally, the theoretical Debye equations as a function of temperature, for both internal friction and dynamic modulus, have been applied, using the measured activation parameters, to perform a deconvolution of the relaxation and precipitation contributions. The obtained results agree well with the experimental ones at different frequencies, allowing a global interpretation of the involved atomic processes.

토양의 유전율 특성을 고려한 정보통신설비용 수평접지전극의 임피던스 계산

정보통신설비용 접지전극의 임피던스는 접지전극이 매설되어 있는 토양의 전기적 특성과 밀접한 관계가 있다. 특히 인가된 전계의 주파수에 따른 토양의 유전율과 도전율 특성이 접지전극의 임피던스에 직접적으로 영향을 준다. 접지전극의 임피던스를 계산할 수 있는 상용프로그램은 유전율과 도전율을 수정하여 시뮬레이션하는 것이 불가능하기 때문에 전자계 이론을 적용한 프로그램을 MATLAB으로 구현하였다. 토양의 유전율은 유전완화 모델인 디바이(Debye)식을 적용하였으며, 도전율은 실험에서 얻어진 수식을 다른 논문에서 인용하였다. 시뮬레이션 결과의 신뢰성을 확인하기 위해서 실험계를 구성하여 접지전극의 임피던스를 측정하고, 시뮬레이션 결과와 서로 비교하였다. 그 결과, 토양의 유전율과 도전율 특성을 고려한 본 논문 결과가 고려하지 않은 상용프로그램(NEC) 결과 보다 측정값과 더욱 잘 일치하는 것을 확인하였다.

Domain structure investigation of non-stoichiometric strontium ferrites and cobaltites

Monte Carlo domain structure simulation and Debye equation calculation of XRD patterns were used to confirm the formation of domain structure and investigate its peculiarities. Correspondence of simulated XRD patterns with synchrotron powder diffraction experiments is achieved on the conditions that beside of 90o rotations of brownmillerite-like domains inside perovskite-like matrix each domain contains areas with perpendicularly oriented tetrahedral chains. Influence of such parameters as stoichiometry, average domain size, orthorhombic distortion degree on the XRD patterns is considered.

Dielectric properties and microwave heating of oil palm biomass and biochar

The conversion of the electromagnetic energy into heat depends largely on the dielectric properties of the material being treated. Therefore, the fundamental understanding of these properties is necessary for designing industrial microwave processing unit. The objective of this study is to investigate the dielectric properties of oil palm biomass and biochar at varying frequency in the range 0.2–10GHz. The dielectric properties were measured using a coaxial probe attached to a network analyzer. The results indicate the dielectric constant was found to be inversely proportional to the frequency. However, the biomass in the present study did not obey the famous Debye equation and hence, the loss factor was found to be directly proportional to the frequency. The dielectric properties of oil palm shell (OPS) and its biochar were found to be almost similar and higher than oil palm fiber (OPF). Relaxation time and static dielectric constant were also presented in the paper. Lastly, the heating characteristics under MW irradiation confirmed poor microwave absorbing properties of oil palm biomass.

RECONSTRUCTION OF SAXS PROFILES FROM PROTEIN STRUCTURES

Small angle X-ray scattering (SAXS) is used for low resolution structural characterization of proteins often in combination with other experimental techniques. After briefly reviewing the theory of SAXS we discuss computational methods based on 1) the Debye equation and 2) Spherical Harmonics to compute intensity profiles from a particular macromolecular structure. Further, we review how these formulas are parameterized for solvent density and hydration shell adjustment. Finally we introduce our solution to compute SAXS profiles utilizing GPU acceleration.

Sound velocities for hexagonally close‐packed iron compressed hydrostatically to 136 GPa from phonon density of states

AbstractThe phonon density of states of pure iron (57Fe) was measured under hydrostatic conditions using nuclear resonant inelastic X‐ray scattering (NRIXS) at pressures up to 136 GPa. Extracting shear (Vs) and compressional (Vp) wave speeds from the Debye velocity and equation of state, we find the hydrostatic shear wave speed trend above previously collected NRIXS data under nonhydrostatic conditions by roughly 5%–6% in the measured pressure range. Using the Birch Murnaghan finite strain approach to fit pressure‐dependent adiabatic bulk and shear moduli, we extrapolated our velocities to inner Earth core densities and found that our shear wave speeds are 3% higher than those in previous studies. Our results on pure iron provide a more accurate and precise baseline to which added complications (e.g., Ni concentration, inclusion of various light elements, and temperature effects) can be considered when comparing experimental elasticity measurements to inner core seismic data.

X-ray scattering from amorphous solids

The main objective of this work is to verify the proposed models by comparing computed outcomes with experimental results. For metallic glasses the novel ideal amorphous solid model is used to simulate the structure and the atomic positions which are input into the Debye equation. Computations predict structure factor or scattered intensity which agree well with the experimentally obtained data. For covalent materials, such as amorphous silica or amorphous polyethylene with short range order the Warren approach offers a simple method to predict X-ray scattering in good agreement with experimental data. Neither of the two above methods works well for chalcogenide glasses which require calculations involving spherical harmonics.

Ambient Heat Capacities and Entropies of Ionic Solids: A Unique View Using the Debye Equation

Entropies of solids are obtained experimentally as integrals of measured heat capacities over the temperature range from zero to ambient. Correspondingly, the Debye phonon distribution equation for solids provides a theoretical connection between these two chemical thermodynamic measures. We examine how the widely applicable Debye equation illuminates the relation between the corresponding experimental measures using more than 250 ionic solids. Estimation of heat capacities for simple ionic solids by the Dulong-Petit heat capacity limit, by the Neumann-Kopp elemental sum, and by the ion sum method is examined in relation to the Debye equation. We note that, and explain why, the ambient temperature heat capacities and entropies of ionic solids are found to be approximately equal, and how deviations from equality may be related to the Debye temperature, ΘD, which characterizes the Debye equation. It is also demonstrated that Debye temperatures may be readily estimated from the experimental ratio of ambient heat capacity to entropy, C(p)/S(p), rather than requiring resort to elaborate theoretical or experimental procedures for their determination. Correspondingly, ambient mineral entropies and heat capacities are linearly correlated and may thus be readily estimated from one another.

Room-temperature dielectric relaxation and magnetic properties in rutile-type FeTiNbO6

FeTiNbO6 ceramics have been prepared through a solid-state reaction route. The room-temperature dielectric relaxation and magnetic characteristics of FeTiNbO6 were investigated together with the crystal structure. The present ceramics were characterized by tetragonal rutile structure in space group P42/mnm. An obvious dielectric relaxation with strong frequency dispersion and following the modified Debye equation was detected in low temperature range, which can be assumed to the carrier hopping process between Fe2+ and Fe3+. Temperature dependence of the dc conductivity (σdc) follows well to Mott variable range hopping (VRH) mechanism. The comparison of the dielectric behaviors between the as-sintered samples and the O2-annealed samples shows that the low-temperature relaxation in FeTiNbO6 is indeed polarnic in nature. Moreover, the slim magnetic hysteresis loop was detected at room temperature, indicating the weak ferromagnetism in FeTiNbO6 ceramics.

Lattice energies and polarizabilities of lanthanide gallium garnets (Ln3Ga5O12)

Lattice energies ΔLHθ of lanthanide gallium garnets Ln3Ga5O12 (Ln=Nd–Lu) have been determined from the Born–Haber thermochemical cycle and compared with those previously obtained by atomistic simulations in the Born model or calculated by an empirical equation. The Born–Haber cycle yields the lowest values among the three methods. Molar polarizations Pm of Ln3Ga5O12 have been calculated by the Debye equation. It has been found that the partial derivative (∂ΔLHθ/∂Pm) corresponds by magnitude to the shear moduli of these crystals.

Water uptake of a low-κ dielectric film: Combining capacitance and gravimetric measurements

Moisture uptake of a benzocyclobutene (BCB) film has been investigated by using the capacitance-time (C-t) measurement method. The change in the permittivity at 80% relative humidity (RH) at room temperature in saturation is about 1.54%. To derive the absolute amount of water molecules from the change in capacitance an appropriate electrical model is required. For the direct measurement of the amount of water molecules in the BCB film gravimetric measurements have been performed at the same environmental conditions by using a quartz crystal microbalance (QCM). In saturation the change in mass induced by the moisture uptake is only about 0.14%. However, the application of the Debye equation using the dipole moment of water vapor yielded an excellent agreement between electrical and physical measurements.

Short-range and long-range order of phyllomanganate nanoparticles determined using high-energy X-ray scattering

High-energy X-ray scattering (HEXS) is used to explore the pH-dependent structure of randomly stacked manganese oxide nanosheets of nominal formula δ-MnO2. Data are simulated in real space by pair distribution function (PDF) analysis and in reciprocal space by both the Bragg-rod method and the Debye equation in order to maximize the information gained from the total scattering measurements. The essential new features of this triple-analysis approach are (1) the use of a two-dimensional supercell in PDF modeling to describe local distortions around Mn layer vacancies, (2) the implementation in Bragg-rod calculations of a lognormal crystal size distribution in the layer plane and an empirical function for the effect of strain, and (3) the incorporation into the model used with the Debye equation of an explicit elastic deformation of the two-dimensional nanocrystals. The PDF analysis reveals steady migration at acidic pH of the Mn atoms from layer to interlayer sites, either above or below the Mn layer vacancies, and important displacement of the remaining in-layer Mn atoms toward vacancies. The increased density of the vacancy–interlayer Mn pairs at low pH causes their mutual repulsion and results in short-range ordering. The layer microstructure, responsible for the long-range lateral disorder, is modeled with spherically and cylindrically bent crystallites having volume-averaged radii of 20–40 Å. Thebunit-cell parameter from the hexagonal layer has different values in PDF, Bragg-rod and Debye equation modeling, because of the use of different weighting contributions from long-range and short-range distances in each method. The PDFbparameter is in effect a measure of the average inlayer Mn...Mn distance and consistently deviates from the average structure value determined by the Bragg-rod method by 0.02 Å at low pH, as a result of the local relaxation induced by vacancies. The layer curvature increases the Bragg-rod value by 0.01–0.02 Å with the cylindrical model and as much as 0.04–0.05 Å with the spherical model. Therefore, in principle, the diffraction alone can unambiguously determine with good accuracy only a volume-averaged apparent layer dimension of the manganese oxide nanosheets. Thebparameter is model dependent and has no single straightforward interpretation, so comparison ofbbetween different samples only makes sense if done in the context of a single specified model.

Theoretical study of some thermodynamical properties for solid under high pressure using finite-strain EOS

This work involves the influence of high pressure on some thermodynamical properties of solid aluminum (Al) using a 3rd and 4th order Birch–Murnaghan equation of state based on the finite Eulerian strain theory.The comparison results for relative compression volume in the range of 1–0.65 versus applied high pressure for the 3rd and 4th order B–M EOS and experimental data indicated that up to 20GPa are in good agreement. But beyond this and up to 100GPa, the results for the 3rd order B–M EOS do diverge from the 4th order B–M EOS as well as from the experimental data.The isothermal bulk modulus (KT) has been worked out by using the 3rd and 4th order B–M EOS. Results were not found in good agreement above 20GPa. However, the data for first pressure derivative (KT′) for both 3rd and 4th order B–M EOS show a big divergence starting from 20GPa.Finally, the effect of high pressure on (Al) melting temperature has been studied. The Mie–Gruneison–Debye equation (based upon the 3rd and 4th order B–M EOS) and Lindemann and Kumar’s equations were investigated. Comparison results for melting temperature as a function of melting pressure by using the above mentioned equations and the experimental data have been found to be in good agreement.

New Method for Determining Dielectric Properties of Skin and Phantoms at Millimeter Waves Based on Heating Kinetics

Recent progress in millimeter-wave (MMW) wireless body-centric applications triggered an increasing interest to characterize the interactions between the millimeter waves and the human body. The determination of the dielectric properties of skin and phantoms (artificial models with tissue-equivalent dielectric properties) at MMW is crucial for the accurate evaluation of the power absorption and distribution in the skin. In this study, we show that the heating kinetics resulting from the MMW exposure can be used for the accurate determination of the penetration depth (δ) and power density (I) in different samples (1% and 4% agar phantoms, 20% and 25% polyethylene powder (PEP) phantoms, and human skin). The samples have been exposed at 60.4 GHz using an open-ended waveguide. The temperature distribution and dynamics are recorded using an infrared camera. The values of δ and I are defined by fitting the analytical solution of the bio-heat transfer equation to the experimental heating kinetics. The values of δ are further used to retrieve the permittivity spectra of materials described by Debye equation. Simultaneously, δ is calculated using the permittivity directly measured using a slim coaxial probe. Both results are in good agreement. Finally, our results demonstrate that the permittivity of a 20% PEP phantom is close to that of skin. Hence, this phantom can be used to model the MMW interactions with skin and to characterize on-body wearable MMW antennas.

Influence of zinc on electrical and microstructural properties of CaCu3Ti4O12 ceramics prepared by sol–gel process

Zn-substituted CaCu3Ti4O12 ceramics were prepared by the sol–gel method. Their microstructures and electrical properties were investigated. XRD patterns showed that the CaCu3−xZnxTi4O12 (CCZTO) (x=0.00, 0.06, 0.10, 0.20) ceramics, after sintering at 1050°C for 20h, were single phase with no Cu-rich phase. SEM results indicated that the samples had smaller grain sizes than those synthesized by traditional solid-state reaction methods. The dielectric and varistor properties of CCZTO were analyzed by a precision impedance analyzer and a varistor tester, respectively. According to Debye's equation, which states that the smaller the leakage current, the smaller the dielectric loss will be in the low-frequency region, we were able to roughly predict the relative value of the dielectric loss at low frequency by the leakage current. The best overall properties were obtained for x=0.06 (CaCu2.94Zn0.06Ti4O12), which has several prospective applications, such as low voltage varistor switchings, gas-sensing devices, and varistor–capacitor double property devices.

Novel microwave dielectric response of Ni/Co-doped manganese dioxides and their microwave absorbing properties

A facile redox reaction between KMnO4 and MnSO4 was carried out to investigate the dielectric response and microwave absorbing properties of Ni/Co-doped MnO2. The samples were characterized by X-ray powder diffraction (XRD), X-ray fluorescence spectrometry (XRF), scanning electron microscopy (SEM), and vector network analysis. The analysis results revealed that the powders were α-MnO2 with one-dimensional nanostructure. The doping of Ni/Co had a certain effect on the dielectric properties: the relative complex permittivity showed a more distinct dielectric response characteristic, and the imaginary part exhibited a great enhancement of 2–18 GHz, which resulted in controllable wave-absorbing properties. The microwave absorbing bandwidth (RL < −10 dB) for Co-doped MnO2 was located at 10.96–16.13 GHz with a thickness of 2 mm. Furthermore, the Debye equation was introduced to explain the novel microwave dielectric response of doped MnO2. Some other properties derived from dielectric performances were also investigated, such as dielectric loss tangent and dielectric conductivity. In particular, first-principles calculations based on density functional theory (DFT) were used to uncover the relationship of electronic structure and dielectric properties on the microscopic scale.