Frequency Dependence Of Modulus Research Articles

Frequency-dependent dielectric, electric modulus, and ac conductivity features of Au/n-Si Schottky diodes (SDs) with PVC and (PVC:Graphite/Graphene-Oxide) interlayer

To determine the interlayer effect on dielectric features and conductivity, Au/n-Si (S0), Au/PVC/p-Si (S1), and Au/PVC:Gt-GO/p-Si (S2) type SDs were grown onto the same n-Si wafer and their admittance measurements performed between 100 Hz and 1 MHz. The observed decrease in C and G/ω values as frequency increases shows that the charges at the interface-states (N ss) can easily follow ac-signal and supply an excess capacitance and conductance at lower frequencies. Using C and G/ω data at 1.5 V, the dielectric-constant (ϵ′), dielectric-loss (ϵ″), and loss-tangent (tan δ) were obtained as a function of frequency. To determine the relaxation processes in (PVC:Gt-GO) nanocomposite, complex-dielectric (M′ and M′′) formalism was also explored in the whole frequency range. The value of ac electrical conductivity (σ ac) remained independent of frequency until 0.1 MHz and then started to increase exponentially which corresponds to dc and ac conductivity. As compared to S1 and S2 with So SD, the conductivity and ϵ′ values increase due to the PVC and (PVC:Gt-GO) interlayer. The Ln(σ ac)-Ln(ω) plots were also drawn to analyze the conduction process and their slopes were found as 0.09, 0.39, and 0.58 for S0, S1, and S2 SD, respectively. These results show that the interaction and trap levels of the electron–hole pairs at lower frequencies, as well as from the well-localized relaxation mechanism at higher frequencies.

Optical and dielectric properties of divalent copper based double perovskite compound, Gd2CuTiO6

In this work, we have investigated high temperature dielectric properties and room temperature optical properties on rare earth ion based orthorhombic Gd2CuTiO6 (GCTO). Optical properties like reflectance and band gap were determined from ultra-violet visible (UV–Vis) diffuse reflectance spectroscopy technique and photoluminescence (PL) spectrum. The compound exhibited substantial optical absorption and emission in the visible region. Our findings reveal the presence of an intermediate band, as evidenced by the difference between the band gap values obtained from the Tauc plot using the diffuse reflectance spectrum (3.07 eV) and the PL spectrum (2.4 eV). Furthermore, thermogravimetric analysis demonstrated high thermal stability with <0.4% change in mass over a wide temperature range of 30 °C–1200 °C in air environment. Moreover, lead-halide free compound, GCTO is highly thermally stable oxide double perovskite with wide band gap and absorption in the UV–Vis range are highly suitable for optical applications In addition, dielectric properties of the compound have been examined using impedance spectroscopy as a function of frequency ranging from 500 Hz to 1 MHz and temperature between 300 K and 550 K. Compounds with relaxor behaviour at high temperatures and high thermal stability are desired for several applications. Because of the cation disorders present in this compound, GCTO displays dielectric relaxor behaviour indicative of a distribution of relaxation times. Furthermore, the frequency-dependent modulus illustrated a thermally activated conduction mechanism. Cole–Cole plots of electrical modulus suggest prominent grain contribution above 350 K.

Exact analytical solution for shear horizontal wave propagation through locally periodic structures realized by viscoelastic functionally graded materials

The paper presents a novel comprehensive exact analytical solution for modeling linear shear-horizontal (SH) wave propagation in an isotropic inhomogeneous layer made of functionally graded material, using local Heun functions. The layer is a composite of two materials with varying properties represented by spatial variations following the square of the sine function. The Voigt–Kelvin model is used to account for material losses. The study focuses on SH waves incident at a specific angle and employs the wave splitting technique to analyze forward and backward waves, facilitating the computation of reflection and transmission coefficients at any point in the inhomogeneous structure. The proposed solution utilizes the periodic nature of material functions and employs the Floquet–Bloch theory to derive an exact analytical solution. This approach is particularly suited for cases where SH waves encounter locally periodic functionally graded material. A Riccati equation-based verification is conducted to compare the frequency-dependent modulus of the reflection coefficient obtained from the analytical solution with numerically solved results. The presented work provides a comprehensive and versatile analytical solution for studying linear SH wave propagation in locally inhomogeneous isotropic layers, contributing to the theoretical understanding of elastic wave fields and practical applications.

Model order reduction of time-domain vibro-acoustic finite element simulations with non-locally reacting absorbers

Time-domain vibro-acoustic finite element simulation gained considerable interest in recent years because of the rise of some applications such as auralization and virtual sensing. Efficiency and stability are of great importance for this topic. The number of elements needed per wavelength to reach acceptable accuracy often results in a large model size, which requires lots of computational resources and cannot run efficiently. Model order reduction can significantly alleviate this problem by reducing the size of these models, while maintaining the high-fidelity property. However, many model order reduction techniques fail to preserve the stability for non-locally reacting absorbers, which are often accounted for by using the Helmholtz equation with frequency-dependent density and bulk modulus, known as the equivalent fluid method. When discretized into a finite element model, frequency-dependent mass and stiffness matrices are introduced, which hinder the preservation of stability in the context of model order reduction. This paper presents a method that enables the creation of a stable reduced order model of a vibro-acoustic system with non-locally absorbers. This method reforms the Helmholtz equation and considers it as the interconnection of several passive systems. Stacking the states of these subsystems gives the final descriptor representation of the non-locally reacting absorbers. Furthermore, a possible second-order representation of the descriptor model is chosen such that it satisfies the stability-preserving condition under model order reduction. The resulting second-order model is coupled with a vibro-acoustic system in a velocity potential-displacement formulation, leading to a second-order model satisfying the aforementioned stability-preserving condition. The proposed method is successfully verified by several numerical simulations.

Strain glass transition in Nb nanowire toughened NiTiHf shape memory alloy composite wires

In this work, we successfully prepared Nb nanowire toughened NiTiHf composite wires with different diameters. The strain glass transition was found in the as-drawn 0.1 mm diameter wire characterized by the Vogel-Fulcher type frequency-dependent modulus anomaly. However, the strain glass transition was not detected in 0.3 mm diameter wires. Microstructural characterization reveals that densely distributed Nb nanowires with small diameter and discontinuous orientation impose both physical confinement and heterogeneous stress fields on the matrix, which interrupt the long-range ordered martensitic transformation, leading to a continuous, high-order like strain glass transition. This work provides a new design strategy for searching new strain glass systems.

Investigation on electrical transport and dielectric relaxation mechanism in TbCrO3 perovskite orthochromite

Herein, the TbCrO3 (TCO) chromite was synthesized by the sol-gel auto-combustion route and sintered at 900 °C. The Rietveld analysis of the room temperature powder X-ray diffraction profile confirmed the single-phase formation of the material crystallized in the orthorhombic phase of the perovskite structure with Pbnm space group symmetry. The surface morphology, the elemental composition, and the chemical states of the compound were investigated by field emission scanning electron microscopy, energy dispersive X-ray analysis, and X-ray photoelectron spectroscopy, respectively. The electronic density of states, band structure, and electron density were analyzed by Density Functional Theory. The electrical transport and dielectric relaxation mechanism were investigated using complex impedance spectroscopy over the experimental frequency and temperature ranging from 40-1.2x106Hz and 138−273 K, respectively. Two semicircular arcs in the impedance complex plane plots were modeled to an equivalent circuit configured by RG∥QG+RGB∥QGB which were attributed to the contributions of the highly resistive grain boundaries and relatively conducting grains in the material. The electrical conductivity as a function of frequency followed Jonscher’s universal power law behavior and an increasing nature of the temperature-dependent frequency exponent suggested small polaron hopping as the electrical conduction mechanism of the material. The least capacitive response of the TCO system was investigated by the complex electrical modulus formalism and the frequency-dependent imaginary modulus spectra were modeled by the Kohlrausch–Williams–Watts function, which resolved the thermally activated peaks of bulk and interface effects to the dielectric relaxation mechanism. The dielectric constant exhibited Maxwell-Wagner interfacial polarization effects and the dielectric loss factor showed frequency dispersion at all temperatures.

Geotechnical and thermal analysis and complex impedance spectroscopy characterization of pure Moroccan bentonite material for civil engineering applications

Combined modulus and impedance spectra are employed in the present work to explore electrical inhomogeneity and carriers’ behaviors in a pure bentonite Moroccan clay based on equivalent circuit. It has been clearly observed that the electrical properties change due to the increase of temperature from 300 °C to 700 °C. The frequency-dependent imaginary modulus M" and imaginary impedance Z" curves has only one peak at each temperature indicating the predominance of the contribution of grains to the total electrical conduction in bentonite. The positions of these peaks move to higher frequencies when the temperature increases in relation with the distribution of relaxation time. Moreover, the activation energy for the conduction process in bentonite is determined from the slope of ln(ρdc) versus of 1/T in the order of 700 meV in good agreement with that obtained from the proposed equivalent circuit. On the other hand, let’s present a geotechnical study that show that our material is a swelling clay, very plastic and could be used as a binder. The external stress dependence of the bulk density, Young’s module and maximum stress are analysed. The thermal conductivity determined following the device of Lee's disks where two copper disks of thickness of 15 mm and diameter of 30 mm were used

Investigation of multiferroic properties of dysprosium substituted bismuth ferrite (Bi1-xDyxFeO3) prepared by auto combustion technique

A simple and inexpensive auto combustion procedure was used to create the Bi1-xDyxFeO3 (x=0.0, 0.015, 0.03, 0.045, 0.060) multiferroics samples. In bismuth ferrite, the average crystallite size increased with growing Dy3+ concentration in BFO, revealing a rhombohedral distorted perovskite structure of space group R3c. During morphological analyses of the produced samples, a spherical structure with little aggregation was found. When Dy3+ is substituted at the B-site, the Raman modes widen and the cation site occupancy changes even more. The frequency-dependent dielectric properties (εr, tanδ), electric conductivity (ac), impedance (Z), and electric modulus (M' and M′′) of the samples were assessed using an impedance analyzer at frequencies between 20 Hz and 20 MHz. All samples had the maximum dielectric constant, which was discovered at a relatively low frequency. The highest value of impedance was found at low frequency and it lowers with increasing frequency as a result of the contributions from the grain and grain boundary. It is discovered that the samples' ac conductivity is frequency-dependent and changes depending on how much Dy3+ is doped into the BFO.

Comparison between longitudinal viscoelastic relaxation and sound dispersion of molecular liquids on the molecular scale.

Molecular dynamics simulation on some molecular liquids was performed to study sound dispersion on the molecular scale. The sound velocity was determined from the intermediate scattering function, and the relation between the longitudinal modulus and frequency was compared with the frequency-dependent longitudinal modulus in the q = 0 limit evaluated by the Kubo-Green theory. The sound dispersion of a monoatomic liquid up to qσ ≅ 2 was almost quantitatively explained by the viscoelasticity in the q = 0 limit when the wavenumber dependence of the heat capacity ratio was taken into account. The situation was similar for a polyatomic molecular liquid for which the intramolecular degrees of freedom were fixed. For a polyatomic liquid with intramolecular degrees of freedom, the sound dispersion on the molecular scale was connected to the high-frequency limit of the ultrasonic relaxation mode assigned to the vibrational energy relaxation. After subtracting the contribution of the vibrational energy relaxation, both the longitudinal viscoelasticity and the sound dispersion depended little on the presence of intramolecular degrees of freedom.

The effects of frequency change on dielectric characteristics in dye-based organic layers

In order to examine the dielectric properties of the Au/B1/p-Si, Au/B2/p-Si, Au/B3/p-Si and Au/B4/p-Si structures, BODIPY dye-based organic layers was coated as a thin film between the metal-semiconductor as the interface. Electrical conductivity, real and imaginary parts of the electrical module, dielectric loss and dielectric constant parameters were calculated in the frequency range of 100–1000 kHz at room temperature. The effect of frequency on dielectric constant and dielectric loss values was not regular in forward bias for Au/B1/p-Si and Au/B2/p-Si at low frequency, but was consistent with frequency for Au/B3/p-Si and Au/B4/p-Si. Dielectric parameters generally behaved as functions of voltage and frequency. The changes in the frequency-dependent electrical modulus were attributed to the relaxation process, polarization, and surface conditions.

Nonlinear eigenvalue topology optimization for structures with frequency-dependent material properties

Eigenvalue topology optimization problem has been a hot topic in recent years for its wide applications in many engineering areas. In the previous studies, the applied materials are usually assumed as elastic, and the resulting structural eigenfrequencies are obtained by solving a linear eigenvalue problem. However, many engineering materials, such as viscoelastic materials, have frequency-dependent modulus, which results in a more complicated nonlinear eigenvalue problem. This paper presents a systematic study on the nonlinear eigenvalue topology optimization problem with frequency-dependent material properties. The nonlinear eigenvalue problem is solved by a continuous asymptotic numerical method based on the homotopy algorithm and perturbation expansion technique, which involves higher-order differentiation of the nonlinear term and shows a fast convergence. Several schemes are proposed to improve the computational accuracy, applicability, and robustness of the method for the application in topology optimization, including Faà di Bruno's theorem, bisection method, and inverse iteration based eigenvector modification method. Three optimization problems are solved to demonstrate the effectiveness of the developed methods, including the maximization of the fundamental frequency, the eigenfrequency separation interval between two adjacent eigenfrequencies of given orders, and the eigenfrequency separation interval at a given frequency. Numerical examples show the large influence of the frequency-dependent material properties on the optimized results and validate the effectiveness of the developed method.

Characterization of a Volcanic Gas Reservoir Using Seismic Dispersion and Fluid Mobility Attributes

Abstract Seismic dispersion and fluid mobility attributes are used to characterize a volcanic gas reservoir in the Songliao Basin of China. A rock physics model is constructed to describe poroelastic behaviors associated with heterogeneous fluids saturation within the volcanic gas reservoirs, where velocity dispersion and attenuation of propagating waves are attributed to the wave-induced fluid flow described by the patchy saturation theory. Modeling results indicate that the frequency-dependent bulk modulus at the seismic frequency is more sensitive to gas saturation than the P-wave velocity dispersion. Accordingly, a new inversion method is developed to compute bulk-modulus-related dispersion attribute DK for improved characterization of volcanic gas reservoirs. Synthetic tests indicate that DK is more sensitive than traditional P-wave dispersion attribute DP to the variations of reservoir properties. The high value of dispersion attribute DK indicates the volcanic gas reservoirs with high porosity and gas saturation. At the same time, fluid mobility attribute FM can discriminate the volcanic gas reservoir as DK. Field data applications illustrate that DK and FM exhibit anomalies to the gas zones in the volcanic gas reservoir on the cross-well section. However, DK is more robust than FM to identify favorable zones on horizontal slices for specific target layers. Overall, rock physical modeling provides insights into the poroelastic behaviors of volcanic gas reservoirs, and inversion for seismic dispersion attribute DK improves hydrocarbon detection in the volcanic gas reservoir.

Study of the optical properties and frequency-dependent electrical modulus spectrum to the analysis of electric relaxation and conductivity effect in zinc oxide nanoparticles

Study of the optical properties and frequency-dependent electrical modulus spectrum to the analysis of electric relaxation and conductivity effect in zinc oxide nanoparticles

Simulations of poroelastic materials in a complex acoustic system using frequency-dependent parameters in the mid-frequency range

Efficiency requirements prompt manufacturers to develop ever lighter acoustic packages in vehicles. Poroelastic materials are essential to achieve the desired interior noise level targets and thus the simulation of their effects is of utmost importance in NVH analyses. However, it is challenging to achieve good validation between finite element method (FEM) based simulation results and measurements in the mid-frequency range (400-1000 Hz). One possible reason could be the lack of using frequency-dependent Biot-paremeters describing the poroelastic materials (PEM) characteristics of trims. The present research aims to employ frequency-dependent Biot-parameters for the PEM materials to investigate the acoustic response of a scaled car-like steel structure composed of flat plates and U-section stiffeners enclosing an air cavity. Porous acoustic material is applied to the walls of the cavity. The focus of the study is to understand the effect of applying frequency-dependent Young's modulus and damping values for the PEM parameters in the 100-1000 Hz range. Simulation results obtained from ESI VPS FEM solver are compared with measurements, with particular focus on the interior sound pressure levels. The simulation methodology, including discretization techniques, structural damping and fluid damping applications are described in detail.

Seismic wave modeling in vertically varying viscoelastic media with general anisotropy

Seismic anisotropy, wave attenuation, and dispersion are critical phenomena of wave propagation in real media. Full-wavefield modeling of wave behavior in such media plays an important role in investigating dynamic features of the earth’s interior and in full-waveform inversion of anisotropic parameters and velocity dispersion. We have developed a numerical scheme to model the full-waveform response from a point source in a vertically varying viscoelastic medium of arbitrary anisotropy. The method is implemented in the frequency domain, so the complexity of anelasticity and anisotropy can be described by a complex elastic stiffness matrix and frequency-dependent moduli can also be readily incorporated. In our scheme, we solve the elastodynamic equations for general anisotropy through finite-element method in the frequency-wavenumber domain and we use the stiffness reduction method to suppress reflections from artificial boundaries along the depth direction. A nonuniform 2D Fourier transform strategy is developed to reconstruct the spatial-domain counterparts from the wavenumber-domain solutions. The time-domain responses are then obtained by taking inverse fast Fourier transform with respect to frequency. We validate the method by comparing the numerical results with the exact solutions for a homogeneous transversely isotropic model and a two-layered model. In the application example, we further proved the feasibility and generality of the scheme using an attenuative, dispersive model with velocity and attenuation anisotropy. Our scheme enjoys significant advantages in incorporating various viscoelastic/dispersive behaviors and general anisotropy, and thus provides a useful tool for numerical simulation of dynamic responses in practical application.

Investigation on Electrical Properties of Solid Polymer Sheets (HDPE AND LDPE) at Audio Frequency Range

Two different groups of solid polymer sheets: low density polyethylene (LDPE) sample of thickness 0.006 cm and 0.007 cm along with high density polyethylene (HDPE) sample of the thickness of 0.009 cm, 0.010 cm were taken in this work. The measurement of electrical properties such as dielectric constant, ε' and dielectric loss, ε'' for LDPE and HDPE polymer sheets have been measured using a dielectric cell. The dielectric cell has been fabricated which consists of two circular parallel plates of pure stainless steel each of 5 cm diameter and 2 mm thickness. An impedance bridge (GRA 650A) was used for measurement of capacitance, C, and dissipation factor, D in the audio frequency (AF) range, 100 Hz to 10 kHz. Different samples were loaded in between the two plates of the cell and the capacitance as well as the dissipation factor were estimated from the dial readings of the bridge. Effect of frequency variation on ε', ε'', relaxation time, τ , dissipation factor, tanδ and ac conductivity, σ were also discussed at audio frequency range. The complex permittivity, ε*, related to free dipole oscillating in an alternating field and loss tangent, tanδ were calculated. The frequency-dependent conductivity, dielectric behavior, and electrical modulus, both real (M') and imaginary (M") parts of LDPE and HDPE have been studied in this work. The values of the real part of the electrical modulus (M') did not equal to zero at low frequencies and it is expected that the electrode polarization may develop in both sheets. These findings reveal an increased coupling among the local dipolar motions in a short-range order localized motion. The analysis of real (ε') and imaginary (ε'') parts of dielectric permittivity and that electrical modulus real (M') and imaginary (M") parts signify poly dispersive nature of relaxation time as observed in Cole-Cole plots.

Investigation of frequency characteristics of biological tissues impedance

The problem of identifying informative signs of biological tissues viability using the impedance measurement method is formulated. At present there is no instrumental base that makes it possible in an operational setting to diagnose the ability of biological tissue to heal itself after injury and damage as a result of thermal exposure, gunshot wound or prolonged compression. It is shown in this article that development of methods and tools for instrumental diagnostics in medical diagnostic practice is an important modern challenge.&#x0D; The results of experimental measurements of impedance characteristics in the frequency range of 20 Hz – 2.0 MHz are presented. The frequency dependences of the modulus of voltage on biological tissues of plant origin are analyzed in its intact state, as well as after exposure of biological tissue samples in a freezer at time intervals from 15 minutes to 2 hours.&#x0D; A comparative analysis of the obtained frequency dependences is carried out. A significant difference between the frequency dependences of the voltage modulus on biological tissues and the frequency dependence of the voltage modulus on an isotonic solution is shown. The concept is introduced that the degree of difference between the frequency distribution of the biological tissue impedance module from the impedance module of an isotonic solution can serve as a criterion for assessing the degree of damage to biological tissue.&#x0D; A conclusion is made about the advisability of developing the impedance measurement method as a method for diagnosing the viability of biological tissue; it is shown that the most promising approach to the development of impedance measurement methods is the analysis of transient processes when biological tissue is disturbed by small electric current pulses.

Sol-gel derived cobalt containing Ni–Zn ferrite nanoparticles: Dielectric relaxation and enhanced magnetic property study

A systematic study of transitional metal ion doped nickel-zinc ferrite (NZF) nanoparticles with its magnetic properties and conductivity relaxation mechanism are the objectives of this research. We have prepared cobalt doped NZF nanoparticles (NZCo) via a facile chemical route. X-Ray Diffraction (XRD) and Transmission Electron Microscopy (TEM) analyses suggest the formation of single phase nearly spherical nanoparticles around 60 nm in size. UV–Vis study reveals the redshift of the optical band gap for doped samples. Estimation of particle size using the effective mass model agrees well with TEM/XRD results. The electrical modulus spectra have been analyzed using Harvilliak-Negami model function. Migration energy has been found to be the minimum for 10 mol % doped sample. Frequency-dependent modulus spectra have been converted to time domain data and the relaxation process shows Kohlrausch–Williams–Watts (KWW) type behavior. Carrier motion inside the lattice has been found to be strongly correlated. Room temperature magnetization curve shows that very weak AFM/PM contribution and strong FM interaction inside the system as well as non-collinear spin arrangements between interstitial sites. Law of Approach (L.A.) analysis of the AFM/PM part subtracted hysteresis curve delineates the enhanced magnetic properties such as saturation magnetization, anisotropy constant and coercivity. Multi-functional materials of such kind with optimum behavior at specific doping percentages can be fruitful for electronic industries.

Damping control in viscoelastic beam dynamics

Viscoelasticity plays a key role in many practical applications and in different research fields, such as in seals, sliding-rolling contacts, and crack propagation. In all these contexts, a proper knowledge of the viscoelastic modulus is very important. However, experimental characterization of the frequency-dependent modulus, carried out through different standard procedures, still presents some complexities; then possible alternative approaches are desirable. For example, experimental investigation of viscoelastic beam dynamics would be challenging, especially for the intrinsic simplicity of this kind of test. This is why a deep understanding of damping mechanisms in viscoelastic beams is found to be a quite important task to better predict their dynamics. With the aim to enlighten damping properties in such structures, an analytical study of the transversal vibrations of a viscoelastic beam is presented in this article. Some dimensionless parameters are defined, depending on the material properties and the beam geometry, which enable to accurately design the beam dynamics. In this way, by properly tuning such disclosed parameters, for example the dimensionless beam length or a chosen material, it is possible to enhance or suppress some resonant peaks, one at a time or more simultaneously. This is a remarkable possibility to efficiently control damping in these structures, and the results presented in this article may help in elucidating experimental procedures for the characterization of viscoelastic materials.

Poly(acrylic acid) grafted soy carbohydrate as thickener for waterborne paints

Thickeners are widely used to change rheological properties of latex paints. Soy carbohydrate is an abundant, but a rarely utilized agricultural by-product. The grafting of poly(acrylic acid) onto soy carbohydrate particles forms gel particles that can change rheological properties of latex paints. The grafting polymerization of acrylic acid onto carbohydrate particles using ammonium cerium (IV) nitrate as initiator increased the particle size and viscosity of the aqueous particle dispersion. The viscosity increased with the increased amount of grafted poly(acrylic acid). Strain and frequency dependent moduli show a difference in dispersion-properties between the grafted soy carbohydrate and hydroxyl ethyl cellulose. The latex paint with poly(acrylic acid) grafted soy carbohydrate shows similar viscosity at low shear rate region and lower viscosity at higher shear rates when compared to the latex paint with hydroxyl ethyl cellulose. High-shear-recovery measurements of the latex paints predict sagging properties that are consistent with the ASTM sagging tests.