Determining the relaxation polarization parameters in dielectrics with high electrical conductivity

In dielectrics with high steady leakage of conductivity, the frequency–temperature dependences of the dielectric loss tangent generally allow us to determine the relaxation time and activation energy of relaxation process only when they are strong. With weak relaxation processes, there are no extrema in the frequency dependence of the dielectric loss tangent. In such cases, the parameters of the relaxation processes are initially determined from the frequency behavior of the imaginary parts of the electrical module or impedance. However, the frequency dependences of these quantities when there is electrical conduction can contain three extrema. Identifying the maxima associated with relaxation polarization therefore requires additional research.     

Strong and weak polarization relaxation processes in solid dielectrics

It is established that an increase in the reach-through electrical conductivity of a dielectric can affect the frequency characteristics of the quantity tanδ in different ways when relaxation polarization processes occur: the extrema of the frequency characteristics can be either suppressed or intensified. In the former case, relaxation processes are referred to as weak; in the latter case, they are referred to as strong. Strong processes lead to the emergence of extrema in the frequency dependence of the imaginary part of complex conductivity. The causes underlying the two polarization relaxation processes are identified.     

AC conductivity and dielectric relaxation in Ba(Sm1/2Nb1/2)O3 ceramic

The complex perovskite oxide a barium samarium niobate (BSN) synthesized by solid-state reaction technique has single phase with cubic structure. The scanning electron micrograph of the sample shows the average grain size of BSN∼1.22 μm. The field dependence of dielectric response and loss tangent were measured in the temperature range from 323 to 463 K and in the frequency range from 50 Hz to 1 MHz. The complex plane impedance plots show the grain boundary contribution for higher value of dielectric constant in the low frequency region. An analysis of the dielectric constant (ε′) and loss tangent (tan δ) with frequency was performed assuming a distribution of relaxation times as confirmed by the scaling behaviour of electric modulus spectra. The low frequency dielectric dispersion corresponds to DC conductivity. The logarithmic angular frequency dependence of the loss peak is found to obey the Arrhenius law with an activation energy of 0.71 eV. The frequency dependence of electrical data is also analyzed in the framework of conductivity and electric modulus formalisms. Both these formalisms show qualitative similarities in relaxation times. The scaling behaviour of imaginary part of electric modulus M″ and dielectric loss spectra suggest that the relaxation describes the same mechanism at various temperatures in BSN. All the observations indicate the polydispersive relaxation in BSN.     

Electrical conductivity and dielectric relaxation studies on microwave synthesized Na<Subscript>2</Subscript>SO<Subscript>4</Subscript>·NaPO<Subscript>3</Subscript>·MoO<Subscript>3</Subscript> glasses

Electrical conductivity and dielectric relaxation studies on SO₄ ^2? doped modified molybdo-phosphate glasses have been carried out over a wide range of composition, temperature and frequency. The d.c. conductivities which have been measured by both digital electrometer (four-probe method) and impedance analyser are comparable. The relaxation phenomenon has been rationalized using electrical modulus formalism. The use of modulus representation in dielectric relaxation studies has inherent advantages viz., experimental errors arising from the contributions of electrode-electrolyte interface capacitances are minimized. The relaxation observed in the present study is non-Debye type. The activation energies for relaxation were determined using imaginary parts of electrical modulus peaks which were close to those of the d.c. conductivity implying the involvement of similar energy barriers in both the processes. The enhanced conductivity in these glasses can be attributed to the migration of Na⁺, in expanded structures due to the introduction of SO₄ ^2? ions.     

Ac conductivity study of lithium and potassium diphosphate LiK3P2O7 using impedance spectroscopy

In this work, a LiK₃P₂O₇ ceramic material was prepared by the solid-state reaction method and identified by X-ray diffractometry. The dielectric properties, impedance characteristics, and modulus were studied over a range of frequency (200 Hz to 5 MHz) and temperature (615–708 K). The frequency and temperature dependence of dielectric permittivity, dielectric loss, and electric modulus is studied. The frequency analysis of modulus properties showed a distribution of relaxation times. Conductivity plots against frequency at a higher frequency suggested the response obeying the universal power law. The temperature behavior of the frequency exponents shows that the correlated barrier hopping CBH model is well adapted to this material. The activation energy associated with the impedance relaxation and the electric modulus spectra is close to the activation energy for dc conductivity indicating the similar nature of relaxation and conductivity. Thermodynamic parameters such as free energy of activation, enthalpy, and entropy have been calculated.     

Dielectric relaxation in complex perovskite oxide BaCo1/2W1/2O3

Polycrystalline BaCo_1/2W_1/2O₃ (BCW) is prepared by the solid-state reaction technique. The X-ray diffraction study of the compound at room temperature reveals the monoclinic phase. The field dependence of the dielectric constant and the conductivity are measured in the frequency range from 50 Hz to1 MHz and in the temperature range from 300 to 413 K. An analysis of the real and imaginary parts of the dielectric permittivity with frequency is performed. The frequency-dependent maxima in the imaginary impedance are found to obey an Arrhenius law with an activation energy=0.86 eV. The frequency-dependent electrical data are also analysed in the framework of the conductivity and modulus formalisms.     

Structural and AC conductivity study of CdTe nanomaterials

Cadmium telluride (CdTe) nanomaterials have been synthesized by soft chemical route using mercapto ethanol as a capping agent. Crystallization temperature of the sample is investigated using differential scanning calorimeter. X-ray diffraction and transmission electron microscope measurements show that the prepared sample belongs to cubic structure with the average particle size of 20 nm. Impedance spectroscopy is applied to investigate the dielectric relaxation of the sample in a temperature range from 313 to 593 K and in a frequency range from 42 Hz to 1.1 MHz. The complex impedance plane plot has been analyzed by an equivalent circuit consisting of two serially connected R-CPE units, each containing a resistance (R) and a constant phase element (CPE). Dielectric relaxation peaks are observed in the imaginary parts of the spectra. The frequency dependence of real and imaginary parts of dielectric permittivity is analyzed using modified Cole–Cole equation. The temperature dependence relaxation time is found to obey the Arrhenius law having activation energy ~0.704 eV. The frequency dependent conductivity spectra are found to follow the power law. The frequency dependence ac conductivity is analyzed by power law.     

The electrical impedance,AC conductivity and dielectric properties of phenol red compound investigated and modeled by an artificial neural network

The impedance spectroscopy, electrical conductivity and electric modulus of bulk phenol red were measured, as a function of both frequency and temperature. Artificial neural networks (ANNs) were used for modeling its electrical properties. The two parts (real and imaginary) of its complex impedance (Z*) were analyzed and the activation energy related to the electrical relaxation process was evaluated. Nyquist curves were plotted showing semicircles for the different temperatures. The AC electrical conductivity follows a power law σ_ac(ω) α ω^η. The maximum barrier height B_m was derived for specific temperatures. A plausible mechanism for the AC conduction of bulk phenol red was deduced from the temperature reliance of the frequency exponent. The dielectric data was analyzed using electric modulus as a tool. In addition, ANNs were used to model the impedance parts and the total electrical conductivity. Numerous runs were tried, to obtain the best performance. The training and prediction results were compared to the equivalent experimental results, with a good match obtained. An equation describing the experimental results was obtained mathematically, based on the use of ANNs. The outputs demonstrated that ANNs are an admirable tool for modeling experimental results.     

Structural and electrical characteristics of rare earth simple perovskite oxide La0.57Nd0.1Pb0.33Mn0.8Ti0.2O3

Polycrystalline La_0.57Nd_0.1Pb_0.33Mn_0.8Ti_0.2O₃ (LNPMT) is prepared by the solid-state reaction technique. The formation of single phase material was confirmed by X-ray diffraction studies, and it was found to be a rhombohedral phase at room temperature. The impedance plane plot shows semicircle arcs at different temperatures and an electrical equivalent circuit has been proposed to explain the impedance results. The frequency dependent conductivity spectra follow the universal power law. The activation energy deduced from analysis of the imaginary part of electric modulus and imaginary impedance is found to be ∼75 meV. Such a value of activation energy indicates that the conduction mechanism for the sample is due to electron hopping. The imaginary part of the electric modulus suggests that the relaxation describes the same mechanism at various temperatures.     

Dielectric relaxation of samarium aluminate

A ceramic SmAlO₃ (SAO) sample is synthesized by the solid-state reaction technique. The Rietveld refinement of the X-ray diffraction pattern has been done to find the crystal symmetry of the sample at room temperature. An impedance spectroscopy study of the sample has been performed in the frequency range from 50 Hz to 1 MHz and in the temperature range from 313 K to 573 K. Dielectric relaxation peaks are observed in the imaginary parts of the spectra. The Cole–Cole model is used to analyze the dielectric relaxation mechanism in SAO. The temperature-dependent relaxation times are found to obey the Arrhenius law having an activation energy of 0.29 eV, which indicates that polaron hopping is responsible for conduction or dielectric relaxation in this material. The complex impedance plane plot of the sample indicates the presence of both grain and grain-boundary effects and is analyzed by an electrical equivalent circuit consisting of a resistance and a constant-phase element. The frequency-dependent conductivity spectra follow a double-power law due to the presence of two plateaus.     

Complex impedance spectroscopic studies of Ba(Pr1/2Ta1/2)O3 ceramic

The polycrystalline sample of Ba(Pr_1/2Ta_1/2)O₃ was prepared by a high-temperature solid-state reaction technique. The crystal symmetry, space group and unit cell dimensions were derived from the experimental results using FullProf software. XRD analysis of the compound indicated the formation of a single-phase tetragonal structure with the space group P4/mmm (1 2 3). Impedance and electric modulus analysis were used as tools to analyze the electrical behavior of the sample as a function of frequency at different temperatures. The impedance analysis of the compound indicated a typical negative temperature coefficient of resistance behavior, and dielectric relaxation was found to be of non-Debye type. The frequency dependent maximum of the imaginary part of the electric modulus follows the Arrhenius law with activation energy of 0.15 eV. The ac conductivity data obeys double power law.     

Electrical properties and dielectric relaxation of thermally evaporated zinc phthalocyanine thin films

The electrical transport properties and dielectric relaxation of Au/zinc phthalocyanine, ZnPC/Au devices have been investigated. The DC thermal activation energy at temperature region 400-500 K is 0.78 eV. The dominant conduction mechanisms in the device are ohmic conduction below 1 V and space charge limited conduction dominated by exponential trap distribution in potentials >1 V. Some parameters, such as concentration of thermally generated holes in valence band, the trap concentration per unit energy range at the valence band edge, the total concentration of traps and the temperature parameter characterizing the exponential trap distribution and their relation with temperatures have been determined. The AC electrical conductivity, σ_ac, as a function of temperature and frequency has been investigated. It showed a frequency and temperature dependence of AC conductivity for films in the temperature range 300-400 K. The films conductivity in the temperature range 400-435 K increased with increasing temperature and it shows no response for frequency change. The dominant conduction mechanism is the correlated barrier hopping. The temperature and frequency dependence of real and imaginary dielectric constants and loss tangent were investigated.     

Dielectric relaxation of ZnO nanostructure synthesized by soft chemical method

Thioglycerol capped nanoparticles of ZnO have been prepared in methanol through chemical technique. Nanostructures of the prepared ZnO particles have been confirmed through X-ray diffraction measurement. The Debye–Scherrer formula is used to obtain the particle size. The average size of the prepared ZnO nanoparticles is found to be 50 nm. The frequency-dependent dielectric dispersion of the sample is investigated in the temperature range from 293 to 383 K and in a frequency range from 100 Hz to 1 MHz by impedance spectroscopy. An analysis of the complex permittivity (ε′ and ε′′) and loss tangent (tan δ) with frequency is performed assuming a distribution of relaxation times. The frequency-dependent maxima of the imaginary part of impedance are found to obey Arrhenius law with activation energy ∼1 eV. The scaling behavior of dielectric loss spectra suggests that the relaxation describes the same mechanism at various temperatures. The frequency-dependent electrical data are analyzed in the framework of conductivity and modulus formalisms. The frequency-dependent conductivity spectra obey the power law.     

Electrical properties,equivalent circuit,and dielectric relaxation studies on [(C<Subscript>3</Subscript>H<Subscript>7</Subscript>)<Subscript>4</Subscript>N]<Subscript>2</Subscript>Cd<Subscript>2</Subscript>Cl<Subscript>6</Subscript> polycrystalline

The Ac electrical conductivity and the dielectric relaxation properties of the [(C₃H₇)₄N]₂Cd₂Cl₆ polycrystalline sample have been investigated by means of impedance spectroscopy measurements over a wide range of frequencies and temperatures, 209 Hz–5 MHz and 361–418 K, respectively. The purpose is to make a difference between the electrical and dielectric properties of the polycrystalline sample and single crystal. Besides, a detailed analysis of the impedance spectrum suggests that the electrical properties of the material are strongly temperature-dependent. Plots of (Z" versus Z') are well fitted to an equivalent circuit model consisting of a series combination of grains and grains boundary elements. Moreover, the temperature dependence of the electrical conductivity in the different phases follows the Arrhenius law and the frequency dependence of σ (ω) follows the Jonscher’s universal dynamic law. Furthermore, the modulus plots can be characterized by full width at half height or in terms of a nonexperiential decay function φ(t) = exp(t/t)^β. Finally, the imaginary part of the permittivity constant is analyzed with the Cole–Cole formalism.     

Dielectric Relaxations and Structures of Nanoclay in Solution Cast Poly(Ethylene Oxide)– Montmorillonite Clay Nanocomposites

The relative complex dielectric function, electric modulus and alternating current electrical conductivity spectra and complex impedance plane plots of aqueous solution cast poly(ethylene oxide)–montmorillonite clay (PEO–MMT) nanocomposite films were investigated over the frequency range 20 Hz to 1 MHz at ambient temperature. The intercalated and exfoliated structures of nanoclay dispersed in PEO matrix were recognized by the significant change in real part of dielectric function with clay concentration in the range 0%–20 wt%. The relaxation times corresponding to PEO chain segmental motion and ionic conduction relaxation processes were used to explore the interactions compatibility between PEO molecules and the dispersed MMT clay nanoplatelets and their effect on PEO chain dynamics. Real part of conductivity spectra of these nanocomposites over five decades of frequency has nonlinear behavior, which is influenced by the MMT clay concentration. The complex impedance plane plots confirm the bulk properties of these nanocomposites over the experimental frequency range.     

Structural,dielectric, electrical and magnetic properties of chemicothermally synthesized material: BiCaFeCeO6

In this communication, detailed studies of structural, micro-structural, dielectric, electrical (impedance, modulus and conductivity) and magneto-electric characteristics of a chemico-thermally synthesized sample of a double perovskite bismuth calcium iron cerate (BiCaFeCeO₆) have been reported. Preliminary structural analysis of room temperature X-ray diffraction data shows orthorhombic structure of the material. The homogeneous distribution of the grains of different dimensions (shape, size, etc) with a small number of voids observed in the scanning electron micrograph suggests the formation of high-density sample. Detailed analysis of dielectric and impedance experimental data, collected at different frequency and temperatures, have provided many important characteristics of the material, such as (a) grains, grain boundaries, and electrode dependent capacitive and impedance parameters, (b) co-relation between the structure, micro-structure and physical properties and (c) the relaxation characteristics of the tested samples. The nature of frequency dependence of AC conductivity of the material obeys the Jonscher's universal power law. The temperature dependence of conductivity provides the conduction mechanism in the material. Detailed studies of field dependence of electric polarization, magnetization and magneto-electric coefficient at room temperature exhibit the multiferroic characteristics of the material.     

Electronic transport mechanisms in tetraphenyleprophyrin thin films

Thermally-evaporated thin films of tetraphenylporphyrin, TPP, with thickness range from (175 to 735) nm had been prepared. Annealing temperatures ranging from (273–473) K do not influence the amorphous structure of these films. The influence of environmental conditions: film thickness, temperature and frequency on the electrical properties of TPP thin films had been reported. It was found that dc conductivity increases with increasing temperature and film thickness. The extrinsic conduction mechanism is operating in temperature range of (293–380) K with activation energy of 0.13 eV. The intrinsic one is in temperatures >380 K via phonon assisted hopping of small polaron with activation energy of 0.855 eV. The ac electrical conductivity and dielectric relaxation in the temperature range (293–473) K and in frequency range (0.1–100) kHz had been also studied. It had been shown that theoretical curves generated from correlated barrier hopping (CBH) model gives the best fitting with experimental results. Analysis of these results proved that conduction occurs at low temperatures (300–370) K by phonon assisted hopping between localized states and it is performed by single polaron hopping process at higher temperatures. The temperature and frequency dependence of both the real and imaginary parts of dielectric constant had been reported.     

The special features of the frequency dependence of phononless hopping conduction

Within the framework of perturbation theory the imaginary part of the phononless conduction of a lightly doped compensated semiconductor is calculated. It is shown that when the basis of localized atomic-like functions is used, the superlinear frequency dependence of the real part of the conduction corresponds to the approximately linear frequency dependence of the imaginary part of the conductivity. It has been found that at frequencies below the transition (crossover) frequency ??_cr from the linear to quadratic frequency dependence of the real part of conductivity, the dielectric loss tangent depends weakly on the frequency and it is determined by the relationship of ???_cr to the width of the impurity band. It is shown that measurements of the dielectric loss tangent can provide information on the localization radius of impurity states.     

Structural and ac electrical properties of a newly synthesized single phase rare earth double perovskite oxide: Ba2CeNbO6

A single phase rare earth double perovskite oxide Ba₂CeNbO₆ (BCN) is synthesized by solid-state reaction technique for the first time. The X-ray diffraction pattern of the sample at room temperature shows monoclinic structure, with the lattice parameters, a=5.9763 Å, b=5.975 Å and c=8.48 Å and β=90.04°. Impedance spectroscopy is used to study the ac electrical behavior of this material as a function of frequency (10²-10⁶ Hz) at various temperatures (30-450 °C). A relaxation is observed in the entire temperature range. Conduction mechanism is investigated by fitting the complex impedance data to Cole-Cole equation. Complex impedance plane plots show only one semicircular arc, indicating only the grain contribution of dielectric relaxation. The scaling behavior of imaginary part of electric modulus (M″) and imaginary part of electrical impedance (Z″) suggests that the relaxation describes the same mechanism at various temperatures. The frequency dependence of conductivity is interpreted in terms of the jump relaxation model and is fitted to Jonscher's power law. The values of dc conductivities extracted from the Jonscher power law varies from 2.79×10⁻⁷ to 3.5×10⁻⁵ Sm⁻¹ with the increase in temperature from 100 to 450 °C. The activation energies (0.37 eV) extracted from M″(ω) and Z″(ω) peaks are found to follow the Arrhenius law.     

Electron beam induced modifications in conductivity and dielectric property of polymer electrolyte film

This paper describes the effect of 8 MeV of electron beam (EB) energy irradiation on the electrical conductivity and dielectric properties of sodium fluoride NaF-doped polyethylene oxide (PEO) film. The structural and chemical characterizations were employed using X-ray diffractometry (XRD) and Fourier Transform Infrared (FTIR) techniques respectively before and after irradiation. The morphology study carried out using Scanning Electronic Microscopy (SEM) analysis. The DC electrical conductivity showed increases with dose and temperature and was consistent with Arrhenius behavior. The maximum conductivity of 1.1 × 10⁻⁵ S/cm and minimum activation energy of 0.25 eV were obtained at 25 kGy, 338 K; further increases in the dose resulted in a reduction in conductivity. The real (ε′) and imaginary (ε″) part of the dielectric constant suddenly decreased in a low frequency region (40–640 Hz), subsequently independent at higher frequency. The AC conductivity showed increases with frequency and temperature for all films. The dielectric constant and AC conductivity increased at the 25 kGy dose due to chain scission. Further increases in dose such as 50 and 75 kGy, resulted in a decrease in dielectric constant and AC conductivity due to cross-linking. The electric modulus approach was used to calculate the dielectric relaxation time (τ), which decreased at 25 kGy and then increased at 50 and 75 kGy doses. The modulus data were fitted using a non-exponential Kohlrausch–Williams–Watts (KWW) function ϕ (t), and the results indicate the existence of a non-Debye relaxation.