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.     

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 relaxation spectroscopy of phlogopite mica

An in-depth investigation of the dielectric characteristics of annealed phlogopite mica has been conducted in the frequency range 0.1 Hz–10 MHz and over the temperature range 653–873 K through the framework of dielectric permittivity, electric modulus and conductivity formalisms. These formalisms show qualitative similarities in relaxation processes. The frequency dependence of the M″ and dc conductivity is found to obey an Arrhenius law and the activation energy of the phlogopite mica calculated both from dc conductivity and the modulus spectrum is similar, indicating that same type of charge carriers are involved in the relaxation phenomena. The electric modulus and conductivity data have been fitted with the Havriliak–Negami function. Scaling of M′, M″, ac conductivity has also been performed in order to obtain insight into the relaxation mechanisms. The scaling behaviour indicates that the relaxation describes the same mechanism at different temperatures. The relaxation mechanism was also examined using the Cole–Cole approach. The study elaborates that the investigation regarding the temperature and frequency dependence of dielectric relaxation in the phlogopite mica will be helpful for various cutting edge applications of this material in electrical engineering.     

Investigation of Relaxation Process of Nylon 1212 Using Dielectric Relaxation Spectroscopy

The relaxation processes of α-form nylon 1212 from 50°C up to 160°C were studied by dielectric relaxation spectroscopy (DRS) in a wide frequency range of 63 Hz to 5 MHz. The α relaxation, the electrode relaxation, and the conductivity relaxation of nylon 1212 were observed and analyzed in detail using permittivity and modulus formalism. Electrode polarization and dc conductivity were the origin of high dielectric permittivity values at low frequencies and high temperatures. The strength of the imaginary part of the electric modulus of conductivity relaxation M″ _max was nearly independent of temperature. The distribution of local conductivity and relaxation time became broader with decreasing temperature.     

Study of the superionic system AgI-PbI2-Ag2O-B2O3

The superionic system AgI-PbI₂-Ag₂O-B₂O₃ with two compositions has been prepared. The pelletised samples were investigated with regard to conductivity, modulus and dielectric analysis at various temperatures and frequencies. The activation energy determined for the samples was found to be varying between 0.09 to 0.10 eV. The effect of polarization at the electrode has been analyzed from conductivity spectra. From the impedance and modulus analysis it has been found that the system is non-ideal and there exists a distribution of relaxation times which is independent of temperature.     

Synthesis, electrical and electromechanical properties of a tungsten-bronze ceramic oxide: Pb0.68K0.64Nb2O6

A tungsten-bronze ceramic oxide, Pb_0.68K_0.64Nb₂O₆, has been prepared by a standard solid-state reaction technique. Compound formation and phase identification has been confirmed by X-ray diffraction (XRD) studies. The dielectric permittivity and the loss tangent of the sample have been measured in a frequency range 45 Hz–5 MHz and a temperature range 35–590 °C. Electrical properties of the material were studied using an impedance spectroscopic technique. Detailed analysis of the impedance spectrum suggested that the electrical properties of the material are strongly temperature dependent. The Nyquist plots clearly showed the presence of bulk and grain boundary effect in the compound. The imaginary part of modulus at different temperatures shows a relaxation peak and its position shifts to higher frequency with increase in temperature. This suggests a temperature-dependent relaxation. The frequency dependent ac conductivity at different temperatures indicated that the conduction process is thermally activated process.     

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.     

Study of (Bi2O3)(BaxMo1−xO3) polycrystalline ceramic as relaxor ferroelectric

Solid solutions of bismuth layered (Bi₂O₃)(Ba_xMo_1−xO₃) (0.2≤x≤0.8, x is in step of 0.2) ceramics were prepared by conventional solid-state reaction of the constitutive oxides at optimized temperatures with a view to study its electrical properties. Powder X-ray diffraction has been employed for physical characterization and an average grain size of ∼16 to 22 nm was obtained. XRD study reveals the single phase structure of the samples. Dielectric properties such as dielectric constant (ε′), dielectric loss (tanδ) and ac electrical conductivity (σ_ac) of the prepared ceramics sintered at various temperatures in the frequency range 10¹–10⁷ Hz have been studied. A strong dispersion observed in the dielectric properties shows the relaxor type behavior of the ceramic. The presence of maxima in the dielectric permittivity spectra indicates the ferroelectric behavior of the samples. Impedance plots (Cole–Cole plots) at different frequencies and temperatures were used to analyze the electric behavior. The value of grain resistance increases with the increase in Ba ion concentration. The conductivity mechanism shows a frequency dependence, which can be ascribed to the space charge mainly due to the oxygen vacancies. The relaxation observed for the M″ (ω) or Z″ (ω) curves is correlated to both localized and long range conduction. A single ‘master curve’ for the normalized plots of all the modulus isotherms observed for a given composition indicates that the conductivity relaxation is temperature independent.     

Effect of the film thickness on the impedance behavior of sol–gel Ba0.6Sr0.4TiO3 thin films

Perovskite Ba_0.6Sr_0.4TiO₃ sol–gel thin films with different thicknesses are fabricated as MFM configuration to study the effect of the film thickness on the dielectric relaxation phenomenon and the ionic transport mechanism. The frequency dependent impedance, electric modulus, permittivity and AC conductivity have been investigated in this context. Z? plane for all the tested samples shows two regions, corresponding to the bulk mechanism and the distribution of the grain boundaries–electrodes process. Electric modulus versus frequency plots reveal non-Debye relaxation peaks. The observed decrease in both the impedance and permittivity with the increase in film thickness is attributed to the grain size effect. The frequency dependent conductivity plots show three regions of conduction processes, i.e. low-frequency region due to DC conduction, mid-frequency region due to translational hopping motion and high-frequency region due to localized hopping and/or reorientational motion.     

AC conductivity and dielectric studies of (C5H10N)2BiCl5 compound

The bis (3-dimethylammonium-1-propyne) pentachlorobismuthate (III) exhibits a structural phase transition at T₁?=?(337?±?2?K), which has been characterized by differential scanning calorimetric, X-ray powder analysis, AC conductivity and dielectric measurements. The dielectric dispersion yielded the real and imaginary parts of impedance of (C₅H₁₀N)₂BiCl₅ in the form of a semicircle in a complex plane. Besides, a Cole?CCole plot was observed at frequencies ranging from 209?Hz to 5?MHz, whose result was found to fit the theoretical resistor?Ccapacitor parallel circuit model. The temperature dependence of the electrical conductivity in the different phases follows the Arrhenius law. The frequency-dependent conductivity data were fitted in the modified power law: $ \sigma = {\sigma_{dc}} + {B_1}(T){\omega^{{s_1}}} + {B_2}(T){\omega^{{s_2}}} $ . The imaginary part of the permittivity constant is analyzed with the Cole?CCole formalism. With regard to the modulus plot, it can be characterized by full width at half height or in terms of a non-exponential decay function $ \phi (t) = \exp {\left( {\frac{{ - t}}{{{\tau_\sigma }}}} \right)^\beta } $ . Besides, the activation energy responsible for relaxation has been evaluated and found to be close the DC conductivity.     

Ac conductivity and dielectric behavior of hydrated homoionic alkali-cations-exchanged montmorillonite

The dielectric properties of a series of homoionic alkali-exchanged montmorillonites were studied at different treatment temperatures and various water loadings by means of complex impedance spectroscopy. To date, however, this method has been underutilized in clay minerals studies. The main objective of the present work is to understand the relaxation mechanisms of water molecules interacting with different hydration centers in clay minerals, with a view to eventually control their interactions with the alkali extra-framework cations. The other part of our study is to study the dielectric properties such as real and imaginary parts of dielectric permittivity, loss tangent, and ac conductivity in the frequency range 10^?2–10⁶?Hz and temperature range 173–333?K of these clay minerals. The obtained results have been discussed in terms of the Jonscher model.     

Oxygen-vacancy-related high-temperature dielectric relaxation and electrical conduction in 0.95K0.5Na0.5NbO3-0.05BaZrO3 ceramic

The crystal structure and dielectric properties of 0.95K_0.5Na_0.5NbO₃-0.05BaZrO₃ (KNN-BZ) ceramic have been investigated by X-ray diffraction and dielectric measurement. A rhombohedral distortion was caused and the dielectric permittivity near Curie temperature was significantly enhanced by introducing BZ into KNN. The dielectric and conductivity properties of the sample were studied by using AC impedance spectroscopy and universal dielectric relaxation law in detail. The typical high-temperature dielectric relaxation process was confirmed to be related to the oxygen vacancies inside the ceramic. The effect of lattice distortion on the activation energy for oxygen vacancy migration in KNN-BZ was discussed by comparing with KNN and KNN-BaTiO₃.     

Dielectric relaxation and dc conductivity on the PVOH-CF3COONH4 polymer system

In the present paper, the ionic conductivity and the dielectric relaxation properties on the poly(vinyl alcohol)-CF₃COONH₄ polymer system have been investigated by means of impedance spectroscopy measurements over wide ranges of frequencies and temperatures. The electrolyte samples were prepared by solution casting technique. The temperature dependence of the sample’s conductivity was modeled by Arrhenius and Vogel-Tammann-Fulcher (VTF) equations. The highest conductivity of the electrolyte of 3.41×10^− 3 (Ωcm)^− 1 was obtained at 423 K. For these polymer system two relaxation processes are revealed in the frequency range and temperature interval of the measurements. One is the glass transition relaxation (α-relaxation) of the amorphous region at about 353 K and the other is the relaxation associated with the crystalline region at about 423 K. Dielectric relaxation has been studied using the complex electric modulus formalism. It has been observed that the conductivity relaxation in this polymer system is highly non-exponential. From the electric modulus formalism, it is concluded that the electrical relaxation mechanism is independent of temperature for the two relaxation processes, but is dependent on composition.     

Dielectric properties of CdS nanoparticles synthesized by soft chemical route

CdS nanoparticles have been synthesized by a chemical reaction route using thiophenol as a capping agent. The frequency-dependent dielectric dispersion of cadmium sulphide (CdS) is investigated in the temperature range of 303-413 K and in a frequency range of 50 Hz-1 MHz by impedance spectroscopy. An analysis of the complex permittivity (ɛ′ and ɛ″) and loss tangent (tan δ) with frequency is performed by assuming a distribution of relaxation times. The scaling behaviour of dielectric loss spectra suggests that the relaxation describes the same mechanism at various temperatures. The frequency-dependent electrical data are analysed in the framework of conductivity and modulus formalisms. The frequency-dependent conductivity spectra obey the power law.     

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.     

Electrical and electrochemical properties of nanocrystalline LiFePO4 cathode

Lithium iron phosphate (LiFePO₄) cathode material has been prepared by hydrothermal synthesis. The XRD spectrum exhibited different characteristic peaks along with (311) predominant orientation corresponding to orthorhombic crystal structure with Pnma space group. Electric and dielectric properties were studied over a frequency range of 1 Hz–1 MHz at different temperatures. The conductivity was found to be increased with increasing temperature following Arrhenius relation with an estimated activation energy of 0.44 eV. The dielectric properties were analyzed in the framework of complex dielectric permittivity and complex electric modulus formalisms. The complex permittivity as a function of frequency and temperature was investigated. Several important parameters, such as activation energy, ionic hopping frequency, carrier concentration, ionic mobility, and diffusion coefficient, etc., were determined. The electrochemical characteristics of LiFePO₄ are examined in aqueous region. It exhibited a good reversible cyclic voltammogram on sweeping the potential upward and downward with discharge capacity of 140 mAh/g.     

Dielectric properties of lead zirconate titanate films synthesized through oxidation of metal layers

Films of the composition Pb(Zr _x Ti_1?x )O₃ are prepared by magnetron sputtering of metal layers onto titanium substrates with subsequent heat treatment in an oxygen atmosphere. The electrical properties of the samples prepared are investigated using impedance spectroscopy in the frequency range from 10² to 5 × 10⁵ Hz at temperatures of 300–750 K. The temperature dependences of the permittivity and the dielectric loss tangent at different frequencies exhibit a behavior typical of ferroelectrics and indicate the occurrence of a ferroelectric phase transition at temperatures close to T = 663 K. Analysis of the imaginary part of the electric modulus has revealed two possible relaxation mechanisms. The activation energy for dc electrical conduction in the paraelectric phase is determined.     

Synthesis and electrical properties of Y2O3: Dy3+ & Eu3+ nanoparticles

Yttrium oxide (Y₂O₃) doped with Dy³⁺ & Eu³⁺ nanoparticle has been synthesized by solution combustion method. The formation of the compounds has been checked by X-ray diffraction method. The crystallite/particle size has been measured using Scherrer formula as well as by transmission electron microscopy which show that the size of the particles are in the nanorange. The frequency and temperature dependent variation of impedance Z*, dielectric constant (ε′), dielectric loss (ε″) and AC conductivity (σ) of Y₂O₃: Dy³⁺ & Eu³⁺ nanoparticles were also measured. The real and imaginary part of complex impedance makes semicircle in the complex plane. The center of semicircle arc is found to be shifted toward higher value of real part of impedance with increasing temperature. This indicates that the conductivity of the material increases with the increase in temperature. Cole–Cole plots demonstrate that the dielectric relaxation process occurs in the material. The AC conductivity (σ _AC) increases with the increase in temperature within the frequency range of 10³–10⁷ Hz confirming the hopping of the electrons in the conduction process. The value of impedance decreases sharply with increasing frequency and attains minimum value after 10⁵ Hz at all temperatures.     

Synthesis,structural and complex impedance spectroscopy studies of Ni0.4Co0.4Mg0.2Fe2O4 spinel ferrite

Spinel ferrite having composition Ni_0.4Co_0.4Mg_0.2Fe₂O₄ was prepared by sol-gel method. X-ray diffraction result indicates that the ferrite sample has a cubic spinel type structure. FT-IR showed two absorption bands (ν₁ and ν₂) that are attributed to the stretching vibration of tetrahedral and octahedral sites. Complex impedance properties have been investigated in 200–420 K temperature range with varying frequency between 40 and 10⁷ Hz. Frequency and temperature dependency of imaginary part of permittivity (?″) and dielectric loss (tanδ) has been discussed in terms of hopping of charge carriers between Fe²⁺ and Fe³⁺ ions. Activation energy has been estimated from both temperature dependency of dc conductivity and relaxation time data, which indicates that the relaxation process and conductivity have the same origin. Nyquist plots of impedance show semicircle arcs for sample and an electrical equivalent circuit has been proposed to explain the impedance results.     

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.