Electric Modulus Formalism Research Articles

Phase transformation and impedance spectroscopic study of Ba substituted Na0.5Bi0.5TiO3 ceramics

(Na0.5Bi0.5)1−xBaxTiO3 (x = 0.05, 0.1 and 0.15) ceramics abbreviated as (NBBT1, NBBT2 and NBBT3) are fabricated by conventional ceramic fabrication technique. The analysis of X-ray diffraction pattern of the prepared ceramic performed by Rietveld refinement indicate that crystal structure is rhombohedral for NBBT1, tetragonal for NBBT3 and a phase boundary occurs for NBBT2. Impedance spectroscopy has been employed to study the electrical properties of these ceramics in the frequency range of 10 Hz to 5 MHz and in a temperature range of 303 K–723 K. Frequency and temperature dependent electrical data is analyzed in the framework of conductivity, impedance and electric modulus formalisms. Conductivity spectrum obeys double power law for NBBT1, which is evidenced from two different dispersion regions. While for NBBT2 and NBBT3 only single power law is observed. Relaxation frequency for impedance is found to increase with temperature and obeys Arrhenius relationship with activation energy ≈0.764, 0.527 and 0.471 eV for NBBT1, NBBT2 and NBBT3 respectively. Variation of dielectric constant and tanδ with frequency at different temperatures was analyzed with the help of Maxwell–Wagner and Koop's phenomenogical theory. The presence of peaks in plots showing frequency dependence of tanδ for NBBT2 and NBBT3 indicates relaxor behavior of these compositions.

Structural studies and impedance spectroscopy of sol–gel derived Bi0.9Pr0.1FeO3 nanoceramics

Nano-crystalline Bi0.9Pr0.1FeO3 (BPFO) ceramics have been synthesized by a sol–gel technique. The Rietveld refinement of the room temperature powder X-ray diffraction pattern confirms that the BPFO crystallizes in the rhombohedral R3c space group symmetry. SEM image of the sintered BPFO ceramic shows particles with same shape and fine grain morphology with the average grain size of 53±12nm. The electrical properties of the ceramic are analysed by impedance spectroscopy. Grain and grain-boundary effect is observed in the material at lower temperature range which has been confirmed by electric modulus formalism. The ac conductivity spectrum obeys the Johnscher's power law. The activation energy calculated from dc conductivity is found to be 0.373eV, which represents the conduction of small polaron over barrier between two sites of the lattice.

The ionic transport mechanism and coupling between the ion conduction and segmental relaxation processes of PEO20-LiCF3SO3 based ion conducting polymer clay composites.

A series of ion conducting polymer-clay composites has been prepared using a solution casting technique. Relaxation dynamics and the ionic transport mechanism are systematically studied employing broadband dielectric spectroscopy over a wide frequency and temperature range. Among different phenomenological and theoretical models for ion conduction in disordered ionic conductors, conductivity isotherm spectra are analysed using the modified Almond-West and random free energy barrier model. Conductivity scaling suggests that the ionic transport mechanism is independent of temperature, and a similar inference is also obtained using scaled electrical modulus spectra. DC conductivity along with conductivity and segmental relaxation time following the Vogel-Tammann-Fulcher relationship suggests coupling between the ionic transport and segmental relaxation processes. Electrical modulus and dielectric formalism are used to understand the conductivity and segmental relaxation processes, respectively. The presence of first and second universality in the ionic transport mechanism is discussed using the real part of conductivity spectra and dielectric loss spectra. The crossover between the first and second universality is explained using the Kramer-Krönig approach. The ion diffusion coefficient is investigated using Ratner's classical approach in combination with the modified Stokes-Einstein relationship to correlate the coupled nature of the ion conduction mechanism and polymer segmental motion.

Sublinear dispersive conductivity in polyetherimides by the electric modulus formalism

It can be seen by Dynamic Electrical Analysis that the electrical properties of polyetherimide at temperatures above the glass transition are strongly influenced by space charge. We have studied space charge relaxation in two commercial grades of polyetherimide, Ultem 1000 and Ultem 5000, using this technique. The electric modulus formalism has been used to interpret their conductive properties. In both grades of polyetherimide, asymmetric Argand plots are observed, which are related to a sublinear power-law dependency ($\omega^{n}$ with $n<1$) in the real part of the conductivity. This behaviour is attributed to correlated ion hopping. The imaginary part of the electric modulus exhibits a peak in the low frequency range associated to conduction. Modelling of this peak allows us to obtain the dependence, among other parameters, of the conductivity ($\sigma_0$), the fractional exponent ($n$) and the crossover frequency ($\omega_\mathrm{p}$) on the temperature. The $\alpha$ relaxation, that appears at higher frequencies, has also to be modelled since it overlaps the conductivity relaxation. The study of the parameters in terms of the temperature allows us to identify the ones that are thermally activated. The difference between the conductivity relaxation time and the Maxwell relaxation time indicates the presence of deep traps. The coupling model points out that the correlation of the ionic motion diminishes with temperature, probably due to increasing disorder due to thermal agitation.

Investigation of relaxation process in poly(vinylidene fluoride–hexafluoropropylene) using dielectric relaxation spectroscopy

Dielectric relaxation behavior of poly(vinylidene fluoride–hexafluoropropylene) [P(VDF–HFP)] is investigated on the basis of dielectric relaxation spectroscopy at 20–200 °C and 20–5 MHz after conversion to complex electric modulus formalism. It is found that imaginary modulus spectra exhibit asymmetry peak with peak-width much broader than that of the Debye peak. The peaks are skewed toward the high frequency sides due to the effect of the conductivity. The complex electric modulus data have been fitted using non-exponent Kohlrausch–Williams–Watts and Cole–Cole functions. The results show that the non-exponent parameter (β) and the shape parameter (α) are all lower than idealized Debye-type, indicating a wide relaxation distribution of P(VDF–HFP). Both the activation energies Ea from $${\text{M}}^{\prime \prime }$$ spectra and conductivity are all due to the contribution of dc and ac conductive relaxation process.

Electrical conductivity and dielectric relaxation studies on microwave synthesized Na2SO4·NaPO3·MoO3 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.

Electric modulus formalism and electrical transport property of ball mill synthesized nanocrystalline Mn doped ZrO2 solid solution

Here we report the formation of Mn doped nanocrystalline ZrO2 solid solution synthesized by high energy ball-milling method and the transport mechanism in the temperature range 298K<T<523K and in the frequency range 20Hz–2MHz. Rietveld method is employed for analysis of phase formation mechanism, structural and microstructural characterization of different phases and relative phase abundances using XRD patterns. The electrical study shows the dc conductivity enhances as the doping percentage increases. Complex electric modulus study shows low frequency region approaches to ideal Debye type behaviour while the high frequency side deviates. Alternating current conductivity is found to follow the power law σ‘(f,T)∝fsTn. A transformation from small polaron hopping to correlated barrier hopping has been observed from the temperature dependence frequency exponent study. The contribution of grain boundary resistance is found to be dominating over the grain resistance in the ac conduction process.

Structural Properties, Impedance Spectroscopy and Dielectric Spin Relaxation of Ni-Zn Ferrite Synthesized by Double Sintering Technique

Structural properties, impedance, dielectric and electric modulus spectra have been used to investigate the sintering temperature (Ts) effect on the single phase cubic spinel Ni0.6Zn0.4Fe2O4 (NZFO) ceramics synthesized by standard ceramic technique. Enhancement of dielectric constants is observed with increasing Ts. The collective contribution of n-type and p-type carriers yields a clear peak in notable unusual dielectric behavior is successfully explained by the Rezlescu model. The non-Debye type long range dielectric relaxation phenomena is explained by electric modulus formalism. Fast response of the grain boundaries of the sample sintered at lower Ts sample leading to small dielectric spin relaxation time, t (several nanoseconds) have been determined using electric modulus spectra for the samples sintered at different Ts. Two clear semicircles in impedance Cole-Cole plot have also been successfully explained by employing two parallel RC equivalent circuits in series configuration taking into account no electrode contribution. Such a long relaxation time in NZFO ceramics could suitably be used in nanoscale spintronic devices.

Dielectric Relaxation of NiFe2O4/Gd2O3 Core-Shell Nanoparticles.

Gd2O3 encapsulated NiFe2O4 core-shell nano-particles (CSNPs) have been synthesized by chemical route. The phase formation of the materials is confirmed by X-ray diffraction analysis. The average particle size is found to be 60 nm by transmission electron microscope. The band gap of NiFe2O4/Gd2O3 CSNPs is obtained by UV-visible absorption spectroscopy. The observed band gap of 4.38 eV lies in between the individual band gap of Gd2O3 and NiFe2O4. The frequency-dependent dielectric relaxation of the material is investigated in the temperature range from 303 K to 543 K. The temperature dependent relaxation times are found to obey Arrhenius law having activation energy of 0.3 eV. The Nyquist plots of impedance data are analyzed by the RC equivalent circuit having a constant phase element. The dielectric relaxation is modelled by Havriliak-Negami technique in the electric modulus formalism. The frequency dependent conductivity spectra follow the double power law.

Conductivity studies on microwave synthesized glasses

Conductivity measurements have been made on x V 2O5 − (100−x) [0.5 Na2O + 0.5 B2O3] (where 10 ≤ x ≤ 50) glasses prepared by using microwave method. DC conductivity (σ) measurements exhibit temperature-and compositional-dependent trends. It has been found that conductivity in these glasses changes from the predominantly ‘ionic’ to predominantly ‘electronic’ depending upon the chemical composition. The dc conductivity passes through a deep minimum, which is attributed to network disruption. Also, this nonlinear variation in σ dc and activation energy can be interpreted using ion–polaron correlation effect. Electron paramagnetic resonance (EPR) and impedance spectroscopic techniques have been used to elucidate the nature of conduction mechanism. The EPR spectra reveals, in least modified (25 Na2O mol%) glasses, conduction is due to the transfer of electrons via aliovalent vanadium sites, while in highly modified (45 Na2O mol%) glasses Na+ ion transport dominates the electrical conduction. For highly modified glasses, frequency-dependent conductivity has been analysed using electrical modulus formalism and the observations have been discussed.

Magnetic and dielectric properties of orthoferrites La1−x PrxFeO3 (x = 0, 0.1, 0.2, 0.3, 0.4 and 0.5)

The Pr doped LaFeO3 are synthesized by the sol–gel citrate method. The crystal structure of the samples can be described by the Pbnm space group. The Raman spectra of the materials show that the vibrational modes are heavily influenced by the magnitude of the orthorhombic distortion. The antiferromagnetic nature of the samples is examined by temperature dependent magnetisation measurements and the corresponding hysteresis loop. A signature of weak ferromagnetic phase is observed in the samples at low temperature due to the canting of the iron sublattices. The frequency dependent dielectric relaxation of the sample has been investigated in the temperature range from 303 K to 513 K in the framework of conductivity and electric modulus formalisms. The complex impedance plots are explained by an electrical equivalent circuit consisting of constant phase element and resistance. A significant change of the conductivity is observed with the increase of Pr concentration.

Electrochemical Impedance Spectroscopy Data from Solid Oxide Cells Undergoing Co-Electrolysis: The Influence of Rig Inductance

High temperature solid oxide cells (SOCs) can be used for co-electrolysis of carbon dioxide and steam to produce carbon monoxide and hydrogen: key reactants for the production of synthetic fuels. During co-electrolysis, two electrochemical reactions occur at the fuel electrode, in addition to the reverse water gas shift reaction (rWGSR). It is currently not well understood which processes relating to these reactions are rate-limiting. Here we propose a method that enables rate-limiting processes to be identified using electrochemical impedance spectroscopy (EIS). SOCs were operated at 850oC under varied fuel concentrations and current densities. Inductance effects were accounted for and the resulting EIS data was de-convoluted using the Distribution of Relaxation Times (DRT) method, giving the characteristic frequencies of rate-limiting processes occurring during cell operation. The resistances and capacitances associated with these processes were quantified using the impedance and electric modulus formalisms, respectively. DRT results in combination with the analysis of differences in spectra (ADIS) associated with the EIS data, plotted in both impedance and electric modulus formalisms, were used to justify the number of processes associated with the cell polarization resistance and to develop a meaningful equivalent circuit to model cell performance.

Dielectric and Conduction Mechanisms of Parylene N at High Temperature: Phase-Transition Effect.

Dielectric and electrical properties correlated with the structure analysis have been studied on 27% semicrystalline parylene-N (-H2C-C6H4-CH2-)n thin films. Transition-phase, AC- and DC-conduction mechanisms, and the MW-interfacial polarization were identified in parylene N at high temperature by experimental and theoretical investigations. The dielectric analysis based on the dc conductivity highlights a temperature of 230 °C as a transition temperature from the α-form to the β1-form. This structure transition is accompanied by a modification on the DC-conduction mechanisms from ionic to electronic conduction in the α-form and the β1-form, respectively. The AC conduction mechanism is governed by the small polaron tunneling mechanism (SPTM) with WH,α = 0.23 eV and a tunneling distance of 7.71 Å in the α-form, while it becomes a correlated barrier-hopping (CBH) mechanism with a WM,β1 = 0.52 eV in the β1-form. The imaginary part of the electrical modulus formalism obeys the Kohlrausch-Williams-Watt (KWW) model and shows the presence of the interfacial polarization effect. The theoretical Kohlrausch exponent (βKWW) confirms the existence of the transition phase on the parylene N in the vicinity of the 230 °C as deduced by the DC- and the AC-conduction parameters. The correlations between the experimental results and the theoretical models are very useful knowledge and tools for diverse parylene N applications at high temperature.

Temperature and frequency dependent conductivity and electric modulus formulation of manganese modified bismuth silicate glasses

The ac conductivity and electric modulus formalism of bismuth silicate glasses containing manganese with compositions xMnO2·(60−x)Bi2O3·40SiO2, (x=0, 5, 10, 15 and 20) have been studied in the frequency range 10−1Hz to 1MHz and temperature range 583K to 703K. The ac conductivity is found to increase with an increase in MnO2 content. The frequency dependent conductivity for manganese doped bismuth silicate glassy system shows a single plateau for samples with x=0 and 5, but for glasses with x=10, 15 and 20, the temperature and frequency dependent conductivity shows a double plateau in the whole temperature range 583K to 703K. The observed dispersive behavior of ac conductivity of bismuth silicate glasses containing manganese is discussed in the framework of Jonscher's universal power law fitted to the experimental data of samples showing single as well as two plateau regions. The results show that the ac conductivity increases with the increase in the frequency of applied field. Further, it is observed that small polaron conduction mechanism is more or less suitable to explain the conduction in the present glass samples with x=10, 15 and 20 in the high frequency region. However, the temperature dependent behavior of the frequency exponent s for glass samples with x=0 and 5 seems to follow CBH conduction mechanism. The electrical relaxation is rationalized using the electric modulus formulation in the presently studied glasses at all the temperatures. The values of activation energy for dc conduction (EA) and electric modulus (ER) were estimated. For glass sample with x=0 and 5, the activation energy associated with electric modulus is almost equal to that of the dc conductivity at the low frequency range, whereas for glass samples with x=10, 15 and 20, the values of ER are equal to the activation energy due to dc conduction in the high frequency region.

Dielectric Properties of Polyaniline Emeraldine Base

Dielectric properties such as permittivity, loss factor and conductivity of pure polyaniline emeraldine base PANI-EB pellets are measured as a function of electric field and frequency. Dielectric properties are measured in the electric field range from 0.2 kV/mm to 2.45 kV/mm and in the frequency range from 0.1 Hz to 1 kHz. Measurement results clearly show that relative permittivity, loss factor and conductivity of PANI EB increase as a function of increasing electric field. Relative permittivity of PANI EB is also quite high, approx. 20 even in the lowest electric field at 50 Hz. On the other hand relative permittivity also increases as a function of decreasing frequency range as well as the loss factor. Only conductivity increases as a function of increasing frequency. The formalism of electric modulus is also studied in the paper.

Dielectric relaxation of PVC/PMMA/NiO blends as a function of DC bias

We have prepared poly vinyl chloride (PVC)/poly-methyl methacrylate (PMMA) blend with loading of Nickel oxide (NiO) by solution cast technique. X-ray diffraction reveals the interaction between NiO, PVC and PMMA in the blend form. The weak interaction between PVC, PMMA and NiO was confirmed by Fourier transform infrared spectroscopy. The miscibility of PVC and PMMA has been confirmed by differential scanning calorimetry. The results demonstrate that the 2 wt% NiO loaded PVC/PMMA blend exhibits lowest crystallinity which leads to better NiO dispersion, also observed by atomic force microscopy and scanning electron microscopy. The performance of electrical properties were evaluated under wide band of frequency (10–107 Hz) as a function of DC bias voltage (0–25 V). The dielectric property was characterized via electrical modulus formalism. The present blend systems show good dielectric property as well as considerable conductivity which differs by frequency and DC bias. The variation of AC conductivity as a function of frequency and DC bias shows plateau shape at higher frequency which obeys Jonscher’s power law. It demonstrates that the AC electrical conductivity is directly proportional to the applied DC bias potential. It may be developed for electrolyte application.

Dielectric Behavior and Magnetic Properties of Mn-Substituted Ni–Zn Ferrites

Nanocrystalline spinel ferrites of nominal stoichiometry Ni0.5Zn0.5Mn x Fe2−x O4 (x = 0.0, 0.1, 0.2, 0.3, 0.4) were synthesized by chemical co-precipitation. X-ray diffraction analysis revealed formation of a single cubic phase with no metal oxide secondary phase; increased intensity of peaks of the doped samples suggests that, in the range studied, substituents are completely dissolved in the cubic lattice. Grain size was measured by scanning electron microscopy, by use of the line intercept method. Dielectric measurements were obtained as a function of frequency in the range 20 Hz to 3 MHz. It was found that hopping conduction was the predominant mechanism of conduction in frequency-dependent alternating current conductivity. Conductivity relaxation of the charge carriers was examined by use of the electrical modulus formalism; the results were indicative of the presence of the non-Debye-type relaxation in the ferrites. The grain boundary contribution was clearly apparent from Cole–Cole plots. Hysteresis loops for all the samples were narrow with low values of coercivity and retentivity, indicative of the superparamagnetic nature of these samples. On the basis of these sample characteristics it is suggested that Ni–Zn–Mn ferrites may be potential candidates for hyperthermia applications.

Crystal structure refinement, dielectric and magnetic properties of Ca/Pb substituted SrFe12O19 hexaferrites

SrFe12O19 (SFO), Sr0.5Ca0.5Fe12O19 (SCFO) and Sr0.5Pb0.5Fe12O19 (SPFO) hexaferrites have been synthesized by a conventional solid state reaction technique. Powder X-ray diffraction and Rietveld refinement confirm the presence of M-type hexagonal phase in prepared samples. However in SCFO, secondary phase was also present with main phase. Analysis of Nyquist's plots of SFO hexaferrite revealed the contribution of many electrically active regions corresponding to bulk mechanism, distribution of grain boundaries and electrode processes also. Both conductivity and electric modulus formalisms have been employed to study the relaxation dynamics of charge carriers. A perfect overlapping of the normalized plots of modulus isotherms on a single ‘super curve’ for all the studied temperatures reveals a temperature independence of dynamic processes involved in conduction and for relaxation. In SPFO sample coercivity is reduced effectively but accompanied with increase in magnetization, which is requirement for hexaferrites to be used as magnetic recording media.

Dielectric relaxation of CdO nanoparticles

Nanoparticles of cadmium oxide have been synthesized by soft chemical route using thioglycerol as the capping agent. The crystallite size is determined by X-ray diffraction technique and the particle size is obtained by transmission electron microscope. The band gap of the material is obtained using Tauc relation to UV–visible absorption spectrum. The photoluminescence emission spectra of the sample are measured at various excitation wavelengths. The molecular components in the material have been analyzed by FT-IR spectroscopy. The dielectric dispersion of the material is investigated in the temperature range from 313 to 393 K and in the frequency range from 100 Hz to 1 MHz by impedance spectroscopy. The Cole–Cole model is used to describe the dielectric relaxation of the system. The scaling behavior of imaginary part of impedance shows that the relaxation describes the same mechanism at various temperatures. The frequency-dependent electrical data are also analyzed in the framework of conductivity and electrical modulus formalisms. The frequency-dependent conductivity spectra are found to obey the power law.

Surfactant mediated synthesis of ZnO nanospheres at elevated temperature, and their dielectric properties

ZnO colloidal spheres were prepared using a simple surfactant mediated approach via a two-stage reaction process, involving the synthesis of nanoparticles and the assembly of the nanoparticles to obtain nanospheres. The present work pointed out a simple and ‘green’ way of converting ZnO nanoparticles into ZnO nanospheres. The structural properties and the crystalline phase of the synthesized nanospheres were characterized by transmission electron microscopy (TEM), scanning electronic microscopy (SEM), and powder X-ray diffraction (XRD). The morphology of the colloidal ZnO nanosphere observed at high resolution showed a nanocrystalline substructure, and XRD indicated the hexagonal phase of zinc oxide with a high purity. The dielectric properties were studied over a frequency range of 1Hz–1MHz at room temperature, and in the framework of complex dielectric permittivity and complex electric modulus formalisms. The evolution of the complex dielectric permittivity as a function of frequency at room temperature was investigated.