Jonscher's Power Law Research Articles

Thickness-dependent structural and growth evolution in relation to dielectric relaxation behavior and correlated barrier hopping conduction mechanism in Ni0.5Co0.5Fe2O4 ferrite thin films.

Ferrite thin films are explored due to their promising properties, which are essential in various advanced electronic devices. However, depositing a film with pure phase and uniform microstructure is challenging. The Ni0.5Co0.5Fe2O4 ferrite thin films are deposited using pulsed laser deposition (PLD) technique to explore the effect of thickness on structural properties, growth evolution, temperature-dependent dielectric behavior, and conduction mechanisms. Microstructural analysis revealed that the films are uniformly grown, exhibiting surface roughness ranging from  2 to 4 nm. The dielectric response, adhering to a modified Debye model, exhibited multiple relaxation processes, with notable changes in the dielectric constant and loss as film thickness increased. Impedance spectra exhibited both space charge and dipolar relaxation phenomena, corroborated by Cole-Cole and electrical modulus plots. The analysis of the imaginary electric modulus using the Kohlrausch-Williams-Watts (KWW) function revealed non-Debye-type relaxation in all deposited films, characterized by thermally activated broad peaks. Conductivity decreased up to a certain film thickness, and the frequency exponent derived from Jonscher's power law suggested a correlated barrier hopping model for AC conduction. Activation energies improved with film thickness up to 125 nm, consistent with a constant energy barrier for polarons during relaxation and conduction phases. The film with 125 nm thickness exhibited the optimal dielectric properties, with the maximum dielectric constant, minimum dielectric loss, and highest activation energy. These findings highlight the potential of dense, uniformly grown films with high dielectric constants and low dielectric losses for advanced electronic device applications.

Exploring the Multifunctional Properties of (Sr, Ni)‐Co‐Doped BaTiO3: Structural Characterization and Electromagnetic Characteristics

The structural and electromagnetic properties of various Ba1−x(Sr0.5Ni0.5)xTiO3 are extensively investigated. X‐ray diffraction and Rietveld refinement are used to perform a structural study. With doping substances, bulk and theoretical densities decrease. The crystallite size is calculated using Scherrer and Williamson–Hall method. The microstructural properties are examined using images from field‐emission scanning electron microscope. The observed values of dielectric constants are found to agree with the porosity‐corrected dielectric constants. The nonlinear modified Debye equation (NLMDE) displays a reasonable goodness of fit value for the first five samples. A small polaron hopping mechanism may be responsible for the frequency‐dependent AC conductivity observed in all samples confirming the Jonscher power law. It is discovered that permeability initially increases and then decreases with doping substances. Initial permeability, experimental data from the magnetic hysteresis (M–H) curve, and law‐of‐approach‐to‐saturation techniques show that Ba0.85(Sr0.5Ni0.5)0.15TiO3 and Ba0.75(Sr0.5Ni0.5)0.25TiO3 ceramics have enhanced electromagnetic properties. These ceramics are useful for fabricating electromagnetic sensors.

Temperature-dependent dielectric measurements of polypyrrole/zinc cobalt oxide nanocomposites by impedance spectroscopy

This study characterizes the conduction mechanism in Zinc Cobalt oxide/Polypyrrole nanocomposites (ZCO/PPy NCs) concerning temperature (303–453 K) and frequency (100 Hz–1 MHz). To obtain the ZCO/PPy nanocomposites for the experiments, we used the in-situ chemical polymerization technique to disseminate varying weight percentages of ZCO nanoparticles (ZCO NPs) in the PPy matrix. The total electrical conductivity graph consists of a step-like feature of a plateau and dispersive regimes. The dispersive zone, which follows Jonscher's power law, correlates to AC conductivity, whereas the plateau region, which corresponds to DC conductivity, is thermally activated. The extracted DC conductivity values are of the order of 10‐4 S/m at 303 K. The conduction mechanism in ZCO/PPy nanocomposites is depicted by the Non-Overlapping Large Polaron Tunneling (NSPT) model. The dielectric studies confirm the non-Debye-like relaxation in PPy and ZCO/PPy NCs. In addition, the complex impedance and equivalent circuit analysis showed maximum contribution from grain and grain boundaries. The grain and grain boundary resistances are of the order of 103 Ω, depicting the electrical homogeneity in the PPy and ZCO/PPy nanocomposites.

Electrical conduction and optical characteristics of Li2O and Bi2O3 Co-doped zinc-phosphate glassy nanocomposites: A critical observation of mixed ionic electronic effect

In the present report, the combined effects of the co-doping of metal oxide (Bi2O3) and Lithium oxide (Li2O) into the glassy matrix with chemical composition xLi2O-(0.45-x)Bi2O3-(0.15ZnO-0.40P2O5) (x = 0.05, 0.15, 025, and 0.35 mol%) are investigated thoroughly. The FESEM and X-ray diffraction data affirm the crystalline nature of the studied glassy composites. The obtained band gap energy values are declined from (3.68–3.17) eV, while the Urbach energy values are declined from (0.38–0.27) eV. Moreover, the mechanism responsible for AC conductivity has been analyzed using Almond–West formalism and Jonscher's universal power law. The observed rise in both AC and DC conductivity in the glass samples is attributed to the mixed ionic electronic effect. In the ionic diffusion model, an increased defect site concentration improves Li+ ion migration through percolation channels. The reduction in both electrostatic binding energy and strain energy lowers the Anderson-Stuart activation energy, facilitating Li+ ion migration and enhancing conductivity. Additionally, in the small polaron hopping model, an increase in the density of defect states suggests more defect sites that facilitate electronic hopping, creating deep localized states and transitions between localized and extended states. Replacing a Bismuth atom with a Lithium atom increases the number of non-bridging oxygen, enhancing the conduction band tail, reducing the energy needed for hopping conductivity, and increasing conductivity.

Correlated barrier hopping transport and non-Debye type dielectric relaxation in Zn2V2O7 pyrovanadate

Herein, the Zn2V2O7 electro-ceramic pyrovanadate was synthesized via a conventional solid-state reaction technique and calcined at 700 °C. The single phase formation of Zn2V2O7 pyrovanadate crystallized in the monoclinic structure with C12/c1 space group was confirmed by X-ray diffraction (XRD). The XRD powder diffraction profile was analyzed by Rietveld refinement to investigate the structural details of the compound. The complex impedance analysis was carried out in the frequency domain of 83−2×106 Hz over a temperature range of 453–613 K to study the electrical charge conduction and dielectric relaxation mechanism in the material which revealed the presence of the distribution of relaxation times with thermal charge activation. Depressed semicircles in the Nyquist plots were modeled by an equivalent circuit with configuration (RGCG)(RGBQGB) which resolved the contributions of grains and grain boundaries towards the transport properties of the material. The electrical conductivity spectra followed Jonscher's power law behavior and the temperature variation of frequency exponent suggested correlated barrier hopping (CBH) as the governing transport mechanism in the Zn2V2O7 pyrovanadate system. The comparison between scaling behaviors of imaginary parts of impedance and modulus advocated the temperature-independent nature of relaxation time distribution. The imaginary electrical modulus spectra were reproduced by the Kohlrausch, Williams, and Watt formulism, and the fitted parameters confirmed the non-Debye type nature of the dielectric relaxation. Further, the Haveriliak-Negami function was employed to investigate the dielectric response of the material which was found to be consistent with impedance, conductivity, and modulus analyses. The frequency dispersion of the tangent loss verified that the hopping mechanism was thermally activated.

Dielectric Relaxation, Electrical Conductivity, Dielectric Permittivity, and Correlated Barrier Hopping Conduction Mechanism Analysis in Ag Doped Bi2S3 at Low Temperatures

AbstractPure and 6% Ag doped bismuth sulfide (Bi2S3) were synthesized via solid‐state reaction method at 500 °C. The X‐ray diffraction method confirmed the orthorhombic phase with average crystallite size ∼25 nm and average lattice strain ∼0.5% and ∼0.6% for pure and 6% Ag doped Bi2S3. The scanning electron microscope (SEM) images confirmed nanobelt morphology. A direct bandgap of ∼3.3 and ∼3.4 eV for pure and doped Bi2S3 was estimated using UV–vis spectroscopy, respectively. AC measurements were performed from 200 Hz to 2 MHz at temperature 223–298 K. Investigation of Nyquist plots of 6% Ag doped Bi2S3 nanobelts suggested space‐charge‐dependent behavior and indicated an negative temperature coefficient of resistance (NTCR). AC conductivity adhered to Jonscher's power law in which the decreasing trend of s‐parameter with increasing temperature indicates correlated barrier hopping conduction mechanism. From this model, hopping distance (∼10−9–10−11 m) and density of states (∼1022–1023 eV−1 cm−3) were estimated. The dielectric permittivity exhibited dispersion at low frequencies due to the combined effect of electronic, ionic, and interfacial polarizations. Presence of two semicircular arcs in the complex modulus analysis suggested the presence of both grain and grain‐boundary effects.

Electrical properties and evaluation of band tail states in Mg doped p-type multilayer hBN

A series of Mg doped p-type multi-layered hBN films were prepared by atmospheric pressure chemical vapor deposition. Temperature dependent conductivity measurements were performed from 0.1 Hz to 10 MHz to analyze the characteristics of tail states close to the valence band edge. Jonscher's power law (Aωs) is successfully applied to understand charge carrier transport through these states. In this work, exponent S increases from 0.6 → 0.8, 0.8 → 0.995, and 1.4 → 1.6 for samples B (precursor temperature, 750 °C), D (850 °C), and E (900 °C), indicating that non-overlapping small polaron tunneling dominates to 548 K. Polaron binding energies of 0.2–0.40 eV and tunneling distances <4.9 Å are calculated, confirming transport through localized states. The density of states near the Fermi level N(EF) was extracted from a fit to the AC conductivity data, yielding values of 1015 and 1017eV−1cm−3 as the precursor temperature increases. Singular Mg acceptor levels of 74, 30, and 17 meV are identified for each sample. A hole concentration from 6.5 × 1017 to 1 × 1018 cm−3 and carrier mobility from 18 to 25 cm2/V s is measured at 300 K. From RC fitting, carrier recombination lifetimes of 1.2, 0.4, and 0.35 μs are determined. Fermi's golden rule is used to determine an optical joint density of states of 1.1 × 1021 eV−1 cm−3 at a band edge. Overall, we show that AC conductivity is an effective method to evaluate midgap states in 2D (two-dimensional) materials at EF and p-type hBN possesses sufficient electrical properties to be integrated into a wide range of semiconductor applications.

Polaron assisted hopping mechanism in microwave processed Nd doped second layered aurivillius SrBi2Nb2O9 ceramics

The polycrystalline Sr0.8Sn0.2Bi1.75Nd0.25Nb2O9 (NdSBN) was synthesized using the green synthesis microwave sintering method, which significantly reduced the processing parameters of the NdSBN ceramics. Orthorhombic crystal structure with A21am symmetry was revealed by Rietveld refinement study, whereas the doping-induced strain and crystallite size was studied using the Williamson Hall method. Crossectional SEM micrographs confirm the plate-like structure, with an average grain size of 273.7 nm. A diffuse type of phase transition was observed at 345 °C, which usually arises due to compositional fluctuations and mobile oxygen vacancies; further, the diffusiveness of the NdSBN was studied using Uchino and Nomura function, a modified version of Curie-Weiss law (CW). The frequency and temperature-dependent dielectric study of NdSBN ceramics display a Maxwell-Wagner relaxation with a high loss in a low frequency regime, possibly due to the presence of leakage current in the solid solution. Frequency dependent AC conductivity obeys Jonscher's power law, whereas DC conductivity supports polaron assisted hopping in NdSBN composition with dual activation energies of 0.55 eV and 0.75 eV, which correspond to electrons and ions, respectively. The non-Debye type relaxation mechanism in conjunction with negative temperature coefficient of resistance (NTCR) behavior was demonstrated by temperature dependent impedance spectroscopy, while modulus spectroscopy confirmed the multiple relaxation processes in NdSBN ceramics.

Upheaval of Negative Dielectric Permittivity and Semiconductor to Metallic Transition in a Thermally Induced Sn-Doped β-Ga2O3 (-201) Single Crystal.

Thermally induced dielectric and conductivity properties of an Sn-doped β-Ga2O3 (-201) single crystal were investigated by frequency-domain impedance spectroscopy in the frequency window from 100 Hz to 1 MHz with temperatures between 293 and 873 K. The (-201) plane-orientated single crystalline nature and the presence of an Sn dopant in β-Ga2O3 were confirmed by X-ray diffraction (XRD) and X-ray photoelectron (XPS) spectroscopy. Two different trends of impedance spectra have been discussed by the modulation of relaxation times and semiconductor to metallic transition after ∼723 K due to activation of a significant number of Sn dopants and their movements with temperature. The negative impedance values were encountered in the Nyquist plots (Z' vs Z″) after 573 K and constitute a reverse movement after 723 K with temperature. The average normalized change (ΔZ'/Δf)/Z0 of impedance exhibits a broad downward relaxation plateau near 723 K, indicating a weak electrical transition. The increases in the positive value of the dielectric constant (εr') below a percolating threshold temperature 573 K is attributed to the interfacial and dipolar polarizations, and the plasma oscillation of delocalized electrons governed by the Drude theory is responsible for the negative dielectric constant above 573 K. The 3D projections of the real dielectric constant create a sharp downward sinkhole near 723 K, indicating the existence of negative dielectric permittivity. The electrical conductivity dramatically changes its trends after 523 K and confirms a transition from hopping conduction (dielectric or semiconductor) following Jonscher's power law to metallic conduction by Drude theory. Below the percolating threshold temperature, a nonoverlapping small polaron tunneling conduction mechanism was unveiled with defect-induced activation energy of 0.21 eV. The Sn-doped β-Ga2O3 exhibits unique and tailored electromagnetic responses with temperatures that can be associated with a variety of applications in electromagnetic wave manipulations, cloaking devices, antennas, sensors, medical imaging, seismic wave propagation, etc.

Microwave absorption properties of β-type ferrites: Influence of Nd-loading percentage on structural, spectral, elemental, and electrical features

Hexagonal ferrites have drawn significant attention due to a broad range of telecommunication and stealth technology applications. β-Type hexagonal ferrites are rarely used in various technological applications. In the current work, Nd3+ substituted polycrystalline β-type hexagonal ferries with composition LiFe11-x NdxO17 (x = 0.0–0.04, ∇ x = 0.01) were prepared using the sol-gel method. All prepared samples were sintered at 1000 °C for 4 h. The influence of Neodymium (Nd3+) on its structural, electrical, and dielectric properties was investigated. Lattice parameters (a, c) and Vcell increased with varying Neodymium substitution levels. The crystallite size was measured in the range of 38–42 nm. Fourier Transform IR (Infrared) spectroscopy exposed the presence of two spectral bands at 416 to 449 cm−1 and 449 to 489 cm−1. XPS (x-ray photoelectron spectroscopy) analysis verified the presence of metal ions and their chemical states in all prepared samples. The dielectric constant, loss, tan δ, and σac (ac-conductivity) decreased by increasing Nd3+ content. Jonscher's power law explains the conduction mechanism of charge carriers in all fabricated samples. The influence of relaxation time and grain boundaries on the electrical characteristics of prepared nanomaterials was investigated by impedance analysis. SEM (scanning electron microscopy) confirms the successful formation of β-hexaferrite nanomaterials. A minimum reflection loss of −32.08 dB was observed at 1.5 GHz for the x = 0.04 sample. This minimum reflection loss evidenced the novelty of the research and suggested their usefulness in high-frequency microwave applications. All samples investigated in this research work are suitable for high-frequency applications, multilayer chip inductors, and EM interference shielding.

Dielectric relaxation and electrical conductivity in lead-free organic ferroelectric diisopropylammonium bromide (dipaBr)

In this communication, we explore the dielectric relaxation behavior of the novel organic salt Diisopropylammonium Bromide (dipaBr), focusing on the universal relaxation law. We conduct dielectric relaxation and conductivity analyses across a broad spectrum of temperatures (325K–443K) and frequencies (20 Hz–20 MHz). The irregularity in peak broadening observed in complex modulus spectroscopy indicates a distribution of relaxation periods with varying time constants, confirming that the relaxation is of the non-Debye type. To interpret the experimental findings, we utilize the Havriliak-Negami (HN) formula in our investigation of dielectric relaxation. The parameters derived from the model are discussed. The relaxation process in the material appears to depend on temperature. The ac conductivity profile follows Jonscher's universal power law, and the relationship between bulk DC conductivity and temperature follows an Arrhenius-like pattern.

Investigation of thermal, optical properties, AC conductivity and broadband dielectric spectroscopy of poly(ethyl methacrylate)/poly(vinyl chloride) polymer blend

This work reports the structural, thermal, optical and electrical properties of PEMA, PVC and their polyblends. These properties are investigated by FTIR, TGA, UV/Vis and broadband dielectric spectroscopy. FTIR spectra showed that the characteristic bands of PEMA and PVC are affected by blending and displayed red and blue shifts confirming that an intermolecular interaction between PEMA and PVC is occurred. Thermal degradation kinetics of PEMA, PVC and its polyblend samples is investigated in details and the thermal properties of each decomposition stage are estimated. UV measurements analysis revealed that Urbach energy (EU) is increased while optical bandgap decreased upon increasing the PVC content. The indirect and direct band gap (Eig/Edg) values are decreased from (3.95/4.21) to (3.10/3.92) eV. Also, upon increasing the content of PVC, the lattice dielectric constant (εL) is increased from 2.71 to 7.83. Wemple-DiDomenico model is applied for investigating the refractive index dispersion and to calculate the oscillator and dispersion energies. It is observed that the linear/nonlinear parameters are increased nonlinearly with increasing the PVC content. χ(1), χ(3) and n2 values are found to increase from 0.104, 0.213 × 10−13 and 4.01 × 10−12 to 0.363, 31.26 × 10−13 and 5.33 × 10−12. These results make PEMA/PVC polyblend strong candidates for use in the development and design of advanced optoelectronic devices. AC conductivity (σac) and dielectric measurements are carried out at various temperatures in wide frequency range. Jonscher power law is applied and showed that the predominant conduction mechanism in our samples is overlapping large-polaron tunneling (OLPT). The dielectric constant and electrical impedance are found to be frequency and temperature dependent. The investigation of the electric modulus (M*) revealed that M′ is increased non-linearly with increasing the frequency, while M″ spectra displayed two different modes of relaxation. The interfacial polarization (IP) is observed in low frequency region, while, dipolar relaxation is detected in high frequency region.

Oxygen vacancy modulated optical and dielectric properties of photoactive γ-Fe2WO6

Ferrite compounds have gained scientific attention for their multifunctional attributes. This investigation explores the structural, optical, dielectric and conductivity properties of polycrystalline γ-Fe2WO6 synthesized by the solid state route. The X-ray diffraction confirmed the orthorhombic structure and single-phase formation, while the electron microscopy showed uniform distribution of dense micrometer-sized grains in γ-Fe2WO6. The FTIR spectroscopy analysis validated the presence of active stretching and bending modes, signifying oxygen anion vibration at both Fe and W sites. The simultaneous presence of Fe2+ and Fe3+ ions in the matrix, as confirmed by X-ray photoelectron spectroscopy (XPS), results in an augmented optical energy band gap and contributes to dielectric permittivity due to the charge carrier hopping mechanism between the trap sites. The compound manifests semiconductor attributes, evident in its indirect optical band gap measuring 1.7 eV. It is observed that the compound has effectively degraded the Methylene Blue (MB) under the visible light within 40 min with a degradation efficiency up to 63 %. The material's electrical conductivity, follows the Jonscher's power law, signifies its semiconductor nature and adheres to the Small Polaron tunneling model for charge conduction between neighboring sites. The impedance (Z′) curves exhibit dielectric relaxation (≤ 10 kHz) with a similar activation energy to the dc conductivity study. The activation energy, determined from both the impedance and conductivity analyses, indicates a connection with the migration of oxygen vacancies within the material. Our observation reveals the presence of oxygen vacancies, which possibly act as in-gap electron traps, enhancing the correlated optical and ac conductivity properties, making it an appealing material for diverse multifunctional applications.

Electrical transport characteristics of rare earth ions (Er³⁺, Sm³⁺) exchanged cobalt-manganese ferrite using impedance spectroscopy

This study presents findings on the AC impedance characteristics of rare earth-doped Co0.5Mn0.5RExFe2-xO4 ferrites (where RE = Er and Sm, and 0.0 ≤ x ≤ 0.1), synthesized utilizing the citrate auto-combustion process. Employing impedance spectroscopy at frequencies ranging from (100 −1 MHz) and temperatures between 30°C and 120°C, we distinguished the impact of grains (Gs) and grain boundaries (GBs) in these compositions. The Jonscher power law was applied to characterize the AC conductivity results. The dielectric constant έ and dielectric loss ε” decline as the frequency rises and reach a stable state at higher frequencies, indicating the characteristic dielectric dispersion. This phenomenon manifests the Maxwell-Wagner polarization, as described by Koop's hypothesis. The modified Debye formula provides a good match for the frequency-dependent dielectric permittivity fluctuation. The Cole-Cole plots revealed a single semicircle for the unaltered sample and lower Er³⁺ concentrations (up to x=0.02), but two semicircles appeared at higher Er³⁺ concentrations and in the Sm³⁺ doped samples. The G and GB resistances increased with higher concentrations of Er³⁺/ Sm³⁺ but showed a decrease at x=0.1 in Sm³⁺-doped samples. The data examination designates that the resistive and capacitive possessions are predominantly affected by G and GB processes. A relaxation phenomenon in the existing samples is shown by the frequency-dependent of the imaginary portion of impedance (Z"). Remarkably, the relaxation time (τz) showed linear temperature dependence. Additionally, studies of the electrical modulus (M’ and M”) highlighted non-Debye sort dielectric relaxation in all compositions, with peaks in the imaginary modulus indicating a shift in charge carrier mobility from long-range toward short-range. The investigation focused on the non-Debye relaxation, which was analyzed by determining the stretching exponential parameter (β). This factor was obtained by fitting the modified Kohlrausch-Williams-Watts (KWW) formula to the graph of the imaginary electric modulus. The substitution of Fe3+ by Er3+ and Sm3+ ions substantially enhanced the dielectric properties, particularly Co-Mn-Sm ferrite series, suggesting their potential use in high-frequency devices.

Investigating the potential of Nd and Co modified bismuth ferrite (BiFeO3) nanoparticles for advanced energy storage and electronic applications

In this study, we synthesized and characterized Nd and Co modified bismuth ferrite nanoparticles (BNFCO) using mechanical milling. X-ray diffraction (XRD) analysis has provided confirmation of the distorted rhombohedral, mixed rhombohedral-tetragonal and tetragonal perovskite structure with space group R3c and P2mm. Notably, these nanoparticles exhibited a high dielectric constant and low loss values at low frequencies and high temperatures, remaining around 103 up to 373 K before increasing to approximately 104, which opens new avenues for exploring temperature-sensitive dielectric properties. The AC conductivity adhered to Jonscher's power law, with dc conductivity values ranging from 10−5 to 10−3 s/cm, representing a significant advance in understanding electrical conduction in nanomaterials. Furthermore, we assessed the electrochemical behavior of the fabricated samples at varying concentrations using cyclic voltammetry, Galvanostatic charge and discharging (GCD), and electrochemical impedance spectroscopy (EIS) on a modified electrode. BNFCO (0.20) displayed exceptional properties with a capacitance of 510 F g−1 and a capacitance retention of 93.9 % after 5k cycles, making BNFCO nanomaterials potential candidates for supercapacitor applications. The multifunctional properties of Nd and Co modified bismuth ferrite nanoparticles presented in this study offer unparalleled opportunities for transformative applications in supercapacitors and optoelectronic devices.

Dynamics of charge carriers in La2CuO4 cuprates: Conductivity variation, scaling formalisms, and electric modulus study

In this work, we conducted a detailed investigation of the structural properties and the dynamics of the charges in the La2CuO4 Ruddlesden–Popper system that is prepared via the conventional solid-state process. Via the X-ray diffraction data and using the Rietveld refinement, we found that the compound exhibits a single crystallographic phase with a Bmab space group. The DC-conductivity investigation shows that the studied ceramic exhibits two electrical behaviors. Below 460 °C, the occurrence of a semiconductor behavior is attributed to the effect of the Variable range hopping conduction process. At high temperatures, the electrical nature of the material is linked to the thermally activated small polaron hopping conduction process via an activation energy Ea = 1.40 eV. Over the explored temperature range, conductivity spectra of the Ruddlesden–Popper are analyzed using the universal Double Jonscher power law. The dispersion region can be attributed to the coexistence of both hopping and tunneling processes. The conductivity spectra of the La2CuO4 Ruddlesden–Popper nicely follow the time-temperature superposition (TTSP) principle. This confirms that similar sources are responsible for relaxation and conduction processes. Using the Summerfield scaling approach, the superposition of the conductivity spectra into a single master curve confirms that the relaxation process is the microstructure's response independent. From the electrical modulus investigation, we found that the studied compound exhibits a non-Debye relaxation nature, over the explored temperature interval. Contribution of grain and grain boundary were resolved by complex modulus spectroscopy analysis. In addition, we found the absence of the electrode contribution at low frequencies. The correlation between both Z″ and the M″ peaks indicates that the conduction and relaxation processes are not related to the same origins.

Rietveld refinement, core level electron shell structure and frequency-dependent dielectric behavior of vanadium bismuth oxide microstructures

Solid-state reaction method was employed to synthesize a series of complex compound system V2-xBi2xO5-δ (0.01 ≤ x ≤ 0.04), and their electrical properties at room temperature were examined through impedance spectroscopy within the frequency range of 40 Hz to 10 MHz. The X-ray diffraction (XRD) is refined to obtain the complete crystallographic profile of the compounds. The frequency-dependent conductivity exhibited adherence to Jonscher's universal power law across all compositions. As the bismuth concentration increased from x = 0.01 to 0.04, both AC and DC conductivity showed a systematic increase. AC conductivity raised from 3.17 × 10−4Sm−1 to 4.3 × 10−4 Sm−1 at 10 MHz, while DC conductivity increased between 1.56 × 10−4Sm−1 and 2.28 × 10−4Sm−1. The dielectric constant (εr') decreased with increasing frequency, stabilizing around 100 kHz. The electric modulus peaks at higher frequencies, reflecting relaxation processes, and approaches zero at lower frequencies due to the absence of electric polarization.

Innovative Nanostructuring of Li–Zn ferrite/graphene composites with tunable properties

The Li-ferrite and graphene oxide (GO) nanocomposites, denoted as (Li0.5-x/2ZnₓFe2.5-x/2O4: x = 0.25), were produced through ultrasonication. The wet method generated Li-ferrite, while the Hummers' method synthesized the GO. X-ray diffraction (XRD) was used to validate the development of Li-ferrite and GO in the nanocomposites. The dimensions of the crystal were determined between 41 and 52 nm, and the porosity of the composites increased with the higher quantity of GO. The scanning electron micrographs (SEM) of ferrites illustrated the formation of uniform and well-defined grains with consistent shapes, exhibiting properties well-suited for effective microwave absorption. The electrical resistance of spinel ferrite was measured at approximately 3.34 × 1011 Ω-cm and significantly lowered as the fraction of GO increased at ambient temperature. As per Maxwell Wagner's model, the electrical permittivity exhibited interfacial polarization with distinct real and imaginary components. The AC conductivity exhibited a positive correlation with the GO content due to the conductive properties of GO and the improved charge hopping mechanism. The frequency exponent parameter's value falls from 0.36 to 0.95 b y the Jonscher's Power law. The magnetic susceptibility of all the samples exhibited a progressive decrease as the temperature increased. The choice of using lithium-based ferrite as filler is made to strengthen the ferrite/GO composites and improve their magnetic and electrical properties. This is undertaken to harness these composites for high-frequency applications, such as their use as microwave absorbers in microwave devices.

Rietveld refined structural, optical and temperature dependent impedance spectroscopy of NiO–ZnO heterostructure composite: Synthesized through solid state method for high-frequency devices

Multifunctional NiO–ZnO heterostructure composite powder is economically synthesized through a solid-state route having a crystallite size of 23 (±2) nm. Chemical composition is identified through FTIR, the peak associated with Zn–O is detected at 1049 cm−1. However, the peaks detected at 870 cm−1 and 590 cm−1 show Ni–O stretching vibrations. UV-DRS technique is employed to estimate the energy band gap (Eg) around 3.18 eV. The impedance studies confirmed the presence of a non-Debye-type relaxation mechanism, electrical parameters confirm the contribution of electroactive regions i.e. grains and interfaces. An equivalent circuit model (R-CPE) is employed to measure various electrical parameters. Adiabatic small polaron hopping model is applied to estimate activation energies for Ni+2 (0.30 eV), Zn+2 (0.35 eV), and bulk (0.32 eV) respectively. The hopping length at the interface is estimated at around 0.8 Å by employing Mott's variable range hopping model. Jonscher's power law (JPL) is used to fit ac conductivity data, and conclude activation energy around 0.3 eV. The conduction mechanism through the whole frequency range (1–107 Hz) is governed by correlated barrier hopping. Various physical parameters i.e. binding energy (Wm), hopping length, and barrier height compared throughout the whole temperature range (313–393 K). The rate of increase in real permittivity at low frequency is related to the disorder of the cation at sublattices. These results deduced potential for NiO–ZnO heterostructure composite for high dielectric permittivity with low tangent loss for high energy storage applications.

Electrical transport and dielectric relaxation mechanism in Zn0.5Cd0.5Fe2O4 spinel ferrite: A temperature- and frequency-dependent complex impedance study

In the present study, the frequency-dependent dielectric relaxation and electrical conduction mechanisms in sol-gel-derived Zn0.5Cd0.5Fe2O4 (ZCFO) spinel ferrite were studied in the temperature range of 343–438 K. The formation of the ZCFO spinel ferrite phase with space group Fd3m was confirmed by X-ray diffraction analysis. The dielectric relaxation and electrical conduction mechanisms were studied using complex impedance spectroscopy (CIS). In the Nyquist plots, depressed semicircles were fitted with an equivalent circuit model with configuration (RGBQGB) (RGQG), signifying the contributions from grain boundaries and grains to the charge transport mechanism in the sample. The frequency-dependent AC conductivity was found to follow Jonscher's power law, and the frequency exponent term depicted the overlapping large polaron hopping (OLPH) model as the dominant transport mechanism. The activation energies for conductivity, electric modulus and impedance were calculated to identify the nature of the charge carriers governing the relaxation and conduction mechanisms in the prepared sample. Complex modulus studies confirmed the non-Debye type of dielectric relaxation, whereas tangent loss and dielectric constant analyses confirmed the thermally activated hopping mechanism of charge carriers in Zn0.5Cd0.5Fe2O4 spinel ferrite.