Debye-type Relaxation Behavior Research Articles

Structural, magnetic and impedance dynamics of multiferroic high entropy garnet ceramics

We have synthesized (Gd0.2Y0.2Nd0.2Dy0.2R0.2)3Fe5O12(R=Er,Sm and Pr) high entropy garnet ceramic samples via solid-state reaction route for the first time. All the samples are formed in a single phase and exhibit a simple cubic crystal structure with an Ia3‾d space group. The lattice constant of these samples varies as per the ionic radii of the substituted element and ranges in between 12.4458Å to 12.5062Å. The morphology and elemental contributions are also investigated for all the high entropy samples. Additionally, magnetization data reveal a similar value of room temperature saturation magnetization i.e., ∼16emu/g for (Gd0.2Y0.2Nd0.2Dy0.2R0.2)3Fe5O12(R=Sm and Pr) samples and it becomes 13.67emu/g for Er doped sample. This variation is understood with Dionne's sublattice magnetization model where the molecular weight of the substituent will affect the saturation magnetization. Furthermore, a deviation from ideal Debye-type relaxation behavior is noticed in room temperature Nyquist plots for all three samples. An anomaly in the dielectric plot around ferrimagnetic transition temperature indicates the multiferroic behavior of these high entropy ceramic materials.

Low-frequency electrical response related to oxygen vacancies in Al3+ substituted M-type hexaferrite

The presence of oxygen vacancies is unavoidable in many complex metal oxide materials such as hexaferrites. This article investigates the role of crystal defects, such as oxygen vacancies, and different oxidation states of Fe ions, on the electrical conduction behaviors of Al3+ substituted Ba0.4La0.1Sr0.5Al x Fe12−x O19 hexaferrites by analyzing the temperature dependent AC impedance and AC conductivity. The optimal substitution of La3+ ions and high-temperature sintering is responsible for forming oxygen vacancies while reducing Fe from Fe3+ to Fe2+ cations, as observed in structural and XPS analysis, which affects electrical conduction behaviors. The departure from ideal Debye-type relaxation behavior is also one of the effects of crystal defects. Temperature variation of relaxation time shows a sharp change at around 403 K. This may be due to different electrical entities influencing the mode of electron hopping with temperature. The activation energy calculated from the temperature dependent relaxation time confirmed the presence of electron hopping through the bridging effects of the first ionization of oxygen vacancies Fe2+––Fe3+ below a temperature of 403 K. Above 403 K, electron hopping through different oxidation states of Fe3+ + e− → Fe2+ and migration of oxygen vacancies toward the bulk surface are responsible for the conduction mechanism. The DC resistivity and AC conductivity show that the bridging effects of oxygen defects can also induce Coulomb interaction between the defect sites resulting in Efros–Shklovskii variable range hopping and correlation barrier hopping below 403 K. Above 403 K, polaron-assisted electron hopping is more desirable, as confirmed by the non-overlapping small polaron tunneling model.

Conductivity, Dielectric and Modulus Study of NH4PF6 Based Zwitterionic Polymer Electrolyte

Background and Objective:Zwitterionic polymer electrolyte has been successfully synthesized using NH4PF6salt. The conductivity of the synthesized polymer membrane is found to be of the order of 10-3Scm-1. Dielectric and Modulus properties of the polymer electrolyte have also been studied which shows well relaxation peaks with both temperature and salt concentrations.Result:Debye type relaxation behavior has observed from the electric modulus.Conclusion:Frequency dependent conductivity data (fitted with Jonscher’s power law equation) confirmed the presence of NCL/SLPL type behavior in the studied frequency range.

Towards superior optical and dielectric properties of borosilicate glasses containing tungsten and vanadium ions

Transparent glasses of the composition (20–x)V2O5–xWO3–20SiO2–60Li2B4O7, x = 2, 4, 8 and 16 mol %, have been successfully synthesized by a popular melt quenching technique. The main features regarding the structure of these glasses were determined via Fourier transform infrared (FTIR) spectroscopy. The structure change was occurred in the glasses containing 8 and 16 mol% of WO3 which, in turn, decreased non-bridging oxygen (NBO) atoms with further WO3 additions. In addition, the density of these glasses provided higher values with WO3 additions. Optical measurements were achieved through different ranges of wavelength, revealing that the degree of transparency improved, while the absorption decreased, with WO3 additions. Remarkably, the optical transitions of tungsten and vanadium ions embedded in lithium borosilicate glasses were examined. The energy of optical band gaps was decreased by introducing WO3 until 8 mol %, and then increased with further WO3 additions. Furthermore, the conductivity was slightly increased by introducing WO3 until 8 mol %, and then decreased with further WO3 additions, whereas the activation energy demonstrated the opposite behavior with WO3 additions. The dependence of dielectric permittivity, dielectric loss and electrical conductivity on temperatures at varying frequencies was applied. The loss factor revealed a peak that moves towards higher temperature as the frequency increased, indicating the Debye-type relaxation behavior. Finally, the outcomes demonstrated that WO3–V2O5–SiO2–Li2B4O7 glasses are promising optically and electrically tunable materials.

The synthesis and dielectric characterization of a low temperature smectic a liquid crystal

In the present paper, we have been synthesized a new salicylaldimine-based rod-like liquid crystal 4-((S)-3,7-Dimethyloctyloxy)-2-[[[4-(S)-2-methylbutoxyphenyl]imino]methyl]phenol (DMIP) exhibiting an enantiotropic Smectic A mesophase in the narrow temperature range. We have also evaluated the dielectric parameters of this liquid crystal DMIP as a function of temperature from 25 °C–50 °C and frequency range from 1 Hz to 1 MHz. It is observed that dielectric constant (ε′) and dielectric loss factor (ε″) depends on frequency and temperature. Relative dielectric parameters, such as the dielectric strength, relaxation times and absorption coefficient change at phase transition temperature of the DMIP have been analyzed from the dielectric data of the Cole-Cole equation. Molecular reorientation mechanism has been investigated in the Smectic A mesophase temperature range by Debye type relaxation behaviour.

Structural, electrical and ferroelectric properties of lithium niobate-bismuth ferrite solid solutions

In this present communication, a polycrystalline lead-free system with composition Bi0.60Li0.40Fe0.60Nb0.40O3 (BLFNO termed further) is synthesized using a cheap conventional ceramic processing route. It featured with resistive, capacitive and dielectric properties of the synthesized composition. Room temperature XRD (X-ray diffraction) technique used to determine the single phase formation, structure and lattice parameters. The SEM micrograph reveals the non-uniform distribution of grains with highly dense grain growth. The complex impedance and modulus technique help to analyze the electrical properties of the sample. The frequency and temperature dependent electrical characteristics occurring in the sample were carried out in a wide temperature (25–500 °C) and frequency (1 kHz-1MHz) range. The Nyquist plot depicts the contribution of both grain and grain boundary effect in the prepared composition. The temperature dependent AC conductivity shows the activation energy for conduction. The frequency dependent electrical modulus and impedance analysis suggest non–Debye type relaxation behavior in the sample.

Na+ ion migration on the surface of reduced graphene oxide

The increasing demand of sodium ion batteries (SIBs) remarkably accelerates the study of solid-state sodium ion conductors due to their potential application as solid-state electrolytes in SIBs. In the present work, the sodium ion is attached to reduced graphene oxide (rGO) to realize a sodium ion conductor. Tuning the activation energy of migration for Na+ and Li+ ions on rGO surface is investigated by varying the concentration of both ions. The lowest values of activation energies for Na+ and Li+ conduction are found to be 0.28 eV and 0.37 eV, respectively. It is seen that the activation energy of migration of the Na+ ion is smaller than that of the Li+ ion. The lower positive charge density of Na+ compared to Li+ causes this lowering of activation energy in Na+ due to the comparatively weak cation–π interaction between the Na+ ion and the carbon hexagon. From the relaxation study, the relaxation exponent (β) value of the Na+ ion is found to be smaller than that of the Li+ ion. This deviation from Debye-type relaxation behavior of the Na+ ion also agrees well with the decreasing value of activation energy as mentioned above. We hope that this study will aid the design of ion conductors for solid-state SIBs.

A comprehensive study of electrical and optical properties of phosphate oxide-based glasses doped with Er2O3

In this study, the radiative parameters were acquired from the UV absorption spectra and the luminescence spectra of Er3+ ions doped Er2O3–Al2O3–Na2O–P2O5 glasses. The intensity of each absorption spectrum was utilized to deduce the radiative parameters and the parameters (Ω2, Ω4 and Ω6) of Judd–Ofelt theory. The FTIR and the elastic moduli of the quaternary glasses are also investigated. Analysis of the FTIR suggested that the presence of Er3+ ions created bridging oxygens and polymerized the local structure around atoms. This procedure manifested itself from decreasing the bond length of O–P and increasing the O/P ratio. The polymerization of the phosphate structure increased the ultrasonic velocity and the rigidity of the network. The electrical parameters of the phosphate glasses, such as the frequency and temperature dependence AC conductivity, dielectric loss and dielectric modulus were carried out. The Er3+ ions affected the carrier mobility by decreasing the electrical conductivity and increasing the activation energy. In addition, the frequency and temperature dependence of the dielectric modulus exhibited a Debye-type relaxation behavior.

A structural insight into the electrical properties of Dy-Ho co-doped phase stabilized Bismuth Oxide based electrolytes

A novel Dy-Ho co-doped face centered cubic (FCC) phase stabilized bismuth oxide solid electrolyte has been developed using low temperature auto – ignition method. XRD analysis confirms that complete phase stabilization has been achieved for all co-doped systems. The decrease in lattice parameter for doped system has been attributed to lower ionic radii of dopants Dy3+ and Ho3+ in comparison with Bi3+. Crystallite size has been found to be maximum and microstrain is minimum for the composition Bi0.88Dy0.06Ho0.06O1.5−δ having equal proportion of dopant content. The same composition shows higher ionic conductivity at lower temperature regime. The electrical modulus study using Havriliak–Negami (HN) formalism indicates non – Debye type relaxation behavior. Comparable values of different types of activation energies indicate that relaxation, hoping mechanism, dc and ac conduction process follow the same kind of transport mechanism. The scaling of the conductivity and modulus spectra verifies the time–temperature superposition principle (TTSP).

Size-dependent studies in ferromagnetic nanoparticles dispersed ferroelectric liquid crystal mixtures

ABSTRACTIn the present study, ferromagnetic nickel nanoparticles (NiNPs) of size (~20 nm, 40 nm) into ferroelectric liquid crystal (FLC) mixture has been dispersed and investigated. Effect of size of NiNPs on the electro-optic, dielectric and optical properties of FLC mixture have been studied and discussed. A minor improvement in spontaneous polarisation, rotational viscosity and faster response time in NiNPs-FLC samples than pure FLC is noticed. Goldstone mode of relaxation frequency ~100 Hz is detected in all samples and follow a Debye type relaxation behaviour. In addition, it is observed that size of NiNPs does not have any remarkable effect on relaxation frequency and dielectric strength. A single absorption peak at 363, 362 Hz is also noticed in pure FLC and NiNPs-FLC samples.

Computational and experimental studies on dielectric relaxation and dipole moment of some anilines and phenol

In the present study, the dielectric relaxation behaviour of four polar molecules namely 2-Nitroaniline, 4-Bromoaniline, 4-Chloroaniline and 4-Chlorophenol were studied in dilute solutions of benzene using microwave bench at 9.59GHz frequency. The different parameters like, dielectric constant (ε′), dielectric loss (ε″), static dielectric constant (ε0) and optical permittivity (ε∞) have been determined. Further from these values, dipole moment (μ) and relaxation time (τ) were calculated for all the molecules following Gopalkrishna, microwave conductivity and the Higasi method. The dipole moment for all the molecules were also estimated theoretically from ab initio computations by using Density Functional Theory (DFT) calculations with the help of Gaussian 09W software. Dipole moments determined experimentally and through DFT computations are in good agreement with the dipole moments estimated by taking vector sum of group moments of Aniline, Nitrobenzene, Bromobenzene, Chlorobenzene and Phenol by neglecting interaction between pendant groups. The experimentally determined relaxation times were analyzed in terms of Stokes-Einstein-Debye (SED) theory and the results are compared with molecular radii estimated from DFT and Edward's atomic increment methods. Further, in order to understand the chemical stability and reactivity of all these molecules, highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO) and HOMO-LUMO energy gap were also estimated from DFT computations. Our experimental findings suggest that, 2-Nitroaniline exhibits simple Debye type relaxation behaviour while the other three samples exhibit Higasi's distribution of relaxation times which may be due to both overall and intra-molecular rotation of the molecules. Further, the HOMO-LUMO studies revealed that, 2-Nitroaniline is more chemically reactive having least energy gap and 4-Chlorophenol is least chemically reactive having highest energy gap among the four samples.

Electro-optic, dielectric and optical studies of NiFe2O4-ferroelectric liquid crystal: a soft magnetoelectric material

ABSTRACTIn the present study, magnetic nanoparticles (NP, nickel ferrite) in different concentrations into ferroelectric liquid crystal (FLC) mixture have been prepared and studied. The effect of nickel ferrite concentration on the electro-optic, dielectric and optical properties of FLC mixture has been studied and discussed. An improvement in spontaneous polarization, response time in nickel ferrite-FLC-doped samples compared to FLC is observed and explained on the basis of dipole moment and anchoring phenomena. The Goldstone mode (GM) is detected in all samples and follows a Debye-type relaxation behaviour. A twofold increase in relaxation frequency for the doped sample rather than the pure sample has been observed. The band gap was found more or less independent of doping concentration. The activation energy (Ea) also decreases on increasing the doping amount.

1-Aza-15-Crown-5 Functionalized Graphene Oxide for 2D Graphene-Based Li⁺-ion Conductor.

Attachment of Li(+) ion on graphene surface to realize Li(+)-ion conductor is a real challenge because of the weak interaction between the ions and the functional groups of graphene oxide; although, a large number of theoretical results are already available in the literature. To overcome this problem, graphene oxide is functionalized by 1-aza-15-crown-5, the cage-like structure containing four oxygens that can bind Li(+) ion through electrostatic interaction. Li(+) migration on graphene surface has been investigated using ac relaxation mechanism. Perfect Debye-type relaxation behavior with β (relaxation exponent) value ≈1 resulting from single ion is observed. The activation energy of Li(+) migration arising due to cation-π interaction is found to be 0.37 eV, which agrees well with recently reported theoretical value. It is believed that this study will help to design isolated ion conductors for Li(+)-ion battery.

Paraelectric Response of Water in the Range 0–100°C

Water exhibits unique physical and chemicals properties and its low frequency dielectric response is not an exception. The large directionable dipole moment of the water molecule results in a relatively high dielectric constant whose temperature dependence above 0°C follows well a Curie-Weiss law (ɛs-ɛei)−1 = (1/C)(T-TC), with ɛei ≅ 6.6, C = 1.49 × 104 and TC = 90.4 K. The frequency dependence of the permittivity of pure water has recently been measured at various temperatures with high accuracy in the frequency range of 0 – 25 THz, showing a well-defined Debye-type relaxation behaviour, which can be described reasonably well by means of a paraelectric-like temperature dependence relaxation time given by τ−1 = υD e−ϕ/kBT [(T-TC)/T], where υD = 1.877 × 1014 and ϕ = 0.180 eV. The combined pressure and temperature dependence of the dielectric constant is described approximately by means of a generalized Curie-Weiss state-law.

Permittivity of ice at radio frequencies: Part II. Artificial and natural polycrystalline ice

Abstract Precise knowledge of the absolute value and frequency dependence of the dielectric permittivity of ice is the basis for interpretation of radio echo sounding data on glaciers and ice sheets. However, in the range of radio-frequencies, data from direct measurements of the permittivity are sparse, and partially lacking uncertainty estimates. Here, we present new results for artificial and natural ice samples obtained by means of frequency-dependent measurements from 10 MHz to 1.5 GHz with a coaxial transmission line cell. Measurements on eight artificial ice samples grown from ultra-pure water within the cell yield a mean value for the real part of the relative permittivity of 3.18 ± 0.01 at − 20 °C. Sole evidence for dispersion is detected for frequencies below 10 MHz, possibly attributed to the Debye-type relaxation behavior. Investigation of the crystal orientation of the artificial ice samples reveals the c-axes to be predominantly parallel to the electric field inside the cell and allows to calculate a value representative for isotropic crystal orientation of 3.16 ± 0.01. Measurements on acid-doped artificial ice show a linear dependence of the real part with acidity with a gradient of (21.1 ± 3.9) [1/M]. The real part of the relative permittivity of natural firn and ice samples from a high Alpine glacier range from 2.02 at a density of 0.515 g/cm 3 to 3.08 at 0.875 g/cm 3 . Quasi-continuous measurements with the present setup on an alpine firn core are now possible, with resolution depending on the coaxial cell's length, for direct comparison with the established dielectric profiling method.

Supramolecular Bola-Like Ferroelectric: 4-Methoxyanilinium Tetrafluoroborate-18-crown-6

Molecular motion is one of the structural foundations for the development of functional molecular materials such as artificial motors and molecular ferroelectrics. Herein, we show that pendulum-like motion of the terminal group of a molecule causes a ferroelectric phase transition. Complex 4-methoxyanilinium tetrafluoroborate-18-crown-6 ([C(7)H(10)NO(18-crown-6)](+)[BF(4)](-), 1) shows a second-order ferroelectric phase transition at 127 K, together with an abrupt dielectric anomaly, Debye-type relaxation behavior, and the symmetry breaking confirmed by temperature dependence of second harmonic generation effect. The origin of the polarization is due to the order-disorder transition of the pendulum-like motions of the terminal para-methyl group of the 4-methoxyanilinium guest cation; that is, the freezing of pendulum motion at low temperature forces significant orientational motions of the guest molecules and thus induces the formation of the ferroelectric phase. The supramolecular bola-like ferroelectric is distinct from the precedent ferroelectrics and will open a new avenue for the design of polar functional materials.

Density and Enthalpy Relaxation Behavior in a Bulk Pd<sub>40</sub>Ni<sub>40</sub>P<sub>20</sub> Metallic Glass

The kinetics of structural relaxation in a Pd40Ni40P20 bulk metallic glass was investigated by the volume relaxation due to density experiments and the enthalpy relaxation due to specific heat experiments. A two-step relaxation process was found in the volume relaxation, while the enthalpy relaxation seemed to be one-step relaxation process with a spectrum of relaxation times. First-step volume relaxation only in as-quenched glass was the process with a spread of relaxation times at lower relaxing temperature, while a Debye-type relaxation behavior was observed at higher temperature near Tg and in pre-annealed glass. The comparison of the kinetics of volume and enthalpy relaxations at the same temperature showed a disagreement with the prediction of free volume theory.

Transport and dielectric properties of V2O5-MnO-TeO2 glasses

The frequency (1-10 kHz) and temperature (80-350 K) dependences of the ac conductivity and dielectric constant of the V2O5-MnO-TeO2 system, containing two transition-metal ions, have been measured. The dc conductivity dc measured in the high-temperature range (200-450 K) decreases with addition of the oxide MnO. This is considered to be due to the formation of bonds such as V--O--Mn and Mn--O--Mn in the glass. The conductivity arises mainly from polaron hopping between V4+M and V5+ ions. It is found that a mechanism of adiabatic small-polaron hopping is the most appropriate conduction model for these glasses. This is in sharp contrast with the behaviour of the Mn-free V2O5-TeO2 glass, in which non-adiabatic hopping takes place. High-temperature conductivity data satisfy Mott's small-polaron hopping model and also a model proposed by Schnakenberg in 1968. A power-law behaviour ( ac = Aωs , with s < 1) is well exhibited by the ac conductivity σac data of these glasses. Analysis of dielectric data indicates a Debye-type relaxation behaviour with a distribution of relaxation times. The MnO-concentration-dependent σac data follow an overlapping large-polaron tunnelling model over the entire range of temperatures studied. The estimated model parameters are reasonable and consistent with changes in composition.

Debye-type dielectric behavior of Bi-Sr-Ca-Cu-O-based transition-metal oxide glasses: Precursors for oxide superconductors.

Detailed measurements of the frequency- (50 Hz to 10 kHz) and temperature (80 loss (\ensuremath{\epsilon}'') have been performed for the ${\mathrm{Bi}}_{4}$${\mathrm{Sr}}_{3}$${\mathrm{Ca}}_{3}$${\mathrm{Cu}}_{\mathit{y}}$${\mathrm{O}}_{\mathit{x}}$ (y=0 to 5) glasses. Some of these glasses become high-temperature superconducting oxides in their respective glass-ceramic phases. The dielectric properties of these glasses are found to follow a Debye-type relaxation behavior with relaxation frequency ${\mathit{f}}_{\mathit{c}}$ [=${\ensuremath{\nu}}_{\mathit{c}}$ exp(-${\mathit{W}}_{\mathit{c}}$/${\mathit{k}}_{\mathit{B}}$T)]. The relaxation behavior is thermally activated in nature similar to the dc electrical-conduction process of these glasses observed in our earlier investigation.

Frequency and temperature dependence of sound velocity in TGS near Tc

Abstract Ultrasonics (10 MHz and 50 MHz) and Brillouin (18.2 Hz and 19.2 Ghz) measurements of the longitudinal sound velocity in TGS propagating along the crystallographic c-axis (⊥ to the ferroelectric b-axis) have been performed in the vicinity of the transition temperature Tc=49.3°C. The data confirm a Debye type relaxation behavior with a polarization relaxation time of the form τ=A(Tc-T)−1 for T < Tc which is in fair quantitative agreement with the relaxation time from dielectric measurements at high frequencies.