non-Debye Dielectric Relaxation Research Articles

Trap-controlled fractal diffusion model of an atypical dielectric response

• New model of non-Debye dielectric relaxation, which leads to a new expression for an atypical two-power-law dielectric response, is developed. • A new expression for the complex dielectric permittivity in the frequency domain, which describes well the experimental dielectric spectra demonstrating atypical relaxation behavior, is obtained. • Relationships that relate microscopic parameters of the medium and parameters of atypical dielectric response, such as relaxation time and fractional-power exponents characterizing the shape of the dielectric loss peak are obtained. Within the framework of the multiple trapping and the fractal diffusion equation models a new expression for the complex dielectric permittivity in the frequency domain is found. The new expression allows us to describe an atypical two-power-law dielectric response. An analytical expression for the relaxation time, which is expressed through microscopic parameters of the structural and energy disorder of the system is obtained. Good agreement of the new expression for the complex dielectric permittivity with observed dielectric responses of porous glass composite ADP and nanoscale Si-layered system is demonstrated.

Frequency- and temperature-dependent dielectric features of multi-component electronic material: (Pb0.8Dy0.1Bi0.1)(Fe0.2Ti0.8)O3

A multiple cation containing sample as [(Pb0.8Dy0.1Bi0.1)(Fe0.2Ti0.8)O3] is fabricated by adopting the solid-state reaction process. The crystallographic structure, crystallite size, morphology, dielectric behavior, conductivity, polarization, impedance as well as electric modulus spectroscopy are experimentally observed for this fabricated composition. The crystal structure of the specimen is observed to be tetragonal from X-ray diffraction. The micrograph shows the presence of polycrystalline microstructure with uniform distributed grains. The impedance spectroscopy analysis as a function of temperature (100–450 °C) and frequency (1–1000 kHz) helps to signify the resistive and capacitive behavior of the compound. The nature of the prepared specimen and conduction mechanism is illustrated through AC conductivity study. The modulus analysis elucidates the existence of non-Debye dielectric relaxation nature in the synthesized compound. The compound possesses appreciable value of loss tangent and remnant polarization, i.e., 0.02 and 0.014 µC/cm2, with high value of dielectric constant at room temperature. The dysprosium doping entails stability with interesting electrical and dielectric properties. The preliminary capacitive characteristic has been elucidated, thus making it a stronger contender for functional device applications.

Probing the ionic transport dynamics in ionic liquid incorporated CuBTC-Metal-Organic Framework based PVdF-HFP nanocomposite membranes

CuBTC-Metal-Organic Framework (MOF) has been prepared by solvothermal synthesis method and ionic liquid (IL) 1-butyl-3 methylimidazolium tetrafluoroborate (BMIMBF4) has been incorporated at different wt% into the CuBTC-MOF. The composite nanofiller has been dispersed in poly (vinylidene fluoride-co-hexafluoropropylene) (PVdF-HFP) polymer electrolyte system. Shifting of FTIR vibrational modes of carboxylate group is due to metal-ligand bond elongation upon interaction of ions of IL with CuBTC-MOF. The binding energy of Cu spin-orbit peak increases with incorporation of IL as obtained from XPS spectra suggesting motion of BF4− anions of IL towards the Cu metal nodes of MOF. Periodic oscillation and coordination structure of Cu K-edge are observed in k-space and R-space scanning EXAFS data. Non-Debye dielectric relaxation dynamics is observed from dielectric permittivity and modulus spectra with ionic conductivity of 8.7 × 10−3 Scm−1at 50 wt% of IL incorporation in the composite polymer electrolyte at 380 K. The electrochemical stability profile increases with increasing IL concentration and attains 6.1 V at 50 wt% of IL.

Trap-controlled fractal diffusion model of the Havriliak-Negami dielectric relaxation

A new model of non-Debye dielectric relaxation, which leads to the popular in broadband dielectric spectroscopy Havriliak-Negami expression for two-power-law dielectric response, is proposed. The new model is based on the multiple trapping model and the fractal diffusion model. Explicit analytical expressions for experimentally measured values such as dielectric strength, characteristic relaxation time, and power-law exponents, which include the microscopic parameters of the medium, are obtain. The comparison of the expression for the relaxation time with the experiment is demonstrated. A clear physical interpretation of the power-law exponents of the Havriliak-Negami relaxation function is found, one makes it possible to extend the area application of this function and to use it for the fitting of dielectric data, which exhibit atypical relaxation behavior.

Development and excitation performance of lead free electronic material: Eu and Fe doped Bi0.5Na0.5TiO3 for filter application

The polycrystalline samples with chemical formula Bi0.49Na0.49Eu0.02Ti0.98Fe0.02O3 (BENFTO-2 abbreviated ahead), Bi0.48Na0.48Eu0.04Ti0.96Fe0.04O3 (BENFTO-4 abbreviated ahead) and Bi0.47Na0.47Eu0.06Ti0.94Fe0.06O3 (BENFTO-6 abbreviated ahead) have been processed using a mixed oxide method. The refinement of XRD data suggests that all prepared materials exhibit tetragonal crystal system with perovskite structure. The surface morphology denotes a high density of grain growth without any cracks. This finding can contribute to grain and grain boundary associated with resistive and capacitive characteristics. The impedance and modulus are performed at various temperatures and frequencies in order to discern the relaxation as well conduction mechanism in these samples. The non-Debye dielectric relaxation is confirmed by the complex impedance formalism in all the composition. The activation energies are estimated from the AC conductivity versus inverse temperature according to the Arrhenius equation. The excitation of materials is investigated by application of a generated electric waveform. The application of series RC filter highlights Eu and Fe doped Bi0.5Na0.5TiO3 as a base for device engineering.

Doping effect of SrZrO3 on KNLN ceramics structure and their dielectric properties

In this work, lead-free systems; ([Formula: see text]) (K[Formula: see text]Na[Formula: see text]Li0.07) NbO3–[Formula: see text]SrZrO3 ([Formula: see text], 0.005, 0.050, 0.095 and 0.14) were synthesized by the conventional solid-state reaction technique. XRD, SEM, densification parameter as well as dielectric parameters of the obtained KNLN ceramics were investigated. XRD analysis showed the formation of orthorhombic perovskite structure in all investigated specimens. SrZrO3 (SZ) inhibited the grain growth and increased the distribution of grains uniformly in the microstructure. In addition, SZ changed the crystalline system of KNLN ceramics abnormally. As a consequence, the permittivity, dielectric loss as well as AC conductivity decreased remarkably. The ceramics of [Formula: see text] are characterized by low conductivity (10[Formula: see text][Formula: see text]S/cm), low dielectric loss (0.005) and relatively high permittivity (34). They can be useful for the electrical capacitors fabrication and filtering out noise from signals in resonant circuits. At frequencies lower than 105[Formula: see text]Hz, DC conductivity and separation of the charges at the interfaces were found to dominate the electrical behavior of ceramics, whereas at higher frequencies, a faster or dipole polarization may become more dominated. A broad peak has been observed in the imaginary part of electric modulus revealing to the non-Debye dielectric relaxation behavior. Quantum mechanical tunneling (QMT) was found to be the most suitable to characterize the electrical conduction mechanism in the ceramic compounds.

Effect of annealing temperatures on the electrical conductivity and dielectric properties of Ni1.5Fe1.5O4 spinel ferrite prepared by chemical reaction at different pH values

The electrical conductivity and dielectric properties of Ni1.5Fe1.5O4 ferrite has been controlled by varying the annealing temperature of the chemical routed samples. The frequency activated conductivity obeyed Jonscher’s power law and universal scaling suggested semiconductor nature. An unusual metal like state has been revealed in the measurement temperature scale in between two semiconductor states with different activation energy. The metal like state has been affected by thermal annealing of the material. The analysis of electrical impedance and modulus spectra has confirmed non-Debye dielectric relaxation with contributions from grains and grain boundaries. The dielectric relaxation process is thermally activated in terms of measurement temperature and annealing temperature of the samples. The hole hopping process, due to presence of Ni3+ ions in the present Ni rich ferrite, played a significant role in determining the thermal activated conduction mechanism. This work has successfully applied the technique of a combined variation of annealing temperature and pH value during chemical reaction for tuning electrical parameters in a wide range; for example dc limit of conductivity ~10−4–10−12 S cm−1, and unusually high activation energy ~0.17–1.36 eV.

Structural and Dielectric Properties of Ionic Liquid Doped Metal Organic Framework based Polymer Electrolyte Nanocomposites

Metal Organic Frameworks (MOFs) are mesoporous materials that can be treated as potential hosts for trapping guest molecules in their pores. Ion conduction and phase behavior dynamics of Ionic Liquids (ILs) can be controlled by tunable interactions of MOFs with the ILs. MOFs incorporated with ionic liquid can be dispersed in the polymers to synthesize polymer electrolyte nanocomposites with high ionic conductivity, electrochemical and thermal stability for applications in energy storage and conversion devices such as rechargeable Li-ion batteries. In the present work we have synthesized Cu-based MOF [Cu3(l,3,5-benzene tricarboxylate)2(H2O)] incorporated with the ionic liquid 1-Butyl-3-methylimidazolium bromide at different weight ratios of MOF and IL. The synthesized MOF-IL composites are dispersed in Poly (ethylene oxide) (PEO). Frequency dependent behavior of permittivity and dielectric loss of the nanocomposites depict the non-Debye dielectric relaxation mechanism. The room temperature Nyquist plots reveal decreasing bulk resistance upto 189 Ω with optimum ionic conductivity of 1.3×10-3S cm-1at maximum doping concentration of IL in the nanocomposite system.

Complex dielectric and impedance behavior of magnetoelectric Fe2TiO5

We have investigated the complex dielectric and impedance properties of magnetoelectric compound Fe2TiO5 (FTO) as a function of temperature (T) and frequency (f) to understand the grain (G) and grain boundary (Gb) contributions to its dielectric response. The temperature and frequency dependent dielectric permittivity (ε′) data shows a sharp increase in permittivity above 200 K accompanied with a frequency dependent peak in tanδ. At T < 175 K, only G contribution dominates even at lower frequency (∼100 Hz), but for T ≥ 175 K, the Gb contribution starts appearing at low frequency. The value of critical frequency distinguishing these two contributions increases with increasing temperature. The observed non-Debye dielectric relaxation follows thermally activated process and is attributed to polaron hopping. Further the frequency dependence of ac conductivity follows the Jonscher's power-law. The temperature dependency of critical exponent ‘s’ shows that the correlated barrier hopping model is appropriate to explain the conductivity mechanism of FTO in the studied temperature regime.

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 and ionic conductivity studies of (C6H20N3)BiCl6·H2O

The dielectric and the conduction characteristics of (C6H20N3)BiCl6·H2O from room temperature (290 K) to 355 K have been investigated by using impedance spectroscopy. The temperature-dependent conductivity and the relaxation times show a break in both the conductivity and the relaxation time around 335 K corresponding to the (I → II) phase transition temperature. Combined impedance and modulus plots were used as tools to analyze the sample behavior as a function of frequency at different temperatures. The modulus analysis and impedance studies showed the non-Debye dielectric relaxation nature. The Z′ and Z″ versus frequency plots in both phases I and II can be modeled as a parallel contribution of bulk resistance Rp and a constant phase element (CPE). The frequency dependence of the complex conductivity and the electric modulus spectra are analyzed by the “universal dielectric response” (UDR) and Kohlrausch, Williams, and Watts (KWW) approaches, and a comparison between the parameters derived from the two approaches has been discussed.

Dielectric relaxation and magnetic characteristics of the Bi0.5La0.5MnO3 ceramics

The complex permittivity ɛ* of ceramics of bismuth-lanthanum manganite Bi0.5La0.5MnO3 has been measured in ranges of temperatures T = 10–200 K and frequencies f = 102–106 Hz. Clearly pronounced regions of the non-Debye dielectric relaxation have been revealed at low temperatures (T < 90 K). To describe them, the possible mechanisms have been proposed and discussed. The temperature dependences of magnetization, the anomalous behavior of which can be associated with the phase transition from the paramagnetic phase into the ferromagnetic phase occurring at T ∼ 40–80 K, have been measured in the temperature range T = 10–120 K.

Conductivity and dielectric relaxation of Li salt in poly(ethylene oxide) and epoxidized natural rubber polymer electrolytes

Two types of polymer electrolytes were studied: poly(ethylene oxide) (PEO) and epoxidized natural rubber (ENR) both filled with lithium perchlorate. Universal dielectric behavior and impedance relaxation were investigated at room temperature over a wide range of salt concentration. Complex impedance plots exhibit one semicircle in some cases (PEO polymer electrolytes) with an extended spike at low frequencies. This implies a double layer capacity strongly influences conductivity at low frequencies. In the ENR–salt system, semicircles can be obtained only at very high concentrations. This points towards stable resistor dominated networks only develop at very high salt concentrations for this system. Centers of the semicircles lie below real axis indicating non-Debye dielectric relaxation. The relaxation peak broadens and shifts to higher frequencies with increasing salt content. It indicates that the relaxation time of polarization relaxations decreases with ascending salt content. Relaxations occur at extremely low salt concentrations in PEO and only at very high salt concentrations in ENR. Hence, conductivity of ENR–salt is one to two orders of magnitude lower as for PEO–salt.

Microscopic model of a non-Debye dielectric relaxation: The Cole-Cole law and its generalization

Based on a self-similar spatial-temporal structure of the relaxation process, we construct a microscopic model for a non-Debye (nonexponential) dielectric relaxation in complex systems. In this model, we derive the Cole-Cole expression for the complex dielectric permittivity and show that the exponent α involved in that expression is equal to the fractal dimension of the spatial-temporal self-similar ensemble characterizing the structure of the medium and the relaxation process occurring in it. We find a relation between the macroscopic relaxation time and the micro- and mesoparameters of the system. We obtain a generalized Cole-Cole expression for the complex dielectric permittivity involving log-periodic corrections that occur because of a discrete scaling invariance of the fractal structure generating the relaxation process on the mesoscopic scale. The found expression for the dielectric permittivity can be used to interpret dielectric spectra in disordered dielectrics.

Electrical Studies on PZT Ceramic

Polycrystalline sample of PZT (52/48) was prepared by solid-state reaction method. X-ray analysis indicated the formation of single-phase. Electrical and impedance-spectroscopy plots were employed to analyze the electrical behavior of the sample, as a function of frequency, in the range of 0.01 Hz to 1 M Hz at different temperatures. Spectroscopic and complex plots indicated non-Debye dielectric relaxation. Detailed electrical studies revealed that the conduction is through hoping of electrons (extrinsic region) at lowers temperature and migration of oxygen vacancies at high temperature (intrinsic region). The results are explained using Euryod’s conduction model and confirmed with pyroelectric and ferroelectric data.

Conductivity and dielectric studies on LiCeO 2

LiCeO 2 was prepared by a solid-state reaction method using microwave heat treatment and identified by X-ray diffractometry. LiCeO 2 has monoclinic crystal structure whose conductivity and dielectric properties were studied over a range of frequency (42 Hz to 1 MHz) and temperatures (30–500 °C) using ac technique of complex impedance analyzer HIOKI 3532. Combined impedance and modulus plots were used as tools to analyze the sample behaviour as a function of frequency at different temperatures. The d.c. conductivity (σ dc) followed the Arrhenius relation. The modulus analysis and dielectrics studies showed the non-Debye dielectric relaxation nature.

Mesoscopic nonequilibrium thermodynamics approach to non-Debye dielectric relaxation

Mesoscopic nonequilibrium thermodynamics is used to formulate a model describing nonhomogeneous and non-Debye dielectric relaxation. The model is presented in terms of a Fokker-Planck equation for the probability distribution of noninteracting polar molecules in contact with a heat bath and in the presence of an external time-dependent electric field. Memory effects are introduced in the Fokker-Planck description through integral relations containing memory kernels, which in turn are used to establish a connection with fractional Fokker-Planck descriptions. The model is developed in terms of the evolution equations for the first two moments of the distribution function. These equations are solved by following a perturbative method from which the expressions for the complex susceptibilities are obtained as a function of the frequency and the wave number. Different memory kernels are considered and used to compare with experiments of dielectric relaxation in glassy systems. For the case of Cole-Cole relaxation, we infer the distribution of relaxation times and its relation with an effective distribution of dipolar moments that can be attributed to different segmental motions of the polymer chains in a melt.

Ferroelectric and anisotropic electrical properties of BaMgF4 single crystal for vacuum UV devices

Ferroelectric and anisotropic electrical behaviors of barium magnesium fluoride (BaMgF4) single crystal grown under CF4 atmosphere by the Czochralski method are comprehensively studied by polarization hysteresis and impedance spectroscopy measurements, respectively. The coercive field (Ec) varies not only with applied frequency but also with ramp rates, while spontaneous polarization Ps∼6.9 C/cm2 remains the same. Dielectric polarization and ionic conductivity measurements at various temperatures and frequencies reveal quasi-one-dimensional ionic conduction phenomena along the c-axis and non-Debye dielectric relaxation along the axes.

Investigation of the shear-mechanical and dielectric relaxation processes in two monoalcohols close to the glass transition

Shear-mechanical and dielectric measurements on the two monohydroxy (monoalcohol) molecular glass formers 2-ethyl-1-hexanol and 2-butanol close to the glass-transition temperature are presented. The shear-mechanical data are obtained using the piezoelectric shear-modulus gauge method covering frequencies from 1 mHz to 10 kHz. The shear-mechanical relaxation spectra show two processes, which follow the typical scenario of a structural (alpha) relaxation and an additional (Johari-Goldstein) beta relaxation. The dielectric relaxation spectra are dominated by a Debye-type peak with an additional non-Debye peak visible. This Debye-type relaxation is a common feature peculiar to monoalcohols. The time scale of the non-Debye dielectric relaxation process is shown to correspond to the mechanical structural (alpha) relaxation. Glass-transition temperatures and fragilities are reported based on the mechanical alpha relaxation and the dielectric Debye-type process, showing that the two glass-transition temperatures differ by approximately 10 K and that the fragility based on the Debye-type process is a factor of 2 smaller than the structural fragility. If a mechanical signature of the Debye-type relaxation exists in these liquids, its relaxation strength is at most 1% and 3% of the full relaxation strength of 2-butanol and 2-ethyl-1-hexanol, respectively. These findings support the notion that it is the non-Debye dielectric relaxation process that corresponds to the structural alpha relaxation in the liquid.

Dielectric relaxation of 4-cyano-4-n-pentylbiphenyl (5CB) thin layer adsorbed on carbon nanotube – MD simulation

The ultra-thin layer of mesogenous molecules 5CB adsorbed on a single walled carbon nanotube (SWNT) has been studied by molecular dynamics (MD) simulation method. The focus was on the temperature dependence (200K<T<350K) and time evolution of the total dipole moment autocorrelation function. The frequency dependence of the dielectric loss of ultra-thin mesogene layer covering carbon nanotube has been also studied. The layer reveals a non-Debye dielectric relaxation. The shape of dielectric loss spectrum significantly depends on the temperature of the system studied.