Universal Relaxation Law Research Articles

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.

Non‐destructive thermal ageing evaluation of P (VDF‐HFP) film based on broadband dielectric response

Capacitors and sensors based on polymer dielectric materials are key components in electrical systems and electronic devices. Considering the temperature rise during operation, an effective evaluation method for the thermal ageing of polymer matrix is urgently needed. P(VDF-HFP) film with a thickness of 20 μm is manufactured by solution casting and a thermal ageing experiment up to 1000 h is conducted. Dielectric responses of wide ranges of temperatures and frequencies are measured for samples with different ageing durations. The universal relaxation law and Dissado–Hill dielectric response model are applied to further investigate the results. The characteristics of individual processes are obtained, which demonstrate that the main chain relaxation following the Vogel−Fulcher−Tammann equation and side chain relaxation following the Arrhenius equation both remain unchanged after thermal ageing. However, the activation energies of those two processes change significantly during the process and show different variation trends. The activation energy of the side chain relaxation gets larger monotonically due to the influence of annealing and the breaking of crystalline region. As a result, a non-destructive evaluation method for the thermal ageing of P(VDF-HFP) is proposed accordingly.

High-temperature electrical conductivity in piezoelectric lithium niobate

Lithium niobate is a promising candidate for use in high-temperature piezoelectric devices due to its high Curie temperature (≈1483 K) and strong piezoelectric properties. However, the piezoelectric behavior has, in practice, been found to degrade at various temperatures as low as 573 K, with no satisfactory explanation available in the literature. We, therefore, studied the electrical conductivity of congruent lithium niobate single crystals in the temperature range of 293–1273 K with an 500 mV excitation at frequencies between 20 Hz and 20 MHz. An analytical model that generalizes the universal dielectric relaxation law with the Arrhenius equation was found to describe the experimental temperature and frequency dependence and helped discriminate between conduction mechanisms. Electronic conduction was found to dominate at low temperatures, leading to low overall electrical conductivity. However, at high temperatures, the overall electrical conductivity increases significantly due to ionic conduction, primarily with lithium ions (Li+) as charge carriers. This increase in electrical conductivity can, therefore, cause an internal short in the lithium niobate crystal, thereby reducing observable piezoelectricity. Interestingly, the temperature above which ionic conductivity dominates depends greatly on the excitation frequency: at a sufficiently high frequency, lithium niobate does not exhibit appreciable ionic conductivity at high temperature, helping explain the conflicting observations reported in the literature. These findings enable an appropriate implementation of lithium niobate to realize previously elusive high-temperature piezoelectric applications.

Investigation of the dielectric relaxation mechanisms for Pb(Fe1/2Nb1/2)O3 single crystal based on the universal relaxation law

Large-sized multiferroics Pb(Fe1/2Nb1/2)O3 (PFN) single crystal was grown by Bridgeman method in order to understand the giant dielectric response by investigating the electrical conductivity and dielectric properties. The synchrotron radiation soft x-ray absorption spectrum revealed the valence states of Fe in PFN crystal. PFN exhibits semiconductor behaviors in the thermal active electrical conductivity investigation. Besides, the frequency-dependent dielectric constants were measured in the frequency range from 100 Hz to 1 MHz to study the dielectric relaxation behaviors. Two relaxation processes were found and described by Havriliak-Negami equation. The origin of dielectric relaxation in PFN with semiconductor characters was discussed based on the universal relaxation law for a dipolar system.

Hydraulic transmissivity inferred from ice-sheet relaxation following Greenland supraglacial lake drainages

Surface meltwater reaching the base of the Greenland Ice Sheet transits through drainage networks, modulating the flow of the ice sheet. Dye and gas-tracing studies conducted in the western margin sector of the ice sheet have directly observed drainage efficiency to evolve seasonally along the drainage pathway. However, the local evolution of drainage systems further inland, where ice thicknesses exceed 1000 m, remains largely unknown. Here, we infer drainage system transmissivity based on surface uplift relaxation following rapid lake drainage events. Combining field observations of five lake drainage events with a mathematical model and laboratory experiments, we show that the surface uplift decreases exponentially with time, as the water in the blister formed beneath the drained lake permeates through the subglacial drainage system. This deflation obeys a universal relaxation law with a timescale that reveals hydraulic transmissivity and indicates a two-order-of-magnitude increase in subglacial transmissivity (from 0.8 ± 0.3 {rm{m}}{{rm{m}}}^{3} to 215 ± 90.2 {rm{m}}{{rm{m}}}^{3}) as the melt season progresses, suggesting significant changes in basal hydrology beneath the lakes driven by seasonal meltwater input.

Relaxor ferroelectric behavior: An approach considering both the dipolar and electrical conductivity contributions

The relaxor behavior of PLZT ferroelectric ceramics has been analyzed in a wide frequency and temperature ranges, below and above the temperature for the formation of the so-called polar nano-regions (PNRs). An approximation to the dynamical behavior of the PNRs has been discussed using Cole–Cole’s relaxation model and Jonscher’s Universal Relaxation Law. The analysis considers both the dipolar contribution and those ones associated with DC and AC electric conductivities, this latter not being previously reported in the literature for relaxor materials. The effectiveness of the developed model has been verified from the agreement between the experimental data and the theoretical calculations. This study also offers an indirect method to predict the DC component of the electrical conductivity.

The abnormal multiple dielectric relaxation responses of Al3+ and Nb5+ co-doped rutile TiO2 ceramics

Al3+ and Nb5+ co-doped rutile TiO2 ceramic samples were prepared by solid state reaction. Raman spectra, element mapping and EDX confirmed that (Al + Nb) dissolved into grain. The samples showed colossal permittivity (ε′≈3.8 × 104) with low dielectric loss (under 0.08) over frequency (20 Hz–100 kHz) and temperature (80 K–240 K) ranges. Abnormal multiple dielectric relaxation properties were obtained around 5 K. Using universal relaxation law and thermal polaron hopping, we concluded that high dielectric constant of (Al1/2Nb1/2)0.05Ti0.95O2 was due to thermal activation of electrons in defect-dipoles, polaron hopping polarization and interfacial polarization. This investigation could increase our understanding models of multiple dielectric relaxation and inhomogeneous composition in co-doped rutile TiO2.

Jonscher indices for dielectric materials

Two parameters are proposed as Jonscher indices, named after A. K. Jonscher for his pioneering contribution to the universal dielectric relaxation law. Time domain universal dielectric relaxation law is then obtained from the asymptotic behavior of dielectric response function and relaxation function by replacing parameters in Mittag–Leffler functions with Jonscher indices. Relaxation types can be easily determined from experimental data of discharge current in barium stannate titanate after their Jonscher indices are determined.

Defect driven d0 ferromagnetism and colossal dielectric behavior in Bi(Zn0.5Ti0.5)O3–PbTiO3 ceramics

We report room temperature ferromagnetism and colossal dielectric behavior in non-magnetic polycrystalline samples of x (BiZn0.5Ti0.5O3) – (1-x) (PbTiO3) with x = 0.25, 0.50. These samples are synthesized by mechanical alloying followed by heating the samples at elevated temperatures. Room temperature X-ray diffraction study reveals the formation of BZT-PT samples in perovskite phase and in the tetragonal system. The magnetic properties of these samples are studied by using SQUID. Intriguingly, exotic room temperature ferromagnetism has been observed in non-magnetic BZT-PT samples by vacuum annealing of the samples. In addition, a substantial high dielectric constant has also been observed in vacuum annealed samples. The unprecedented magnetic and dielectric behavior has been attributed to the formation of oxygen vacancies which is explained by further studying the magnetic and dielectric behavior in air annealed samples. Furthermore, the dielectric relaxation and frequency response of ac conductivity in BZT-PT samples found to follow universal dielectric relaxation and Johnscher's power law response, respectively. A detailed density functional calculations show that the exotic magnetism BZT-PT is mainly due to the partial occupancy of t2g and eg states of Ti ion by the delocalized electrons generated due to oxygen vacancy.

A New Look at Formulation of Charge Storage in Capacitors and Application to Classical Capacitor and Fractional Capacitor Theory


 
 
 
 In this study, we revisit the concept of classical capacitor theory-and derive possible new explanations of the definition charge stored in a capacitor. We introduce the capacity function with respect to time to describe the charge storage in a classical capacitor and a fractional capacitor. Here we will describe that charge stored at any time in a capacitor as ‘convolution integral’ of defined capacity function of a capacitor and voltage stress across it which comes from causality principle. This approach, however, is different from the conventional method, where we multiply the capacity and voltage functions to obtain charge stored. This new concept is in line with the observation of charge stored as a step function and the relaxation current in form of impulse function for ‘ideal geometrical capacitor’ of constant capacity; when an uncharged capacitor is impressed with a constant voltage stress. Also this new formulation is valid for a power-law decay current that is given by ‘universal dielectric relaxation law’ called as ‘Curie von-Schweidler law’, when an uncharged capacitor is impressed with a constant voltage stress. This universal dielectric relaxation law gives rise to fractional derivative relating voltage stress and relaxation current that is formulation of ‘fractional capacitor’. A ‘fractional capacitor’ we will discuss with this new concept of redefining the charge store definition i.e. via this ‘convolution integral’ approach, and obtain the loss tangent value. We will also show how for a ‘fractional capacitor’ by use of ‘fractional integration’ we can convert the fractional capacity a constant that is in terms of fractional units (Farads per sec to the power of fractional number); to normal units of Farads. From the defined capacity function, we will also derive integrated capacity of capacitor. We will also give a possible physical explanation by taking example of porous and non-porous pitchers of constant volume holding water and thus, explaining the various interesting aspects of classical capacitor and a fractional capacitor that we arrive with this new formulation; and also relates to a capacitor breakdown theory-due to electrostatic forces.
 
 
 
 

Influence of defects on the dielectric relaxation and electrical conductivity behavior for Sr0.70Ba0.30Bi2Nb2O9 ferroelectric ceramic

Sr0.7Ba0.3Bi2Nb2O9 ferroelectric ceramic system is studied concerning the dielectric relaxation and electrical conductivity processes in wide temperature and frequency ranges. The dielectric relaxation analysis is carried out by using the Cole-Cole model and the Universal Relaxation Law. From the activation energy value for the relaxation time, the dielectric relaxation processes at low temperatures (T < 90 °C) has been associated to polarons. For temperatures between 90 °C and 300 °C the contribution of polarons increases and the dielectric parameters follow the Universal Relaxation Law. From 300 °C to 450 °C, a strong influence of the electrical conductivity in the dielectric relaxation processes has been observed. The frequency dependence of the electrical conductivity was analyzed by using the Universal Dielectric Response (UDR) model. The electrical conductivity processes have been related to the presence of polarons in correspondence with the dielectric analysis for temperatures below 300 °C. For temperatures above 300 °C the main contribution to both dielectric relaxation and electrical conductivity is the hopping of electrons from the ionization of oxygen vacancies.

Joint effect of the tube sizes and Fe-filling process on microwave dielectric properties of carbon nanotubes

To explore the effect of tube sizes and filling process on dielectric properties of carbon nanotubes (CNTs), CNTs with various diameters and lengths were applied to synthesize Fe-filled CNTs through wet-chemical method. The permittivities of the composites of CNTs and paraffin rely on the dispersion state (agglomeration) of CNTs in polymer matrices. During the filling process, CNTs with diverse tube parameters and dispersibility experienced different structural transformations, and different iron oxides (either Fe3O4 or Fe2O3) particles (depending on the dispersibility of CNTs) were observed adhering to walls of CNTs after filling. The discrepancies along with the dispersibility of CNTs per se alter the order of the permittivity (from high to low) within samples. The smallest agglomerates and the largest permittivity were obtained for CNTs with diameters of 10–20 nm and lengths of 10–30 μm, both before and after the filling of CNTs. The role that the shape parameters played in the dielectric properties during the whole filling process was analyzed. The frequency-dependent permittivity spectrum was also examined and it obeyed Jonscher’s universal dielectric relaxation law.

Revisiting the Curie-Von Schweidler Law for Dielectric Relaxation and Derivation of Distribution Function for Relaxation Rates as Zipf’s Power Law and Manifestation of Fractional Differential Equation for Capacitor

The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations; and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.

Microstructures and Properties of 3Y‐TZP/Ba0.5Sr0.5Fe12O19 Composites Prepared by Two Methods

Two composites of Ba0.5Sr0.5Fe12O19 grains dispersed in a 3 mol% yttria‐doped zirconia (3Y‐TZP) matrix are prepared by two methods. The mechanical and electromagnetic properties of the both composites are investigated. The maximum values of the bending strength and the fracture toughness are 786 MPa and 8.6 MPa m1/2, respectively. The maximum value of the magnetization is 17.2 emu/g. In addition, the distribution of the Ba0.5Sr0.5Fe12O19 phase is described using the box dimension of the fractal theory. The impedance spectra of the both composites are fitted using the equivalent circuit model with a constant phase element (CPE). The obtained p value of the CPE can indirectly reflect the morphology of the Ba0.5Sr0.5Fe12O19 phase in both composites according to the universal relaxation law.

Magnetic and dielectric properties of 3Y-TZP/strontium doped barium ferrite composite

Magnetic and dielectric properties of 3Y-TZP/20 wt.% Ba 1-x Sr x Fe 12 O 19 (x = 0, 0.25, 0.5, 0.75) composites prepared by solid state reaction method are investigated. The magnetic properties are improved in the composites with the strontium doped barium ferrite. When x = 0.25, the saturation magnetization of the ferrite reaches the maximum. This is due to the migration of Fe 3+ induced by the Sr 2+ doping. The dielectric properties are also improved in the composite with the strontium doped barium ferrite. When x = 0.5, the dielectric constant and dielectric loss possess the maximum. This is caused by the lattice distortion resulting from the Sr 2+ doping. The dielectric properties are analyzed by the universal relaxation law.

Time domain dielectric relaxation study on charging and discharging current of barium stannate titanate ferroelectric ceramics

Time domain measurement is an indispensable experimental method for ultralow frequency region (even lower than 1 Hz) and nonlinearity study of ferroelectric materials. The charging and discharging currents of BaTi1-xSnxO3 (BTS) ceramics have been collected in both paraelectric and ferroelectric phases. Kohlrausch-Williams- Watts (KWW) relation with two parameters (β and τ) was employed in discharging current analysis. Our results show that the higher β values in paraelectric phase indicate near Debye relaxation behavior, and lower βvalues in ferroelectric phase tie with possible diffusion controlled universal relaxation law (URL).

Magnetoelectric Coupling in BaTiO3–CoFe2O4 Nanocomposites Studied by Impedance Spectroscopy Under Magnetic Field

BaTiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> -CoFe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> nanocomposites with a 1/1 molar ratio were prepared by a combination of polyol synthesis (chimie douce) and a subsequent consolidation by spark plasma sintering. The nanocomposite samples, with a grain size about 50 nm showed a good mixing and a high density. Their impedance response was measured in the 5 Hz-1 MHz frequency range, under magnetic fields up to 1200 kA/m. Measurements were carried out in the 40-210 °C temperature range. We used the Jonscher's universal relaxation law to analyze the electric conductivity results. Significant changes in the activation energies for long range conductivity and hopping conductivity were observed both at the coercive magnetic field of the ferrite and the Curie transition of the titanate. We show that the use of impedance spectroscopy, based on a wide frequency range, provides a far larger view of electric phenomena allowing a separation of the several contributions to the conductivity phenomena, as a function of the magnetic field.

On the theory of the universal dielectric relaxation

Dielectric relaxation has been investigated within the framework of a modified mean field theory, in which the dielectric response of an arbitrary condensed matter system to the applied electric field is assumed to consist of two parts, a collective response and a slowly fluctuating response; the former corresponds to the cooperative response of the crystalline or noncrystalline structures composed of the atoms or molecules held together by normal chemical bonds and the latter represents the slow response of the strongly correlated high-temperature structure precursors or a partially ordered nematic phase. These two dielectric responses are not independent of each other but rather constitute a dynamic hierarchy, in which the slowly fluctuating response is constrained by the collective response. It then becomes clear that the dielectric relaxation of the system is actually a specific characteristic relaxation process modulated by the slow relaxation of the nematic phase and the relationship governing such a process can be defined as the universal dielectric relaxation law. Furthermore, we have shown that seemingly different relaxation relationships, such as the Debye relaxation law, the Cole-Cole equation, the Cole-Davidson equation, the Havriliak-Negami relaxation, the Kohlrausch-Williams-Watts function, Jonscher’s universal dielectric relaxation law, etc. are only the variants of this universal law under different circumstances.

Dielectric properties and high-temperature dielectric relaxation of Ba4Gd2Fe2Nb8−xTaxO30 ceramics

Several ferrum oxides of formula Ba4Gd2Fe2Nb8−xTaxO30 (x = 2, 4, 6 and 8) with tetragonal tungsten-bronze structure have been synthesized by the conventional solid state sintering method. Dielectric response of the samples was studied using AC impedance spectroscopy and universal dielectric relaxation law in detail. The dielectric anomaly at high temperature is attributed to the mobility of oxygen vacancies. Arrhenius activation energy associated with the migration of oxygen vacancies is estimated from impedance spectroscopy, which is 0.77, 1.11, 1.26 and 1.02 eV for x = 2, 4, 6 and 8, respectively.

Dielectric and optical properties of Ba5AFe0.5Ta9.5O30 (A = K, Li) tungsten bronze ceramics

Two novel Ba5AFe0.5Ta9.5O30 (A = K, Li) ceramics were fabricated through a conventional solid-state sintering process. Both samples were paraelectric phase with tetragonal tungsten bronze structure at room temperature. Dielectric response of the samples was studied by using AC impedance spectroscopy and universal dielectric relaxation law in detail. Dielectric relaxation at high temperatures is attributed to the oxygen vacancies induced by the evaporation of alkali oxide. The relaxation activation energy of the ceramics is lower than half of the band gap Eg obtained by UV–Vis spectroscopy, which resulted from the emergence of oxygen vacancies at high temperatures. In the visible light region, the samples showed strong absorption with a band gap of about 2.7 eV, which could be applied as a visible light irradiation photocatalyst.