Heavy-tail properties of relaxation time distributions underlying the Havriliak–Negami and the Kohlrausch–Williams–Watts relaxation patterns

A detailed discussion of asymptotic properties of the Havriliak–Negami and the Kohlrausch–Williams–Watts relaxation time distributions is presented. The heavy-tail property of the Havriliak–Negami relaxation time distribution, leading to the infinite mean relaxation time, is discussed. In contrast, the existence of the finite mean relaxation time for the Kohlrausch–Williams–Watts response is shown. The discussion of the Cole–Davidson and the Cole–Cole cases is also included. Using the Tauberian theorems we show that these properties are determined directly by the asymptotic behavior of the considered empirical functions.     

Design,Synthesis and Analysis of Chlorohydroquinone Derivatives—Liquid Crystalline Complexes

A novel linear double hydrogen-bonded liquid crystalline material is designed and isolated. The ingredients of the mesogens synthesized are chloro hydroquinone (ClHQ) and p-n alkyloxy benzoic acid (nBAO) where n varied from pentyl to dodecyl alkyloxy carbon numbers. The series is abbreviated as ClHQ + nBAO, and seven of eight synthesized complexes are found to exhibit liquid crystalline phases. These liquid crystalline complexes are characterized by Fourier Transformation Infrared spectroscopy (FTIR) in order to confirm the formation of hydrogen bond. Mesophases and their corresponding transition temperatures are studied by polarizing optical microscopy (POM) and their respective enthalpy values along with the order of the transitions are determined by Differential Scanning Calorimetry (DSC). The experimental measurement of tilt angle is carried out by optical extinction method and fitted to the theoretically predicted mean field exponent which is found to be in good agreement. Dielectric relaxations at different temperatures in nematic phase for the complexes have been carried out and their corresponding activation energy values are calculated from Cole–Davidson plots. Light filtering action in the liquid crystalline complexes is done to validate the commercial applications of these mesogens.     

The physical mechanisms of relaxation times distribution in inorganic and organic disordered ferroelectrics

We discuss the physical background for relaxation times distribution in organic and inorganic disordered ferroelectrics. We show that such background is a disorder which is believed to be a reason for relaxor behavior. Due to this disorder the internal electric and elastic fields are of a random nature being characterized by certain distribution function. Having the distribution function f(E) of random field E, we can obtain the distribution function of relaxation times F(τ) with the help of relation between τ and E. Latter relation can be obtained considering the dynamics of a single electric dipole in a random field created by the ensemble of defects and impurities in a sample. We show that in our approach the known empirical relaxation laws like Cole–Cole, Davidson–Cole, Havriliak–Negami etc correspond to different concentrations and kind of defects in the above substances. The character of interaction between them also plays an important role. The comparison of our theory with experiment shows that our approach captures the main relaxation properties of disordered ferroelectrics. Our formalism can be easily generalized on the other nonferroelectric disordered substances, both organic and inorganic.     

Electrical properties of interdigitated partially bent like shaped liquid crystalline compound

This article represents the electrical studies of an interdigitated highly skewed N(4-n-pentyloxybenzylidene) 4-n-alkylaniline (5O.16) compound. Interestingly the compound is partially bent like and unsymmetrical in alkyl chain length. Dielectric and impedance spectroscopy studies indicate the coupling between the liquid crystal and the electrical field. Studies were carried out as a function of temperature as well as frequency. Semicircular nature of the Cole–Cole plots indicates the reorientation of the molecule with the applied field. Using the experimental data and the theoretically fitted results the effective equivalent model circuit was designed. Which used to explain the behavior of the compound under the external electric effect and the influence of the electrodes with different variable represent the resistor circuit. However, the effect of the conductivity of temperature and frequency are also reported.     

Dielectric relaxation and morphologic properties of CaCu3Ti4O12 doped with GeO2

CaCu₃Ti₄O₁₂ (CCTO) is a material with giant dielectric constant, presenting good stability over a wide temperature and frequency ranges. The preparation method and doping has a great influence on the microstructure and dielectric properties of this material. In this work, doping CCTO with 2–10 wt% GeO₂ has been shown to increase the dielectric constant. We studied the prepared samples by X-ray diffraction (XRD), scanning electron microscopy (SEM) and impedance spectroscopy. X-ray diffraction shows the presence of nanocristals. Grains and grain boundaries compositions have been observed by scanning electron microscopy with energy dispersive X-ray spectrometry mapping. Impedance spectroscopy measurements, in the frequency range from 75 kHz to 30 MHz, and temperature from 250 to 325 K, have been performed. The data were analyzed using the Cole–Cole model of dielectric relaxation.     

Indexing of double reflection peaks

A numerical and a graphical method for indexing double reflections is described. The conditions for the applicability of the graphical method are discussed.     

Dielectric characteristics of Ce3+ doped Sr0.61Ba0.39Nb2O6 with Cole‐Cole plots technique

In this paper, we have investigated two‐relaxator mechanism and dielectric characteristics of Ce³⁺ doped Sr_0.61Ba_0.39Nb₂O₆ with dielectric spectroscopy measurements. The crystal undergoes a ferroelectric phase transition at 340 K. The temperature dependence of the real and imaginer part of the complex dielectric susceptibility in vicinity of ferroelectric‐paraelectric phase transition has been studied in the frequency region 0.1 kHz–10 MHz. The measurements of the dielectric constant of the real and imaginer parts show strongly frequency dependence. The investigations of the dielectric constant revealed a non‐Debye type dielectric relaxation for Ce⁺³ doped SBN61 by using Cole‐Cole plots. It reveals the coexistence of the two dielectric relaxators in vicinity of the phase transition. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermally stimulated currents in disordered solids at fractional heating

Thermally stimulated currents (TSCs) in disordered solids, registered at fractional sample heating, are investigated theoretically. The Gobrecht–Hofmann method of determining trap distribution in energy gap is extended to the case of significant carrier retrapping. Two specific cases, when the TSCs are limited either by carrier recombination or by carrier neutralization on collecting electrode, are considered. The accuracy of proposed method is estimated from the analysis of TSC curves, calculated numerically for exponential and Gaussian trap distributions.     

Atomic and electronic structures of nanometer sized silica particles

The Austin Model 1 semi-empirical method combined with geometry optimization procedure was used to study atomic and electronic structures of nanoscale silica particles containing up to 192 atoms (64 Si and 128 O). Twofold Si–O rings were found to dominate in nanometer sized particles. The fraction of larger rings increases with increasing particle sizes. Bond length and bond angle distributions were calculated. The shortest Si–O, O–O and Si–Si interatomic distances are approximately 1.7, 3.0 and 3.3 Å, respectively. Average O–Si–O and Si–O–Si bond angles are approximately 110^∘ and 130^∘. Average electronic energy band gap is 6.9 eV.     

Dielectric relaxation of Al/Lu2O3/Al thin film structures from 10 μHz to 10 MHz

Results of dielectric studies of lutetium sesquioxide layers examined in Al/Lu₂O₃/Al thin film sandwiches are reported. The dielectric measurements were carried out in the frequency range 10⁻⁵–10⁷ Hz and for temperatures from 292 K to 500 K. Results are presented as plots of frequency functions: the capacitance, the dielectric loss factor, tan δ(f) and also on the complex plane as Cole–Cole plots and Nyquist plots. The influence of the external voltage on C(U) and tan δ(U) was examined. Experimental data were analyzed taking into account thin insulating Lu₂O₃ film, near-electrode regions of Al/Lu₂O₃ and Lu₂O₃/Al interfaces and series resistance of electrodes and leads. The parameters of Lu₂O₃ film, near-electrode regions and resistance of contacts and leads were determined.     

Relaxation behavior of supra-molecular hydrogen-bonded liquid crystal phase structures: SA:11OBA

Low-frequency (20 Hz–10 MHz) dielectric response in liquid crystalline (LC) phases of hydrogen-bonded (HB) complex, SA:11OBA, is studied. Synthesis of SA:11OBA with non-mesogenic succinic acid (SA) and mesogenic p-n-undecyloxy benzoic acid (11OBA) and its spectroscopic confirmation are detailed. Phase transition temperatures (T_C) involving nematic, smectic-C (SmC), and smectic-G (SmG) phases by capacitance C(T) and loss tanΔ(T) anomaly agree with the microscopy (polarizing optical microscope) and calorimetry (differential scanning calorimetry) results. Low-frequency dispersion infers two types of reorientation processes, viz. higher frequency (～MHz) and lower frequency (kHz) processes. Distinct time scale mechanism are presented. Arrhenius behavior infers influence of HB on activation energy (E_a). Off-centered dispersion, viz. ?′(ω) with ?″(ω), analyzed through the Cole–Cole plots in N, SmC, and SmG phases infers a strong temperature trend for dielectric strength (Δ?) and distribution (α) parameters. Temperature dependence of α-parameter reveals on LC phases increasing fixture of molecular dipole in LC phase structure. Results are discussed in the wake of the body of data reported in LC phases exhibited by other LC compounds.     

Calculation of the atomic scattering factors of fast electrons at zero angle of incidence of an electron beam and mean inner crystal potentials

The atomic scattering factors of fast electrons at zero angle of incidence of an electron beam, f _el(0), are calculated for neutral atoms with Z = 1?54, using the mean-square radii of electron-density distributions in atoms and ions, derived on the basis of the Hartree-Fock wave functions. The values of f _el(0) have been calculated for the first time for some positive and negative ions. The obtained values of f _el(0) were used to determine the mean inner potentials V₀ of metallic, covalent, and ionic crystals. The calculated values of V₀ are compared with the experimental data in the literature. The values of V₀ calculated for III–V and II–VI compounds are reported.     

Effect of devitrification on ion motion in lithium-disilicate glass

Li-disilicate glass-ceramics consist of microcrystallites imbedded in the glassy Li₂O · 2SiO₂ matrix where the number and size of the crystallites depend on the devitrification heat treatment. To assess ion motion in these model glass-ceramics, we have measured the temperature dependence of the dc conductivity, σ_dc, and the ⁷Li nuclear spin relaxation (NSR) rate, 1/T₁, in samples with various crystalline fraction, c, ranging from c = 0 (pure glass) to c = 1 (fully devitrified polycrystalline ceramic). The Cole–Cole presentation of the complex impedance shows two separate arcs caused by the remarkable difference of the ionic motion in the glassy and crystalline phase. These two arcs correspond to a bi-exponential decay of the ⁷Li nuclear spin magnetization where the resulting two NSR rates are induced by the ionic motion in the two phases. Thus the NSR and σ_dc data provide a comprehensive picture of the ionic motion in the glassy and crystalline phases. In particular, the ionic motion is the fastest in the glass; then at lower values of c we observe a metastable crystalline phase with ionic motion much greater than in the stable (LS₂) crystalline phase existing at large c-values.     

Elastic Behaviour of Mn–Zn and Mg–Zn Ferrites

The elastic moduli of four different composition of mixed Mn–Zn and Mg–Zn ferrites in the polycrystalline form have been measured at the room temperature using the ultrasonic pulse transmission method. The values of Young's modulus and the rigidity modulus are corrected to theoretical density using the method of Mackenzie. From the values of longitudinal and shear velocities, the Debye temperature has been calculated.     

A method for the calculation of the magnetization of random high anisotropy amorphous materials

We introduce a procedure for the calculation of the magnetization distribution for a random anisotropy amorphous ferromagnetic material using a steepest descent method. The technique is applied to several anisotropy distributions, and the magnetization of each is presented as a function of temperature for realistic values of molecular field constant and anisotropy.     

Bias field induced impedance relaxation of TlGaSe2 semiconducting layered crystal at room temperature

Complex Impedance Spectroscopy has been employed for the study of absorption kinetics at TlGaSe₂ layered crystal under Bias voltage at room temperature. Two relaxations mechanisms have been observed. The crystal has “slow” and “fast” relaxation mechanisms in low and high frequency region, respectively. The complex impedance spectra were fitted by the superposition of two Cole‐Cole types of relaxations. The fast relaxation in the higher frequency region may be due to dipolar relaxation and the slow relaxation in the low frequency region may be due to Maxwell‐Wagner type relaxation. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Probleme röntgenografischer Teilchengrößen- und Verzerrungsbestimmung an verformten Polykristallen

For given models of distortion (displacement fields) and given particle sizes intensity distributions of Debye-Scherrer lines were calculated and from these by the method of WARREN and AVERBACH such as by the variance method particle sizes and mean square strains were determined. For particle sizes values were obtained which were in good agreement with those predetermined. The mean square strains on the contrary partly strongly deviate from the predetermined values. This deviation can be explained by an investigation of the specific averaging, occurring with application of the method of WARREN and AVERBACH .     

Anomalous thermal expansion of osmium dioxide

The precision lattice parameters of osmium dioxide have been determined at different temperatures, in the temperature range 30–444 °C, using a Unicam high temperature powder camera 19 cm in diameter and CuKα radiation. The data have been used to evaluate the coefficients of thermal expansion at various temperatures by a graphical method. The ‘a’ parameter increases non-linearly with increasing temperature while the ‘c’ parameter remains constant throughout the range of temperature studied indicating a zero coefficient of expansion along the c-direction. The abnormal thermal behaviour of this compound is explained in terms of the electronic configuration of the d-shell of the cation.     

Untersuchungen zur röntgenografischen Verzerrungsverteilung von Versetzungen

For cylindrical crystallites with a dislocation on the axis are calculated deformation moments and with him the X-ray distribution function of deformations. The obtained deformation distributions deviates – except of special cases – from a Gaussian distribution, especially in the cases of the screw dislocation and the edge dislocation with inserted planes in interference position appears intense minimum values at small deformations and a dependence of all distributions on the Fourier order. – By the ratios of moments are compared the deformation distributions of dislocation models with the corresponding quantities of predetermined model distributions.     

Particle size distribution in FeAg granular alloy

A combination of Langevin and hyperbolic tangent functions weighted by a log-normal particle size distributions were used to fit the magnetization curves of Fe₁₀Ag₉₀ granular alloys, produced by a sol–gel process under different chemical conditions. The fitting technique allows one to get both the superparamagnetic and the blocked particle size distributions. The average size of the Fe particles obtained from the fit were in good agreement with those obtained by X-ray diffraction. The correlation between the coercive field and the particle distribution was also investigated. Zero-field cooling dc magnetic susceptibility measurements were fitted using a similar technique to that used for fitting the magnetization curves. The saturation magnetization and mean Fe particle size values obtained from the two fittings were in good agreement.