Dielectric parameters in Se70Te30 and Se70Te28Zn2 chalcogenide glasses

Temperature and frequency dependence of dielectric constant (ε′) and dielectric loss (ε″) are studied in glassy Se₇₀Te₃₀ and Se₇₀Te₂₈Zn₂. The measurements have been made in the frequency range (8-500 kHz) and in the temperature range 300 to 350 K. An analysis of the dielectric loss data shows that the Guintini's theory of dielectric dispersion based on two-electron hopping over a potential barrier is applicable in the present case.No dielectric loss peak is observed in glassy Se₇₀Te₃₀. However, such loss peaks exist in the glassy Se₇₀Te₂₈Zn₂ in the above frequency and temperature range. The Cole-Cole diagrams have been used to determine some parameters such as the distribution parameter (α), the macroscopic relaxation time (τ₀), the molecular relaxation time (τ) and the Gibb's free energy for relaxation (ΔF).     

Dielectric dispersion studies of mixtures of aniline and benzonitrile in benzene solutions

Dielectric behavior of aniline, benzonitrile and their binary mixtures of different concentrations were studied in benzene at 293, 303, 313 and 323 K. The complex permittivity (∈′, ∈″) at microwave frequencies 7.22, 9.1, 19.61 GHz, static permittivity ∈₀ at 455 KHz and high frequency limiting dielectric constant ∈_∞ = n_D² at optical frequency of these molecules and their binary mixtures were measured. The average relaxation time (τ₀), distribution parameter (α) and thermodynamical parameters were determined. The plot of relaxation time (τ₀) against concentration of benzonitrile in the mixtures is nonlinear indicating complex formation.     

Multivariate pressure effects on an electron hopping process in ferroelectric KTa<Subscript>1−x</Subscript>Nb<Subscript>x</Subscript>O<Subscript>3</Subscript>

The effect induced by the presence of a polaron related relaxation process on the dielectric properties of a ferroelectric KTa_1?x Nb _x O₃ (KTN) crystal was investigated (10^-2?10⁶ Hz, at 300?375 K) using broadband dielectric spectroscopy. Characterization of the process using just the standard frequency domain dielectric parameters can nonetheless provide penetrating insight into its nature and origins. The three parameters, namely: relaxation time (τ), Cole-Cole loss broadening (α), and dielectric strength (Δ?) provide each one in its own way, much useful and often overlooked information. The Activation Energy along with the Meyer-Neldel dependance, both extracted from τ serve to illuminate the dynamic properties. At the same time, α and especially the combined α(lnτ) relationship, expose the fractal structure of the underlying landscape. Finally, the static parameter Δ?, enables quantification of the dipolar correlations. Hydrostatic pressure (up to 7.5 kbar) was applied to gently perturb the system and observe the outcome on all of the various parameters. This additional degree of freedom allows for a much more comprehensive exploration of the phase space behavior of the system.     

Associated relaxation time and the correlation function for a tumor cell growth system subjected to color noises

The associated relaxation time Tc and the normalized correlation function C(s) for a tumor cell growth system subjected to color noises are investigated. Using the Novikov theorem and Fox approach, the steady probability distribution is obtained. Based on them, the expressions of Tc and C(s) are derived by means of projection operator method, in which the effects of the memory kernels of the correlation function are taken into account. Performing the numerical computations, it is found: (1) With the cross-correlation intensity |λ|, the additive noise intensity α and the multiplicative noise self-correlation time τ₁ increasing, the tumor cell numbers can be restrained; And the cross-correlation time τ₃, the multiplicative noise intensity D can induce the tumor cell numbers increasing; However, the additive noise self-correlation time τ₂ cannot affect the tumor cell numbers; The relaxation time Tc is a stochastic resonant phenomenon, and the distribution curves exhibit a single-maximum structure with D increasing. (2) The cross-correlation strength λ weakens the related activity between two states of the tumor cell numbers at different time, and enhances the stability of the tumor cell growth system in the steady state; On the contrast, τ₁ and τ₃ enhance the related activity between two states at different time; However, τ₂ has no effect on the related activity between two states at different time.     

Low frequency dielectric relaxation in lightly doped VO2 single crystals

The relative effects of intrinsic and extrinsic defects on the dielectric relaxation of VO₂ crystals have been investigated by measurement of the dielectric parameters of undoped crystals and crystals doped with Ti, Cr and Al. Measurements have been made in the temperature range 77–250 K and the frequency range 50–100 kHz. The dielectric data is described by a Cole-Cole distribution function with a distribution parameter α ? 0.45 which decreases with increasing temperature. However, the distribution of activation energies g(E) derived from α is almost independent of temperature. The overall dielectric relaxation behaviour is determined primarily by the intrinsic defect structure of VO₂, and the effect of impurities is observed only in changes in the low frequency limiting (static) value of the dielectric constant. The same transport mechanism is found to determine the dc conductivity and the dielectric relaxation and evidence is presented that the dielectric relaxation is of dipolar origin.     

Dielectric characterization of semiconducting ZnPc films sandwiched between Gold or Aluminum electrodes

The dependencies of complex dielectric functions (the dielectric constant, ε ₁, and the dielectric loss, ε ₂), on frequency and temperature of zinc phthalocyanine (ZnPc) thin films sandwiched between either gold or aluminum Ohmic-electrode contacts have been investigated in the temperature range of 93–470 K and frequency range 0.1–20 kHz. It is found that both values of ε ₁ and ε ₂ decrease with increasing frequency and increase with decreasing temperature. The rate of change depends greatly on the temperature and frequency ranges under consideration. Around room temperature, neither ε ₁ nor ε ₂ show any appreciable change through the whole range of frequencies. Thus, the dielectric dispersion is found to include of both dipolar and interfacial polarizations. The dependencies of both dielectric functions on frequency at different temperatures were found to follow a universal power law of the form ω ⁿ , where the index 0<n≤?1. This indicates that the correlated barrier hopping (CBH) model is a suitable mechanism to describe the dielectric behavior in ZnPc films. Furthermore, the results of the dielectric response indicate that polarization in these films could be in the form of non-Debye polarization. However, the Debye polarization can be traced below room temperature. The obtained results of the relaxation-time, τ, dependency on temperature have shown that a thermally-activated process may be dominated in ZnPc thin films conduction at high temperatures. Partial phase transition (from α- to β-phase) has been observed around 400 K in molecular relaxation-time, τ, and optical dielectric constant, ε _∞. Arrhenius behavior has been observed for all the dielectric loss and conductivity relaxation-times above room temperature and their activation energies are explained and reported. The optical dielectric constant ε _∞ was found to increase with temperature.     

Investigation on crystalline structure and dielectric relaxation behaviors of hot pressed poly(vinylidene fluoride) film

The dielectric relaxation behaviors of hot pressed poly(vinylidene fluoride) (PVDF) film have been studied using dielectric spectroscopy in the frequency domain from 20 Hz to 5 MHz at temperatures between 20 °C and 200 °C. Crystalline/amorphous interphase is suggested with methods of FTIR, XRD, and DSC. Frequency and temperature dependence of dielectric spectroscopy reveals the relaxation behavior and structural dynamics of the samples, and three types of relaxation processes are suggested, α_Ac relaxation process contributed by the hopping transport process near the periphery of conduction band or valence zones at Fermi energy, α_c relaxation process related to the structure change of crystal lattice trapped dipoles in crystalline regions, and α_a relaxation process arising from segmental dipole rearrangement of interphases in amorphous regions. Cole-Cole and Havriliak-Negami experimental equations were utilized to analyze these relaxation processes, and differences of Arrhenius parameters for α_Ac and α_c relaxation processes obtained from Cole-Cole and Havriliak-Negami equations were discussed in detail. Activity energy of different relaxation processes obtained from Arrhenius equation and VFT equation indicates non-single thermal activation mechanism for hot pressed PVDF film.     

Effects of time-delay in stationary properties of a logistic growth model with correlated noises

A time-delayed tumor cell growth model with correlated noises is investigated. In the condition of small delay time, the stationary probability distribution is derived and the stationary mean value (〈x〉_st) and normalized varianceλ₂ of the tumor cell population and state transition rate (κ) between two steady states are numerically calculated. The results indicate that: (i) The delay time (τ) enhances the coherence resonance in 〈x〉_st as a function of the multiplicative noise intensity (D) and increases 〈x〉_st as a function of the additive noise intensity (α), i.e., τ enhances fluctuation of the system, however, the strength (λ) of correlations between multiplicative and additive noise plays a contrary role to τ on these; (ii) τ enhances the coherence resonance in κ as a function of D and increases κ as a function of α, i.e., τ speeds up the rate of state transition, however, λ also plays a contrary role to τ on these.     

A new method for determining relaxation energies by means of aes and xps and its application to silicon compounds

A new method is presented for the determination of the absolute dynamic relaxation energy R_D from experimental Auger parameters, the static dielectric constant and the plasmon energy of the solids. The relaxation energies of the Si 1s and 2p core levels in Si, SiC, SiO₂, Si₃N₄ and Na₂SiF₆ are investigated by comparing the experimental values with theoretical results from a semiempirical dielectric theory. Both the experimental and theoretical results are valid only for the least-bound Si 2p state. The calculated relaxation shifts ΔR_D^ea(1s) and ΔR_D^ea(2p) are in reasonable agreement with the experimental values, and describe the extraatomic polarization effect well also for a deep level.     

Clarifying the nature of the Johari-Goldstein β-relaxation and emphasising its fundamental importance

ABSTRACT

Since 1998 the primitive relaxation time τ ₀(T,P) of the Coupling Model (CM) and the Johari-Goldstein (JG) β-relaxation time τ_JG (T,P) are shown approximately equal in many glass-formers. The CM relation between τ ₀(T,P) and τ_α (T,P) at any T and P is exact. Additionally from the CM relation τ_α (T,P)/τ ₀(T,P) is exactly invariant to variations of T and P while τ_α (T,P) is kept constant, and τ ₀ is exactly a function of ρ ^γ/T like τ_α . However, since τ_JG (T,P) ≈ τ ₀(T,P), the exact invariance of τ_α (T,P)/τ ₀(T,P) leads to approximate invariance of τ_α (T,P)/τ_JG (T,P), and τ_JG is approximately a function of ρ ^γ/T. Notwithstanding, the CM prediction of the approximate relations between τ_β and τ_α were mistaken as exact relations by some researchers. In this paper, we remove this misunderstanding by demonstrating via simulations and experiments that the JG β-relaxation is comprised of processes with different length-scales and degrees of cooperativity, and the process is heterogeneous. The distribution of processes makes τ_JG (T,P) equivocal, because it is just a single relaxation time used to represent the different processes within the distribution, which may change on varying T and P, at constant τ_α (T,P). The problem is compounded if the β-relaxation is not resolved, and fitting procedure used to extract τ_JG (T,P) and τ_α (T,P). Despite the relations of τ_JG (T,P) to τ_α (T,P) are approximate, we show these properties of τ_JG (T,P) are truly remarkable, fundamental, general, and important.     

A comparative study of non-polar solvents effect on dielectric relaxation and dipole moment of binary mixtures of mono alkyl ethers of ethylene glycol and of diethylene glycol with ethyl alcohol

Dielectric relaxation and dipole moment of binary mixtures of homologous series of mono alkyl ethers of ethylene glycol and of diethylene glycol, i.e., mono methyl, mono ethyl and mono butyl ethers of ethylene glycol (ROCH₂CH₂OH) and mono methyl, mono ethyl and mono butyl ethers of diethylene glycol (ROCH₂CH₂OCH₂CH₂OH) with ethyl alcohol (C₂H₅OH) of different concentrations were studied in dilute solutions of benzene, dioxane and carbon tetrachloride at 35 °C. Permittivity (ε′) and loss (ε″) at 10.1 GHz, static dielectric constant ε_o at 1 MHz and high frequency limiting dielectric constant ε_∞ = n_D² at optical frequency of these molecules and their binary mixtures at different concentration were measured in dilute solutions of non-polar solvents. The average relaxation time τ_o, relaxation times corresponding to overall molecular reorientation τ₁ and group rotations τ₂ were determined using Higasi's single frequency measurement equations for dilute solutions. The evaluated values of relaxation times and free energy of activation ΔF were used to explore the solvent effect on molecular dynamics of these polar binary systems in non-polar solvents. The excess inverse relaxation time and excess free energy of activation were determined to confirm the existence of hydrogen-bonded heterogeneous cooperative domains of the ethers and alcohol molecules at different concentration their binary mixtures in non-polar solvents. The dipole moment of the binary mixtures was evaluated using Higasi's and Guggenheim's equation for dilute solutions. The evaluated values of dipole moments and computed dipole moment values using a simple mixing equation of the polar molecules binary mixture were used to explore the effect of non-polar solvent environment on heterogeneous molecular interactions between ethers and alcohol molecules. The effect of number of carbon atoms in the molecular structure of these homologous series molecules was also considered for the interpretation of various evaluated dielectric parameters.     

Random walks in a simple percolation model with two jump frequencies

We consider transport properties of the system in which the good-conducting bonds lie in parallel planes linked by poor-conducting bonds and the concentration p of good-conducting bonds is close to the two-dimensional percolation threshold p_c. The diffusion coefficient D(τ) which describes the random walking in directions along the planes is calculated as a function of variable τ = p − p_c. For τ → 0 the asymptotic relation D(τ)/D(0) − 1 | ∼ |τ|^α is found w α = 2ν − s. Here s is the superconductivity exponent and ν is the correlation length exponent. It is argued that such behavior is to be expected also for more general models.     

On the Physical Meaning of Disperse Parameters of Frequency Dependence of Dielectric Permittivity in the Havriliak–Negami Model

This paper is devoted to an analysis of the frequency dispersion of dielectric permittivity in order to establish the physical meaning of the dispersion parameters α and β in the Havriliak–Negami model. It is found that parameter α is associated with the spectrum broadening of relaxation time τ. Examples with the appearance of a dispersion with parameter α of about 0.4 and 0.7 are presented. A conclusion is drawn that disorder creates a broadening of the relaxation times. Dispersion parameters α and β are introduced to preserve the unified relaxation time. The possibility of the analysis of experimental results on the basis of the Debye model in order to obtain the relaxation time distribution and determine parameters α and β according to the log(τ_HN/τ) chart is shown.     

The critical phenomenon and the re-entrance phenomenon in the anti-tumor model induced by the time delay

The effects of time delay τ on an anti-tumor model driven by a multiplicative noise and a periodic signal are investigated. The results obtained from the small delay approximation and numerical simulations indicate: (i) For the absence of the periodic signal in the system, the two-peak structure of the stationary probability distribution transforms into the single-peak structure with the increasing τ, and τ exists a critical value τc. For τ<τc, the stationary mean value 〈x〉_st of the cell population decreases as the noise intensity D increases, however, for τ>τc, the 〈x〉_st increases as the D increases; (ii) For the presence of the periodic signal in the system, the structure of the signal-to-noise ratio with changes of the D exhibits the transitions of one peak → two peaks → one peak as τ increases.     

Microwave dielectric response of binary mixture of N,N-dimethylformamide with propylene glycol using TDR method

Dielectric relaxation study of N,N-dimethylformamide (DMF) has been carried out with propylene glycol (PLG) at different temperatures. Time domain reflectometry (TDR) in reflection mode has been used to measure the reflection coefficient in frequency range of 10 MHz to 20 GHz. The dielectric parameters static dielectric permittivity (? ₀) and relaxation time (τ) have been obtained by Fourier transform and least squares fit methods. The experimental results show nonlinear variation in dielectric permittivity and relaxation time with volume fraction of PLG confirm the structural formation due to the intermolecular interaction between N,N-dimethylformamide and PLG. The variation in excess permittivity (ε ^E), excess inverse relaxation times (1/τ)^E, Kirkwood correlation factors (g ^eff, g ^f), activation enthalpy (ΔH) and entropy (ΔS) are also calculated to study the binary mixture interaction.     

Zur Definition von Relaxationszeit und Korrelationszeit in magnetischen Resonanzexperimenten

Kubo's general definition of relaxation and correlation times in magnetic spin systems, applicable to non-exponential processes, is evaluated for several non-exponential relaxation and correlation functions known from nmr experiments. The new definition eliminates the arbitrary factors usually encountered in the time constants of nonexponential irreversible processes. For the correlation time of the well-known “translational two-spin model”, three different values are used in the literature; our definition leads toτ _t =1/5 d²/D (d=distance of closest approach between the two spins,D=diffusion coefficient of the related molecules), which is an intermediate value to the conventional abbreviationsτ _t =1/5d ²/D andτ _t =1/6d ²/D.     

Relaxation times in dissipative heavy-ion collisions

The classical model introduced earlier for analyzing experimental data on dissipative heavy-ion collisions, is generalized to include effects from the gradual dissipation of radial kinetic energy and from the development of fragment deformations during the collision. Relaxation times for the dissipation of radial kinetic energy (τ _R ) and relative angular momentum (τ _l ) as well as for the development of deformations (τ_α) are fitted to the reaction⁸⁶Kr (8.18 MeV/u) +¹⁶⁶Er and applied to three other reactions. A consistent set of relaxation times isτ _R = 0.3 · 10^?21 s,τ _l =1.5 · 10^?21 s andτ _α = 5 · 10^?21 s. Empirical mass transport coefficients are deduced from comparisons with experimental element distributions. Effects from fluctuations in the deflection function are discussed. Evidence is found for the existence of a relaxation time of the order 10^?21 s in the mass-drift coefficient.     

Dielectric relaxation and AC conduction of an AgTlSe2 semiconductor in the solid and liquid states

Measurements of the dielectric properties of AgTlSe₂ in the solid and liquid states were carried out in a wide range of frequencies and temperatures. The material displayed dielectric dispersion, and a loss peak was observed. Cole-Cole diagrams have been used to determine the distribution parameter (a) and the molecular relaxation time (). The process of dielectric relaxation (loss) and ac conduction was attributed to the correlated barrier hopping model suggested by Elliott for amorphous solids, where two carriers simultaneously hop over a barrier between charged defectD ⁺ andD ^– states.     

Dielectric dispersion studies of aromatic ketones in non-polar solvents

Measurements of dielectric constant (ε′) and loss (ε″) have been made at five different microwave frequencies from 1000 MHz to 67.7 GHz for acetophenone, benzophenone and propiophenone in four different non-polar solvents namely benzene, cyclohexane, 1-4-dioxane and n-heptane. Results are reported at five different temperatures from 25°C to 60°C. The dielectric data of these ketones in different solvents are analysed in terms of the Cole-Cole arc plots and superposition of two Debye-type absorptions. Values of mean relaxation times (τ_o), dipolement (μ), overall relaxation time (τ₁) and group relaxation time (τ₂) have been obtained and presented here. The values of relaxation time and dipolemoment are in reasonable good agreement, at the temperatures, at which there are available known data.     

Beyond the pulse-area theorem: Role of the absorption and the dispersion in the propagation of weak ultrashort resonant pulses

We present here some fundamental but yet underlooked features of the propagation of weak ultrashort pulses (with Δ_dτ << 1, where Δ_d is the Doppler width and τ is the pulse duration) in resonant atomic media. We show that the pulse area behaviour and the pulse spectrum at resonance are governed by the usual optical depth (α₀L, where α₀ is the absorption coefficient at resonance and L the length of the medium), whereas the pertinent parameter that governs the severity of the dispersion effects and the distortion of the pulse is the dispersion parameter e_disp = (α₀L)Δ_dτ that we introduce. Paradoxical effect such as distortionless propagation (e.g. e_disp << 1) with vanishing pulse area (when α₀L >> 1) can then explained within this formalism.