Dielectric study and ac conductivity of iron sodium silicate glasses

A series of glasses with formula (SiO₂)_0.7−x(Na₂O)_0.3(Fe₂O₃)_x with ( 0.0 ≤ x ≤ 0.20) were prepared and studied by means of AC measurements in the frequency range 20 kHz to 13 MHz at room temperature. The study of frequency dependence of both dielectric constant ε' and dielectric loss ε" showed a decrease of both quantities with increasing frequency. The results have been explained on the basis of frequency assistance of electron hopping besides electron polarization. From the Cole-Cole diagram the values of the static dielectric constant ε_s, infinity dielectric constant ε_∞, macroscopic time constant τ, and molecular time constant τ_m are calculated for the studied amorphous samples. The frequency dependence of the ac conductivity obeys a power relation, that is σ_ac (ω) = Α ω^s. The obtained values of the constant s lie in the range of 0.7 ≤ s ≤ 1 in agreement with the theoretical value which confirms the simple quantum mechanical tunneling (QMT) model. The increase in ac conductivity with iron concentration is likely to arise due to structural changes occurring in the glass network. The structure of a glass with similar composition was published and showed clustering of Fe²⁺ and Fe³⁺ ions which favor electron hopping and provide pathways for charge transport.     

Studies on electrical and the dielectric properties in MS structures

In this study, we investigated frequency dependent electrical and dielectric properties of metal-semiconductor (MS) structures using capacitance-voltage (C-V) and conductance-voltage (G/ω-V) characteristics in the frequency range 100 kHz-10 MHz in the room temperature. The dielectric constant (ε′), dielectric loss (ε″), dielectric loss tangent (tan δ) and ac electrical conductivity (σ_ac) were calculated from the C-V and G/ω-V measurements and plotted as a function of frequency. In general, ε′, ε″ and tan δ values decreased with increasing the frequency, while σ_ac increased with increasing frequency. Furthermore, the voltage and frequency dependence of series resistance were calculated from the C-V and G/ω-V measurements and plotted as functions of voltage and frequency. The distribution profile of R_S-V gives a peak in the depletion region at low frequencies and disappears with increasing frequencies. Also, series resistance values decreased with increasing frequency. The experimental results show that both frequency dependent electrical and dielectric parameters were strongly frequency and voltage dependent.     

Experimental confirmation of oscillating properties of the complex conductivity: Dielectric study of polymerization/vitrification reaction

Clear evidence of the existence of fractional kinetics containing the complex power-law exponents were obtained by conductivity measurements of polymerization reaction of polyvinylpyrrolidone (PVP) performed inside a dielectric cell. We established the relationship between the Fourier image R(jω) of the complex memory function K(t) and the time-dependent mean square displacement 〈r²(t)〉. This relationship helps to understand the origin of the different power-law exponents appearing in the real part of complex conductivity Re[σ(ω)] and find a physical/geometrical meaning of the power-law exponents that can form the complex-conjugated values. The complex-conjugated values of the power-law exponents leading to oscillating behavior of conductivity follows from the fractional kinetics suggested by one of the authors (R.R.N.). The relationships [R(jω)⇔Re[σ(ω)]⇔〈r²(t)〉] are becoming very efficient in classification of different types of collective motions belonging to light and heavy carriers involved in the relaxation/transfer process. The conductivity data obtained for Re[σ(ω)] during the whole polymerization process of the PVP at different temperatures (80, 90, 100 °C) are very well described by the fitting function that follows from the suggested theory. Original fitting procedure based on the application of the eigen-coordinates (ECs) method helps to provide a reliable fitting procedure in two stages and use the well-developed and statistically stable linear least square method (LLSM) for obtaining the correct values of the fitting parameters that describe the behavior of Re[σ(ω, T_r)] in the available frequency range for the current time of the chemical reaction T_r measured during the whole process of polymerization. The suggested theory gives a unique possibility to classify the basic types of motions that take place during the whole polymerization process.     

Electrical conductivity and dielectric relaxation in non-crystalline films of tungsten trioxide

Amorphous tungsten trioxide (a-WO₃) thin films were prepared by thermal evaporation technique. The electrical conductivity and dielectric properties of the prepared films have been investigated in the frequency range from 100 Hz to 100 kHz and in the temperature range 293–393 K. In spite of the absence of the dielectric loss peaks, application of the dielectric modulus formulism gives a simple method for evaluating the activation energy of the dielectric relaxation. The frequency dependence of σ(ω) follows the Jonscher’s universal dynamic law with the relation σ(ω) = σ_dc + Aω^s, where s is the frequency exponent. The conductivity in the direct regime, σ_dc, is described by the small polaron model. The electrical conductivity and dielectric properties show that Hunt’s model is well adapted to a-WO₃ films.     

ac conductivity in a-Ge–Se–Bi glasses

In the present paper the effect of Bi impurity (low ∼4 at.% and high ∼10 at.%) on the ac conductivity (σ_ac) of a-Ge₂₀Se₈₀ glassy alloy is studied and the experimentally deduced values are fitted with theoretically deduced values by using correlated barrier hopping model (CBH). Frequency dependent ac conductance of the samples over a frequency range of 100–50 kHz has been taken in the temperature range (268–360 K). At frequency 2 kHz and temperature 298 K, the value of ac conductivity (σ_ac) decreases at low concentration of Bi (4 at.%). However, the value of σ_ac increases at higher concentration of Bi (10 at.%). The ac conductivity is proportional to ω^s for undoped and doped samples. The value of frequency exponent (s) decreases as the temperature increases. These results have been explained on the basis of some structural changes at low and high concentration of Bi impurity.     

Effect of proton irradiation on electrical properties of a-As2S3

This paper reports the effect of proton irradiation on the electrical properties of a-As₂S₃ in the temperature range of 323–418 K and frequency range 0.1–100 kHz. The variation of transport property is studied with proton irradiation dose (1 × 10¹³ ions/cm² and 1 × 10¹⁵ ions/cm²). It has been observed that proton irradiation changes the dc conductivity (σ_dc), dc activation energy (ΔE_dc) and ac conductivity (σ_ac(ω)). The σ_dc and σ_ac(ω) increases with dose of proton irradiation. The value of frequency exponent (s) decreases with the temperature and irradiation dose. These results are explained in terms of change in density of defect states in these glasses.     

Electronic relaxation in zinc iron phosphate glasses

The electrical and dielectric properties of 10ZnO-30Fe₂O₃-60P₂O₅ (mol%) glasses, melted at different temperatures were measured by impedance spectroscopy in the frequency range from 0.01 Hz to 3 MHz and over the temperature range from 303 to 473 K. It was shown that the dc conductivity strongly depends on the Fe(II)/[Fe(II) + Fe(III)] ratio. With increasing Fe(II) ion content from 17% to 37% in these glasses, the dc conductivity increases. Procedure of scaling conductivity data measured at various temperatures into a single master curve is given. The conductivity of the present glasses is made of conduction and conduction-related polarization of the polaron hopping between Fe(II) and Fe(III), both governed by the same relaxation time, τ. The high frequency dispersion in electrical conductivity arises from the distribution in τ caused by the disordered glass structure. The evolution of the complex permittivity as a function of frequency and temperature was investigated. At low frequency the dispersion was investigated in terms of dielectric loss. The thermal activated relaxation mechanism dominates the observed relaxation behavior. The relationship between relaxation parameters and electrical conductivity indicates the electronic conductivity controlled by polaron hopping between iron ions.     

Hopping conduction in amorphous Nb2O5 thin films

The low field conduction mechanism in amorphous Nb₂O₅ doped with Nb is investigated by measurements of the ac conductivity as a function of frequency (3 Hz?6 × 10⁶ Hz), dc conductivity as a function of temperature (100–400 K), capacitance as a function of frequency (3 Hz?6 × 10⁶ Hz) and conductance G as a function of voltage at 10³ Hz. Loss tangent and quality factor data are also given because of their technical and scientific relevance. Evidence for hopping conduction at low applied fields is presented by the following results: (1) a monotonic increase in ac conductivity σ(ω)αωⁿ where 0.5 < n < 1.0 in the range 3 Hz?6 × 10⁶ Hz; (2) a linear dependence of current on voltage at low fields; and (3) low activation energy for dc conduction with a transition at 210 K to a still lower activation energy; and (4) a decrease in polarizability with frequency. At high fields, E > 10⁵ V/cm, dc conductivity is dominated by the field emission mechanism of the Poole-Frenkel or Poole type.     

Novel feature of the universal power law dispersion of the ac conductivity in disordered matter

The ac conductivity σ_ac of different types of materials as a function of angular frequency ω is approximated by a ‘universal’ power law σ_ac = Aωⁿ, A and n are fitting parameters .The exponent and the pre-exponential factor depend on temperature, in general. In the present Letter, we suggest an empirical law that states that the temperature evolution of log A is proportional to the temperature evolution of n. Data reported on different materials ascertain that the ratio −log A/n is constant, regardless the nature of the material and the type of conductivity.     

Comparison of analysis of dielectric spectra of PCL in the ε1 and the M1 formalism

The complex dielectric modulus, M¹(ω, T), for poly(ε-caprolactone) has been obtained by inverting the complex dielectric permittivity data, ε¹(ω, T) recorded in a wide temperature and frequency range. The analysis of the dielectric loss modulus spectra M″(ω, T) have been performed by using a simulated annealing Monte Carlo procedure in order to extract the relaxation parameters for each relaxation mode. Besides the local modes γ and β, the segmental α mode associated to the glass transition, the conductivity and the interfacial polarization peaks could be analyzed with a better precision than by using the conventional non-linear least squares method in ε″ domain. The merging of the α and β modes at high temperatures is much better defined due to the less significant contribution of the ionic conductivity in M¹ formalism.     

ac Conductivity of 4.5 TiO2−x · 2 P2O5

The ac conductivity of a member of the family of glasses 4.5 TiO_2?x · 2 P₂O₅ has been measured between 77 and 300 K, and up to 100 kHz. The dc conductivity was measured over only part of this temperature range. The measured ac conductivity can be represented by σ_ac = σ₀ + σ₁ω^s, with s < 1, and temperature dependent. A similar equation describes the ac dielectric constant, ?_ac = ?₀ + ?₁ω^s?1, where $\text{?}{}_1\text{= σ}{}_1\text{tan}\text{1}\text{2}\text{sπ}$. A simple proportionality of s to temperature holds at low temperature; at the higher temperatures, the T-dependence of s is no longer simple. The observed behaviour of the ac properties of this glass is in general accordance with a recently proposed model for systems where transport occurs by hopping. The over-all behaviour is comparable to other transition metal glasses.Using the model and treating the carriers as polarons yields an expression for s in terms of temperature. Values for the polaron radius and the effective dielectric constant are then extracted from the measurements. These values are in good agreement with values for similar systems obtained by other means.     

AC conductivity in amorphous germanium

The ac conductivity in evaporated amorphous germanium films has been measured as a function of annealing and has been found to obey the ω^0.8 law, in accordance with the hopping model. The dc conductivity measurements on the same samples show a $\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ law behaviour. The densities of localized states near the Fermi level g(E_F), obtained from both experiments are in reasonable agreement with each other. Both the measurements show a reduction by about a factor of 2 in g(E_F) when a freshly prepared film is fully annealed. High-temperature substrate films also show the ω^0.8 behaviour. This suggests that the frequency dependence of the ac conductivity is not caused by voids alone. Other possible explanations of our results are also discussed.     

Frequency dependence of conduction and polarization in conductive polymers

We report the results of the measurement and analysis of the complex conductivities of two high polymers over the frequency range 10²–10⁶ Hz, and temperature range 70–300 K. Giant polarization of the nomadic type is observed, with dielectric constants ranging from about 50 to 6000 in these aromatic hydrocarbon polymers. The complex conductivities resemble power law behavior, σ_ac = Aω^s (with s in the range 0.7–1.0) in some temperature ranges, and deviates from this in others. The dc conductivity and the real part of the ac conductivity at various frequencies follow a $\text{T}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>4</mtext>}}$ law. The dielectric constant varies as expected for nomadic polarization in long-chain molecules. An attempt is made to develop an understanding of the observed dependences of the complex conduction or polarization on temperature and frequency in terms of interchain and intrachain transport processes.     

Fragility in mixed alkali tellurites

Linear viscoelastic stress relaxation and calorimetric measurements were performed on a series of mixed alkali tellurite glasses of composition 0.3([xNa₂O+(1−x)Li₂O])+0.7TeO₂ at temperatures near and above the glass transition temperature, T_g. The stress relaxation data were well described by the stretched exponential function, G(t)=G₀exp[−(t/τ)^β], where τ is the relaxation time, β is the distribution of relaxation times and G₀ is the high frequency modulus. The fragility, determined from the temperature dependence of τ, exhibited a minimum in the middle of the mixed alkali composition. A possible connection between the kinetic and the thermodynamic dimensions of this system was established, wherein the heat capacity change at the T_g, ΔC_p(T_g), and the fragility are correlated.     

Longitudinal acoustic compliance and tagged particle susceptibility in liquid and supercooled glycerol

Brillouin spectra of glycerol measured in the visible, ultraviolet and X-ray frequency regions allow us to reckon the imaginary part of acoustic compliance, J″(ω), over a broad frequency range from fraction of GHz to tens of THz. We observe that J″(ω) suitably mimic the shape of the tagged particle susceptibility, χ″_INS(ω), measured by incoherent neutron spectra for both the liquid and supercooled states. The proportionality between these two quantities suggests a strict relationship between acoustic dissipation and generalized density of states.     

The Raman coupling function in v-GeO2 and v-SiO2: A new light and neutron scattering study

We report inelastic Raman and neutron scattering spectra for the network glass formers vitreous silica (v-SiO₂) and vitreous germania (v-GeO₂) measured at temperature from 10 to 300 K. The ability to determine the temperature dependence of the luminescence background in Raman scattering has allowed to obtain the Raman coupling function C(ω) and in particular, its low-frequency limit. This study indicates that C(ω) has a linear behavior near the Boson peak maximum and below.     

Relaxation times and viscosity

On the basis of parallel Maxwell models having partial shear moduli G_i and relaxation times τ_i, mechanical relaxation processes including viscous flow can be easily described. Viscosity, e.g., equals the sum of the products of the above quantities, i.e. η = ΣG_iτ_i. The temperature dependence of each i term rigorously follows Arrhenius' las as logτ_i = logτ_{i, ∞} + Q_i/MRΘ. The assumption that a relation logτ_∞ = f(Q) exists between the activation energy Q_i and the relaxation time limit τ_∞ correlated to Θ = ∞ and that it varies with composition and cooling rate of the glass, proves useful. The usual function for the distribution of shear moduli over relaxation times [φ(logτ) ≡ G^?1dG/dlogτ] can thus be complemented by a corresponding one for the distribution over activation energies [Ψ(Q) ≡ G^?1dG/dQ]; which is temperature independent — the same as logτ_∞(Q)The corresponding functions Ψ (Q) are determined for the solid (?100 deg/h) and ‘liquid’ (L) glass states. Measurements of relaxation and viscosity are employed for that purpose.Application of the temperature-dependent functions logτ_∞ (Q) and Ψ (Q) are useful in several respects, as exemplified by calculating the freezing temperature, the change of activation energy with cooling rate, and the damping of mechanical vibrations in the transformation range.     

Dielectric study of the segmental relaxation of low and high molecular weight polystyrenes under hydrostatic pressure

In this work we analyze by means of dielectric spectroscopy the dynamics of the α-relaxation process of low and high molecular weight polystyrene over a wide range of pressures and temperatures. The results are interpreted in terms of a recently proposed equation which describes the behavior of the structural relaxation time, τ(T, P), as a function of both pressure and temperature. This equation has been derived from the Adam–Gibbs (AG) theory by writing the configurational entropy, S_c, in terms of the excess thermal heat capacity and of the excess thermal expansion. Consequently, the molecular dynamic of glass-forming liquids can be linked to its thermodynamic properties. The pressure dependence of the segmental dynamics for both polymers is here measured and analyzed in the AG framework for the first time. τ(T, P) was found to be very well described using the extended AG equation. Additionally, the pressure dependence of the fragility and glass transition temperature (T_g) is analyzed and discussed in terms of the role of chain length and end groups.     

Study on the influence of isotope exchange of hydrogen with deuterium on the vibrational spectrum of lysozyme by inelastic neutron scattering

The influence of isotope exchange of hydrogen with deuterium on the lysozyme dynamics was studied by incoherent inelastic neutron scattering. The generalized vibrational densities of states G(ω) were constructed from experimental results for protonated and deuterated protein samples at 200, 280, and 311 K. The major isotope effect was observed in G(ω) in the frequency region higher than 100 cm^?1. At all temperatures, both the Debye mode and the region of G(ω), whose spectral dimension corresponds to the fracton mode, are observed in the low-frequency region of the densities of states of both protonated and deuterated lysozyme. The influence of the hydrogen isotope exchange on the low-frequency region of G(ω) is insignificant.