Acoustic damping in Li2O–2B2O3 glass observed by inelastic X-ray and optical Brillouin scattering

The dynamic structure factor of lithium-diborate glass has been measured at several values of the momentum transfer Q using high resolution inelastic X-ray scattering. Much attention has been devoted to the low-Q-range, below the observed Ioffe–Regel crossover q_IR ≃ 2.1 nm⁻¹. We find that below q_IR, the linewidth of longitudinal acoustic waves increases with a high power of either Q, or of the frequency Ω, up to the crossover frequency Ω_IR ≃ 9 meV that nearly coincides with the center of the boson peak. This new finding strongly supports the view that resonance and hybridization of acoustic waves with a distribution of rather local low frequency modes forming the boson peak is responsible for the end of acoustic branches in strong covalent glasses. Further, we present high resolution Brillouin light-scattering data obtained at much lower frequencies on the same sample. These clearly rule out a simple Ω²-dependence of the acoustic damping over the entire frequency range.     

Asymptotic description of schematic models for CKN

The fits of 0.4Ca(NO₃)₂0.6 K(NO₃) (CKN) by schematic mode-coupling models [V. Krakoviack, C. Alba-Simionesco, J. Chem. Phys. 117 (2002), 2161] are analyzed by asymptotic expansions. The validity of both the power-law and the Cole–Cole-peak solutions for the critical spectrum are investigated. It is found that the critical spectrum derived from the fits is described by both expansions equally well when both expansions are carried out up to next-to-leading order. The expansions up to this order describe the data for 373 K over two orders of magnitude in frequency. In this regime an effective power-law ω^a can be identified where the observed exponent a is smaller than its calculated value by about 15%; this finding can be explained by corrections to the leading-order terms in the asymptotic expansions. For higher temperatures, even smaller effective exponents are caused by a crossover to the alpha-peak spectrum.     

Low frequency Raman scattering in chalcogenide glasses

Low frequency Raman spectra of chalcogenide glasses are analyzed in terms of matrix element effects and modes of a layered structure. The spectra of GeSe₂ at low temperature shows no peaks which can be assigned to layer modes. The reduced spectra indicates that the density of states exhibits nearly ω² dependence for ω < 60 cm^?1, and the coupling constant approaches ω² dependence at frequencies less than 20 cm^?1.     

High frequency acoustic attenuation of vitreous silica: New insight from inelastic x-ray scattering

We present new experimental results on the propagation and damping of the high frequency acoustic-like modes in vitreous silica. The new data are measured by means of the inelastic x-ray scattering technique down to an exchanged wavevector Q ∼ 0.9 nm ^− 1, at the limit of the instrument capabilities. Thanks to the continuous development of the technique, the new spectra are characterized by a very high signal to noise ratio when compared to previous experiments. The higher data quality finally allows for a reliable determination of the position and width of the inelastic excitations. The new data show that the sound damping Γ is marked by a frequency dependence compatible with the Rayleigh law, Γ ∼ ν⁴, for frequencies below the position of the excess vibrational modes at the boson peak. We show that the new data are in good agreement with estimates of the acoustic mean free path from the thermal conductivity, which take into account the peculiar plateau at a few Kelvin. The connection between the boson peak and the Rayleigh law is further confirmed by a comparison of the present data with literature data for the sound attenuation in a permanently densified silica sample.     

Ultrasound propagation in glasses in the metastable immiscibility region of the sodium borosilicate system

Measurements of ultrasound wave velocity and attenuation have been made between 1.3 K and 400 K in a series of both quenched and heat-treated Na₂OB₂O₃SiO₂ glasses. As in many other inorganic glasses, the ultrasound attenuation of both longitudinal and shear waves below room temperature is dominated by a broad and intense loss peak; the height and temperature of the peak maximum are frequency sensitive. The loss peak characteristics are consistent with a structural relaxation mechanism with a distribution of activation energies and this model is used to analyse the data. The features of the acoustic loss peak and also the absolute value and temperature coefficient of ultrasound velocity are strongly dependent on the total Na₂O network modifier content of the glasses. The ultrasound wave propagation is also affected by phase-separation inducing heat treatment: a steady rise in the height of the acoustic loss peak and an upward shift in the peak temperature takes place with increasing time of heat treatment at 550°C, a finding which suggests that structural rearrangements are still occurring in the individual glassy phases even after long periods of heat treatment. It is proposed that heat treatment causes migration of Na⁺ ions away from BOB bonds in the B₂O₃ rich phase.     

Electrical conductivity and dielectric constant of heat-treated polyacrylonitrile in an AC regime

The electrical conductivity σ(ω) and the dielectric constant ?(ω) of heat-treated polyacrylonitrile (PAN) samples obtained by pyrolysis at temperatures up to 550°C, were measured in the frequency range from 500 Hz to 250 MHz at room temperature. For samples treated at temperatures below 300°C and for frequencies up to 200 MHz, the conductivity obeys a ω^s law (s = 1) while ? does not change significantly. For heat-treatment temperatures above 300°C, the behaviour of σ(ω) is greatly modified. In fact, ?(ω) greatly increases at low frequencies for increasing heat-treatment temperatures, and is strongly dependent frequency. Our results can be explained with the help of two randomly distributed phases in the medium and by introducing percolation theory.     

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.     

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.     

The boson peak in melt-formed and damage-formed glasses: A defect signature?

We describe the preparation and characterization of a glassy form of the moderately good glassformer PbGeO₃, by mechanical damage, and compare its properties with those of the normal melt-quenched glass and the crystal. The damage-formed glass exhibits a DSC thermogram strikingly similar to that of a hyperquenched glass, implying that it forms high on the energy landscape. The final glass transition endotherm occurs within 4 K (0.006T_g) of that of the melt-quenched glass, but crystallization occurs at a lower temperature, as if pre-nucleated. In particular, we have studied the low frequency vibrational dynamics of the alternatively prepared amorphous states in the boson peak region, and find the damage-formed glass boson peak to be almost identical in shape to, but more intense than, that of the normal melt-formed glass, as previously found for hyperquenched glasses. In view of the quite different preparation procedures, this similarity would seem to eliminate equilibrium liquid clusters as a source of the boson peak vibrations, but leaves plausible a connection to force constant fluctuations or to specific vitreous state defects.     

The AC conductivity of superionic conducting glasses (AgI)x−(Ag4P2O7)1−x (x = 0.8, 0.75, 0.7): Experiment and analysis based on the generalized Langevin equation

The frequency-dependent complex impedance of superionic conducting glasses (AgI)_x − (Ag₄P₂O₇)_1−x (x = 0.3, 0.25, 0.20) was measured from 5 Hz to 500 kHz below room temperature. The frequency dependence of the conductivity and the electric modulus observed here cannot be expressed by a single relaxation equation, but it is well described by an equivalent circuit involving a contribution due to Jonscher's universal law σ [ω] ∼ ωⁿ (0 < n < 1). A linear relation between the DC conductivity and the relaxation time was observed irrespective of the sample compositions. These results are explained on the basis of the generalized Langevin equation associated with a non-exponential memory function. The physical basis of this approach is discussed in terms of the distribution of transition times arising from non-periodic potentials formed by immobile anions and many-body interactions among mobile cations at very high concentration in the superionic conducting glass.     

On the analysis of the vibrational Boson peak and low-energy excitations in glasses

Implications of reduction procedures applied to the low energy part of the vibrational density of states in glasses and supercooled liquids are considered by advancing a detailed comparison between the excess – over the Debye limit – vibrational density of states g(ω) and the frequency-reduced representation g(ω)/ω² usually referred to as the Boson peak. Analyzing representative experimental data from inelastic neutron and Raman scattering, we show that reduction procedures distort to a great extent the otherwise symmetric excess density of states. The frequency of the maximum and the intensity of the excess experience dramatic changes; the former is reduced while the latter increases. The frequency and the intensity of the Boson peak are also sensitive to the distribution of the excess. In the light of the critical appraisal between the two forms of the density of states (i.e. the excess and the frequency-reduced one) we discuss changes of the Boson peak spectral features that are induced under the presence of external stimuli such as temperature (quenching rate, annealing), pressure, and irradiation. The majority of the Boson peak changes induced by the presence of those stimuli can be reasonably traced back to simple and expected modifications of the excess density of states and can be quite satisfactorily accounted for by the Euclidean random matrix theory. Parallels to the heat capacity ‘Boson peak’ are also briefly discussed.     

Low-frequency Raman scattering and small-angle X-ray scattering of glasses inclined to phase decomposition

Low-frequency (<1000 cm⁻¹) Raman scattering of lithium aluminosilicate (12Li₂O : 15Al₂O₃ : 73SiO₂ with 4 mol% TiO2) glasses with addition of titanium dioxide has been studied. With a heat treatment at temperatures 660°C, 700°C, 720°C and 820°C and for various times and sequences of temperature, our samples decompose into nanometer sized dispersed aluminotitanate particles. In Raman spectra of these glasses an evolution of a boson peak was observed. The width of the relatively broad boson band decreases as does the frequency of the band. From small-angle X-ray scattering data we conclude that the boson peak is connected with elastic vibrations of amorphous or crystalline regions of inhomogeneity with a dimension of ∼1.7 nm in initial glasses or larger depending on the heat treatment sequences.     

Supercooled liquids and plastically crystalline phases: Indications for a similar manifestation of a crossover in the evolution of the dielectric spectra

We compare the susceptibility spectra (10⁻⁶ Hz–10¹² Hz) of glass forming liquids and plastically crystalline (PC) phases. In both the cases, a similar spectral change is observed while cooling. Whereas at high-temperatures the frequency-temperature superposition (FTS) principle holds for the α-process with a stretching parameter significantly below 1 it fails below a certain temperature T_x. Below T_x, in the case of supercooled liquids, in addition to a broadening of the α-relaxation peak the excess wing appears, and the corresponding power-law exponents β (α-peak) and γ (excess wing) of the distribution of correlation times show a similar dependence on the time constant τ_α, explicitly 1/β and 1/γ both are linear in lg τ_α. In the PC systems studied, an excess wing is missing and the failure of the FTS principle for the α-relaxation peak directly shows up below T_x. Again, the parameter of the Cole–Davidson susceptibility 1/β_CD is linear in lg τ_α below T_x, and constant above, allowing to identify T_x. In PC phases the crossover temperature T_x may be found much closer to the glass transition temperature T_g as compared to supercooled liquids, and thus can be well studied by standard dielectric spectroscopy.     

AC conductivity of (As2Te3)95Ge5

The elctrical conductivity of amorphous chalcogenide (As₂Te₃)₉₅Ge₅ is investigated at variable frequency, from 1 kHz up to 35 GHz, and a variable temperature, from 77 to 300 K. The low-temperature conductivity is constant with temperature at a fixed frequency. At a fixed temperature, it obeys a ω^0.8 law only at low frequencies. The results are analysed with respect to the polaron problem, but also with a simple model of several dilute localized levels having a wide energy distribution in the forbidden band.     

Temperature dependence of dielectric losses in chalcogenide glasses

The frequency (2 × 10⁴?2 × 10⁷ Hz) and temperature (250–600 K) dependence of the imaginary part of the permittivity, ?′', of As₂Se₃ and Tl₂SnSe_8.61 is explained within a theoretical model. The dielectric premittivities of these compounds are correctly explained by means of a model of a hopping process over a potential barrier between localized sites.We have found that the glassy system of chalcogenide can exist in the form of dipoles. The theory shows, in agreement with the experimental results, that ?′' = Aω^m, where m is a function of temperature.     

Dielectric behaviour in a vanadium phosphate glass

The dielectric constant and conductivity of 80% V₂O₅: 20% P₂O₅ glass has been measured in the frequency range 10² to 10⁹Hz and in the temperature range 80 to 350°K. It is shown that the dielectric behaviour over these ranges is described by a Debye type relaxation process with distribution of relaxation times. A method is proposed to determine the width of distribution from the data at fixed frequencies and different temperatures. The width of distribution increases at frequencies ω > 10/τ, which leads to an a.c. conductivity at these frequencies almost linearly proportional to frequency and independent of temperature. The estimated value of the static dielectric constant of about 30 was found to decrease with temperature while the infinite frequency dielectric constant of 10 was independent of temperature. The carrier concentration calculated from the dielectric relaxation time and the d.c. conductivity through a thermal diffusion model shows reasonable agreement with direct measurement using electron paramagnetic resonance.     

Crossover region of dynamic glass transition: general trends and individual aspects

The dynamic glass transition of many substances is characterized by significant changes and peculiarities in a narrow frequency temperature range, the crossover region. Crossover temperatures and frequencies as obtained from different experimental methods are compiled for 38 glasses of a variety of substance classes. The crossover temperatures obtained from different methods (T_B, T_t−r, T_on, T_c, T_β) are usually similar for a given substance. We attempt to relate the crossover parameters for different substances to typical properties of conventional α relaxation and Johari–Goldstein-process β below the crossover. The parameters are discussed with respect to empirical concepts from the literature. An attempt is presented to quantify the old, intuitive idea that molecular cooperativity starts in the crossover region and increases for lower temperature.     

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.     

Phase-matched frequency doubling in a LiNbO3-sapphire waveguide

An rf-sputtered thin film of LiNbO₃ on a sapphire substrate was used as a waveguide for optical frequency doubling. Employing a Nd:YAG laser and a tunable dye laser, whose output was used to pump a stimulated Raman cell, the TM^ω₀→TM^2W₂ up-conversion process was investigated in detail and the phase matched nature of this process was demonstrated. The conversion efficiency was estimated to be about 10^?3.     

Thin layers deposited from V2O5 gels: I. A conductivity study

The conductivity ? of V₂O₅ layers deposited from gels of various V⁴⁺ content C was measured over a very large temperature range. The observed variations agree with Mott predictions on polaron hopping. Indeed below ≈ 50 K we reached a new conductivity regime with a well-defined activation energy. The fit of the experimental data to the Schnakenberg model was excellent and thus we could determine the polaron energy W_p, the disorder energy W_D and the mean optical phonon frequency v₀. All these values decrease with increasing C. In contrast whatever C the coupling constant γ was ≈ 10. The variation of W_D with C agrees quantitatively with the values calculated by means of Miller and Abrahams' theory and this led us to the conclusion that in those amorphous V₂O₅ layers disorder is mainly a potential disorder related to non-stoichiometry.