A low-frequency Raman study of glassy,supercooled and molten silica and the preservation of the Boson peak in the equilibrium liquid state

A temperature dependent Raman spectroscopic study of the Boson peak in silica is being presented. For the first time experimental data are obtained not only above the glass transition temperature but also above the melting point. The intriguing temperature dependencies exhibited by the Boson peak frequency and intensity are examined in detail. A comparison of the above features between the frequency-reduced and the true excess density of vibrational states revealed that the spectrum of the latter does not exhibit the anomalous trend of the Boson peak as regards the temperature dependence of its frequency, and further the number of the excess modes decreases with increasing temperature. The observability of the Boson peak in the normal liquid state as a well-resolved peak is also discussed in the context of recent theoretical and simulation works that relate the Boson peak with the details of the potential energy landscape of the supercooled liquid.     

Pressure dependence of the Boson peak in glassy As2S3 studied by Raman scattering

A detailed pressure dependence study of the low energy excitations of glassy As₂S₃ is reported over a wide pressure range, up to 10 GPa. The spectral features of Boson peak are analyzed as a function of pressure. Pressure effects on the Boson peak are manifested as an appreciable shift of its frequency to higher values, a suppression of its intensity, as well as a noticeable change of its asymmetry leading to a more symmetric shape at high pressures. The pressure-induced Boson peak frequency shift agrees very well with the predictions of the soft potential model over the whole pressure range studied. As regards the pressure dependence of the Boson peak intensity, the situation is more complicated. It is proposed that in order to reach proper conclusions the corresponding dependence of the Debye density of states must also be considered. Comparing the low energy modes of the crystalline counterpart of As₂S₃, as well as the experimental data concerning the pressure dependencies of the Boson peak frequency and intensity, a structural or glass-to-glass transition seems to occur at the pressure ∼4 GPa related to a change of local dimensionality of the glass structure. Finally, the pressure-induced shape changes of the Boson peak can be traced back to the very details of the excess (over the Debye contribution) vibrational density of states.     

Non-Debye excess heat capacity and boson peak of binary lithium borate glasses

The non-Debye excess heat capacities of binary lithium borate glasses with different Li₂O compositions of x = 8, 14 and 22 (mol%) are investigated to understand origin of the boson peak. The low-temperature heat capacities are measured between 2 and 50 K by a relaxation calorimeter. The experimental non-Debye heat capacities with x = 14 is successfully reproduced using the excess vibrational density of states measured by inelastic neutron scattering. This finding indicates that the non-Debye heat capacities of lithium borate glasses originate from the excess vibrational density of states measureable by inelastic neutron scattering. Moreover, it is demonstrated that all of the excess heat capacity spectra lie on a single master curve by the scaling using boson peak temperature and intensity.     

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.     

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.     

Observing the twinkling fractal nature of the glass transition

A fundamental understanding of the nature and structure of the glass transition in amorphous materials is currently seen as a major unsolved problem in solid-state physics. A new conceptual approach to understanding the glass transition temperature (T_g) of glass-forming liquids called the twinkling fractal theory (TFT) has been proposed in order to solve this problem. The main idea underlying the TFT is the development of dynamic rigid percolating solid fractal structures near T_g, which are said to be in dynamic equilibrium with the surrounding liquid. This idea is coupled with the concept of the Boltzmann population of excited vibrational states in the anharmonic intermolecular potential between atoms in the energy landscape. Solid and liquid clusters interchange or “twinkle” at a cluster size dependent frequency ω_TF, which is controlled by the population of intermolecular oscillators in excited energy levels. The solid-to-liquid cluster transitions are in accord with the Orbach vibrational density of states for a particular fractal cluster g(ω) ~ ω^df − 1, where the fracton dimension d_f = 4/3. To an observer, these clusters would appear to be “twinkling.” In this paper, experimental evidence supporting the TFT is presented. The twinkling fractal characteristics of amorphous, atactic polystyrene have been captured via atomic force microscopy (AFM). Successive two-dimensional height AFM images reveal that the percolated solid fractal clusters exist for longer time scales at lower temperatures and have lifetimes that are cluster size dependent. The computed fractal dimensions, ≈ 1.88, are shown to be in excellent agreement with the theory of the fractal nature of percolating clusters in accord with the TFT. The twinkling dynamics of polystyrene within its glass transition region are captured with time-lapse one-dimensional AFM phase images. The autocorrelation cluster relaxation function was found to behave as C(t) ~ t^− 4/3 and the cluster lifetimes τ versus width R were found to be in excellent agreement with the TFT via τ ~ R^1.42. This paper provides compelling new experimental evidence for the twinkling fractal nature of the glass transition.     

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.     

Atomic dynamics in liquid KxSb1−x alloys

The atomic dynamics of liquid K_xSb_1−x alloys are studied using cold neutron inelastic scattering. Dynamical properties extracted from the experimental spectra, like the dispersions obtained from the maxima of the longitudinal current correlation function, J_l(Q, ω), and the vibrational spectra, show a strong dependence on concentration. With increasing content of Sb, higher frequency modes are observed in the vibrational spectrum. For the Sb-rich compositions the dispersion is split into two branches. This indicates the de-coupling of the dynamics of the two components, due to the difference in atomic mass, already around the position of the principal peak of the static structure factor, S(Q). The observations are consistent with results from earlier experiments on similar systems and from ab initio molecular dynamics simulations.     

Raman study of lattice dynamics in quasicrystals

We present the first Raman investigation of icosahedral quasicrystals. Broad structured bands in the energy range up to ~500 cm^− 1 have been observed in a series of AlCuFe, AlPdMn and AlPdRe systems. Original information on the vibrational density of states g(ω) was obtained for AlPdRe; for AlCuFe and AlPdMn estimated g(ω) shows a good agreement with the previous neutron results, but demonstrates finer structure. Strong increase in the parameter of electron-vibrational coupling for the low-energy vibrations and its correlation with changes in electronic conductivity has been observed in the series from AlCuFe to AlPdRe. This suggests the increase of the degree of localization for these vibrational excitations and involved electronic states.     

Space charge capacitance spectroscopy in amorphous silicon Schottky diodes: Theory,modeling, and experiments

Numerical modeling of capacitance spectroscopy of hydrogenated amorphous silicon Schottky diodes is carried out. We test the accuracy of the determination of the density of states at the Fermi level, g(E_F), from an analytical treatment of the temperature (T) and frequency (f) dependence of the capacitance (C). Assessment of the position of the Fermi level and the attempt-to-escape frequency of states at E_F is also addressed. It is shown that the precision and reliability of the determination of g(E_F) is strongly dependent on the position of the Fermi level and the shape of the DOS and that the attempt-to-escape frequency is overestimated. Numerical calculations are then used to fit experimental capacitance data. Material parameters that provide the best fits are found in quite good agreement with independent modulated photocurrent and constant photocurrent measurements. Again, the attempt-to-escape frequency deduced from the simplified analytical treatment of capacitance data is found to be overestimated.     

Inelastic neutron scattering on silica xerogel porous systems

New coherent inelastic neutron scattering measurements on silica xerogels in the 300–1000 K temperature range are presented and compared with those obtained in vitreous silica (heralux). The spectra show the presence of the Boson peak, at temperatures, where the quasi-elastic contribution due to absorbed water is negligible. The Boson peak in silica xerogels is at a frequency of around 5 meV (40 cm⁻¹) and has a shape similar to that of melted silica, even in the smaller density xerogels. This important result seems to indicate that the disorder introduced by the presence of pores does not affect the density of states in frequency region. This evidence is also confirmed by changes in the inelastic structure factor S(Q,ω), measured at the frequencies of the Boson peak as a function of the exchanged Q.     

Simulation and scaling of ac conductivities in ion-conducting glasses

Simulation is made about ac conductivity, σ(ω), in ion-conducting glass by recurring to one of the Maxwell’s equations. It is concluded that (1) σ(ω) is made of conduction and conduction-related polarization of the mobile ions, both governed by the same relaxation time, τ, and that (2) high frequency dispersion in σ(ω), high frequency dispersion in the electric modulus peak, and distortion of a semicircle in the complex impedance plane, all arise from a distribution in τ, caused by the disordered structure of glass. Finally, a procedure of scaling ac data measured at various temperatures into a single master curve is given.     

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.     

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.     

Influence of pressure on fast dynamics in polyisobutylene

Influence of pressure on fast dynamics and elastic properties in polyisobutylene is studied using Raman, Brillouin and neutron scattering spectroscopy. Analysis of the results shows that the boson peak frequency increases with pressure stronger than the longitudinal sound velocity measured by Brillouin scattering. Moreover, the boson peak intensity decreases under pressure stronger in Raman scattering than in neutron scattering suggesting a decrease in the light-to-vibrations coupling coefficient C(ν). The strong decrease of the microscopic peak intensity under pressure in Raman spectra supports this suggestion. We argue that variations in C(ν) might be related to amplitude of structural fluctuations. We speculate that change in disorder and/or overall density under pressure is the main cause for the observed variations.     

Replica field theory for anharmonic sound attenuation in glasses

A saddle-point treatment of interacting phonons in a disordered environment is developed. In contrast to crystalline solids, anharmonic attenuation of density fluctuations becomes important in the hydrodynamic regime, due to a broken momentum conservation. The variance of the shear modulus Δ² turns out to be the strength of the disorder enhanced phonon-phonon interaction. In the low-frequency regime (below the boson peak frequency) we obtain an Akhiezer-like sound attenuation law Γ ∝ Τω². Together with the usual Rayleigh scattering mechanism this yields a crossover of the Brillouin linewidth from a ω² to a ω⁴ regime. The crossover frequency ω_c is fully determined by the boson peak frequency and the temperature. For network glasses like SiO₂ at room temperature this crossover is predicted to be situated one order of magnitude below the boson peak frequency.     

Vibrational entropy near glass transition in a chalcogenide glass and supercooled liquid

Raman spectroscopic measurements have been performed on Ge₂₀Se₈₀ glass and supercooled liquid at temperatures ranging between 298 and 500 K. Temperature dependent softening of vibrational mode frequencies has been used in conjunction with the available vibrational density of states data at ambient temperature to estimate the relative contributions of vibrational and configurational entropies across glass transition. Nearly 20% of the additional entropy above glass transition is estimated to be vibrational. Thermal expansion effect on vibrational mode softening is found to be insufficient to account for the anharmonic component of vibrational entropy implying possible coupling between the vibrational and configurational entropies at temperatures above T_g. These results may have important consequences in shaping our understanding of various aspects of glass transition.     

Physical aging effect on the boson peak and heterogeneous nanostructure of a silicate glass

The effect of physical aging on a silicate glass has been investigated by low-frequency Raman scattering. It was observed that the low-frequency side of the excess of Raman scattering, or boson peak, due to harmonic vibration modes decreases in intensity with the thermal annealing (aging) at a temperature lower than the glass transition temperature (T_g), after quenching (rejuvenation) from a temperature higher than T_g. Moreover, it was found that the lowering of the very low-frequency scattering mainly due to anharmonic modes becomes more pronounced when the aging temperature is decreased. These observations are interpreted in the frame of the energy landscape, and by considering the model of the glass heterogeneous cohesion at the nanometric scale.     

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.