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.     

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.     

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.     

Manifestation of thermodynamic glass transition by structure and picosecond dynamics in alkali tellurite glasses

The Raman spectra of the 0.1Cs₂O–0.9TeO₂ melt were measured and analyzed over a broad temperature range including the glassy, supercooled and molten state in an effort to follow the varying structural and dynamical aspects caused by temperature and alkali modifier. The network structure of the glass/melt is formed by mixing TeO₄ trigonal bipyramid and TeO₃ trigonal pyramid units. Changing alkali content and/or temperature results to conversion of the TeO₄ units to TeO₃ units with a varying number of non-bridging oxygen atoms. The low-frequency Raman spectra reveal a well-resolved Boson peak whose frequency also depends on temperature. The variation of the maximum of the Boson peak has been determined and discussed in the framework of current phenomenological models. The short-time dynamics of the system experiences drastic changes when approaching the glass-to-liquid transition. The temperature dependent plot of the correlation times extrapolates to a crossover value, which we assign as spectral evidence of the system's known thermodynamic glass transition temperature. Similar behavior exhibit several spectral features, such as the maximum of the Boson peak, the exponent of the susceptibility and the intensity ratio related to the structural transformation from TeO₄ tbp to TeO₃ tp species occurring in the medium range order structure.     

Boson peak,structural inhomogeneity,light scattering and transparency of silicate glasses

The microscopic origin of the excess of Density of Vibrational States (Boson peak) is discussed, taking into account recent analyses of the properties of glasses that were frozen-in under high pressure. Experimental data reveals a decrease of the Boson peak with increasing pressure of freezing (fictive pressure) and, simultaneously, an increase of the structural homogeneity of the glass. These results suggest new ways to improve the transmission of telecommunication fibers by decreasing the optical loss due to the scattering by the structural inhomogeneities of glasses.     

Octahedral fluoride glasses: Raman spectra and structure of niobium pentafluoride

Raman spectroscopy is used to characterize the NbF₅ phases in the temperature range 80–500 K. A new clear glass is formed by quenching the melt to liquid nitrogen temperatures having a glass transition at ～206 K and crystallization at ～233 K. For all phases including the melt, the glass, the supercooled liquid, the crystalline solid and the gas, the Raman spectra show a rather common high frequency band at ～760 cm^?1 which is attributed to the Nb–F terminal frequency of partially bridged ‘NbF₆’ octahedra. Based on the systematics of the Raman spectra for all phases and the literature physicochemical data a model is proposed for the glass and the liquid phases where ‘NbF₆’ octahedral bridged in cis and/or trans configurations form a variety of cyclic and/or chain structures which intermix building up the overall structure. At exceptionally low energies (<11 cm^?1) a rather weak in intensity Boson peak is observed in the glass which shifts to even lower energies with increasing temperature. Librational and/or tortional motions of the bridged octahedra participating in the glass structure are possible candidates for the origin of this peak.     

Genuine Johari–Goldstein β-relaxations in glass-forming binary mixtures

Broadband dielectric spectroscopy measurements were performed on glass-forming binary mixtures, composed of rigid polar molecules dissolved at low concentration in apolar viscous solvent (tristyrene). Dielectric spectra were dominated by the polar molecule contribution, so enabling the study of its dynamic behavior. A well resolved secondary relaxation, not attributable to internal degrees of freedom, was visible in both the liquid and glassy states: for its intermolecular nature, it can be called a ‘genuine’ Johari–Goldstein (JG) relaxation, in the sense that it is a local and non-cooperative process but entailing the motion of the molecule as a whole. Among our results, the following ones are noteworthy: (a) polar systems in the neat state showed an excess wing that became a well resolved JG-peak on mixing with the apolar solvent; (b) the time-scale distance between structural and JG loss peak increased with the apolar solvent fraction; (c) broader the structural loss peak was, larger was the separation in the frequency scale between structural and JG peak; (d) the JG relaxation time showed a non-Arrhenius temperature behavior above T_g, paralleling that of the structural relaxation time. All the results can be rationalized in the framework of Coupling Model.     

A study of Raman spectroscopy and low-temperature specific heat in gel-synthesized amorphous silica

A comparative study of low-temperature specific heat (1.5–25 K), C_p, and low-frequency Raman scattering (<150 cm⁻¹) has been performed in amorphous silica samples synthesized by sol–gel method (xerogels) and thermally densified in a range of densities, from ρ=1250 kgm⁻³ to ρ=2100 kgm⁻³, close to the density of the melt quenched vitreous silica (v-SiO₂). The present analysis concerns the application of the low-energy vibrational dynamics as an appropriate tool for monitoring the progressive thermal densification of silica gels. By comparison with v-SiO₂, the Raman and thermal properties of xerogels with increasing thermal treatment temperature revealed the following important results: (i) the existence of a critical treatment temperature at about 870°C, where a homogeneous viscous sintering produces full densification of the samples. This effect is detected by the observations of the Boson peak in Raman spectra at about 45 cm⁻¹ and of a peak in C_p(T)/T³, very close to those observed in v-SiO₂; (ii) in silica xerogels treated at temperatures less than about 800°C, the low-frequency Raman scattering is greater, with a continuous decreasing unstructured shape, and the Boson peak is not detected in the spectra.     

Medium range order in sodium silicate glasses: role of the network modifier

The effect of different concentrations of the network modifier Na₂O on the position of the Boson peak, observed in the low frequency Raman scattering experiments, is analyzed. Glasses containing 25% Na₂O (Na₂O · 4SiO₂) and 33% Na₂O (Na₂O · 2SiO₂) are compared with pure SiO₂ glass. The observed shift of the Boson peak is interpreted in terms of a change of a correlation length, ℓ, corresponding to some medium range order. This length, ℓ, decreases when the amount of sodium oxide increases.     

Dynamics of glass-forming bioprotectant systems

In this work the dynamics of glass-forming mixtures showing a bioprotective function towards organisms under stress conditions is investigated. The behaviour of mixtures of two known glass-forming systems, such as α-d-glucopyranosyl α-d-glucopyranoside (trehalose) and 1,2,3-propanetriol (glycerol), are studied as a function of temperature and concentration. Both the fast local dynamics and the diffusive dynamics are determined by Inelastic Neutron Scattering and Quasi Elastic Neutron Scattering, respectively; more specifically the Boson peak behaviour, the mean square displacements and the translational linewidth as a function of temperature, wave-vector Q and concentration are characterized. The findings highlight an anomalous dynamic behaviour when a small amount of the alcohol is added to the disaccharide. This feature could be relevant in understanding the bioprotection mechanisms.     

Silica under hydrostatic pressure: A non continuous medium behavior

The homogeneous/inhomogeneous structure of glasses is still a debated question. Hydrostatic high pressure experiments allow us to determine if a glass behaves as an elastic continuous random network or if a nanometer scale heterogeneity has to be taken into account. In order to get information on the homogeneous/inhomogeneous structure of glasses, in situ high pressure Raman experiments are performed on silica in the elastic domain up to 4.7 GPa. A strong decrease of the Boson peak intensity is observed between 1 bar and 3 GPa. We show that this decrease does not correspond quantitatively to the effect of pressure on a homogeneous elastic medium. From the interpretation of the narrowing of the main Raman band width under pressure as a narrowing of the θ inter-tetrahedral Si–O–Si angle distribution it is shown that the decrease of the Boson peak intensity is correlated to the decrease of the intrinsic inhomogeneity of the silica glass. These results confirm the occurrence of an intrinsic inhomogeneity at a nanometer scale even in a single component glass like SiO₂ which is very important for the interpretation of the optical or mechanical properties of the glasses.     

Stokes to anti-Stokes intensity ratio in Raman spectra of the soft mode in KH2PO4 near the phase transition temperature

We investigate the Stokes to anti-Stokes intensity ratio for the Raman spectrum of a central peak in a potassium dihydrogen phosphate (KDP) crystal. The ratio deviates from the Boltzmann factor as the temperature approaches the phase transition temperature. The response functions evaluated by three ways assuming the fluctuation–dissipation theorem do not agree in a frequency region below ～30 cm^?1. This means that the usual relation based on the fluctuation–dissipation theorem are not directly applicable to the spectral analysis of the soft mode. Further, we compare the result of KDP with that of the cooperative rotational dynamics in liquid carbon disulfide.     

The slow β-relaxation observed in Ce-based bulk metallic glass-forming supercooled liquid

Dynamic mechanical relaxation measurements are performed on a Ce-based metallic supercooled liquid close to its glass transition temperature T_g. An obvious excess wing is observed both in the temperature and frequency dependent loss modulus curves by the calculation the relaxation time of the α-relaxation in supercooled liquid with the fit by the combination of the Kohlrausch–Williams–Watts and Vogel–Fulcher–Tamman equation. The results indicate that the slow β-relaxation process exists in the metallic liquid and arises from the small-scale translational motions of atoms that are linked in its metastable islands.     

Low-temperature specific heats of porous silica xerogels of low densities

Low-temperature specific heat measurements have been performed in porous silica xerogels with densities varying from 670 to 1730 kg m⁻³ to study the low-energy vibrational dynamics. The specific heat, C_p, shows a bump in the temperature range above 4 K, when reported in a plot of C_p/T³ against the temperature, T. The bump is almost independent of the sample density and is close to the boson peak observed in melt-quenched amorphous silica (a-SiO₂). At temperatures <4 K, an additional contribution to that predicted by the Debye theory is observed. It follows an approximately linear temperature dependence (C_exc=aT^1+v, v being equal to about 0.25). In the xerogel with the largest density, specific heat of about a factor 5 larger than that of a-SiO₂ is measured, which increases with decreasing sample density. By comparison with the corresponding properties of a-SiO₂, we conclude that the disorder introduced by the presence of pores does not measurably affect the excess density of vibrational states in a frequency range of the boson peak (BP), but increases the density of the two-level systems (TLS).     

Short-range order and dynamic viscosity of liquid Cu–Ge alloys

We report an investigation of the dynamic viscosity and the atomic structure of liquid Cu–Ge alloys. The concentration as well as the temperature dependence of the viscosity obtained experimentally has been modelled by use of a thermodynamic approach. An excess viscosity above mixing rules has been observed for Cu-rich alloys which – in relation with the diffraction experiments – can be explained in terms of a micro-heterogeneous structure.     

The defect diffusion model and the properties of glasses and liquids

Several previously unexplained relaxation phenomena are interpreted quantitatively in terms of the defect diffusion model (DDM). These include widely different pre-exponentials, exponents and consequently fragility. In addition, the DDM is used to give a qualitative explanation of many properties that glasses and liquids exhibit. This includes interpretations of the glass transition (T_g), the liquid–liquid transition (T_B), the crystalline melting temperature (T_m), and the different values of the characteristic temperature, T_C, that some materials exhibit for different types of physical measurements. Next, qualitative explanations of the origin of secondary relaxations such as the excess wing and the β relaxation are given. In addition, the boson peak is discussed in terms of the DDM. Finally, it is pointed out that in the DDM, universality is embodied in the defects i.e. free volume.     

Effect of temperature and pressure on the structural (α-) and the true Johari–Goldstein (β-) relaxation in binary mixtures

We investigated the microscopic origin of the excess wing through isothermal and isobaric dielectric relaxation measurements for the Quinaldine/tristyrene mixture. Our results show that the excess wing, characteristic of the high frequency side of the structural loss peak in neat Quinaldine, becomes a well resolved Johari–Goldstein secondary relaxation on mixing with the apolar tristyrene. Analyzing the temperature and pressure behavior of the two processes, a clear correlation has been found between the structural relaxation time, the Johari–Goldstein relaxation time and the dispersion of the structural relaxation (i.e. its Kohlrausch parameter). These results support the idea that the Johari–Goldstein relaxation acts as a precursor of the structural relaxation and therefore of the glass transition phenomenon.     

Low-energy excitations in polyvinyl chloride: Raman scattering and thermal properties

The low-energy excitations of a very fragile glass-former (in the sense of Angell), poly(vinyl chloride), have been studied by low-frequency Raman scattering and by measurements of the low-temperature heat capacity and thermal conductivity. Two different samples were investigated : one with a crystallinity of about 15%, the other quenched and amorphous, as measured by small-angle neutron scattering. The boson peak in Raman scattering was observed in both samples even at room temperature. A clear correspondance between the Raman boson peak, the excess of heat capacity and the plateau of thermal conductivity was shown. It is confirmed that the boson peak or the heat capacity excess are relatively small in this very fragile glass-former. However it is deduced that the high concentration of tunnelling systems in the amorphous sample is the result of a rapid quenching rather than an intrinsic property of fragile glass-formers.     

Dependence of the Electrically Controlled Birefringence on Applied Frequency in a Nematic Liquid Crystal

Detailed studies on the dependence of the ECB effect on the applied frequency have been made in a nematic liquid crystal MBBA. It is found experimentally that, when the applied voltage is just above the threshold voltage, there are strong dependences of both the delay time and the mean deformation angle of the molecular director subjected to a constant voltage setup on the applied frequency. Those applied frequency dependences of the ECB effect can be interpreted in terms of the dielectric alignment in an electrically conducting nematic liquid crystal. We have measured the capacitance of the deformed liquid crystal cell varying the applied frequency. The experimental results are compared with the Gruler and Cheung theoretical prediction, and good agreements are obtained between them when the applied voltage is just above the threshold voltage.     

Comparison of amorphous and liquid palladium-silicon alloys

The Pd_82,5Si_17,5 alloy has been investigated by X-ray diffraction in an amorphous state obtained by rapid quenching from the liquid state and also in the liquid state at a temperature just above T_f. The differences seen in the interference functions obtained relative to both states are not only due to a temperature effect. From the two atomic radial distribution functions it was possible to evaluate the Pd–Pd distances and the Pd–Si distances as well as the number of nearest neighbours. These distances have the same values, but the displacements of the atoms are more important in the liquid. The contribution of Pd–Pd bonds, for the metal-metal distances equal to 1.65 times the particle diameter, decreases in the liquid.