Origin of boson peak in glasses: Role of Ioffe–Regel crossover and atomic soft modes

A theoretical ‘complete soft-mode-dynamics’ model of the origin and properties of the boson peak accompanied by a high-frequency sound, observed in glasses of a certain type, is described. The origin is determined by interaction of non-acoustic vibrations with acoustic phonons and a Ioffe–Regel crossover for their inelastic scattering. The non-acoustic excitations are associated with vibrations of atomic soft-mode ‘defects’. Two types of boson peak can be predicted in agreement with experiments.     

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.     

Effect of polymerization on the boson peak, from liquid to glass

Reactive epoxy-amine mixtures during isothermal polymerization have been characterized by Raman scattering measurements in order to follow the modification of the vibrational density of states. In the initially liquid solutions an increasing number of Van der Waals bonds are replaced by stiffer covalent bonds. During the chemical reaction, the molecular diffusion slows down and ultimately the systems are frozen in a glassy structure. The transformation from reactive liquids to chemical glasses is accompanied by microscopic structural changes driven by the bonding process. During the reaction the samples density and the sound velocity increase, both of them contribute to significantly change the Debye level. By combining Raman with Brillouin inelastic X-ray scattering measurements, we compare the relative variations of the boson peak with that of the Debye level. We find that the shift and intensity variation of the boson peak are fully explained by the modification of the elastic properties of the medium and a boson peak master curve is obtained.     

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.     

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.     

Vibrational states and disorder in continuously compressed model glasses

We present in this paper a numerical study of the vibrational eigenvectors of a two-dimensional amorphous material, previously deeply studied from the point of view of mechanical properties and vibrational eigen-frequencies [7], [8], [9] and [10]. Attention is paid here to the connection between the mechanical properties of this material in term of elastic heterogeneities (EH), and how these inherent heterogeneous structures affect the vibrational eigenvectors and their plane waves decomposition. The systems are analysed for different hydrostatic pressures, and using results from previous studies, a deeper understanding of the boson peak scenario is obtained. The vibrational spectrum of a continuously densified silica glass is also studied, from which it appears that the pulsation associated with the boson peak follows the same pressure dependence trend than that of transverse waves with pulsation associated with the EH characteristic size.     

Kovacs effect in PMMA observed by low-frequency Raman scattering (boson peak)

The physical aging of the poly(methyl methacrylate) glass (PMMA) is described by its effects on the refractive index, that reflects the change of mean specific volume, and, on the other hand, on the low-frequency Raman scattering, i.e., on the boson peak. The boson peak depends mainly on the cohesion fluctuations. The memory or so-called Kovacs effect is observed by the appearance of a minimum of refractive index (i.e. a maximum of volume) as a function of the aging time at a higher temperature subsequent to an aging at lower temperature. The minimum of refractive index corresponds to a maximum of the boson peak intensity. However, the cohesion is not directly related to the volume, so that the evolution of the refractive index does not mimic exactly that of the boson peak intensity. Information on the change of cohesion by aging is obtained by enthalpy measurement. The obtained experimental results are discussed in the frame of the heterogeneous cohesion or elasticity at the nanometric scale. This clarifies the phenomenon of physical aging and the consequent Kovacs effect.     

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.     

Effects of permanent densification on the vibrational density of states of vitreous silica

We present a detailed Raman scattering study of the boson peak evolution in vitreous silica as a function of density, from the normal one up to ~ 22% of densification. We show that the distribution of low frequency modes in the boson peak range does not change as a function of density, at least until the densification process starts to modify the glassy network structure from a fourfold coordinated structure into a sixfold coordinated one.     

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.     

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.     

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 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.     

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.     

Third-order elastic constants determination in soda–lime–silica glass by Brillouin scattering

Brillouin light scattering allows the measurement of sound velocity and elastic moduli in transparent materials. The ability to select a small scattering volume and to use specific scattering configurations gives important information about the gradient and anisotropy of mechanical properties. Brillouin experiments are often used to measure the second-order elastic constants. When a high accuracy in frequency measurements is achieved, Brillouin scattering may allow the determination of third-order elastic constants in pre-stressed media. Hence, Brillouin scattering provides in principle, a method for the analysis of stress fields in tempered glasses. In order to validate the technique, samples of float soda-lime–silica glass submitted to controlled stresses by four-point flexion were investigated. The results show the expected profile for the velocity of sound waves propagating in directions parallel and perpendicular to the surface of the samples, respectively. They allow the determination of several third-order elastic constants of the investigated glass. This technique was applied to several samples of tempered glass corresponding to different values of the surface stress. The main result is the observation of the expected general trend, namely, through the thickness of the sample, a parabolic variation of the sound velocity whose amplitude increases with the magnitude of the surface stress.     

Raman spectroscopic investigations of Mn2+ doping effects on the densification of acid-catalyzed silica xerogels

Undoped and Mn²⁺-doped silica xerogels were prepared from hydrolysis and condensation of tetramethyl orthosilicate (TMOS). The xerogels were characterised by density measurements and fluorescence and Raman spectroscopies. Raman measurements over the range 4–1200 cm⁻¹ showed that the number of three- and four-membered rings in the xerogel network depends on the thermal treatment and on the concentration of Mn²⁺ ions. Indeed, both structures are found to be more numerous in the gel network of the doped samples than in the undoped one, showing that doping with Mn²⁺ hampers the destruction of three- and four-membered rings. In the low-wave number region (4–100 cm⁻¹), doping with manganese ions was found to affect the position of the boson peak. The boson peak profiles were used to deduce that the sizes of the cohesive domains in the gel-derived silica network are much larger for doped samples (11 nm for 500 ppm) than for undoped ones (2.1 nm).     

High-frequency excitations in glassy crystals

We present broadband dielectric loss spectra of the orientationally disordered (‘plastic’) crystal ortho-carborane, extending well into the infrared region and compare the results to the low-molecular weight glass former glycerol. Focusing on the high-frequency dynamics beyond 1 GHz, we find a loss minimum showing evidence for excess intensity, quite similar to the findings in canonical glass formers. In the THz region a strongly asymmetric peak shows up, which exhibits marked differences to the corresponding peaks found in glycerol and other glass-forming liquids. We discuss the relation of this feature to the boson peak detected, e.g., in light and neutron scattering experiments.     

Brillouin light scattering study of polymeric glassy sulfur

We present here a study of the acoustic dynamics of polymeric glassy sulfur. The data have been collected in the GHz frequency range by means of Brillouin light scattering for different scattering geometries. The choice of the experimental setup allows us to obtain information on the refractive index, n, that comes out to be close to that corresponding to the high temperature polymeric liquid phase. The longitudinal acoustic excitations have been investigated as a function of temperature from deep into the glassy state up to the glass transition temperature. The temperature dependence of the sound velocity is compared to the one measured in the liquid phase. We find that the sound velocity of the glass can be linearly extrapolated from that of the polymeric liquid measured in the THz frequency range with inelastic X-ray scattering.     

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).     

Inelastic neutron and low-frequency Raman scattering in a niobium-phosphate glass for Raman gain applications

We present measurements of the vibrational spectrum of a binary niobium-phosphate glass in the THz frequency range using inelastic neutron and Raman scattering. The spectra of these glasses show a low-frequency enhancement of the vibrational density of states (“boson peak”). Using a recently developed theory of vibrational excitations in disordered solids we are able to reconcile the measured neutron and Raman spectra using fluctuating elastic and Pockels constants as a model concept. As the spontaneous Raman susceptibility is a key parameter for Raman amplification our results suggest a significant gain profile for application of niobium-phosphate glasses in Raman amplifiers.