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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

The structure of densified As2O3 glasses

In situ high energy X-ray diffraction and Raman experiments have been carried out to probe the structure changes of vitreous As₂O₃ under pressure. The first sharp diffraction peak reduces in intensity up to 10 GPa, indicating a breakdown of intermediate range order with pressure. All features in the Raman spectra broaden with increasing pressure up to 11.6 GPa. The mode at 378 cm⁻¹ associated with As₄O₆ molecule-like vibrations increases in intensity up to 6.2 GPa and decreases at higher pressures. In addition, X-ray and neutron structure factors have been measured for normal density and permanently densified As₂O₃ glasses recovered from 10 and 23 GPa. The results show the local AsO₃ pyramids and 3-membered rings essentially remain intact after compression. The increase in density is mainly associated with an inward shift of the third nearest neighbor peak in the X-ray radial distribution function, which indicates an increased packing of 3-membered AsO₃ rings.     

Raman and luminescence studies of alkali borate tungstate glasses

Raman and luminescence spectroscopy were used to determine the structure of alkali borate tungstate glasses: M₂O(B₂O₃)₂·xWO₃, M = Li or Na (0 < x < 1). Raman scattering results showed the dominant tungstate species in these photochromic glasses to be tetrahedral WO₄⁼. At high concentrations of WO₃, WO₃·H₂O, and W₂O₇⁼ are also present. Luminescence measurements provided evidence for an octahedral WO₃ structure not identified by the Raman results. The results also revealed a possible change in the structure of the glasses similar to that observed in alkali borate glasses and associated with the “borate anomaly”. In addition, preliminary measurements are reported on the variation of the band gap, density, index of refraction, and the elastic coefficient C₁₁ determined by Brillouin scattering with composition.     

Diffraction studies of glass structure III. Limitations of the fourier method for polyatomic glasses

Using the scattering intensity calculated for a simple quasi-crystalline model based on the high-cristobalite structure, for which the structural correlation function is known exactly, the fourier transformation of X-ray and neutron intensity data for a polyatomic glass has been investigated. The effects of termination of the data at finite Q, quadrature interval, data normalisation and various kinds of errors are discussed. The resulting form of the distortions on the derived correlation functions, of errors in peak positions and in peak areas are described and it is shown that a variety of errors give rise to pronounced structure in the correlation function at low values of r, below the first true peak.     

Raman spectroscopy study of the structure of gallium nitride epitaxial layers of different orientations

The composition nonstoichiometry and structural quality of undoped gallium nitride layers grown by the hydride vapor phase epitaxy on sapphire substrates of different orientations have been estimated using Raman spectroscopy. It is found for the first time that the peak position of the phonon mode E₂(high) in the Raman spectra of gallium nitride films at a wave vector of 572 cm^–1 depends on the initial orientation of sapphire substrate and is low-frequency shifted when passing from Ga-polar to partially N-polar orientation. Additional modes are found in the spectra of GaN layers grown on substrates with m and r orientations. It is shown that a decrease in the composition deviation from stoichiometry, caused by reducing the HCl flow through the gallium source during the growth of GaN layers, leads to an increase in the phonon-mode intensity in the Raman spectrum.