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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 \qco{}$\simeq$ 2.1 nm$^{-1}$. We find that below \qco{}, the linewidth of longitudinal acoustic waves increases with a high power of either $Q$, or of the frequency $\Omega$, up to the crossover frequency \OMco{} $\simeq$ 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 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 $\Omega^2$-dependence of the acoustic damping over the entire frequency range., Comment: 5 pages, 5 figures, submitted to the proceedings of IDMRCS 2005, Lille, France

Inelastic neutron-scattering measurements of the dispersion and width of transverse acoustic branches are reported for SixGe1−x, particularly for x=0.51. These alloys form high-quality single crystals. They are strongly disordered dynamically owing to the large Ge/Si mass ratio. This allows to study in function of disorder (x) the relations between the inhomogeneous broadening of acoustic waves, the Boson peak, and low-temperature thermal anomalies common to glasses. For x⩽0.51 we find no boson peak, apparently no plateau in the thermal conductivity, but at large x a Rayleigh law on the phonon width, Γ∝Q4, where Q is the scattering vector.

The interest in measuring acoustic and optic vibrations of glasses at terahertz frequencies is explained. Techniques used for Brillouin spectroscopy at scattering vectors Q⩾1 nm−1 are briefly described and compared. Experimental results, for example on vitreous silicas or glassy selenium, show that plane-wave acoustic excitations exhibit a crossover from propagation to strong scattering as Q is increased. Optical excitations at similar frequencies form a ‘boson peak’. These fairly local excitations can obey ‘molecular-like’ selection rules. The findings reveal a somewhat unexpected strong elastic inhomogeneity in the structure of glasses at the extended length scale of ∼5 nm, about which so little is known otherwise.

Brillouin scattering showing an unusual low temperature softening of some transverse modes in SrTiO3 had been reported previously. The earlier data, complemented by newer Brillouin results, and supplemented by high quality hyper Raman data on the soft mode, demonstrate that this anomalous softening is to a large extent caused by a bilinear coupling of the strain with the gradient of the electrical polarization fluctuations. This coupling had been identified long ago in KTaO3, but at the large momentum exchanges that are achieved in neutron spectroscopy. To our knowledge, it is the first time that the signature of this coupling is observed in any material at the small wave vectors of optical Brillouin scattering. (C) 1999 Elsevier Science B.V, All rights reserved.

New neutron spectroscopic results on glassy selenium are presented. For the first time both Brillouin scattering under kinematic conditions and the boson peak were observed. Both thermal neutron three-axis and cold neutron time-of-flight spectroscopies were necessary. Their absolute calibration reveals the strength of the various spectral contributions in this frequency range. The most plausible interpretation of the overall data is that longitudinal acoustic waves enter a regime of strong scattering between 3 and 4 meV. Umklapp scattering of the neutrons via the static structure factor is also seen. It provides unique information on transverse acoustic modes. Its fast disappearance beyond 5 meV is another strong indication that acoustic excitations cease to propagate.

Three remarkable anomalies related to the acoustic branches of quantum paraelectric (QPE) oxides are presented. In SrTiO 3 , an additional shear-like sheet is observed for modes propagating in the tetragonal plane, and shear branches polarized parallel to the tetragonal axis show an anomalous softening on cooling in the QPE-regime. Both in SrTiO 3 and KTaO 3 , a new doublet is observed in Brillouin scattering which is due to second sound, the wave-like propagation of heat. These effects are discussed in terms of large anharmonic polarization clusters.

Mutual self-similarity of a series of base-catalyzed aerogels was established by comparison of small-angle neutron scattering data and numerical simulations. Investigation of phonon-fracton crossover in these samples by Brillouin scattering allowed determination of the fracton dispersion curve. A fracton dimension d ∼ = 1.1 ± 0.1 was obtained. The correlation between the sharpness of the phonon-fracton crossover and the well-defined structure of the materials is discussed.

Two, significantly different, temperatures are found to be related to the freezing process in the mixed crystal Rb 0.38 (ND 4 ) 0.62 D 2 PO 4 . This observation — based on neutron, Brillouin, and dielectrin methods - indicates a temperature region of enhanced spatial heterogeneity in the relaxational dynamics of the system. A molecular dynamics simulation supports this interpretation.

The fractal character of silica aerogels made under controlled conditions has been investigated by small angle neutron scattering. The conditions involve the selection of the catalysts and the concentration. By a strong dilution, material can be prepared which is fractal over 2 orders of magnitude in length scale. The catalyst allows modification of the spatial arrangement of the elementary particles. The fractal dimension is close to 1.8 under basic conditions and within the range 2.2 to 2.4 under acidic and neutral conditions.

A remarkable softening of a TA-branch in the paraelectric regime of SrTiO3 caused by coupling with the softest TO-mode is observed by inelastic neutron scattering. The simultaneous presence of a nearly forbidden structural soft mode is also found, which depends on how the crystal is cooled through the structural phase transition.

Inelastic neutron and X-ray scattering are used to investigate high-frequency acoustic modes in glasses, in particular glassy selenium and densified silica. Strong scattering takes over above a crossover frequency where the excitations loose their plane-wave character.

Inelastic neutron scattering has been used to study the vibrational excitations of SixGe1−x crystals. Measurements on time-of-flight and triple-axis spectrometers are reported. Local and resonant modes are observed. A strong broadening at high wave vectors is found for some TA-modes.

We have measured the elastic properties of silica aerogels with densities in the range 0.1 to 0.4 g/cm3. The static Young's modulus E was obtained from three-point flexion experiments, while Brillouin scattering allowed the determination of the elastic constants C11 and C44, at hypersonic frequencies. The comparison of these frequency-dependent determinations shows that the samples exhibit large scale homogeneity down to a few μm. The density dependence of the Young's modulus and elastic constants is shown to obey the same power dependence pα with α = ∼- 3.8. The ratio of the compressibility to the shear modulus is similar to that found in bulk vitreous silica. Percolation models are used for the discussion of these elastic behaviour.

Small angle neutron scattering and Brillouin scattering experiments have been performed in porous silica aerogels with densities ranging from 0.1 to 0.4 gcm−3. The results demonstrate the fractal structure of these materials. The fractal dimension is D = 2.40 ± 0.02. The high dispersion observed was interpreted in terms of phonon to fracton crossover. From the scaling exponents, we deduced the spectral dimension d = 1.25 ± 0.12. The numerical value of these exponents raises the interesting question of whichis the proper elasticity theory to be applied to these weakly connected structures.

Small angle neutron scattering results obtained on several series of silica aerogels are presented. It is shown that basic catalysis can produce materials that are fractal over at least two orders of magnitude in length. These have bulk densities lower than ∼ 0.02 g/cm3, corresponding to porosities of 99% or larger. In this case, the constituent particles, whose gyration radii are larger than 10 A, have a fractal surface that cannot be smoothened by oxidation. Densification at elevated temperatures mostly increases the particle size. The fractal structure is destroyed when the particle dimensions equal the correlation length at the gel-glass transformation.

The spectra recently published by Tominaga and Urabe are shown to be in good qualitative agreement with the current coupled-mode models of the KDP transition. The need for a careful quantitative analysis of this type of data over a broad frequency range is discussed.