Search

A general framework for the understanding of Brillouin scattering spectra observed in glasses with light, X-rays, or neutrons is presented. Several sources of acoustic damping are discussed. Crossovers between different damping regimes can occur, depending on the glass and on the temperature. Generally, the damping of sound culminates in the THz frequency range with a Ioffe-Regel limit corresponding to a resonance with the boson peak. This limit should be of direct relevance to BRISP, as the instrument will mostly operate in that region.

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 lattice parameters of tetragonal strontium titanate are determined to about 1 part in 106 with penetrating X-rays. While no peculiarity is detected in a bulk sample, a distinct anomaly at 37 K is observed in an optically polished thin platelet derived from the same single crystal. This suggests that the anomaly is related to a high density of dislocations. A possible mechanism is that dislocations stabilize transverse antiphase boundaries which undergo a ferroelectric transition near 37 K. If so, this transition stresses the boundaries which then strain the bulk leading to the observed anomaly.

The ferroelectric transition of bulk strontium titanate is suppressed by a combination of two effects: (1) the structural changes produced by the antiferrodistortive transition at T-a =105 K and (2) the quantum fluctuations. The structural changes are strongly perturbed within antiphase domain boundaries , and this in such a manner that a ferroelectric transition should occur in boundaries containing the tetragonal c-axis at T-c similar to 35 to 40 K. This provides a possible explanation for a number of anomalies observed in SrTiO3 at those temperatures. We report a new low-T anomaly on the lattice parameter c measured on a thin polished platelet. The above model is consistent with its sign and size, as well as with the sign and size of earlier birefringence measurements on similar samples.

Peter Debye was a scientist of remarkable breath and a founder of material science. This short article summarizes his scientific career, main contributions, and recognitions. A separate longer chapter will give more details on Debye's personal history in the perspective of the scientific life and historical circumstances of his time. It will also describe other aspects of Peter Debye, as a leader, a teacher, and a man.

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.

Hyper-Raman spectroscopy is used to investigate low frequency vibrations of various silica glasses. A strong boson peak is observed. The corresponding modes are inactive in infrared and Raman spectra, and are nonacoustic in nature. The shape of this boson peak essentially matches the total density of vibrational states (DOS), with a constant coupling coefficient C. This and other indications suggest that these modes actually dominate the DOS of silica.

The frequencies of the softest polar optic phonons of tetragonal SrTiO3 are accurately determined using high-resolution hyper-Raman spectroscopy on oriented-domain crystals. The splitting of the polar soft mode in the tetragonal phase is quantitatively related to the 105 K structural transition, i.e., to the rotation of the oxygen octahedra and to the associated macroscopic strains. In addition to quantum fluctuations, these tetragonal distortions are found to be essential in preventing the ferroelectric transition.

Low-T Brillouin spectra of the incipient ferroelectric KTaO3 exhibit a broad central peak (CP), and additional Brillouin doublets (BD), that can both be related to phonon-density fluctuations. On the basis of new high-resolution neutron data obtained of low-lying phonon branches, we analysed the phonon-kinetics mechanisms that are possibly the origin of these unusual features. Firstly, transverse acoustic (TA) phonons whose normal damping is faster than the BD frequency can produce hydrodynamic second sound. Secondly, two-phonon difference scattering from low damping thermal transverse phonons contribute to the spectra with either a sharp or a broader doublet, depending on the phonon group velocity and anisotropy of dispersion surfaces. The position of the observed sharp doublet is consistent with both mechanisms, but a comparison of the computed and experimental anisotropies favours the second process.

Neutron-scattering, ultrasonic, and Brillouin-scattering experiments were performed to clarify the role of domains in the low temperature anomalies of SrTiO3. Ferroelastic domains of the antiferrodistortive transition at 105 K produce many anomalies in ultrasonics which can be eliminated by the application of an orienting pressure on the sample. In this condition, we find that other low temperature spectral anomalies remain which depend on the manner the sample has been cooled through its structural transition. It is suggested that these anomalies might relate to antiphase domains of the structural transition, and that these domains might play a role in the existence of the Muller State.

The attenuation of acoustic phonons in glasses increases with their frequency Ω growing either to internal friction or to scattering by static and dynamical disorder. Friction leads to a finite lifetime, i.e. to homogeneous broadening. Conversely, scattering does not prevent excitations from remaining long-lived, but piane waves become inhomogeneously broadened. In this paper we show that, at very high frequencies Ω ∼ 1THz, acoustic modes enter a regime dominated by strong scattering in which they cease to propagate as piane waves. This is consistent with all available information, whether macroscopic, simulation, or spectroscopic.

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.

Brillouin scattering from transverse-acoustic modes of SrTiO3 is observed, while the frequencies of the soft polar modes are remeasured with hyper-Raman scattering. It is shown that an anomalous decrease of sound velocities at low temperatures results from the.coupling of the strain with the gradient of the electrical polarization fluctuations. The corresponding anomaly in the acoustic width indicates an inhomogeneous broadening of the soft polar mode.

Glasses exhibit well known and apparently universal anomalies in their thermal properties. Their excess specific heat poses the question of the nature of the modes that contribute to the density of vibrational states and to the plateau in their thermal conductivity of the propagation of acoustic phonons. The vibrational modes involved in both anomalies must have frequencies well above 100 GHz, reaching into the terahertz range. This is a difficult region for direct spectroscopic observation of acoustic excitations. New small-angle inelastic neutron and inelastic X-ray scattering spectroscopies now give access to the structure factor S(Q, ω) in this region. Recent results on vitreous silica are discussed in the light of other well established spectroscopic information. We show in some detail that an elementary model, which consists in fitting inelastic spectra simply with a damped harmonic oscillator response, gives the impression that a mode continues to exist at frequencies ω above the strong ph...

Direct spectroscopic information on the frequency and temperature dependences of acoustic-phonon damping in vitreous silica is reconsidered. It points to the essential role played by Rayleigh scattering of the phonons, in quantitative agreement with thermal properties at low temperatures. A picture is proposed that consistently unifies thermal properties with all the available spectroscopic results.

The velocities of acoustic modes have been measured on SrTiO3 by Brillouin and neutron scattering. Anomalies are detected at or below T q, the temperature that marks the onset of the quantum paraelectric regime. It is shown quantitatively that the square of the polarization plays an important role below T q. The dependence on the wavevector square which is found for some of the anomalies indicates the importance of coupling terms proportional to the gradient of the polarization.

Quantum paraelectrics are incipient ferroelectrics whose transition is hindered by the zero-point quantum motion. Recently however, electronparamagnetic-resonance measurements uncovered a phase-transition-like anomaly in the quantum paraelectric SrTiO3 at T q ≈ 37 K. The observed line shifts are accompanied by no measurable splitting or broadening, suggesting that the possible transition would be towards a dynamical state preserving the crystal symmetry. This new “Muller state” generated considerable interest. In this report, we concentrate on data obtained on oxide perovskites. Light and neutron scattering spectroscopies confirmed the existence of T q in SrTiO3 and revealed several anomalies among which a new branch whose origin remains unclear. A new quasielastic doublet was also found, both in SrTiO3 and KTaO3, which is produced by second sound. Although some measurements were interpreted in terms of a coherent quantum state, there seems to be so far no direct evidence for such a state, while ...

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.

Inelastic neutron scattering measurements are reported for Rb0.55 (ND4)0.45D2PO4 at temperatures well above the TDIC where diffuse incommensurate freezing at wave vector qs occurs. They reveal, in addition to a central peak, a branch whose relaxation rate is smallest at qs and which softens on cooling. A weak pseudo-antiferroelectric diffuse scattering is also observed that freezes near TDIC. A scenario is proposed to describe comprehensively the freezing of these proton glasses.

Rayleigh-Brillouin light-scattering spectroscopy performed on oriented samples of tetragonal SrTi${\mathrm{O}}_{3}$ reveals the presence of a new doublet at low temperatures. This scattering, also seen in KTa${\mathrm{O}}_{3}$, appears in addition to the broad central peak already reported by Lyons and Fleury. The likely origin of this spectral component is second sound, the wavelike propagation of entropy.

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.

Fracture surfaces of high-purity silica glasses, finely patterned with small amounts of either GeO2 or P2O5 substituted for SiO2, are investigated by atomic force microscopy under an electrolyte. The samples are cross sections of graded-index optical fibers of the type used for long-distance optical communications. While topography images are featureless, the frictional force is strikingly sensitive to the composition, down to ∼0.1% for the [P]/[Si] ratio. This unexpectedly large contrast depends on the pH of the electrolyte showing its relation to the acid−base properties of the oxides. This result holds considerable promise for the local exploration of acid−base properties of mixed oxides down to the nanometer scale.

The phonon-fracton crossover in a series of fractal aerogels of well-defined microstructure is investigated for the first time. Results of small-angle neutron scattering combined with simulations establish the mutual self-similarity of the series and its fractal dimension D 1.7. Brillouin scattering is used to determine the fracton dimension related to tensorial elasticity, 1.1. Combined with Raman and neutron spectroscopic data, this allows to derive a consistent picture of dynamical scaling in relation with the structure of these materials.

A previous inelastic UV scattering experiment on silica glass is reproduced using a high grade superpolished sample. In the pristine sample condition, surface scattering is not observable compared to Rayleigh scattering from the bulk. However, exposure to a fluence of the order of 100 J/cm${}^{2}$ at photon energies slightly below the electronic gap generates observable surface damage. This occurs after a few hours' illumination with the monochromatic spectrometer beam. No anomaly in the Brillouin linewidth was found up to an excitation energy of 7.8 eV.

International audience; We report picosecond acoustic measurements in silica-glass films grown by wet thermal oxidation on a (111) silicon substrate. The longitudinal acoustic phonons are observed over the range from 150 to 300 GHz using an infrared pump and a second harmonic blue probe. The transducer is an aluminum thin film deposited on top. Multiple interference effects are analyzed and fully taken into account. They lead to a signal presenting rapid oscillations as a function of the sample thicknesses. The latter are determined by separate interferometry. Our remarkably precise acoustic attenuation results are found to follow rather well a model combining thermally activated relaxations and anharmonicity. New values for the optical absorption of silicon in the 400-to-500-nm region of the spectrum are obtained as a by-product.

New inelastic neutron-scattering and Brillouin-scattering results are reported for pressure-oriented SrTiO, crystals at temperatures below the structural transition. The measurements reveal an unexpectedly large number of anomalies at small frequencies and wave vectors in the quantum paraelectric region. The anomalies include a strong depression of a TA-branch at unusually small wave vectors, an apparent splitting of the same branch, the lifting of a selection rule for the structural mode, and an anomalous temperature dependence of the elastic constant C,, .

The position and strength of the boson peak in silica glass vary considerably with temperature $T$. Such variations cannot be explained solely with changes in the Debye energy. New Brillouin scattering measurements are presented which allow determining the $T$-dependence of unrelaxed acoustic velocities. Using a velocity based on the bulk modulus, scaling exponents are found which agree with the soft-potential model. The unrelaxed bulk modulus thus appears to be a good measure for the structural evolution of silica with $T$ and to set the energy scale for the soft potentials., Accepted for publication in Physical Review Letters

A systematic study of the structure and magnetism of epitaxial iron films deposited on Cu(100) is reported. For clean room-temperature growth conditions a succession of four different crystalline reconstructions is observed, which appear to be related uniquely to four different magnetic behaviors, as detected by magnon light scattering and the magneto-optical Kerr effect

The single-length-scale postulate for fractons and the scaling hypothesis for the dynamic structure factor are confirmed for scalar elasticity on bond-percolation clusters. The strain exponent \ensuremath{\sigma} is determined in two and three dimensions. Because of granularity and finite-size effects, these results cannot be obtained from site-percolation models for which the short-range structure fails to scale. Dipole-induced-dipole scattering is particularly sensitive to granularity.

Transverse acoustic (TA) phonons propagating in the basal plane ( ) of Rb1-x(NH4)xH2 PO4 with x=0.25 have been measured by means of coherent inelastic neutron scattering over a temperature range including the dipolar glass transition. These modes seem to be more and more damped as temperature is decreased towardsTg, the width of energy scans reachs a maximum at about 80 K then decreases to a normal value at very low temperatures. During the decrease of temperature no softening of TA phonons is observed. Although measured at higher frequencies, the TA phonons determined by neutron scattering behave exactly as those observed in Brillouin scattering. One has applied the model of piezoelectrically coupled modes which accounts for Brillouin spectra. The agreement with neutron data is good. So the picture of freezing characterized by a wide distribution of relaxation times is valid on a very large scale of frequency.

The current status of our experiments on fractal silica aerogels is reviewed. Remarks are made concerning the direct space observations of the structure compared with reciprocal space measurements. The scaling of the intensities observed in the Raman scattering from fractons is analysed in the light of recent theoretical progess. The origin of, and evidence for, an elasticity cross-over in the fracton frequency range are discussed. The fracton dimension [dtilde] is clearly shown to be an additional dimension to characterize the fractal rather than a universal quantity.

Brillouin and neutron-scattering measurements of TA-phonon branches are reported for SrTiO3 at small wave vectors and at temperatures well below the 105 K structural transition. Anomalous softening in the former measurements, and dispersion in the latter, are found in the quantum paraelectric regime. Furthermore, an unexpected loss of scattered intensity is observed on the TA[100]-phonon branch at temperatures centred around 30 to 40 K.

Low-temperature thermal conductivity and time-dependent specific heat have been measured on mixed crystals of ${\mathrm{Rb}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(${\mathrm{NH}}_{4}$${)}_{\mathit{z}}$${\mathrm{H}}_{2}$${\mathrm{PO}}_{4}$ (x=0.35,0.72), in the composition range in which an electric dipole glass state forms below \ensuremath{\sim}100 K. Glasslike excitations have been observed. In the fully deuterated isomorph with x=0.62, however, the thermal conductivity is that of a crystal, and glasslike excitations are only seen in the specific heat at very long times. This striking isotope effect shows that the low-energy excitations in these crystals relate to tunneling of protons or deuterons, respectively.

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.

International audience; Experimental results on the density of states and on the acoustic modes of glasses in the THz region are compared to the predictions of two categories of models. A recent one, solely based on an elastic instability, does not account for most observations. Good agreement without adjustable parameters is obtained with models including the existence of nonacoustic vibrational modes at THz frequency, providing in many cases a comprehensive picture for a range of glass anomalies.

International audience; There exists a special interest in investigating acoustical and optical vibrations of glasses in the one THz frequency region. The main experimental tools that are used to this effect are briefly discussed. The current understanding of the boson-peak vibrations and of their resonance with acoustic branches are explained. Specific new results on the origin of the boson peak and on the end of acoustic branches are presented for borates.

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.

Hyper-Raman scattering has been measured on vitreous boron oxide, $v-$B$_2$O$_3$. This spectroscopy, complemented with Raman scattering and infrared absorption, reveals the full set of vibrations that can be observed with light. A mode analysis is performed based on the local D$_{3h}$ symmetry of BO$_3$ triangles and B$_3$O$_3$ boroxol rings. The results show that in $v-$B$_2$O$_3$ the main spectral components can be succesfully assigned using this relatively simple model. In particular, it can be shown that the hyper-Raman boson peak arises from external modes that correspond mainly to librational motions of rigid boroxol rings., 13 pages, 11 figures, 2 tables

A Comment on the Letter by T. Scopigno et al., [Phys. Rev. Lett. 96, 135501 (2006)]. The authors of the Letter offer a Reply.

The hydrogen-bond network formed from a crystalline solution of ferroelectric RbH_2PO_4 and antiferroelectric NH_4H_2PO_4 demonstrates glassy behavior, with proton tunneling the dominant mechanism for relaxation at low temperature. We characterize the dielectric response over seven decades of frequency and quantitatively fit the long-time relaxation by directly measuring the local potential energy landscape via neutron Compton scattering. The collective motion of protons rearranges the hydrogen bonds in the network. By analogy with vortex tunneling in superconductors, we relate the logarithmic decay of the polarization to the quantum-mechanical action.

Hyper-Raman scattering spectra of vitreous B$_2$O$_3$ are reported and compared to Raman scattering results. The main features are indexed in terms of vibrations of structural units. Particular attention is given to the low frequency boson peak which is shown to relate to out-of-plane librations of B$_3$O$_3$ boroxol rings and BO$_3$ triangles. Its hyper-Raman strength is comparable to that of cooperative polar modes. It points to a sizeable coherent enhancement of the hyper-Raman signal compared to the Raman one. This is explained by the symmetry of the structural units., 4 pages, 3 figures