Raman scattering and the low-frequency vibrational spectrum of glasses

We present a theory of low-frequency Raman scattering in glasses, based on the concept that light couples to the elastic strains via spatially fluctuating elasto-optic (Pockels) constants. We show that the Raman intensity is not proportional to the vibrational density of states (as was widely believed), but to a convolution of Pockels constant correlation functions with the dynamic strain susceptibilities of the glass. Using the dynamic susceptibilities of a system with fluctuating elastic constants we are able for the first time to describe the Raman intensity and the anomalous vibration spectrum of a glass on the same footing. Good agreement between the theory and experiment for the Raman spectrum, the density of states, and the specific heat is demonstrated at the example of glassy As(2)S(3).     

Raman scattering in ZrB<Subscript>12</Subscript> cage glass

High-precision measurements of the Hall effect and Raman scattering have been performed for single crystals of ZrB₁₂ superconductor in the wide temperature range of 5–300 K. For ZrB₁₂, the boson peak with ω_max ~ 100 cm^–1 has been observed for the first time within the low-frequency range of the Raman spectrum I(ω). The sizes of vibrational clusters with the correlation length ranging from 25 to 35 Å are estimated. The relation between the renormalization of the low-frequency density of vibrational states accompanying the transition to the cage-glass phase (T* ~ 90 K) and the enhancement of superconductivity in ZrB₁₂ is discussed.     

Low frequency Raman scattering of anatase titanium dioxide nanocrystals

TiO₂ nanoparticle of size 7.8 nm are synthesized by wet chemical route and characterized by low-frequency Raman scattering (LFRS), transmission electron microscopy (TEM) and X-ray diffraction. The low frequency peaks in the Raman spectra have been explained using the Lamb's theory that predicts the vibrational frequencies of a homogeneous elastic body of spherical shape. Our results show that the observed low-frequency Raman scattering originates from the spherical (l=0) and quadrupolar vibrations (l=2) of the spheriodal mode due to the confinement of acoustic vibrations in TiO₂ nanoparticles. In addition to the low-frequency peak due to the vibrational quadrupolar and spheriodal modes, a band is also observed, which is assigned to the Raman forbidden torsional l=2 mode originating from the near spherical shape of the TiO₂ nanoparticles. The size distribution is also obtained from LFRS, which is in good agreement with TEM.     

Low-frequency raman scattering in the orientationally disordered phase of a C60 crystal

Low-frequency (3–120 cm^?1) Raman scattering in the orientationally disordered phase and the photopolymerized state of fullerite was investigated. Experimental data suggest that, by analogy with scattering in disordered media (glasses), the low-frequency spectra can be described in terms of scattering by the localized vibrational states.     

Origin of excess low-energy vibrations in densified B2O3 glasses

Low-temperature experiments of Raman scattering and heat capacity have been performed in a B₂O₃ glass, pressure quenched from 1200 °C in order to obtain the density as largest as possible (ρ = 2373 kg/m³). When compared to those of compacted B₂O₃ glasses having smaller density, the Raman spectrum of this glass exhibits a strong decrease of the intensities of the Boson peak and the band at 808 cm^?1, both the features being determined by the decrease of the boroxol ring population. Moreover, the Boson peak exhibits a large shift to 68 cm^?1 (from 26 cm^?1 observed in normal vitreous B₂O₃). The high atomic packing of the glassy network also leads to a marked decrease of the excess heat capacity over the Debye T³-behaviour characterizing the crystal. The density g(ν) of low-frequency vibrational states has been assessed by using the low-frequency Raman intensity to determine the temperature dependence of the low-temperature heat capacity. The observations performed over a wide range of glass densities are compared to the predictions of theoretical models and computer simulations explaining the nature of the Boson peak. Consistency with the results of a simulation study concerning the vibrations of jammed particles leads to evaluate a nanometre length scale which suggests the existence of poorly packed domains formed from several connected boroxols. These soft regions are believed to be the main source of low-frequency optic-like vibrations giving rise to the Boson peak.     

Vibrational anomalies and marginal stability of glasses

The experimentally measured vibrational spectrum of glasses strongly deviates from that expected in Debye’s elasticity theory: The density of states deviates from Debye’s ω² law (“boson peak”), the sound velocity shows a negative dispersion in the boson-peak frequency regime, and there is a strong increase in the sound attenuation near the boson-peak frequency. A generalized elasticity theory is presented, based on the model assumption that the shear modulus of the disordered medium fluctuates randomly in space. The fluctuations are assumed to be uncorrelated and have a certain distribution (Gaussian or otherwise). Using field-theoretical techniques one is able to derive mean-field theories for the vibrational spectrum of a disordered system. The theory based on a Gaussian distribution uses a self-consistent Born approximation (SCBA),while the theory for non-Gaussian distributions is based on a coherent-potential approximation (CPA). Both approximate theories appear to be saddle-point approximations of effective replica field theories. The theory gives a satisfactory explanation of the vibrational anomalies in glasses. Excellent agreement of the SCBA theory with simulation data on a soft-sphere glass is reached. Since the SCBA is based on a Gaussian distribution of local shear moduli, including negative values, this theory describes a shear instability as a function of the variance of shear fluctuations. In the vicinity of this instability, a fractal frequency dependence of the density of states and the sound attenuation ∝ ω^1+a is predicted with a ? 1/2. Such a frequency dependence is indeed observed both in simulations and in experimental data. We argue that the observed frequency dependence stems from marginally stable regions in a glass and discuss these findings in terms of rigidity percolation.     

Theoretical Study of Elastic Properties of Tungsten Disilicide

The plane-wave pseudopotential method using the generalized gradient approximation within the framework of density functional theory is applied to analyse the lattice parameters, elastic constants, bulk moduli, shear moduli and Young's moduli of WSi₂. The quasi-harmonic Debye model, using a set of total energy versus cell volume obtained with the plane-wave pseudopotential method, is applied to the study of the elastic properties and vibrational effects. The athermal elastic constants of WSi₂ are calculated as a function of pressure up to 35GPa. The relationship between bulk modulus and temperature up to 1200K is also obtained. Moreover, the Debye temperature is determined from the non-equilibrium Gibbs function. The calculated results are in good agreement with the experimental data.     

Raman scattering in dried DNA and crystalline amino acids

Raman spectrum characteristics of dried deoxyribonucleic acid (DNA) and two types of crystalline amino acids (L-lysine, D-asparagine) are compared in a wide range of frequencies, including the regions of lattice (7 to 200 cm^?1) and intramolecular (200 to 4000 cm^?1) vibrations. It is found that the spectral position of the low-frequency band in the Raman spectrum of DNA with a peak near 26 cm^?1 correlates with the Raman spectrum of high-Q low-frequency modes that manifest themselves in the crystalline amino acids under investigation. The low-frequency band of DNA refers to a twist-like vibrational mode of nucleobases. The intensities of this DNA mode and the high-Q lattice modes of the crystalline amino acids L-lysine and D-asparagine are several times as high as those of the Raman lines corresponding to the intramolecular modes. Resonant coupling of low-frequency modes of DNA and amino acid molecular chains is analyzed.     

Low-frequency Raman scattering in a polycrystalline C60 film: The role of orientational disorder

Low-frequency Raman scattering in the orientationally disordered phase of a polycrystalline C₆₀ film is investigated. By analogy with disordered media (glasses), the low-frequency Raman spectra are interpreted in terms of light scattering by localized vibrational states.     

First-Principles Calculations of Elastic and Thermal Properties of Molybdenum Disilicide

The first-principles plane-wave pseudopotential method using the generalized gradient approximation within the framework of density functional theory is applied to anaylse the equilibrium lattice parameters, six independent elastic constants, bulk moduli, thermal expansions and heat capacities of MoSi2. The quasi-harmonic Debye model, using a set of total energy versus cell volume obtained with the plane-wave pseudopotential method, is applied to the study of the elastic properties, thermodynamic properties and vibrational effects. The calculated zero pressure elastic constants are in overall good agreement with the experimental data. The calculated heat capacities and the thermal expansions agree well with the observed values under ambient conditions and those calculated by others. The results show that the temperature has hardly any effect under high pressure.     

Calculation of the effect of pressurizing gases on the resonant modes of single-crystal parallelepiped

Resonant ultrasound spectroscopy provides for an experimental determination of the elastic moduli of a solid sample. The moduli are extracted by matching a theoretically computed resonant spectrum to the experimental vibrational spectrum. To determine the pressure dependence of the moduli, the vibrational spectrum can be taken with the sample in a pressurizing gas. Then the extraction of the intrinsic, pressure dependent moduli requires a theoretical treatment which permits removal of the perturbation of the spectrum due to the surface loading by the pressure and shear waves in the gas. In order to illustrate a treatment which accomplishes this removal, the theoretically computed frequency shifts and the quality factors are reported for two single-crystal parallelepiped pressurized by noble gases.     

Features of the formation of silicon nanocrystals upon the annealing of SiO<Subscript>2</Subscript> layers implanted with Si ions

The effect of annealing on the ion-beam synthesis of silicon nanocrystals in Si layers was investigated by low-frequency Raman scattering (RS). The occurrence of crystal nuclei in a matrix of glass results in an additional contribution to density of the acoustic vibrational states associated with the surface vibrational modes of nanocrytals. The low-frequency RS caused by interaction of light with acoustic vibration modes of nanoparticles is an effective method of research. The low-frequency Raman spectra show that the samples do not have a smooth distribution of nanoparticle size, but have two specific sizes of nanoparticles, 3 and 6 nm.     

Elastic properties study of single crystal NH3 up to 26 GPa

Single crystal Brillouin and Raman scattering measurements on NH₃ in a diamond anvil cell have been performed under pressures up to 26 GPa at room temperature. The pressure dependencies of acoustic velocity, adiabatic elastic constants, and bulk moduli of ammonia from liquid to solid III and solid IV phase have been determined. All the nine elastic constants in orthorhombic structure phase IV were presented for the first time, each elastic constant grows monotonously with pressure and a crossover of the off‐diagonal moduli C₁₂ and C₁₃ was observed at around 12 GPa because of their different pressure derivative values. We also performed ab initio simulations to calculate the bulk elastic moduli for orthorhombic ammonia, the calculated bulk moduli agree well with experimental results. In Raman spectra the very weak bending modes ν₂ and ν₄ for orthorhombic ammonia are both observed at room temperature, a transition point near 12 GPa is also found from the pressure evolution of the Raman bands. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of rare earth (Pr2O3, Nd2O3, Sm2O3, Eu2O3, Gd2O3 and Er2O3 ) on the acoustic properties of glass belonging to bismuth-borate system

Bismuth-borate glasses doped with some rare earth ions were studied with respect to the density, molar volume and the elastic moduli, Poisson’s ratio, Debye temperature, microhardness, softening temperature, acoustic impedance, diffusion constant and latent heat of melting. Ultrasonic velocities were measured by the pulse echo overlap technique at a frequency of 10 MHz and at room temperature. From these velocities and density values, various elastic moduli were calculated. The correlation of elastic stiffness, the cross link density, and the fractal bond connectivity of these glasses are discussed. The derived experimental values of shear modulus, bulk modulus, Young’s modulus, and Poisson’s ratio for our glasses are compared with the theoretically calculated values in terms of the bond compression model and Makishima-Mackenize theory.     

Low temperature elastic behaviour of As-Sb-Se and Ge-Sb-Se glasses

The ternary glasses of arsenic and germanium with antimony and selenium can be prepared in large sizes for optical purposes. The elastic behaviour of eight compositions of each glass has been studied down to 4.2 K using a 10 MHz ultrasonic pulse echo interferometer. The glasses have a normal elastic behaviour, with the velocities gradually increasing as the temperature is lowered. An anharmonic solid model of Lakkad satisfactorily explains the temperature variations. The elastic moduli of Ge _x Sb₁₀Se_90?x glasses increase linearly as the Ge content is increased up to 25 at. % and beyond this the increase is nonlinear. (AsSb)₄₀Se₆₀ glasses show a linear increase in elastic moduli with increasing Sb content. The elastic moduli of As _x Sb₁₅Se_85?x glasses exhibit a drastic change near the stoichiometric composition As₂₅Sb₁₅Se₆₀. These behaviours have been qualitatively explained on the basis of the structural changes in glasses.     

Rayleigh-ritz calculation of the resonant modes of a solid parallelepiped in a pressurizing fluid

Resonant ultrasound spectroscopy relies on comparisons of experimentally determined vibrational spectra to theoretically computed spectra for the extraction of the elastic moduli of the solid samples. To determine the pressure dependence of these moduli, resonant spectra are taken for samples pressurized by a surrounding gas and knowledge of the contribution of the surface loading of the sample by the gas is needed in order to extract the intrinsic pressure dependence of the moduli. To facilitate the required comparisons, a Rayleigh-Ritz variational calculation of the vibrational spectrum is formulated which includes the loading of the solid by the pressurizing fluid. This formalism is used to compute the effect of gas loading on the vibrational spectrum of an isotropic, solid parallelepiped.     

Glasses for Raman nonlinear optics

The Raman effect, by which light is frequency shifted by a vibrational mode, enters into a number of phenomena in nonlinear optics. Here, we summarize our progress in identifying glass materials with potentially useful Raman properties, methods for measuring the strength of the Raman effect and its spectral dependence, and the properties of a number of different families of glasses. Glasses with both larger peak Raman susceptibilities and larger bandwidths relative to fused silica are reported.     

Influence of pressure on the boson peak: stronger than elastic medium transformation

We study the changes in the low-frequency vibrational dynamics of poly(isobutylene) under pressure up to 1.4 GPa, corresponding to a density change of 20%. Combining inelastic neutron, x-ray, and Brillouin light scattering, we analyze the variations in the boson peak, transverse and longitudinal sound velocities, and the Debye level under pressure. We find that the boson peak variation under pressure cannot be explained by the elastic continuum transformation only. Surprisingly, the shape of the boson peak remains unchanged even at such high compression.     

Study of the broadening of the rotational Raman lines of CO2 perturbed by rare gases

This paper presents the results of an experimental and theoretical study of the broadening of the rotational Raman lines of the linear molecule CO₂ perturbed by rare gases: helium, neon and argon. In the first part, the experimental set-up and the method to deduce linewidths from the spectra are presented. This method is similar to that used by Welsh et al. although we take into account the contribution of the molecules in the (01¹0) vibrational state for which the rotational quantum number J can be odd. The results for the pressure broadening coefficient are then given for several values of J. We then briefly recall how one can derive collision cross sections from the measured linewidths. The second part is devoted to an attempt to interpret the experimental results in terms of the theory of the Raman linewidths developed by Van Kranendonk. After recalling briefly the assumptions used in that theory and discussing the intermolecular potentials that are used, we present the results of numerical calculations performed with several types of anisotropic interaction potentials between CO₂ and the atom of rare gas. We reach the conclusion that the approximate methods used by Van Kranendonk (matrix elements of the evolution operator S computed by second order perturbation theory) are probably inadequate to calculate the effect of elastic collisions that disorient the molecule. It is suggested that it might be advantageous to consider anisotropic forces of shorter range than the anisotropic London dispersion forces derived from an r^-6 potential.     

Elastic and Raman scattering of 8.5–11.4 MeV photons from 159Tb, 165Ho and 237Np

Differential cross sections for elastic and inelastic Raman scattering from the deformed heavy nuclei ¹⁵⁹Tb, ¹⁶⁵Ho and ²³⁷Np were measured at five energies between 8.5 and 11.4 MeV. Angular distributions at four angles between 90° and 140° for both elastic and inelastic scattering at 9.0 and 11.4 MeV were also measured. The monoenergetic photons were obtained from thermal neutron capture in Ni and Cr. All the angular distributions and the elastic and Raman scattering at the higher energies are in good overall agreement with theoretical predictions. The theory is based on a modified simple rotator model of the giant dipole resonance in which the effect of Delbrück scattering was included. A trend of both the elastic and Raman scattering at lower energies to be stronger than expected are suggested by the data. However, the ratio between the Raman and elastic scattering seem to be in good agreement with theory throughout the whole energy range. This shows that there is no need to introduce a direct nonresonant component to the imaginary part of the elastic scattering amplitude to explain the experimental data.