Scaling the Temperature-dependent Boson Peak of Vitreous Silica with the high-frequency Bulk Modulus derived from Brillouin Scattering Data

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.Comment: Accepted for publication in Physical Review Letter

High frequency sound waves in vitreous silica

We report a molecular dynamics simulation study of the sound waves in vitreous silica in the mesoscopic exchanged momentum range. The calculated dynamical structure factors are in quantitative agreement with recent experimental inelastic neutron and x-ray scattering data. The analysis of the longitudinal and transverse current spectra allows to discriminate between opposite interpretations of the existing experimental data in favour of the propagating nature of the high frequency sound waves.Comment: 4 pages, Revtex, 4 ps figures; to be published in Phys. Rev. Lett., February 198

Acoustic damping in Li2_2O-2B2_2O3_3 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 \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, Franc

Phonons from neutron powder diffraction

The spherically averaged structure function \soq obtained from pulsed neutron powder diffraction contains both elastic and inelastic scattering via an integral over energy. The Fourier transformation of \soq to real space, as is done in the pair density function (PDF) analysis, regularizes the data, i.e. it accentuates the diffuse scattering. We present a technique which enables the extraction of off-center phonon information from powder diffraction experiments by comparing the experimental PDF with theoretical calculations based on standard interatomic potentials and the crystal symmetry. This procedure (dynamics from powder diffraction(DPD)) has been successfully implemented for two systems, a simple metal, fcc Ni, and an ionic crystal, CaF$_{2}$. Although computationally intensive, this data analysis allows for a phonon based modeling of the PDF, and additionally provides off-center phonon information from powder neutron diffraction

Multiple-scattering effects on incoherent neutron scattering in glasses and viscous liquids

Incoherent neutron scattering experiments are simulated for simple dynamic models: a glass (with a smooth distribution of harmonic vibrations) and a viscous liquid (described by schematic mode-coupling equations). In most situations multiple scattering has little influence upon spectral distributions, but it completely distorts the wavenumber-dependent amplitudes. This explains an anomaly observed in recent experiments

Dielectric and thermal relaxation in the energy landscape

We derive an energy landscape interpretation of dielectric relaxation times in undercooled liquids, comparing it to the traditional Debye and Gemant-DiMarzio-Bishop pictures. The interaction between different local structural rearrangements in the energy landscape explains qualitatively the recently observed splitting of the flow process into an initial and a final stage. The initial mechanical relaxation stage is attributed to hopping processes, the final thermal or structural relaxation stage to the decay of the local double-well potentials. The energy landscape concept provides an explanation for the equality of thermal and dielectric relaxation times. The equality itself is once more demonstrated on the basis of literature data for salol.Comment: 7 pages, 3 figures, 41 references, Workshop Disordered Systems, Molveno 2006, submitted to Philosophical Magazin

Observation of Umklapp processes in non-crystalline materials

Umklapp processes are known to exist in cristalline materials, where they control important properties such as thermal conductivity, heat capacity and electrical conductivity. In this work we report the provocative observation of Umklapp processes in a non-periodical system, namely liquid Lithium. The lack of a well defined periodicity seems then not to prevent the existence of these scattering processes mechanisms provided that the local order of the systems i.e. the maxima of the static structure factor supply the equivalent of a reciprocal lattice vector in the case of cristalline materials.Comment: 13 pages P

Energy landscape - a key concept for the dynamics of glasses and liquids

There is a growing belief that the mode coupling theory is the proper microscopic theory for the dynamics of the undercooled liquid above a critical temperature T_c. In addition, there is some evidence that the system leaves the saddlepoints of the energy landscape to settle in the valleys at this critical temperature. Finally, there is a microscopic theory for the entropy at the calorimetric glass transition T_g by Mezard and Parisi, which allows to calculate the Kauzmann temperature from the atomic pair potentials. The dynamics of the frozen glass phase is at present limited to phenomenological models. In the spirit of the energy landscape concept, one considers an ensemble of independent asymmetric double-well potentials with a wide distribution of barrier heights and asymmetries (ADWP or Gilroy-Phillips model). The model gives an excellent description of the relaxation of glasses up to about T_g/4. Above this temperature, the interaction between different relaxation centers begins to play a role. One can show that the interaction reduces the number of relaxation centers needed to bring the shear modulus down to zero by a factor of three.Comment: Contribution to the III Workshop on Nonequilibrium Phenomena in Supercooled Fluids, Glasses and Amorphous Materials, 22-27 September 2002, Pisa; 14 pages, 3 figures; Version 3 takes criticque at Pisa into account; final version 4 will be published in J.Phys.: Condens.Matte

Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega)/\omega^2$ as a precursor of the instability. We argue that this peak is the analogon of the "boson peak", observed in structural glasses. By means of the level distance statistics we show that the peak is not associated with localized states

The crossover from propagating to strongly scattered acoustic modes of glasses observed in densified silica

Spectroscopic results on low frequency excitations of densified silica are presented and related to characteristic thermal properties of glasses. The end of the longitudinal acoustic branch is marked by a rapid increase of the Brillouin linewidth with the scattering vector. This rapid growth saturates at a crossover frequency Omega_co which nearly coincides with the center of the boson peak. The latter is clearly due to additional optic-like excitations related to nearly rigid SiO_4 librations as indicated by hyper-Raman scattering. Whether the onset of strong scattering is best described by hybridization of acoustic modes with these librations, by their elastic scattering (Rayleigh scattering) on the local excitations, or by soft potentials remains to be settled.Comment: 14 pages, 6 figures, to be published in a special issue of J. Phys. Condens. Matte