The propagation and damping of the acoustic excitations in vitreous silica is measured at terahertz frequencies using inelastic x-ray scattering. The apparent sound velocity shows a marked dispersion with frequency while the sound attenuation undergoes a crossover from a fourth to a second power law frequency dependence. This finding solves a recent controversy concerning the location of this crossover in vitreous silica, clarifying that it occurs at the position of the glass-characteristic excess of vibrational modes known as boson peak, and thus establishing a direct connection between boson peak and acoustic dispersion curves.

We measured the density of vibrational states (DOS) and the specific heat of various glassy and crystalline polymorphs of SiO 2 . The typical (ambient) glass shows a well-known excess of specific heat relative to the typical crystal (α-quartz). This, however, holds when comparing a lower-density glass to a higherdensity crystal. For glassy and crystalline polymorphs with matched densities, the DOS of the glass appears as the smoothed counterpart of the DOS of the corresponding crystal; it reveals the same number of the excess states relative to the Debye model, the same number of all states in the low-energy region, and it provides the same specific heat. This shows that glasses have higher specific heat than crystals not due to disorder, but because the typical glass has lower density than the typical crystal. DOI: 10.1103/PhysRevLett.112.025502 PACS numbers: 63.20.-e, 07.85.-m, 76.80.+y The low-temperature thermodynamic properties of glasses are accepted to be anomalously different from those of crystals due to the inherent disorder of the glass structure. At temperatures of ∼10 K, the specific heat of glasses shows an excess relativetothatofthecorrespondingcrystals.Theexcessspecific heat is related to a distinct feature in the spectrum of the atomic vibrations: At frequencies of ∼1 THz, glasses exhibit an excess of states above the Debye level of the acoustic waves, the socalled "boson peak." The excess of specific heat and the boson peak are universally observed for all glasses and by all relevant experimental techniques. However, the results still do not converge to a unified answer to how disorder causes these anomalies.Themajorityofthemodelsexplainthebosonpeakbyappealing tovarious glass-specific features. Theseincludelow-energy optical modes [1], onset of mechanical instability related to saddle points in the energy landscape [2] or to jamming [3][4][5], local vibrationalmodes of clusters [6] or locally favoured structures [7], librations [8] or other coherent motions [9] of molecular fragments, crossover of local and acoustic modes [10], quasilocal vibrations of atoms in an anharmonic potential [11], broadening of vibrational states in the Ioffe-Regel crossover regime [12], spatial variation of the elastic moduli [13], breakdown of the continuum approximation [14,15], and topologically diverse defects [16], to cite the most important ones.Alternatively, the boson peak is identified as the counterpart of the acoustic van Hove singularities of crystals, i.e., explained by the piling up of the vibrational states of the acousticlike branches near the boundary of the pseudoBrillouin zone [17][18][19][20].Diverging in explanations of the boson peak, all models agree that the excess states and the excess specific heat of

We report measurements of the sound attenuation coefficient in vitreous silica, for sound waves of wavelength between 50 and 80 nm, performed with the new inelastic UV light scattering technique. These data indicate that in silica glass a crossover between a temperature-dependent (at low frequency) and a temperature-independent (at high frequency) acoustic attenuation mechanism occurs at Q 0:15 nm ÿ1 . The absence of any signature in the static structure factor at this Q value suggests that the observed crossover should be associated with local elastic constant fluctuations. DOI: 10.1103/PhysRevLett.97.035501 PACS numbers: 61.43.Fs, 63.50.+x The sound attenuation in disordered materials and its frequency and wavelength dependence are the result of the interplay between two physical mechanisms: one is due to the anharmonicity of the interparticle interactions, and the other to the structural disorder.The anharmonic attenuation of an acoustic sound wave, identified by its wavelength , frequency , and wave vector Q 2 = , is characterized by a specific, temperature-dependent, relaxation time r [1]. At low frequency (! r < 1) this process dominates the sound absorption through mechanisms such as, e.g., the Akhiezer mechanism [2,3]. Accordingly, the sound attenuation coefficient, as measured by the broadening ÿ of the Brillouin peak in the dynamic structure factor S Q; ! , scales as ! 2 and Q 2 . At high frequency ÿ! r > 1, i.e., Q > Q r 1=v r , where v is the sound velocity, the anharmonic attenuation becomes frequency independent [1][2][3].The sound attenuation associated with topological disorder gives rise to a steeper Q dependence of ÿ Q . If Rayleigh scattering is responsible for this attenuation, ÿ / Q 4 is expected for wavelengths larger than the typical defects size 2 =Q R . For Q > Q R , when the Rayleigh scattering regime is abandoned, one expects that ÿ Q is no longer / Q 4 . Experimentally, for Q larger than 1 nm ÿ1 , all glasses studied so far show ÿ / Q x , with x very close to 2 [4,5].This scenario can be summarized by a three-regime behavior of ÿ Q : (i) at low Q, ÿ Q is determined by anharmonic processes, and ÿ Q / Q 2 up to a first (temperature-dependent) crossover Q r 1=v r ; (ii) an intermediate regime, where the Q dependence of ÿ Q is determined by the system dependent strengths of anharmonicity and structural disorder processes; (iii) a high-Q regime, where ÿ Q is determined by the topological disorder and ÿ Q / Q 2 with a temperature-independent coefficient. This picture is highly debated because it critically depends on the location of Q r and Q R in different glasses. In densified v-SiO 2 , for example, the crossover Q R has been hypothesized to be around 2 nm ÿ1 [6].In the most studied case of vitreous silica, similarly to what happens in many other glasses, both Q r and Q R belong to a Q region which is not directly accessed by traditional scattering probes. In the case of v-SiO 2 , clear evidence is reported for the low-and high-Q quadratic behaviors of ÿ Q , using Brillouin light scat...

Raman, Brillouin light, and x-ray scattering measurements have been carried out to characterize the low-frequency vibrational dynamics of the SiO(2) glass as function of its density. The obtained results demonstrate that while the distribution of the low-frequency states in the boson peak range is conserved under densification, these modes do not shift as a function of density as the acoustic modes do. The clear difference between the behavior of the vibrational states in the Boson peak range and that of the acoustic modes, could be explained considering the contribution of specific nonacoustic modes (tetrahedra rotation

We study the temperature dependence of acousticlike excitations measured by means of inelastic x-ray scattering at terahertz frequencies in silica glass. The apparent sound velocity shows, between 300 and 1600 K, the same temperature variation measured, at lower frequencies, by Brillouin light scattering. On the contrary the vibrations at the boson peak (BP) present a much stronger temperature dependence, as indicated by neutron scattering data. The measured dispersion and damping are used to compute the contribution to the vibrational density of states (VDOS) coming from the propagating acousticlike modes. This part of the VDOS accounts only for a fraction of the BP intensity, indicating that other kinds of excitation accumulate in this frequency range. It is consequently not surprising that the BP does not follow the temperature evolution of the Debye frequency, which describes the modification of the continuum medium. Finally we present a comparison between the experimentally accessible quantities and a recently proposed model for the vibrations in glasses, based on the assumption of random spatial variations of the shear modulus [Schirmacher, Europhys. Lett. 73, 892 (2006)].

We investigate a $d$-dimensional model ($d$ = 2,3) for sound waves in a disordered environment, in which the local fluctuations of the elastic modulus are spatially correlated with a certain correlation length. The model is solved analytically by means of a field-theoretical effective-medium theory (self-consistent Born approximation) and numerically on a square lattice. As in the uncorrelated case the theory predicts an enhancement of the density of states over Debye's $\omega^{d-1}$ law (``boson peak'') as a result of disorder. This anomay becomes reinforced for increasing correlation length $\xi$. The theory predicts that $\xi$ times the width of the Brillouin line should be a universal function of $\xi$ times the wavenumber. Such a scaling is found in the 2d simulation data, so that they can be represented in a universal plot. In the low-wavenumber regime, where the lattice structure is irrelevant there is excellent agreement between the simulation at small disorder. At larger disorder the continuum theory deviates from the lattice simulation data. It is argued that this is due to an instability of the model with stronger disorder.Comment: 5 pages, 3 figures, to be published in physica status solidi (c) March 200

Still very little is known on the relaxation dynamics of glasses at the microscopic level due to the lack of experiments and theories. It is commonly believed that glasses are in a dynamical arrested state, with relaxation times too large to be observed on human time scales. Here we provide the experimental evidence that glasses display fast atomic rearrangements within a few minutes, even in the deep glassy state. Following the evolution of the structural relaxation in a sodium silicate glass, we find that this fast dynamics is accompanied by the absence of any detectable aging, suggesting a decoupling of the relaxation time and the viscosity in the glass. The relaxation time is strongly affected by the network structure with a marked increase at the mesoscopic scale associated with the ion-conducting pathways. Our results modify the conception of the glassy state and asks for a new microscopic theory.

We present x-ray photon correlation spectroscopy measurements of the atomic dynamics in a Zr 67 Ni 33 metallic glass, well below its glass transition temperature. We find that the decay of the density fluctuations can be well described by compressed, thus faster than exponential, correlation functions which can be modeled by the well-known Kohlrausch-Williams-Watts function with a shape exponent β larger than one. This parameter is furthermore found to be independent of both waiting time and wave-vector, leading to the possibility to rescale all the correlation functions to a single master curve. The dynamics in the glassy state is additionally characterized by different aging regimes which persist in the deep glassy state. These features seem to be universal in metallic glasses and suggest a nondiffusive nature of the dynamics. This universality is supported by the possibility of describing the fast increase of the structural relaxation time with waiting time using a unique model function, independently of the microscopic details of the system.