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    Vibrational Dynamics of Non-Crystalline Solids

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    The boson peak (BP) is an excess of vibrational states over the Debye law appearing at terahertz frequencies. It is found in all glasses and marks the crossover between the long-wavelength behavior, where the solid can be considered as an isotropic continuum, and the region where the wavelength of the sound wave starts to experience the microscopic details of the structure. This chapter is devoted to a review of the main experimental observations regarding the vibrational dynamics of amorphous solids, as detected by neutron and X-ray scattering techniques. A first part of the chapter is devoted to the measurements of the BP and its evolution as a function of external parameters, such as temperature, pressure, or density. The second part of the chapter reviews the wavevector evolution of the dynamic structure factor, which provides evidence of a pseudo-acoustic propagating mode up to frequencies comparable to those of the BP. This longitudinal mode has a sound attenuation which follows ..

    Sound Attenuation at Terahertz Frequencies and the Boson Peak of Vitreous Silica

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    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

    Liquid nitrogen cooled Si crystal monochromator: x-ray focusing by controlled heat load

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    The thermal deformation of a liquid nitrogen cooled silicon crystal under increasing absorbed power undergoes five phases: i) no deformation at zero power, ii) concave shape of the crystal, iii) appearance of a central bump, iv) minimum of the slope error averaged over the beam footprint on the crystal due to the balance between the initial concave shape and the growing central bump, and v) rapid growth of the thermal bump. In general, a liquid nitrogen cooled silicon crystal is designed to operate before the appearance of phase v), and mostly in phase ii) (concave shape). This concave shape of the crystal leads to a focusing effect on the beam, which should be considered in combination with other optical elements in the design and optimization of the beamline optical layout. © 2013 IOP Publishing Ltd

    Elastic anomalies at terahertz frequencies and excess density of vibrational states in silica glass

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    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)]
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