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 the Rayleigh scattering law and a negative dispersion that can partially explain the deviation from the Debye law. At higher frequencies, the inelastic spectrum presents a complex pattern of vibrations, with evidences of two peaks in various systems. To conclude, we will highlight the information that can be gained on the nature of the glass vibrational modes from a comparison with the dynamics of the corresponding polycrystal.
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