High frequency sound and the boson peak in amorphous silica

We present the results: of extensive molecular dynamics computer simulations in which the high frequency dynamics of silica, i.e. for frequencies nu > 0.5 THz, is investigated in the viscous liquid state as well as in the glass state. We characterize the properties of high frequency sound modes by analyzing J(1) (q, v) and J(t) (q, v), the longitudinal and transverse current correlation function, respectively. For wave-vectors q > 0.4 Angstrom (-1) the spectra are sitting on top of a flat background. The dynamic structure factor S(q, v) exhibits for q > 0.23 Angstrom (-1) a boson peak which is located nearly independent of q around 1.7 THz and for which the intensity scales approximately linearly with temperature. We show that the low frequency part of the boson peak is mainly due to the elastic scattering of transverse acoustic modes with frequencies around 1 THz. The strength of this scattering depends on q and is largest around q = 1.7 Angstrom (-1), the location of the first sharp diffraction peak in the static structure factor. By studying S(q, v) for different system sizes we show that strong finite size effects are present in the low frequency part of tire boson peak in that for small systems part of its intensity is: missing. We discuss the consequences of these finite size effects for the structural relaxation.