High frequency sound and the boson peak in amorphous silica

Abstract

We present the results of extensive molecular dynamics computer simulations in which the high frequency dynamics of silica, 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_l(q,nu) and J_t(q,nu), 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 which is due to multiphonon excitations. In the acoustic frequency band, i.e. for nu<20 THz, the intensity of J_l(q,nu) and J_t(q,nu) in the liquid and the glass approximately proportional to temperature, in agreement with the harmonic approximation. In contrast to this, strong deviations from a linear scaling are found for nu>20 THz. The dynamic structure factor S(q,nu) exhibits for q>0.23 Angstrom^{-1} a boson peak which is located nearly independent of q around 1.7 THz. 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,nu) for different system sizes we show that strong finite size effects are present in the low frequency part of the 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.