Vibrational amplitudes in vitreous silica

A model structure of vitreous silica, for which the vibrational frequencies and eigenmodes were calculated from first principles, is used to investiga te vibrational amplitudes. Calculated mean-square displacements for oxygen and silicon atoms are obtained as a function of temperature. The square dis placement tensors of oxygen atoms show a marked anisotropic character, whic h is related to the local geometry. The displacements of oxygen atoms along the three principal directions can be associated to distinct parts of the vibrational spectrum, as evidenced by their thermal dependence. These aniso tropic effects directly affect the elastic and the static structure factors , which are sensitive to the correlation between displacements of different atoms along their connecting direction. This description shows that the ob served widths for Si-O and O-O correlations mainly derive from atomic vibra tions rather than from structural disorder. Anisotropic correlations betwee n different atoms are shown to be important up to a distance of 4 Angstrom, i.e., involving atoms that belong to corner-sharing tetrahedra. The scatte ring functions, calculated at finite temperature and in the harmonic approx imation, show good agreement with experiment. In particular, the comparison between the static and the elastic structure factors yields a characteriza tion of the correlated displacements in accord with experimental observatio ns. The static structure factor is significantly affected by anisotropic co rrelations, but shows only a weak dependence on temperature between 0 and 3 00 K.