Abstract
The dynamical structure factor, S( Q, E), of a model system, based on a percolator and using the harmonic approximation, has been calculated using the moments method especially in the smaller Q region. With this particular growth algorithm we calculate systems with densities as small as few percent of the complete lattice. The variation of the width of the Brillouin peak with density and its dependence on the exchanged wavevector are compared with the experimental data available for amorphous silica at different densities. The results show that the dynamical properties of sparse materials, such as aerogels and xerogels, can be reproduced considering only the dynamic of their network neglecting the contribution of the elemental units forming the network.
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