I have been studying the lattice vibrations of amorphous silicon using a realistic model of the atomic coordinates and the interatomic forces. The picture above shows the vibrational densities of states of both crystalline and amorphous silicon. There is surprisingly little change when crystalline order is lost. However, the nature of the vibrational normal modes does change.
Crystalline silicon has vibrations which can be classified by wavevector and by branch.
Transverse branches involve atom motions perpendicular to the direction of propagation. These vibrations do not stretch the bonds very much. Longitudinal branches cause large stretches of bonds. In the low-frequency part of the spectrum, the crystalline modes clearly separate into these very different categories. The vibrational normal modes of amorphous silicon completely lose this differentiation.