Atomic vibrations in disordered systems: Comparison of disordered diamond lattices and a realistic amorphous silicon model

Force-constant and positional disorder have been introduced into diamond lattice models in an attempt to mimic the vibrational properties of a realistic amorphous silicon model. Neither type of disorder is sufficient on its own to mimic the realistic model. By comparing the spectral densities of these models, it is shown that a combination of both disorders is a better representation, but still not completely satisfactory. Topological disorder in these models was investigated by renumbering the atoms and examining the dynamical matrix graphically. The dynamical matrix of the realistic model is similar to that of a positionally-disordered lattice model, implying that the short-range order in both systems is similar.