We have used the Real Space Green's-function technique to study the vibrational properties of the Si0.5Ge0.5 alloy. Our results reproduce correctly the three-mode behavior, which can not be obtained by the mean field approximation such as CPA. Our calculation also correctly predicts the intensities of the peaks associated with the three modes which can not be easily obtained by the supercell approach.
We have formulated a scheme to study the dynamics of a random overlayer on a substate such as AxB1-x/B(110) where species A or B forms an FCC metal. Detailed formulation for the calculation of the layer density of states from the surface to the deeper layers has been developed.