Coherent-potential approximation for the lattice vibrations of mixed diatomic systems

We generalize the coherent-potential approximation (CPA) for the lattice dynamics of mass-disordered systems to the case of mixed diatomic crystals. Specific results are obtained for a one-dimensional model. We prove that for mass defects on only one sublattice the CPA self-energy is nonzero only on that sublattice. We compare the configuration-averaged density of states calculated by the CPA with computer experiments on several mixed diatomic chains. We compare the CPA dielectric susceptibility for the one-dimensional model with the experimental optical properties of several interesting III-V, II-VI, and I-VII mixed crystals. With some qualifications we conclude that the CPA in one-dimension can explain the switching from one-mode- to two-mode-type behavior observed in some III-V mixed systems and unexplained by previous theories. Finally, we present a one-dimensional CPA phase diagram for the transition from one optic band to two optic bands in the density of states.