Frequencies of Localized Vibrations of a Diatomic Simple Cubic Lattice with a Point Imperfection

Frequencies of localized vibrational modes are calculated for a diatomic simple cubic lattice containing a substitutional impurity atom or a hole. Numerical values of Green's functions are obtained, which will be useful for the investigation of localized modes appearing in the gap between the optical and the acoustical bands. In the case of a substitutional impurity atom diagrams representing the dependence of the squared-frequencies of localized modes on parameters characterizing the impurity atom are obtained according as the case whether an atom of heavier mass or that of lighter mass is replaced by it. In the case of a hole, it is shown that localized modes appear near the bottom of the optical band if and only if an atom of heavier mass is replaced by it.