Lattice Vibrations in Crystals with Molecular Impurity Centers

The Green's function formalism of Lifshitz and others for the calculation of lattice vibrations in impure crystals is restricted to disturbed lattices with an unchanged number of particles (monatomic impurity centers). A method is given here which reduces the problem of polyatomic impurities to the Lifshitz formalism. This is achieved by means of a molecular Green's function which describes the influence of the molecular particles as an effective disturbance among the lattice particles, excluding the molecular coordinates themselves.