TMatrix for a Substitutional Impurity in Diatomic fcc and bcc Lattices

The phonon scattering $T$ matrix is analyzed according to the irreducible representations of the point group pertaining to the perturbation caused by a substitutional impurity in the diatomic fcc and bcc lattices. The effects due to change in mass at the impurity site and the changes in the nearest-neighbor central- and noncentral-force constants for the impurity-host-crystal interaction are taken into account. Relations between lattice Green's functions are derived for the nearest-neighbor interactions in the pure lattice. Simple expressions for the irreducible representations of the $T$ matrix are obtained, by assuming only central forces.