Local vibrational modes in crystal lattices with a simply connected region of the quasi-continuous phonon spectrum

Abstract

It is shown that the use of the mode classification adopted in the Jacobi matrix method and which is the most natural one for describing localized states leads to extremely rapid convergence of the Green functions for frequencies lying outside the quasi-continuum band of the crystal. This has made it possible to obtain rather general analytical expressions for the conditions of formation and the characteristics of local modes due to the presence of light impurity atoms in crystal lattices having a simply connected region of the quasi-continuous phonon spectrum. The accuracy with which the frequencies and intensities of the local modes are determined using these expressions is illustrated for examples of light substitutional impurities (isotopic and weakly coupled) and close-packed structures (fcc and hcp) and also isolated pairs of isotopic impurities in an fcc crystal lattice. In particular, the results permit simple and extremely accurate evaluation of the parameters of the host lattice and defect from the known values of the local frequencies.