Long‐Wavelength Optical Phonons in Mixed Crystals : I. A System of Two Coupled Modes

Abstract

Abstract A model is presented which for the first time provides a description of the long‐wavelength phonons in mixed crystals of the type AB 1−x C x as a system of two coupled modes: a lattice mode in a virtual crystal approximation (VCA) and a localized (or quasi‐localized) mode of the disordered sub‐lattice. These two modes interact by effects beyond the VCA, namely by the difference of the vibrational frequencies of the atoms B and C perceived by the atom A. Two cases will occur: (i) The two modes interact only weakly over the entire composition range. Then a lattice‐like mode and – as a new result — in addition a mode in which the disordered sub‐lattice is nearly involved alone are present over the entire composition range. This leads to the traditionally named one‐mode behaviour. (ii) The two modes become resonant at a certain composition and interact strongly. This leads to the two‐mode behaviour. The dielectric function assumes a form typical for the presence of two oscillators for both types of mode behaviour.