Electronically Driven Lattice Instabilities

A general and physically simple model based on rigorous formulations of the dielectric function is presented and used to explain the phonon anomalies in niobium and niobium carbide. The model contains the explicit $q$ dependence of both the electron-phonon and electron-electron interactions for localized states near the Fermi energy and appears quite useful for explaining the $q$ dependence of phonon anomalies and lattice instabilities in various systems.