Charge-density distortions and lattice dynamics: A general theory and application to Nb

A general formulation is given of phenomenological models for lattice dynamics which use localized electronic variables as additional adiabatic degrees of freedom. This formulation encompasses shell models of all types, bond-charge models, and charge-fluctuation models. Restrictions due to symmetry are discussed. In a specific application to Nb, ${\Gamma }_1$ (scalar), and ${\Gamma }_{{25}^{\prime }}$ (quadrupolar) degrees of freedom are introduced. All symmetry-allowed parameters out to second-neighbor coupling are kept. The resulting 18-parameter model gives a good fit to the measured phonon dispersion, and a number of the parameters are found to be ignorable. The anomalies in the LA branches arise from interatomic-stabilized charge fluctuations, while the anomalies in TA branches are associated with dispersionless quadrupolar fluctuations. It is suggested that in a similar model for $A$ 15 metals, charge fluctuations alone might explain the TA anomalies.