Phonon anomalies in transition-metal nitrides: HfN

Abstract

The phonon dispersion curves in HfN have been measured at room temperature in the high-symmetry directions $\ensuremath{\Delta}$, $\ensuremath{\Sigma}$, and $\ensuremath{\Lambda}$ by coherent inelastic neutron scattering. Anomalies in the dispersion of the acoustic branches have been detected which are similar to those that have already been reported for superconducting transition-metal compounds with nine valence electrons. The experimental results are well described by a double-shell model which is also used to calculate the density of states.