Lattice Dynamics of Transition-Metal Carbides

The phonon dispersion relations of ZrC, NbC, HfC, TaC, and UC are investigated using a phenomenological-model theory. For the transition-metal carbides, a shell model with a free-electron screening is used to describe the over-all shape of the phonon curves. The results strongly support the "covalent model," where the extreme physical properties of these compounds are attributed mainly to strong covalent metal-nonmetal bonding. In contrast, for UC the "interstitial-alloy" picture seems to be more appropriate. The pronounced anomalies in the acoustic branches of TaC and NbC occur at certain $\overrightarrow{\mathrm{q}}$ values which are directly related to definite lattice vectors. We interprete the anomalies as originating from a resonancelike increase of the electronic polarizability due to strong short-range correlations of the $d$ conduction electrons. In a model theory, we represent this $d$ charge density by a further electronic degree of freedom at the metal-ion sites, i.e., a second shell. Calculations with this "double-shell model" show very good agreement with experimental data. It is strongly indicated that the anomalies are caused by $d$ electrons of $T_{2g}$ symmetry. The connections to structural phase transitions are discussed.