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 q⃗ 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.