A TSM study of the phonon dispersion in a high superconducting transition metal carbide TaC

Phonon dispersion in transition metal carbides has recently attracted the attention of a numbers of experimental and theoretical physicists particularly because of their superconducting behaviour. In particular the large superconducting transition temperatures observed in some cases are believed to be directly related to certain anomalies in the phonon dispersion curves. An explanation of these anomalies has been provided by Weber et al. through a resonance effect by a modified shell model called the double shell model which introduces an additional shell of electrons and uses a free electron like screening in the interaction system. It has been shown that the anomalous wiggles in the phonon dispersion are also obtained in a three body force shell model calculation suitably modified to take account of the absence of the LST splitting in the longwave optical vibration modes. The TSM results of TaC are as good as the DSM results and prove the equivalence of the two models. This equivalence has been discussed by comparing the dynamical equations corresponding to the models. (author)