Lattice vibrational properties of transition metal carbides (TiC, ZrC and HfC) have been presented by including the effects of free-carrier doping and three-body interactions in the rigid shell model. The short-range overlap repulsion is operative up to the second neighbour ions. An excellent agreement has been obtained between theory and experiment for their phonon dispersion curves and Debye temperature variations. It is concluded that the contributions of free-carrier doping and three-body interactions are essential for the description of the lattice dynamics of these carbides.

Harmonic dynamical behaviour of thallous halides (TlCl and TlBr) have been studied using the new van der Waals three-body force shell model (VTSM), which incorporates the effects of the van der Waals interaction along with long-range Coulomb interactions, three-body interactions and short-range second neighbour interactions in the framework of rigid shell model (RSM). Phonon dispersion curves (PDC), variations of Debye temperature with absolute temperature and phonon density of state (PDS) curves have been reported for thallous halides using VTSM. Comparison of experimental values with those of VTSM and TSM are also reported in the paper and a good agreement between experimental and VTSM values has been found, from which it may be inferred that the incorporation of van der Waals interactions is essential for the complete harmonic dynamical behaviour of thallous halides.