Investigating Intrinsically Localized Vibrations in crystalline lattices using van-Hove singularities.

Sodium Iodide has a rock salt structure. Intrinsically Localized Modes (ILMs) have supposedly been observed in NaI but only for wave-vectors at the corner of the 3-D Brillouin Zone. It has been suggested that, for high-symmetry q vectors, several van Hove singularities may converge at one critical energy producing a large peak in the two-phonon density of state spectrum and giving rise to ILMs with these q values. First, we fit the experimentally determined acoustic and the optic phonon modes using a nearest neighbor and a next-nearest neighbor force constants. We find that the two-phonon density of states, for fixed q exhibits non-divergent van Hove singularities. The energies of these features vary as q is varied and we have identified the q values at which the two-phonon density of states is enhanced. We intend to introduce anharmonic interactions and examine if it can bind the two-phonon excitations to produce a quantized ILM.