The lattice dynamics of tellurium

Abstract

The phonon dispersion curves along the Δ, Σ, W, R directions have been measured at 298 K in tellurium using the technique of coherent, inelastic neutron scattering. In all these directions the 9 branches for a given wave-vector fall into 3 well defined “bands”. The curves have been analysed in terms of axially-symmetric, tensor and valence force field lattice dynamical models. Several of these models provide a reasonable fit to the experimental dispersion curves, but none gives a very good description of the dynamics. The main features of the dispersion curves are qualitatively fitted by a simple 2 neighbour model, but the best fit to these overall features is given by a valence model which includes “non-diagonal” interactions. The “in-chain” interactions are found to be significantly stronger than the “inter-chain” ones, but not so much stronger that the chains can be considered as rigid. The “best-fit” parameters are used to calculate the phonon distribution function, g v, and the temperature dependence of the specific heat C v , and Debye temperature θ D . The two-phonon distribution functions g(v $ ̄ v') and the temperature dependence of the mean square displacements, together with the Mössbauer fraction for 125Te are also computed from the model.