Lattice Dynamics of Rutile

Abstract

The phonon dispersion relation for rutile (Ti${\mathrm{O}}_{2}$) has been measured by the coherent inelastic scattering of thermal neutrons along principal symmetry directions of the Brillouin zone. Theoretical models based on rigid-ion and shell models, with either axially symmetric or tensor first- and second-neighbor forces, have been fitted to the measured dispersion relation. Only the shell model with tensor forces for all interactions except the second-neighbor oxygen-oxygen interaction was able to give acceptable qualitative agreement with the data, and that agreement is good for only some modes. A frequency distribution and Debye temperature spectrum are presented for that model. The temperature dependence of the frequency of the ${\ensuremath{\Gamma}}_{1}^{\ensuremath{-}}({A}_{2u})$ transverse optic mode is measured from 4 to 300\ifmmode^\circ\else\textdegree\fi{}K, and the behavior of the square of the frequency is in good agreement with that predicted by the static dielectric constant measurements of Parker.