Lattice Dynamics of Rutile

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 ${\Gamma }_1^{-}\left(A_{2u}\right)$ transverse optic mode is measured from 4 to 300°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.