Raman scattering in $\beta -\mathrm{alumina}$

The Raman spectra of the ionic conductor Na $\beta -{\mathrm{Al}}_2{\mathrm{O}}_3$ and several of its cation-substituted isomorphs have been studied at temperatures from 4.2 to 900 °K. For the Na, Ag, K, and Rb isomorphs, but not for Li, lowfrequency vibrations are observed which attributed to vibrations of the mobile cations with displacements parallel to the conducting planes. In several cases the frequencies and widths of these vibrations are quite different from those measured by infrared reflectivity. A calculation of the contribution of dipolar interactions to the in-phase vibrations of the cations shows that the resulting corrections are sizable, but are essentially identical for ir and Raman modes. The differences in the spectra may be due to a difference in the samples used. A quasielastic scattering wing is observed at high temperatures in Ag $\beta -{\mathrm{Al}}_2{\mathrm{O}}_3$. The estimated width of this feature is consistent with the ionic hopping rate caculated from the attempt frequency and activation energy for ionic conduction. Structural distortion modes of the spinel blocks are also observed. These correspond to vibrations observed by neutron scattering. Possible assignments for these modes are suggested by their polarization behavior. Two different possible superlattices in Ag $\beta -\mathrm{alumina}$ and in Na, K, and Rb $\beta -\mathrm{alumina}$ are discussed and related to the splittings in the low-frequency vibrations of the cations.