Vibrational Dynamics of Cadmium Ions in β-Alumina Crystals

Abstract

In the β-aluminas the monovalent conducting cations occupy low density mirror planes between spinel blocks made by aluminum and oxygen ions. The mobile ion may occupy different sites in the conduction plane, denoted as Beever-Ross (BR), anti-Beever-Ross (aBR) and mid-oxygen (mO) [1]. The relative occupation probability depends on the cation properties and changes with both the temperature and the degree of non-stoichiometry. Vibrational frequencies of the cation motions fall in the region below 100 cm−1 [2, 3], while the spinel modes have frequencies up to ~1000 cm−1. In fact the cations feel quite smooth potentials because of the weak bonds with the surrounding ions. On the contrary the Li+ ion vibrational frequency was found to be anomalously higher (~380 cm−1) than that expected on the basis of vibrational frequency of Na+ and the mass ratio [4]. This suggests that the lithium containing (β-alumina has peculiar structural properties. Moreover heat capacity [5], dielectric constant [6], neutron [7] and X-ray [8] diffraction measurements indicate that out of the mirror plane sites are occupied by most of the Li+ ions. KANEDA et al. [4] have calculated the potential energy experienced by the Li+ ion as a function of the displacement from the mirror plane along the crystallographic c direction above and below the BR sites. The results of their calculation are resumed in Fig. 1: the Li+ ion, due to its small radius, tends to escape from the conduction plane approaching the spinel blocks, and feels a potential having two minima at ± 0.8 A away from the mirror plane. The two charged layers of Li+ ions give rise to the asymmetry in the potential energy. By means of this two-wells potential energy, KANEDA et al. were able to fit the anomalously high vibrational frequency observed in the a (c,c) a’ Raman spectrum of Li β-alumina crystals.