The Structure and Lattice Dynamics of Spinel

Abstract

The low energy phonon dispersion system in Spinel, MgAl2O4, has been investigated by neutron inelastic scattering using time of flight spectrometry and the observed data used to refine the twelve adjustable parameters of a theoretical model constructed on the rigid ion harmonic approximation of Kellermann. It is demonstrated that the same approximation may be used to give a good description of the dynamical behaviour of Magnetite, Fe3O4, previously studied by Samuelsen and Steinsvall. Comparison of the ten repulsive parameters which describe the ion overlap interactions and the effective ionic charges shows that the former are very similar in the two cases and correspond to non-central forces. The good electrical conductivity in Magnetite, arising from electron hopping, is apparently accommodated within the rigid ion model primarily through modification of the effective ionic charges. The elastic constants in spinels have contributions from both internal and external strains and expressions have been derived in terms of the model parameters for the latter.  These have been used together with a numerical evaluation of the internal contributions to provide theoretical estimates of the elastic constants of both Spinel and Magnetite, which are in fair agreement with the experimental values. From examination of the eigenvectors of the model at phonon wavevector q ~ 0, two infra-red active modes of vibration have been identified. However the derived frequencies are in poor agreement with those observed and this is believed to be a consequence of assuming the ions to be unpolarisable. Conventionally the crystal structure of cubic spinel compounds is referred to the space group Fd3m, but there is a considerable body of experimental evidence inconsistent with this description. A more general, unified and consistent description is provided by the lower symmetry space group F-43m. Therefore a very careful analysis based on single crystal X-ray and neutron diffraction studies of MgAl2O4 has been carried out and is also presented. Very precise atom positions have been derived from the analysis and it is concluded that the symmetry of magnesium aluminate is more correctly described by the space group F-43m.