Elastic properties of the olivine and spinel polymorphs of Mg 2GeO 4, and evaluation of elastic analogues

Abstract

The single-crystal elastic moduli of the olivine and spinel phases of Mg 2GeO 4 have been measured using Brillouin scattering spectra. The moduli for the olivine phase are: C 11 = 3.12, C 22 = 1.87, C 33 = 2.17, C 66 = 0.71, C 23 = 0.66, C 31 = 0.65 and C 12 = 0.60. The moduli for the spinel phase are: C 11 = 3.00, C 44 = 1.26 and C 12 = 1.18. These data are analyzed to define the best type of elastic analogue for magnesium orthosilicates. The character of the many-bodied, non-central force associated with the divalent cation is found to significantly influence the relative magnitudes of the elastic moduli. Since the nature of the many-bodied, non-central force is quite different for alkaline earth cations than for transition metal cations, we conclude that materials which contain one of these cation types is not a good analogue for materials with the other type. Magnesium orthogermanate, however, is a good analogue of magnesium orthosilicate. On the other hand, the high elastic anisotropy of the spinel phase of the germanate suggests that the germanium tetrahedron is less rigid under shear than the corresponding silicon tetrahedron. The success of the magnesium orthogermanate to model the magnesium orthosilicate is probably a result of the mechanical isolation of the tetrahedra, thus requiring the conclusions of this study to be further tested before applying them to other silicate systems.