Lattice Dynamics of MgO, Al2MgO4 and Mg2SiO4 Spinel

Summary The method of long waves is used to compute the volume dependence of the elastic properties of MgO, γ-Al2MgO4 (spinel), and γ-Mg2SiO4 (spinel structure) from a rigidion, central force model. A comparison of theoretical and experimental elastic constants for the first two compounds shows that the neglect of non-central forces and ionic polarization severely limits the application of the model for oxides and silicates. The Coulombic contributions to the elastic constants for both the 3–2 spinel (γ-Al2MgO4) and the 2–4 spinel (γ-Mg2SiO4) are expressed as dimensionless Madelung-like constants and are computed as a function of the oxygen parameter. The distortion of the two spinels from c.c.p. is shown to be primarily an electrostatic effect. The elastic properties of γ-Mg2SiO4 are predicted using the bond parameters for Mg-O found from data on periclase and for Si-O found from stishovite. Although the rigid-ion model is too restrictive to give geophysically useful predictions, it shows how lattice dynamics may be used as a framework through which laboratory data may be used to interpret seismic velocity and density profiles.