Structures, compressibilities and relative stabilities of the α, β and γ phases of Mg2SiO4 deduced from an electron-gas ionic Hamiltonian

The properties of forsterite (alpha -Mg2SiO4) and its high-pressure polymorphs wadsleyite (beta -Mg2SiO4) and ringwoodite (gamma -Mg2SiO4) play an important role in the chemical, dynamic and elastic behaviour of the upper 660 km of the Earth's mantle. Mineralogists have tended to rationalize their structures in terms of empirical ionic models, guided by Pauling's rules. Modern electron-gas theory of ionic interactions is accurate enough to encourage a detailed study of the structure and properties of these minerals within an intuitively appealing ionic model that is independent of empirical data. We therefore undertook to obtain the minimum-energy lattice structures, and their corresponding equations of state, of electron-gas models of the Mg2SiO4 polymorphs. We find that the model densities compare very well with actual observations, while compressibilities are somewhat underestimated. Unit cell geometries are also accurately represented, but coordination polyhedra tend to be more distorted than those observed, mainly because of excessive bond-angle variance. We also found that Pauling's rules do not offer a complete accounting for the observed stability of olivine at low pressures. Instead, in the model crystals it is a difference in the magnitude of the Mg-O repulsions that give olivine the energetic advantage. The higher density of ringwoodite, and a rapidly increasing Mg-O repulsion energy in olivine stabilize ringwoodite at high pressure.