Structures, compressibilities and relative stabilities of the alpha, beta and gamma phases of Mg2SiO4 deduced from an electron-gas ionic Hamiltonian

The properties of forsterite (alpha -Mg2SiO4) and its high-pressure polymor phs wadsleyite (beta -Mg2SiO4) and ringwoodite (gamma -Mg2SiO4) play an imp ortant role in the chemical, dynamic and elastic behaviour of the upper 660 km of the Earth's mantle. Mineralogists have tended to rationalize their s tructures in terms of empirical ionic models, guided by Pauling's rules. Mo dern electron-gas theory of ionic interactions is accurate enough to encour age a detailed study of the structure and properties of these minerals with in an intuitively appealing ionic model that is independent of empirical da ta. 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 poly hedra tend to be more distorted than those observed, mainly because of exce ssive bond-angle variance. We also found that Pauling's rules do not offer a complete accounting for the observed stability of olivine at low pressure s. Instead, in the model crystals it is a difference in the magnitude of th e Mg-O repulsions that give olivine the energetic advantage. The higher den sity of ringwoodite, and a rapidly increasing Mg-O repulsion energy in oliv ine stabilize ringwoodite at high pressure.