Ab initio investigation of the high pressure elasticity of Mg₂SiO₄ forsterite and ringwoodite

We discuss the behavior of two minerals of the same composition, Mg₂SiO₄ but different structures: forsterite and ringwoodite. Ab initio plane-wave pseudopotential results are discussed in terms of the full elastic constant tensors of these phases and their elastic anisotropy. The structures of the two minerals, based on pseudo-hcp and pseudo-fcc packing of oxygens, respectively, show very different behavior at high pressure. While the elastic anisotropy of olivine depends weakly on pressure between 0 and 25 GPa, the anisotropy of ringwoodite decreases with pressure initially, vanishing at 17 GPa before increasing again at higher pressure. This unusual behavior is understood in terms of a change of sign of the combination of elastic constants c₁₂+2c₄₄-c₁₁, and a resulting interchange of fast and slow directions of acoustic wave propagation. To gain insight into the origin of their elastic behavior, the ab initio results are compared with a simple model based on the O sub-lattice.