Structural, vibrational and thermodynamic properties of Mg2SiO4Mg2SiO4 and MgSiO3MgSiO3 minerals from first-principles simulations

In this paper we report a computational study of the structural and vibrational properties of the Mg-end members forsterite, wadsleyite and ringwoodite   of Mg2SiO4Mg2SiO4, and akimotoite, majorite   and the perovskite phase of MgSiO3MgSiO3. Our calculations have been carried out in the framework of Density Functional Theory (DFT) using a plane wave basis set and the Projector-augmented Wave (PAW) method to account for the core electrons. All structures have been fully relaxed at a series of volumes corresponding to the pressure range relevant to the transition zone in the Earth’s mantle, and at each volume the phonon frequencies have been obtained and classified. Using the quasi-harmonic approximation, we have estimated a series of thermodynamic properties for each structure, including the Gibbs free energy, from which we have computed approximate phase diagrams for Mg2SiO4Mg2SiO4 and MgSiO3MgSiO3. In spite of our reliance on the quasi-harmonic approximation, which is expected to break down at high temperatures, our calculated phase diagrams qualitatively reproduce the main features expected from diagrams fitted to experimental data. For example, from the computed phase diagram for Mg2SiO4Mg2SiO4 we obtain a post-spinel boundary at P = 22.1 GPa at T = 1873 K, with a slope of −3.4 MPa/K.This supports experimental results suggesting a relatively large slope rather than those favouring a much flatter one. It also suggests that vertical deflections of the 660 km discontinuity due to thermal signatures from plumes and slabs should be similar to those at the 410 km, and that a deflection of 35 km as seen in recent seismic studies could be caused by a thermal anomaly as small as 330 K. We also identify the triple point between the ringwoodite, ilmenite (plus periclase) and perovskite (plus periclase) phases to be at P = 22.9 GPa and T = 1565 K. Our results clearly illustrate the stringent requirements made on theoretical models in order to extract predictions compatible with the available experimental data.