High-pressure order-disorder transition in Mg$_2$SiO$_4$: Implications for super-Earth mineralogy

(Mg, Fe)SiO$_3$ post-perovskite is the highest pressure silicate mineral phase in the Earth's interior. The extreme pressure and temperature conditions inside large extrasolar planets will likely lead to phase transitions beyond pPv. In this work we have explored the high-pressure phase relations in Mg$_2$SiO$_4$ using computations based on density functional theory. We find that a partially disordered I-42d type structure would be stable in the interiors of these super-Earth planets. The discovery of a structure where two very dissimilar cations, Mg$^{2+}$ and Si$^{4+}$ occupy the same crystallographic site opens up a domain of interesting crystal chemistry and provides a foundation for other silicates and oxides with mixed occupancy. We have explored the mechanism of the phase transition from the ordered ground state and the effect of the disordering on electronic properties of the silicate phase.