Structure phases of MgSiO$_{3}$ in Earth's lower Mantle: ab initio calculations

The Earth's mantle is divided into five layers with four major phase transitions at 410, 520, 660 and $\sim $2600-km depths, due to a structural and chemical changes of its main constituent minerals. MgSiO$_ {3}$ is believed to be a predominant mineral, at least in the upper part of the lower mantle. MgSiO$_{3}$ has a structural sequence from corundum-type ilmenite to CaIrO$_{3}$-type structure (\textit{Cmcm} symmetry). First-principles calculations have been performed within the full-potential linearised augmented plane-wave method (FP-LAPW). We calculated equilibrium lattice parameters at different pressures up to 150 GPa. Four crystal structures relevant to MgSiO$_{3}$ were considered and they can grouped in two pairs of distinct types:\textbf{ (a)} corundum-like and Rh$_{2}$O$_{3} $(II) structure-like, and \textbf{(b)} perovskite and CaIrO$_{3}$ structure-like. To investigate the structural phase transitions in MgSiO$_{3}$, we calculated the enthalpy (E+PV) of the four-structures as a function of pressure from 0 to 150 GPa. The intersection of the curves indicates which structure is more stable and gives the transition pressure.