Theory of magnesium silicates with bearing Fe and Al in the lower mantle and the Earth's D'' layer

Although iron and aluminum incorporation into Earth's mantle minerals are expected to have important effects, little is known about Fe valence and spin state in such major phases as MgSiO$_{3}$ perovskite (\textit{Pv}, main mineral of the lower mantle) and post-perovskite (\textit{PPv}, main mineral of the Earth's D'' layer). Here, we perform \textit{ab initio} simulations, indicating that $Fe^{2+}\to Fe(metal)+Fe^{3+}$ in \textit{Pv} {\&} \textit{PPv}. A new detailed microscopic picture of MgSiO$_{3}$ \textit{Pv} {\&} \textit{PPv} is presented, including the complexity of Fe-Al incorporation, the spin transitions in Fe$^{3+}$ and lack of such in Fe$^{2+}$, and the effects of Fe$^{2+}$, Fe$^{3+}$, Al$^{3+}$ on the stability of \textit{PPv}. These theory results explain and reconcile the recent diverse experimental results on the iron spin transition in MgSiO$_{3}$ and provide basis for future geodynamical and petrological studies of the mantle and the D'' layer.