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.