Electronic Spin State and Elasticity of (Mg, Fe)(Si, Al)O3-perovskite at high pressure

We investigate the effect of pressure on the electronic spin state of ferric iron in Al-bearing MgSiO$_{3}$-perovskite using first-principle computations (Density Functional Theory with the Generalized Gradient Approximation). We also calculate the single crystal elastic moduli ($c_{ij})$ for (Mg, Fe$^{3+})$(Si, Al)O$_{3}$ perovskite to understand the effect of chemical variations and spin state transitions of the Fe$^{3+}$ ions on these properties. Ferric iron (6.25 mol{\%}) and Al (6.25 mol{\%}) substitute for Mg and Si respectively. Our results show that spin state transition from high spin (HS) to low spin (LS) occurs on the Fe$^{3+}$ ions at high pressure, while there is no stability field for the intermediate spin state. Fe$^{3+}$ alone can be responsible for the spin state transition. The models witness a transition pressure ranging from 97-126 GPa. Differential stress can change the pressure for the spin collapse. These results are one explanation to the reported experimental observations that the spin transition occurs over a wide pressure range. We find that ferric iron lowers the elastic moduli relative to the Al charge-coupled substitution. The spin state of the iron for this composition has a relatively small effect ($<$ 0.5{\%} variation) on both bulk modulus and shear modulus. Replace this text with your abstract body.