Thermoelasticity of Fe${}^{3+}$- and Al-bearing bridgmanite

Abstract

We report \textit{ab initio} (LDA + U${}_{sc}$) calculations of thermoelastic properties of ferric iron (Fe${}^{3+}$)- and aluminum (Al)-bearing bridgmanite (MgSiO${}_3$ perovskite), the main Earth forming phase, at relevant pressure and temperature conditions and compositions. Three coupled substitutions, namely, [Al]${}_{Mg}$-[Al]${}_{Si}$, [Fe${}^{3+}$]${}_{Mg}$-[Fe${}^{3+}$]${}_{Si}$, and [Fe${}^{3+}$]${}_{Mg}$-[Al]${}_{Si}$ have been investigated. Aggregate elastic moduli and sound velocities are successfully compared with limited experimental data available. In the case of the [Fe${}^{3+}$]${}_{Mg}$-[Fe${}^{3+}$]${}_{Si}$ substitution, the high-spin (S=5/2) to low-spin (S=1/2) crossover in [Fe${}^{3+}$]${}_{Si}$ induces a volume collapse and elastic anomalies across the transition region. However, the associated anomalies should disappear in the presence of aluminum in the most favorable substitution, i.e., [Fe${}^{3+}$]${}_{Mg}$-[Al]${}_{Si}$. Calculated elastic properties along a lower mantle model geotherm suggest that the elastic behavior of bridgmanite with simultaneous substitution of Fe${}_2$O${}_3$ and Al${}_2$O${}_3$ in equal proportions or with Al${}_2$O${}_3$ in excess should be similar to that of (Mg,Fe${}^{2+}$)SiO${}_3$ bridgmanite. Excess Fe${}_2$O${}_3$ should produce elastic anomalies though.

Under review with Geophysical Research Letters