Site preference of Fe atoms in ${\text{FeMgSiO}}_4$ and $\text{FeMg}{\left({\text{SiO}}_3\right)}_2$ studied by density functional calculations

Using first-principles density functional calculation we investigate site preference of Fe in ${\text{FeMgSiO}}_4$ olivine and $\text{FeMg}{\left({\text{SiO}}_3\right)}_2$ pyroxene, which are the major constituents of the earth’s upper mantle. A combination of state-of-the-art methods has been used for this purpose. The strong correlation effect at Fe site has been taken care of by means of $\text{local-density}\text{approximation}+U$ calculations, and the crystal structures have been optimized by means of total-energy calculations. Our $T=0\text{K}$ study in the total-energy-minimized structures indicate a strong preference for Fe to occupy $M2$ site in case of pyroxene and a preference for Fe to occupy $M1$ site in case of olivine. We provide the microscopic understanding of our finding in terms of density of states and charge densities.

Figure 1

(Color online) Building units of olivine projected onto $bc$ plane (top panel) and pyroxene projected onto $ab$ plane (bottom panel). (a) ${\text{SiO}}_4$ tetrahedral unit. (b) $M1\text{-O}$ octahedral unit. (c) $M2\text{-O}$ octahedral unit.

Figure 2

(Color online) Complete lattice structure of olivine (left panel) and pyroxene (right panel).

Figure 3

(Color online) Partial DOSs of olivine (top panel) and pyroxene (bottom panel) projected onto $\text{Fe}d$, $\text{O}p$, Si, and Mg. Within each panel the upper(lower) subpanel corresponds to majority (minority) spin. The negative of DOS has been plotted for the minority channel for clarity.

Figure 4

(Color online) Comparison between total DOSs for olivine and pyroxene with Fe at $M1$ and $M2$ sites in olivine (top panel) and pyroxene (bottom panel). The solid and the dashed lines correspond to DOS for Fe at $M1$ and $M2$, respectively. Inset shows an enlarged plot of DOS focused at the bottom of the conduction band.

Figure 5

(Color online) Charge-density plot of olivine projected onto the $ac$ plane. Top panel shows Fe at $M1$ site and Mg at $M2$ site. Bottom panel shows Fe at $M2$ site and Mg at $M1$. Contour values are ${\rho }_n=\delta \times n\times e^{-}/{\left(\text{a}\text{.}\text{u}\right)}^3$, where $\delta =0.002$ and $n$ labels the contours. Note enhanced covalency for Fe at $M1$ (top panel) compared to Fe at $M2$ (bottom panel).