High-pressure order-disorder transition in ${\mathrm{Mg}}_2\mathrm{Si}{\mathrm{O}}_4$: Implications for super-Earth mineralogy

$\left(\mathrm{Mg},\mathrm{Fe}\right)\mathrm{Si}{\mathrm{O}}_3$ post-perovskite is the highest-pressure silicate mineral phase in the Earth's interior. The extreme pressure and temperature conditions inside large extrasolar planets will likely lead to phase transitions beyond post-perovskite. In this work, we have explored the high-pressure phase relations in ${\mathrm{Mg}}_2\mathrm{Si}{\mathrm{O}}_4$ using computations based on density functional theory. We find that a partially disordered $I\overline{4}2d$-type structure would be stable under the conditions expected for the interiors of super-Earth planets. We have explored the mechanism of the phase transition from the ordered ground state and the effect of disordering on the electronic properties of the silicate phase. The discovery of a structure where two very dissimilar cations, ${\mathrm{Mg}}^{2+}$ and ${\mathrm{Si}}^{4+}$, occupy the same crystallographic site opens up a domain of interesting crystal chemistry and provides a foundation for other silicates and oxides with mixed occupancy.

Figure 1

Theoretically computed phase boundaries (solid black lines) in the ${\mathrm{Mg}}_2\mathrm{Si}{\mathrm{O}}_4$ system [15]. Dashed black lines show the pressure and temperature conditions inside terrestrial exoplanets [29] with masses equal to 5 and 10 times that of the Earth $\left(M_E\right)$. Solid red line shows the melting curve of $\mathrm{MgSi}{\mathrm{O}}_3$ [6]. Red rectangles indicate estimated core-envelope $P$ and $T$ conditions in giant planets in the solar system.

Figure 2

Enthalpy differences (Δ$H$) between post-perovskite $\mathrm{MgSi}{\mathrm{O}}_3+\mathrm{MgO}$ (B1/B2) and $I\overline{4}2d$-type ${\mathrm{Mg}}_2\mathrm{Si}{\mathrm{O}}_4$ as a function of pressure for the static lattice (classical 0 K). The dashed black line indicates Δ$H$ = 0; the crossover with the respective phases shows the transition pressure.

Figure 3

Crystal structure (224-atom supercell) of partially and completely ordered $I\overline{4}2d$-type ${\mathrm{Mg}}_2\mathrm{Si}{\mathrm{O}}_4$ at 600 GPa.

Figure 4

Difference in enthalpy ($H_Q-H_{Q1})$ (left) vs order parameter $Q$ at 600, 800, and 1500 GPa, where $H_{Q1}$ is the enthalpy of the completely ordered phase ($Q$ = 1). Configurational entropy at 600 GPa (right).

Figure 5

Change in the order parameter $Q$ with temperature for $I\overline{4}2d$-type ${\mathrm{Mg}}_2\mathrm{Si}{\mathrm{O}}_4$ (solid) and ${\mathrm{Mg}}_2\mathrm{Ge}{\mathrm{O}}_4$ (dashed) [17] at select pressures. $Q$ = 0 and 1 correspond to completely disordered and completely ordered structures, respectively. Black dotted line shows the predicted melting temperature [6] of $\mathrm{MgSi}{\mathrm{O}}_3$ based on extrapolation of shockwave meting data.

Figure 6

Variation in unit-cell volume (left) and c/a (right) of $I\overline{4}2d$-type ${\mathrm{Mg}}_2\mathrm{Si}{\mathrm{O}}_4$ as a function of the order parameter $Q$ at 600, 800, and 1500 GPa.