Demixing Instability in Dense Molten ${\mathrm{MgSiO}}_3$ and the Phase Diagram of MgO

The phase diagrams of ${\mathrm{MgSiO}}_3$ and MgO are studied from first-principles theory for pressures and temperatures up to 600 GPa and 20 000 K. Through the evaluation of finite-temperature Gibbs free energies, using density-functional theory within the generalized gradient approximation as well as with hybrid exchange-correlation functionals, we find evidence for a vast pressure-temperature regime where molten ${\mathrm{MgSiO}}_3$ decomposes into liquid ${\mathrm{SiO}}_2$ and solid MgO, with a volume change of approximately 1.2%. The demixing transition is driven by the crystallization of MgO—the reaction only occurs below the high-pressure MgO melting curve. The predicted transition pressure at 10 000 K is in close proximity to an anomaly reported in recent laser-driven shock experiments of ${\mathrm{MgSiO}}_3$. We also present new results for the high-pressure melting curve of MgO and its $B1\mathrm{\text{−}}B2$ solid phase transition, with a triple point at 364 GPa and 12 000 K.

Figure 1

High-pressure phase diagram of MgO revealed by first-principles free energy calculations. The red triangles show our melting points for $B1$ and $B2$ phases obtained with (downward) and without (upward) HSE corrections to the free energies. Our predicted $B1\mathrm{\text{−}}B2$ transition points are given by red squares. Short black lines underneath our data represent Clausius-Clapeyron slopes. Thick blue lines are Kechin fits to our HSE-corrected data [38], which give rise to a triple point at 364 GPa and 12 000 K. Previous theoretical predictions of $B1$ (diamonds) and $B2$ (circle) melting points are also shown [31, 32]. The black dashed lines indicate theorized high-pressure melting curves [31, 33] as well as $B1\mathrm{\text{−}}B2$ phase boundaries [31, 34, 35]. Inset: Gibbs free energies for MgO phases relative to the $B1$ phase along the 10 000 K isotherm with (solid lines) and without (dashed lines) HSE corrections.

Figure 2

Gibbs free energies of mixing along the (a) 10 000 and (b) 16 000 K isotherms computed using MgO liquid (blue symbols) and MgO solid $B1$ (red symbols) with (squares) and without (circles) HSE corrections. Anomalies measured in shocked ${\mathrm{MgSiO}}_3$ are given by black crosses. (c) Enthalpy and entropy (diamonds) contributions to the Gibbs free energies of mixing at 10 000 K. (d) Total entropies of the various phases considered at 10 000 K.

Figure 3

Proposed high-pressure phase diagram of liquid ${\mathrm{MgSiO}}_3$. The shaded blue region shows the $P\mathrm{\text{−}}T$ region where liquid ${\mathrm{MgSiO}}_3$ phase separates into solid MgO and liquid ${\mathrm{SiO}}_2$. Demixing transition points were calculated with (squares) and without (diamonds) HSE energy corrections. The short black lines underneath our data represent Clausius-Clapeyron slopes. Recent shock measurements are shown with shaded gray regions [15]. The blue square indicates the demixing transition pressure for reaction (1), assuming a systematic $200\mathrm{meV}/\mathrm{atom}$ error in our Gibbs free energy calculations, equivalent to an approximately 1% error in the evaluation of our total entropies. The blue arrow forms the corresponding demixing phase boundary (guide to the eye), taking into account such a systematic error. Previous theoretical [33, 39] and experimental [40, 41] results for the ${\mathrm{MgSiO}}_3$ melting curve are shown by black dashed lines and black dots, respectively. The MgO phase boundaries presented in Fig. 1 are given by solid black lines for comparison.