Anharmonicity and Phase Diagram of Magnesium Oxide in the Megabar Regime

B1-B2 transition in shock-compressed MgO

Magnesium oxide (MgO) is a major component of the Earth's mantle and is expected to play a similar role in the mantles of large rocky exoplanets. At extreme pressures, MgO transitions from the NaCl B1 crystal structure to a CsCl B2 structure, which may have implications for exoplanetary deep mantle dynamics. In this study, we constrain the phase diagram of MgO with laser-compression along the shock Hugoniot, with simultaneous measurements of crystal structure, density, pressure, and temperature. We identify the B1 to B2 phase transition between 397 and 425 gigapascal (around 9700 kelvin), in agreement with recent theory that accounts for phonon anharmonicity. From 425 to 493 gigapascal, we observe a mixed-phase region of B1 and B2 coexistence. The transformation follows the Watanabe-Tokonami-Morimoto mechanism. Our data are consistent with B2-liquid coexistence above 500 gigapascal and complete melting at 634 gigapascal. This study bridges the gap between previous theoretical and experimental studies, providing insights into the timescale of this phase transition.

Double-Shock Compression Pathways from Diamond to BC8 Carbon

Carbon is one of the most important elements for both industrial applications and fundamental research, including life, physics, chemistry, materials, and even planetary science. Although theoretical predictions on the transition from diamond to the BC8 (Ia3[over ¯]) carbon were made more than thirty years ago, after tremendous experimental efforts, direct evidence for the existence of BC8 carbon is still lacking. In this study, a machine learning potential was developed for high-pressure carbon fitted from first-principles calculations, which exhibited great capabilities in modeling the melting and Hugoniot line. Using the molecular dynamics based on this machine learning potential, we designed a thermodynamic pathway that is achievable for the double shock compression experiment to obtain the elusive BC8 carbon. Diamond was compressed up to 584 GPa after the first shock at 20.5  km/s. Subsequently, in the second shock compression at 24.8 or 25.0  km/s, diamond was compressed to a supercooled liquid and then solidified to BC8 in around 1 ns. Furthermore, the critical nucleus size and nucleation rate of BC8 were calculated, which are crucial for nano-second x-ray diffraction measurements to observe BC8 carbon during shock compressions. The key to obtaining BC8 carbon lies in the formation of liquid at a sufficient supercooling. Our work provides a feasible pathway by which the long-sought BC8 phase of carbon can be reached in experiments.

Machine-Learning Accelerated First-Principles Accurate Modeling of the Solid-Liquid Phase Transition in MgO under Mantle Conditions

While accurate measurements of MgO under extreme high-pressure conditions are needed to understand and model planetary behavior, these studies are challenging from both experimental and computational modeling perspectives. Herein, we accelerate density functional theory (DFT) accurate calculations using deep neural network potentials (DNPs) trained over multiple phases and study the melting behavior of MgO via the two-phase coexistence (TPC) approach at 0-300 GPa and ≤9600 K. The resulting DNP-TPC melting curve is in excellent agreement with existing experimental studies. We show that the mitigation of finite-size effects that typically skew the predicted melting temperatures in DFT-TPC simulations in excess of several hundred kelvin requires models with ∼16 000 atoms and >100 ps molecular dynamics trajectories. In addition, the DNP can successfully describe MgO metallization well at increased pressures that are captured by DFT but missed by classical interatomic potentials.

Magnesium oxide-water compounds at megabar pressure and implications on planetary interiors

Magnesium Oxide (MgO) and water (H₂O) are abundant in the interior of planets. Their properties, and in particular their interaction, significantly affect the planet interior structure and thermal evolution. Here, using crystal structure predictions and ab initio molecular dynamics simulations, we find that MgO and H₂O can react again at ultrahigh pressure, although Mg(OH)₂ decomposes at low pressure. The reemergent MgO-H₂O compounds are: Mg₂O₃H₂ above 400 GPa, MgO₃H₄ above 600 GPa, and MgO₄H₆ in the pressure range of 270-600 GPa. Importantly, MgO₄H₆ contains 57.3 wt % of water, which is a much higher water content than any reported hydrous mineral. Our results suggest that a substantial amount of water can be stored in MgO rock in the deep interiors of Earth to Neptune mass planets. Based on molecular dynamics simulations we show that these three compounds exhibit superionic behavior at the pressure-temperature conditions as in the interiors of Uranus and Neptune. Moreover, the water-rich compound MgO₄H₆ could be stable inside the early Earth and therefore may serve as a possible early Earth water reservoir. Our findings, in the poorly explored megabar pressure regime, provide constraints for interior and evolution models of wet planets in our solar system and beyond.

Miscibility of rock and ice in the interiors of water worlds

Super-Earths and sub-Neptunes are the most common planet types in our galaxy. A subset of these planets is predicted to be water worlds, bodies that are rich in water and poor in hydrogen gas. The interior structures of water worlds have been assumed to consist of water surrounding a rocky mantle and iron core. In small planets, water and rock form distinct layers with limited incorporation of water into silicate phases, but these materials may interact differently during the growth and evolution of water worlds due to greater interior pressures and temperatures. Here, we use density functional molecular dynamics (DFT-MD) simulations to study the miscibility and interactions of enstatite (MgSiO₃), a major end-member silicate phase, and water (H₂O) at extreme conditions in water world interiors. We explore pressures ranging from 30 to 120 GPa and temperatures from 500 to 8000 K. Our results demonstrate that enstatite and water are miscible in all proportions if the temperature exceeds the melting point of MgSiO₃. Furthermore, we performed smoothed particle hydrodynamics simulations to demonstrate that the conditions necessary for rock-water miscibility are reached during giant impacts between water-rich bodies of 0.7–4.7 Earth masses. Our simulations lead to water worlds that include a mixed layer of rock and water.

Structural transition and re-emergence of iron's total electron spin in (Mg,Fe)O at ultrahigh pressure

Fe-bearing MgO [(Mg_1−xFe_x)O] is considered a major constituent of terrestrial exoplanets. Crystallizing in the B1 structure in the Earth’s lower mantle, (Mg_1−xFe_x)O undergoes a high-spin (S = 2) to low-spin (S = 0) transition at ∼45 GPa, accompanied by anomalous changes of this mineral’s physical properties, while the intermediate-spin (S = 1) state has not been observed. In this work, we investigate (Mg_1−xFe_x)O (x ≤ 0.25) up to 1.8 TPa via first-principles calculations. Our calculations indicate that (Mg_1−xFe_x)O undergoes a simultaneous structural and spin transition at ∼0.6 TPa, from the B1 phase low-spin state to the B2 phase intermediate-spin state, with Fe’s total electron spin S re-emerging from 0 to 1 at ultrahigh pressure. Upon further compression, an intermediate-to-low spin transition occurs in the B2 phase. Depending on the Fe concentration (x), metal–insulator transition and rhombohedral distortions can also occur in the B2 phase. These results suggest that Fe and spin transition may affect planetary interiors over a vast pressure range.

Iron spin transition occurs at ultrahigh pressure. The total electron spin increases from 0 to 1 as the structural transition of (Mg,Fe)O occurs (~0.6 TPa) and drops back to 0 at higher pressure. Its effects on exoplanet interiors are anticipated.

The phase diagrams of beryllium and magnesium oxide at megabar pressures

We performab initiosimulations of beryllium (Be) and magnesium oxide (MgO) at megabar pressures and compare their structural and thermodynamic properties. We make a detailed comparison of our two recently derived phase diagrams of Be (Wuet al2021Phys. Rev.B104014103) and MgO (Soubiran and Militzer 2020Phys. Rev. Lett.125175701) using the thermodynamic integration technique, as they exhibit striking similarities regarding their shape. We explore whether the Lindemann criterion can explain the melting temperatures of these materials through the calculation of the Debye temperature at high pressure. From our free energy calculations, we find that the melting line of both materials is well represented by the Simon-Glazel fitT_m(P) =T₀(1 +P/a)^1/c, whereT₀= 1564 K,a= 15.8037 GPa andc= 2.4154 for Be, whileT₀= 3010 K,a= 10.5797 GPa andc= 2.8683 for the MgO in the B1. For the B2 phase, we use the valuesa= 26.1163 GPa andc= 2.2426. Both materials exhibit negative Clapeyron slopes on the boundaries between the two solid phases that are strongly affected by anharmonic effects, which also influence the location of the solid-solid-liquid triple point. We find that the quasi-harmonic approximation underestimates the stability range of the low-pressure phases, namely hcp for Be and B1 for MgO. We also compute the phonon dispersion relations at low and high pressure for each of the phases of these materials, and also explore how the phonon density of states is modified by temperature. Finally, we derive secondary shock Hugoniot curves in addition to the principal Hugoniot curve for both materials, and study their offsets in pressure between solid and liquid branches.