Melting phase relation of seifertite and pyrite-type SiO2 determined by machine learning potentials

TL;DR

This work tackles the uncertain high-pressure phase relations of SiO2, focusing on seifertite and pyrite-type polymorphs, by developing two machine-learning potentials trained on SCAN and PBEsol to span 100–400 GPa and 1000–10000 K. Using MTMB-enhanced sampling and DeePMD-based neural networks, the authors perform large-scale two-phase coexistence MD to map melting curves and the seifertite–pyrite-type boundary, including a 0 K transition assessment via DFT. The SCAN-based potential generally yields higher melting temperatures and a phase boundary that better matches experimental data when corrected for Pt EOS, with a strongly negative Clapeyron slope around dP/dT≈−6 MPa/K, suggesting layered mantle convection in super-Earth exoplanets. Overall, the study demonstrates the power of transferable ML potentials to resolve complex phase behavior under extreme conditions and informs models of planetary interiors and their thermal evolution.

Abstract

Silica (SiO2) is fundamental to both industrial technology and planetary science, yet the phase relations of its high-pressure polymorphs remain poorly constrained. Here, we develop two machine learning potentials (MLPs) for SiO2 that faithfully represent the SCAN and PBEsol exchange-correlation functionals over a wide temperature (1000-10000 K) and pressure (100-400 GPa) range using deep neural networks. With large-scale two-phase simulations powered by these potentials, we determine the melting curves of seifertite and pyrite-type SiO2 and infer the solid-solid phase boundary between these two phases. The SCAN functional, which captures intermediate-range van der Waals interactions, reproduces structural and thermodynamic properties with high fidelity, predicting melting temperatures 6-10 % higher and a seifertite to pyrite-type transition pressure 22 % higher than the PBEsol. The strongly negative Clapeyron slope (-6.1 MPa/K) of this transition suggests that mantle convection could be highly layered in super-Earth exoplanets, potentially affecting their long-term thermal evolution and habitability.

Figures (6)

• Figure 1: Comparison between MLP-SCAN predictions and DFT calculations for energies (a), atomic forces (b), and stresses (c) using a test dataset of 10400 96-atom SiO$_2$ configurations over the temperature range 1000–10000 K and pressure range 100–400 GPa. The red dashed lines are given as guides for perfect matches.
• Figure 2: Comparison between MLP-SCAN predictions (thin black lines) and DFT calculations (thick colored lines) of total energies for SiO$_2$ systems with 216 atoms at 200 GPa and 7000 K. None of the configurations in the trajectory were included in the training set. The root-mean-square errors of the MLP are 5.0, 5.0, and 6.5 meV/atom for seifertite, pyrite-type, and liquid, respectively.
• Figure 3: Two-phase simulations of seifertite SiO$_2$ and liquid coexistence using the machine learning potential based on the SCAN functional at 200 GPa and 7220 K (upper panel) and 7230 K (lower panel). The simulation box contains 1728 SiO$_2$ formula units (5184 atoms). The box centers are evenly spaced horizontally and vertically aligned to clearly illustrate the relative volume differences.
• Figure 4: Two-phase simulations of pyrite-type SiO$_2$ and liquid coexistence using the machine learning potential based on the SCAN functional 200 GPa and 7220 K (upper panel) and 7230 K (lower panel). The simulation box contains 1728 SiO$_2$ formula units (5184 atoms). The box centers are evenly spaced horizontally and vertically aligned to clearly illustrate the relative volume differences.
• Figure 5: Melting phase relation of seifertite and pyrite-type SiO$_2$. Melting points determined by two-phase simulations were fitted and extrapolated using the Simon equation (a). The resulting melting curves, along with the solid-solid phase boundary between seifertite and pyrite-type, were plotted together with results from the literature (b). Experimental data points are shown with filled markers kuwayama2005 or half-filled markers andrault2022, with error bars indicating temperature uncertainty. One shock compression experiment is represented separately by a green dashed-dotted line millot2015.