Abstract
Most water in the Universe may be superionic, and its thermodynamic and transport properties are crucial for planetary science but difficult to probe experimentally or theoretically. We use machine learning and free-energy methods to overcome the limitations of quantum mechanical simulations and characterize hydrogen diffusion, superionic transitions and phase behaviours of water at extreme conditions. We predict that close-packed superionic phases, which have a fraction of mixed stacking for finite systems, are stable over a wide temperature and pressure range, whereas a body-centred cubic superionic phase is only thermodynamically stable in a small window but is kinetically favoured. Our phase boundaries, which are consistent with existing—albeit scarce—experimental observations, help resolve the fractions of insulating ice, different superionic phases and liquid water inside ice giants.
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Data availability
The data supporting the findings of this study are available within the paper, and a detailed description of the calculations is included in the Supplementary Information. All original data generated for the study and the machine learning potential for high-pressure water constructed in this study are in the Supplementary Information and available via GitHub at https://github.com/BingqingCheng/superionic-water.
Code availability
All necessary input files for simulations and a Python notebook for data analysis are in the Supplementary Information.
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Acknowledgements
We thank M. Millot, A. Reinhardt and G. Mazzola for reading an early draft and providing constructive and useful comments and suggestions. We thank M. Millot for seeding this collaboration. We also gratefully acknowledge J.-A. Hernandez (European Synchrotron Radiation Facility Grenoble, France) and L. Scheibe (University of Rostock, Germany) for sharing their equation of state data and planetary profiles. B.C. acknowledges resources provided by the Cambridge Tier-2 system operated by the University of Cambridge Research Computing Service funded by EPSRC Tier-2 capital grant number EP/P020259/1. C.J.P. acknowledges support from EPSRC grant number EP/P022596/1. M.B. was supported by the European Horizon 2020 programme within the Marie Skłodowska-Curie actions (xICE grant number 894725). S.H. acknowledges partial support from LDRD grant numbers 19-ERD-031 and 21-ERD-005, and computing support from the Lawrence Livermore National Laboratory (LLNL) Institutional Computing Grand Challenge programme. The Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the US Department of Energy, National Nuclear Security Administration under contract number DE-AC52-07NA27344.
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B.C., M.B. and S.H. conceived the study. B.C. performed the simulations related to the MLP. M.B., C.J.P. and S.H. performed the FP calculations. B.C. M.B. and S.H. analysed the data. All authors wrote the paper.
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Supplementary Information
Supplementary Figs. 1–21, Tables 1 and 2 and methods for the density dunctional theory calculations, fitting of the MLP, the MD simulations using the MLP and the data analysis.
Supplementary Data 1
Data files and a data analysis notebook for reproducing the results.
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Cheng, B., Bethkenhagen, M., Pickard, C.J. et al. Phase behaviours of superionic water at planetary conditions. Nat. Phys. 17, 1228–1232 (2021). https://doi.org/10.1038/s41567-021-01334-9
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DOI: https://doi.org/10.1038/s41567-021-01334-9
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