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Phase behaviours of superionic water at planetary conditions

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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Fig. 1: The diffusion of hydrogen in water with bcc, fcc and hcp lattices of oxygen.
Fig. 2: Modelling hydrogen diffusion in water with an fcc oxygen lattice.
Fig. 3: Hydrogen atoms diffuse easily between the superionic and the liquid phases.
Fig. 4: The phase stabilities for bcc, fcc, hcp and liquid water.

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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.

References

  1. Helled, R., Nettelmann, N. & Guillot, T. Uranus and Neptune: origin, evolution and internal structure. Space Sci. Rev. 216, 38 (2020).

    Article  ADS  Google Scholar 

  2. Millot, M. et al. Nanosecond X-ray diffraction of shock-compressed superionic water ice. Nature 569, 251–255 (2019).

    Article  ADS  Google Scholar 

  3. Demontis, P., LeSar, R. & Klein, M. L. New high-pressure phases of ice. Phys. Rev. Lett. 60, 2284–2287 (1988).

    Article  ADS  Google Scholar 

  4. Millot, M. et al. Experimental evidence for superionic water ice using shock compression. Nat. Phys. 14, 297–302 (2018).

    Article  Google Scholar 

  5. Redmer, R., Mattsson, T. R., Nettelmann, N. & French, M. The phase diagram of water and the magnetic fields of Uranus and Neptune. Icarus 211, 798–803 (2011).

    Article  ADS  Google Scholar 

  6. Soderlund, K. M. & Stanley, S. The underexplored frontier of ice giant dynamos. Phil. Trans. R. Soc. A 378, 20190479 (2020).

    Article  ADS  Google Scholar 

  7. Cavazzoni, C. et al. Superionic and metallic states of water and ammonia at giant planet conditions. Science 283, 44–46 (1999).

    Article  ADS  Google Scholar 

  8. Wilson, H. F., Wong, M. L. & Militzer, B. Superionic to superionic phase change in water: consequences for the interiors of Uranus and Neptune. Phys. Rev. Lett. 110, 151102 (2013).

    Article  ADS  Google Scholar 

  9. French, M., Desjarlais, M. P. & Redmer, R. Ab initio calculation of thermodynamic potentials and entropies for superionic water. Phys. Rev. E 93, 022140 (2016).

    Article  ADS  Google Scholar 

  10. Sun, J., Clark, B. K., Torquato, S. & Car, R. The phase diagram of high-pressure superionic ice. Nat. Commun. 6, 8156 (2015).

    Article  ADS  Google Scholar 

  11. Goncharov, A. F. et al. Dynamic ionization of water under extreme conditions. Phys. Rev. Lett. 94, 125508 (2005).

    Article  ADS  Google Scholar 

  12. Sugimura, E. et al. Experimental evidence of superionic conduction in H2O ice. J. Chem. Phys. 137, 194505 (2012).

    Article  ADS  Google Scholar 

  13. Queyroux, J.-A. et al. Melting curve and isostructural solid transition in superionic ice. Phys. Rev. Lett. 125, 195501 (2020).

    Article  ADS  Google Scholar 

  14. Schwegler, E., Sharma, M., Gygi, F. & Galli, G. Melting of ice under pressure. Proc. Natl Acad. Sci. USA 105, 14779–14783 (2008).

    Article  ADS  Google Scholar 

  15. Hernandez, J.-A. & Caracas, R. Superionic-superionic phase transitions in body-centered cubic H2O ice. Phys. Rev. Lett. 117, 135503 (2016).

    Article  ADS  Google Scholar 

  16. Hernandez, J.-A. & Caracas, R. Proton dynamics and the phase diagram of dense water ice. J. Chem. Phys. 148, 214501 (2018).

    Article  ADS  Google Scholar 

  17. Ceriotti, M. et al. Nuclear quantum effects in water and aqueous systems: experiment, theory, and current challenges. Chem. Rev. 116, 7529–7550 (2016).

    Article  Google Scholar 

  18. Deringer, V. L., Caro, M. A. & Csányi, G. Machine learning interatomic potentials as emerging tools for materials science. Adv. Mater. 31, 1902765 (2019).

    Article  Google Scholar 

  19. Cheng, B., Engel, E. A., Behler, J., Dellago, C. & Ceriotti, M. Ab initio thermodynamics of liquid and solid water. Proc. Natl Acad. Sci. USA 116, 1110–1115 (2019).

    Article  ADS  Google Scholar 

  20. Reinhardt, A. & Cheng, B. Quantum-mechanical exploration of the phase diagram of water. Nat. Commun. 12, 588 (2021).

    Article  ADS  Google Scholar 

  21. Niu, H., Bonati, L., Piaggi, P. M. & Parrinello, M. Ab initio phase diagram and nucleation of gallium. Nat. Commun. 11, 2654 (2020).

    Article  ADS  Google Scholar 

  22. Cheng, B., Mazzola, G., Pickard, C. J. & Ceriotti, M. Evidence for supercritical behaviour of high-pressure liquid hydrogen. Nature 585, 217–220 (2020).

    Article  Google Scholar 

  23. Deringer, V. L. et al. Origins of structural and electronic transitions in disordered silicon. Nature 589, 59–64 (2021).

    Article  ADS  Google Scholar 

  24. Behler, J. & Parrinello, M. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98, 146401 (2007).

    Article  ADS  Google Scholar 

  25. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996); erratum 78, 1396 (1997).

  26. French, M., Mattsson, T. R. & Redmer, R. Diffusion and electrical conductivity in water at ultrahigh pressures. Phys. Rev. B 82, 174108 (2010).

    Article  ADS  Google Scholar 

  27. Rice, M. J., Strässler, S. & Toombs, G. A. Superionic conductors: theory of the phase transition to the cation disordered state. Phys. Rev. Lett. 32, 596–599 (1974).

    Article  ADS  Google Scholar 

  28. Holz, M., Heil, S. & Sacco, A. Temperature-dependent self-diausion coefficients of water and six selected molecular liquids for calibration in accurate 1H NMRPFG measurements. Phys. Chem. Chem. Phys. 2, 4740–4742 (2000).

    Article  Google Scholar 

  29. Gao, Y. et al. Classical and emerging characterisation techniques for investigation of ion transport mechanisms in crystalline fast ionic conductors. Chem. Rev. 120, 5954–6008 (2020).

    Article  Google Scholar 

  30. Bachman, J. C. et al. Inorganic solid-state electrolytes for lithium batteries: mechanisms and properties governing ion conduction. Chem. Rev. 116, 140–162 (2016).

    Article  Google Scholar 

  31. Torrie, G. M. & Valleau, J. P. Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling. J. Comput. Phys. 23, 187–199 (1977).

    Article  ADS  Google Scholar 

  32. Behler, J. Constructing high-dimensional neural network potentials: a tutorial review. Int. J. Quantum Chem. 115, 1032–1050 (2015).

    Article  Google Scholar 

  33. Schwager, B., Chudinovskikh, L., Gavriliuk, A. & Boehler, R. Melting curve of H2O to 90 GPa measured in a laser-heated diamond cell. J. Phys. Condens. Matter 16, S1177 (2004).

    Article  ADS  Google Scholar 

  34. Schwager, B. & Boehler, R. H2O: another ice phase and its melting curve. High Press. Res. 28, 431–433 (2008).

    Article  ADS  Google Scholar 

  35. Van Santen, R. A. The Ostwald step rule. J. Phys. Chem. 88, 5768–5769 (1984).

    Article  Google Scholar 

  36. Oxtoby, D. W. Homogeneous nucleation: theory and experiment. J. Phys. Condens. Matter 4, 7627–7650 (1992).

    Article  ADS  Google Scholar 

  37. Myint, P. C. et al. Nanosecond freezing of water at high pressures: nucleation and growth near the metastability limit. Phys. Rev. Lett. 121, 155701 (2018).

    Article  ADS  Google Scholar 

  38. Myint, P. C. et al. Coupling solidification kinetics with phase-behaviour computations in hydrodynamic simulations of high-pressure, dynamic-compression processes. AIP Adv. 10, 125111 (2020).

    Article  ADS  Google Scholar 

  39. Davidchack, R. L., Morris, J. R. & Laird, B. B. The anisotropic hard-sphere crystal-melt interfacial free energy from fluctuations. J. Chem. Phys. 125, 094710 (2006).

    Article  ADS  Google Scholar 

  40. Goncharov, A. F., Beck, P., Struzhkin, V. V., Hemley, R. J. & Crowhurst, J. C. Laser-heating diamond anvil cell studies of simple molecular systems at high pressures and temperatures. J. Phys. Chem. Solids 69, 2217–2222 (2008).

    Article  ADS  Google Scholar 

  41. Prakapenka, V. B., Holtgrewe, N., Lobanov, S. S. & Goncharov, A. Polymorphism of superionic ice. Preprint at https://arxiv.org/abs/2007.07715 (2020).

  42. Zeng, L. et al. Growth model interpretation of planet size distribution. Proc. Natl Acad. Sci. USA 116, 9723–9728 (2019).

    Article  ADS  Google Scholar 

  43. Scheibe, L., Nettelmann, N. & Redmer, R. Thermal evolution of Uranus and Neptune. Astron. Astrophys. 632, A70 (2019).

    Article  ADS  Google Scholar 

Download references

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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Contributions

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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Correspondence to Bingqing Cheng.

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The authors declare no competing interests.

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Peer review informationNature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

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Supplementary information

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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