Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Melting curve of superionic ammonia at planetary interior conditions

Nature Physics volume 19, pages 1280–1285 (2023)Cite this article

Subjects

An Author Correction to this article was published on 16 June 2023

This article has been updated

Abstract

Under high pressures and temperatures, molecular systems with substantial polarization charges, such as ammonia and water, are predicted to form superionic phases and dense fluid states with dissociating molecules and high electrical conductivity. This behaviour potentially plays a role in explaining the origin of the multipolar magnetic fields of Uranus and Neptune, whose mantles are thought to result from a mixture of H2O, NH3 and CH4 ices. Determining the stability domain, melting curve and electrical conductivity of these superionic phases is therefore crucial for modelling planetary interiors and dynamos. Here we report the melting curve of superionic ammonia up to 300 GPa from laser-driven shock compression of pre-compressed samples and atomistic calculations. We show that ammonia melts at lower temperatures than water above 100 GPa and that fluid ammonia’s electrical conductivity exceeds that of water at conditions predicted by hot, super-adiabatic models for Uranus and Neptune, and enhances the conductivity in their fluid water-rich dynamo layers.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Experimental setup with examples of VISAR and SOP data.
Fig. 2: Liquid and phase III pre-compressed Hugoniots and reflectivity.
Fig. 3: Phase diagram and melting temperature of SI NH3.
Fig. 4: Electrical conductivities and melting curves of NH3 and H2O at planetary interior conditions.

Data availability

Data supporting this study are available in the Supplementary Information, from the online repository66 and from the corresponding author upon request.

Code availability

DFT simulations were performed with the proprietary code VASP.

Change history

References

  1. 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 

  2. Hull, S. Superionics: crystal structures and conduction processes. Rep. Prog. Phys. 67, 1233–1314 (2004).

    Article  ADS  Google Scholar 

  3. Mohn, C. E., Krynski, M., Kob, W. & Allan, N. L. Cooperative excitations in superionic PbF2. Philos. Trans. R. Soc. A 379, 20190455 (2021).

    Article  ADS  Google Scholar 

  4. Boyce, J., Hayes, T. & Mikkelsen Jr, J. Extended-x-ray-absorption-fine-structure investigation of mobile-ion density in superionic AgI, CuI, CuBr, and CuCl. Phys. Rev. B 23, 2876–2896 (1981).

    Article  ADS  Google Scholar 

  5. 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 

  6. Bethkenhagen, M., French, M. & Redmer, R. Equation of state and phase diagram of ammonia at high pressures from ab initio simulations. J. Chem. Phys. 138, 234504 (2013).

    Article  ADS  Google Scholar 

  7. French, M., Mattsson, T. R., Nettelmann, N. & Redmer, R. Equation of state and phase diagram of water at ultrahigh pressures as in planetary interiors. Phys. Rev. B 79, 054107 (2009).

    Article  ADS  Google Scholar 

  8. Stanley, S. & Bloxham, J. Convective-region geometry as the cause of Uranus’ and Neptune’s unusual magnetic fields. Nature 428, 151–153 (2004).

    Article  ADS  Google Scholar 

  9. Stanley, S. & Bloxham, J. Numerical dynamo models of Uranus’ and Neptune’s magnetic fields. Icarus 184, 556–572 (2006).

    Article  ADS  Google Scholar 

  10. 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 

  11. Tian, B. Y. & Stanley, S. Interior structure of water planets: implications for their dynamo source regions. Astrophys. J. 768, 156 (2013).

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. Prakapenka, V. B., Holtgrewe, N., Lobanov, S. S. & Goncharov, A. F. Structure and properties of two superionic ice phases. Nat. Phys. 17, 1233–1238 (2021).

  17. Weck, G. et al. Evidence and stability field of fcc superionic water ice using static compression. Phys. Rev. Lett. 128, 165701 (2022).

    Article  ADS  Google Scholar 

  18. 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 

  19. 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 

  20. 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 

  21. Cheng, B., Bethkenhagen, M., Pickard, C. & Hamel, S. Phase behaviours of superionic water at planetary conditions. Nat. Phys. 17, 1228–1232 (2021).

    Article  Google Scholar 

  22. Robinson, V. N., Wang, Y. C., Ma, Y. M. & Hermann, A. Stabilization of ammonia-rich hydrate inside icy planets. Proc. Natl Acad. Sci. USA 114, 9003–9008 (2017).

  23. Robinson, V. N. & Hermann, A. Plastic and superionic phases in ammonia-water mixtures at high pressures and temperatures. J. Phys. Condens. Matter 32, 184004 (2020).

  24. Ninet, S., Datchi, F. & Saitta, A. M. Proton disorder and superionicity in hot dense ammonia ice. Phys. Rev. Lett. 108, 165702 (2012).

    Article  ADS  Google Scholar 

  25. Wang, Z.-Q. et al. Melting curve and transport properties of ammonia ice up to the deep mantle conditions of Uranus and Neptune. Phys. Rev. B 106, 014108 (2022).

    Article  ADS  Google Scholar 

  26. Queyroux, J.-A. et al. Melting curve and chemical stability of ammonia at high pressure: combined x-ray diffraction and Raman study. Phys. Rev. B 99, 134107 (2019).

    Article  ADS  Google Scholar 

  27. Kimura, T. & Murakami, M. Fluid-like elastic response of superionic NH3 in Uranus and Neptune. Proc. Natl Acad. Sci. USA 118, e2021810118 (2021).

    Article  Google Scholar 

  28. Brygoo, S. et al. Analysis of laser shock experiments on precompressed samples using a quartz reference and application to warm dense hydrogen and helium. J. Appl. Phys. 118, 195901 (2015).

    Article  ADS  Google Scholar 

  29. Brygoo, S. et al. Evidence of hydrogen–helium immiscibility at Jupiter-interior conditions. Nature 593, 517–521 (2021).

    Article  ADS  Google Scholar 

  30. Hanson, R. & Jordan, M. Ultrahigh-pressure studies of ammonia. J. Phys. Chem. 84, 1173–1175 (1980).

    Article  Google Scholar 

  31. Barker, L. M. & Hollenbach, R. E. Laser interferometer for measuring high velocities of any reflecting surface. J. Appl. Phys. 43, 4669–4675 (1972).

    Article  ADS  Google Scholar 

  32. Celliers, P. M. et al. Line-imaging velocimeter for shock diagnostics at the OMEGA laser facility. Rev. Sci. Instrum. 75, 4916–4929 (2004).

    Article  ADS  Google Scholar 

  33. Holmes, N. C. Fiber coupled optical pyrometer for shock wave studies. Rev. Sci. Instrum. 66, 2615–2618 (1995).

    Article  ADS  Google Scholar 

  34. Miller, J. E. et al. Streaked optical pyrometer system for laser-driven shock-wave experiments on OMEGA. Rev. Sci. Instrum. 78, 034903 (2007).

    Article  ADS  Google Scholar 

  35. Ravasio, A. et al. Metallization of shock-compressed liquid ammonia. Phys. Rev. Lett. 126, 025003 (2021).

    Article  ADS  Google Scholar 

  36. Eggert, J. et al. Melting temperature of diamond at ultrahigh pressure. Nat. Phys. 6, 40–43 (2010).

    Article  Google Scholar 

  37. Millot, M. et al. Shock compression of stishovite and melting of silica at planetary interior conditions. Science 347, 418–420 (2015).

    Article  ADS  Google Scholar 

  38. Kormer, S. B. Optical study of the characteristics of shock-compressed condensed dielectrics. Sov. Phys. Uspekhi 11, 229–254 (1968).

    Article  ADS  Google Scholar 

  39. Bethkenhagen, M. et al. Planetary ices and the linear mixing approximation. Astrophys. J. 848, 67 (2017).

    Article  ADS  Google Scholar 

  40. Scheibe, L., Nettelmann, N. & Redmer, R. Thermal evolution of Uranus and Neptune-I. adiabatic models. Astron. Astrophys. 632, A70 (2019).

    Article  ADS  Google Scholar 

  41. Naumova, A. S., Lepeshkin, S. V., Bushlanov, P. V. & Oganov, A. R. Unusual chemistry of the C-H-N-O system under pressure and implications for giant planets. J. Phys. Chem. A 125, 3936–3942 (2021).

    Article  Google Scholar 

  42. Conway, L. J., Pickard, C. J. & Hermann, A. Rules of formation of H-C-N-O compounds at high pressure and the fates of planetary ices. Proc. Natl Acad. Sci. USA 118, e2026360118 (2021).

    Article  Google Scholar 

  43. He, Z. et al. Diamond formation kinetics in shock-compressed C-H-O samples recorded by small-angle x-ray scattering and x-ray diffraction. Sci. Adv. 8, eabo0617 (2022).

    Article  Google Scholar 

  44. Robinson, V. N., Marques, M., Wang, Y. C., Ma, Y. M. & Hermann, A. Novel phases in ammonia-water mixtures under pressure. J. Chem. Phys. 149, 234501 (2018).

  45. 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 

  46. Schwegler, E., Galli, G., Gygi, F. & Hood, R. Q. Dissociation of water under pressure. Phys. Rev. Lett. 87, 265501 (2001).

    Article  ADS  Google Scholar 

  47. Goldman, N. et al. Ab initio simulation of the equation of state and kinetics of shocked water. J. Chem. Phys. 130, 124517 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  49. Duarte, L. D., Gastine, T. & Wicht, J. Anelastic dynamo models with variable electrical conductivity: an application to gas giants. Phys. Earth Planet. Inter. 222, 22–34 (2013).

    Article  ADS  Google Scholar 

  50. Borucki, W. J. Kepler: a brief discussion of the mission and exoplanet results. Proc. Am. Philos. Soc. 161, 38–65 (2017).

    ADS  Google Scholar 

  51. Ninet, S. et al. Experimental and theoretical evidence for an ionic crystal of ammonia at high pressure. Phys. Rev. B 89, 174103 (2014).

    Article  ADS  Google Scholar 

  52. Ninet, S. & Datchi, F. High pressure–high temperature phase diagram of ammonia. J. Chem. Phys. 128, 154508 (2008).

    Article  ADS  Google Scholar 

  53. French, M. & Redmer, R. Electronic transport in partially ionized water plasmas. Phys. Plasmas 24, 092306 (2017).

    Article  ADS  Google Scholar 

  54. Nettelmann, N. et al. Uranus evolution models with simple thermal boundary layers. Icarus 275, 107–116 (2016).

    Article  ADS  Google Scholar 

  55. Dewaele, A., Torrent, M., Loubeyre, P. & Mezouar, M. Compression curves of transition metals in the mbar range: experiments and projector augmented-wave calculations. Phys. Rev. B 78, 104102 (2008).

    Article  ADS  Google Scholar 

  56. Datchi, F., Dewaele, A., Godec, Y. L. & Loubeyre, P. Equation of state of cubic boron nitride at high pressures and temperatures. Phys. Rev. B 75, 214104 (2007).

    Article  ADS  Google Scholar 

  57. Qi, T., Millot, M., Kraus, R. G., Root, S. & Hamel, S. Optical and transport properties of dense liquid silica. Phys. Plasmas 22, 062706 (2015).

    Article  ADS  Google Scholar 

  58. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993).

    Article  ADS  Google Scholar 

  59. Kresse, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 14251–14269 (1994).

    Article  ADS  Google Scholar 

  60. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    Article  ADS  Google Scholar 

  61. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  ADS  Google Scholar 

  62. Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81, 511–519 (1984).

    Article  ADS  Google Scholar 

  63. Baldereschi, A. Mean-value point in the Brillouin zone. Phys. Rev. B 7, 5212–5215 (1973).

  64. Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207–8215 (2003).

    Article  ADS  Google Scholar 

  65. Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207 (2003); erratum 124, 219906 (2006).

  66. Hernandez, J.-A. Melting curve of superionic ammonia at planetary interior conditions. OSF https://doi.org/10.17605/OSF.IO/DETZM (2023).

Download references

Acknowledgements

We acknowledge the crucial contribution of the LULI2000 laser and support teams to the success of the experiments. We also thank S. Brygoo and P. Loubeyre for useful discussions. This research was supported by the French National Research Agency (ANR) through the projects POMPEI (grant no. ANR-16-CE31-0008) and SUPER-ICES (grant ANR-15-CE30-008-01), and by the PLAS@PAR Federation. M.F. and R.R. gratefully acknowledge support by the DFG within the Research Unit FOR 2440. M.B. was supported by the European Union within the Marie Skłodowska-Curie actions (xICE grant 894725) and the NOMIS foundation. The DFT-MD calculations were performed at the North-German Supercomputing Alliance facilities.

Author information

Authors and Affiliations

  1. LULI, CNRS, CEA, Sorbonne Université, École Polytechnique – Institut Polytechnique de Paris, Palaiseau, France

    J.-A. Hernandez, A. Benuzzi-Mounaix, M. Guarguaglini, F. Lefevre, T. Vinci & A. Ravasio

  2. Centre for Earth Evolution and Dynamics, University of Oslo, Oslo, Norway

    J.-A. Hernandez

  3. European Synchrotron Radiation Facility, Grenoble, France

    J.-A. Hernandez

  4. École Normale Supérieure de Lyon, Université Lyon 1, Laboratoire de Géologie de Lyon, Lyon, France

    M. Bethkenhagen

  5. Institute of Science and Technology Austria, Klosterneuburg, Austria

    M. Bethkenhagen

  6. Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie (IMPMC), Sorbonne Université, CNRS, MNHN, Paris, France

    S. Ninet & F. Datchi

  7. Institut für Physik, Universität Rostock, Rostock, Germany

    M. French & R. Redmer

  8. CEA, DAM, DIF, Arpajon, France

    F. Occelli

Authors
  1. J.-A. Hernandez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Bethkenhagen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Ninet
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. French
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Benuzzi-Mounaix
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. F. Datchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. M. Guarguaglini
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. F. Lefevre
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. F. Occelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. R. Redmer
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. T. Vinci
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. A. Ravasio
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.-A.H., A.R., S.N. and F.D. designed the project and the experiments. F.D., S.N., F.O., J.-A.H. and A.R. designed the DAC targets, and J.-A.H., S.N., F.D., F.L. and F.O. prepared them. J.-A.H., A.R., A.B.-M., M.G. and T.V. performed the dynamic compression experiments. J.-A.H. analysed the experimental data. M.B. and M.F. designed, performed and analysed the DFT-MD simulations. All authors discussed the data. J.-A.H., M.B. and A.R. wrote the manuscript, and all authors commented on it and improved it.

Corresponding authors

Correspondence to J.-A. Hernandez or A. Ravasio.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks David Stevenson, Kenji Ohta and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Sections S1–S7, Figs. S1–S9 and Tables S1–S3.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hernandez, JA., Bethkenhagen, M., Ninet, S. et al. Melting curve of superionic ammonia at planetary interior conditions. Nat. Phys. 19, 1280–1285 (2023). https://doi.org/10.1038/s41567-023-02074-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-023-02074-8

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing