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Free electron to electride transition in dense liquid potassium

Nature Physics volume 17, pages 955–960 (2021)Cite this article

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Abstract

At high pressures, simple metals such as potassium have a rich phase diagram including an insulating electride phase in which electrons have a localized, anionic character. Measurements in the liquid phase have shown a transition between two states, but experimental challenges have prevented detailed thermodynamic measurements. Using potassium as an example, we present numerical evidence that the liquid–liquid transition is a continuous transformation from free electron to electride behaviour. We show that the transformation manifests in anomalous diffusivity, thermal expansion, speed of sound, coordination number, reflectivity and heat capacity across a wide range of pressures. The abnormalities stem from a significant change in the local electronic and ionic structure. Although primarily a pressure-induced phenomenon, there is also a thermal expansion anomaly. By establishing the electride nature of the high-pressure liquid phase, we resolve the long-standing mystery of how a liquid can be denser than a close-packed solid. Our work is relevant for high-pressure thermodynamic properties of all alkali metal liquids.

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Fig. 1: Phase diagram of potassium from MLMD simulations.
Fig. 2: Thermodynamic quantities of liquid potassium, shown as a function of pressure for selected temperatures.
Fig. 3: Dynamical properties of liquid potassium from MLMD simulations.
Fig. 4: Structural properties of liquid potassium from AIMD simulations.
Fig. 5: Electronic properties of liquid potassium.

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Data availability

All the data presented in Figs. 1–5 are available as source data. All other data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Code availability

Code is available at https://github.com/zhaolongxjtu/KMLP.

References

  1. Katayama, Y. et al. A first-order liquid–liquid phase transition in phosphorus. Nature 403, 170–173 (2000).

    Article  ADS  Google Scholar 

  2. Ashcroft, N. The hydrogen liquids. J. Phys. Condens. Matter 12, A129 (2000).

    Article  ADS  Google Scholar 

  3. Knudson, M. D. et al. Direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium. Science 348, 1455–1460 (2015).

    Article  ADS  Google Scholar 

  4. McMahon, J. M., Morales, M. A., Pierleoni, C. & Ceperley, D. M. The properties of hydrogen and helium under extreme conditions. Rev. Mod. Phys. 84, 1607 (2012).

    Article  ADS  Google Scholar 

  5. Geng, H. Y., Wu, Q., Marqués, M. & Ackland, G. J. Thermodynamic anomalies and three distinct liquid-liquid transitions in warm dense liquid hydrogen. Phys. Rev. B 100, 134109 (2019).

    Article  ADS  Google Scholar 

  6. London, F. The λ-phenomenon of liquid helium and the Bose–Einstein degeneracy. Nature 141, 643–644 (1938).

    Article  ADS  Google Scholar 

  7. Mishima, O. & Stanley, H. E. The relationship between liquid, supercooled and glassy water. Nature 396, 329–335 (1998).

    Article  ADS  Google Scholar 

  8. Soper, A. K. & Ricci, M. A. Structures of high-density and low-density water. Phys. Rev. Lett. 84, 2881 (2000).

    Article  ADS  Google Scholar 

  9. Strässle, T. et al. Structure of dense liquid water by neutron scattering to 6.5 GPa and 670 K. Phys. Rev. Lett. 96, 067801 (2006).

    Article  ADS  Google Scholar 

  10. Fanetti, S. et al. Structure and dynamics of low-density and high-density liquid water at high pressure. J. Phys. Chem. Lett. 5, 235–240 (2014).

    Article  Google Scholar 

  11. Lapini, A. et al. Pressure dependence of hydrogen-bond dynamics in liquid water probed by ultrafast infrared spectroscopy. J. Phys. Chem. Lett. 7, 3579–3584 (2016).

    Article  Google Scholar 

  12. Bove, L. E. et al. Translational and rotational diffusion in water in the gigapascal range. Phys. Rev. Lett. 111, 185901 (2013).

    Article  ADS  Google Scholar 

  13. Cadien, A. et al. First-order liquid-liquid phase transition in cerium. Phys. Rev. Lett. 110, 125503 (2013).

    Article  ADS  Google Scholar 

  14. Nomura, R. et al. Spin crossover and iron-rich silicate melt in the Earth’s deep mantle. Nature 473, 199–202 (2011).

    Article  ADS  Google Scholar 

  15. Ramo, D. M. & Stixrude, L. Spin crossover in Fe2SiO4 liquid at high pressure. Geophys. Res. Lett. 41, 4512–4518 (2014).

    Article  ADS  Google Scholar 

  16. Gregoryanz, E., Degtyareva, O., Somayazulu, M., Hemley, R. & Mao, H.-K. Melting of dense sodium. Phys. Rev. Lett. 94, 185502 (2005).

    Article  ADS  Google Scholar 

  17. Ma, Y. et al. Transparent dense sodium. Nature 458, 182–185 (2009).

    Article  ADS  Google Scholar 

  18. Guillaume, C. L. et al. Cold melting and solid structures of dense lithium. Nat. Phys. 7, 211–214 (2011).

    Article  Google Scholar 

  19. Narygina, O., McBride, E. E., Stinton, G. W. & McMahon, M. I. Melting curve of potassium to 22 GPa. Phys. Rev. B 84, 054111 (2011).

    Article  ADS  Google Scholar 

  20. Woolman, G. et al. Structural and electronic properties of the alkali metal incommensurate phases. Phys. Rev. Mater. 2, 053604 (2018).

    Article  Google Scholar 

  21. Dawes, S. B., Ward, D. L., Huang, R. H. & Dye, J. L. First electride crystal structure. J. Am. Chem. Soc. 108, 3534–3535 (1986).

    Article  Google Scholar 

  22. Dye, J. L. Electrides: ionic salts with electrons as the anions. Science 247, 663–668 (1990).

    Article  ADS  Google Scholar 

  23. Miyakawa, M. et al. Superconductivity in an inorganic electride 12CaO·7Al2O3:e–. J. Am. Chem. Soc. 129, 7270–7271 (2007).

    Article  Google Scholar 

  24. Sushko, P. V., Shluger, A. L., Hirano, M. & Hosono, H. From insulator to electride: a theoretical model of nanoporous oxide 12CaO·7Al2O3. J. Am. Chem. Soc. 129, 942–951 (2007).

    Article  Google Scholar 

  25. Kitano, M. et al. Ammonia synthesis using a stable electride as an electron donor and reversible hydrogen store. Nat. Chem. 4, 934–940 (2012).

    Article  Google Scholar 

  26. Kitano, M. et al. Electride support boosts nitrogen dissociation over ruthenium catalyst and shifts the bottleneck in ammonia synthesis. Nat. Commun. 6, 6731 (2015).

    Article  ADS  Google Scholar 

  27. Zhang, Y., Wang, H., Wang, Y., Zhang, L. & Ma, Y. Computer-assisted inverse design of inorganic electrides. Phys. Rev. X 7, 011017 (2017).

    Google Scholar 

  28. Tsujia, K., Katayama, Y., Morimoto, Y. & Shimomura, O. Structure of liquid rubidium under high pressure. J. Non Cryst. Solids 205-207, 295–298 (1996).

    Article  ADS  Google Scholar 

  29. Gorelli, F. A. et al. Simple-to-complex transformation in liquid rubidium. J. Phys. Chem. Lett. 9, 2909–2913 (2018).

    Article  Google Scholar 

  30. Tsuji, K. et al. Pressure-induced structural change of liquid cesium. J. Non Cryst. Solids 117–118, 72–75 (1990).

    Article  ADS  Google Scholar 

  31. Falconi, S., Lundegaard, L. F., Hejny, C. & McMahon, M. I. X-ray diffraction study of liquid Cs up to 9.8 GPa. Phys. Rev. Lett. 94, 125507 (2005).

    Article  ADS  Google Scholar 

  32. Hattori, T. Is there a pressure-induced discontinuous volume change in liquid Cs? Phys. Rev. B 97, 100101 (2018).

    Article  ADS  Google Scholar 

  33. Decremps, F. et al. Sound velocity and equation of state in liquid cesium at high pressure and high temperature. Phys. Rev. B 98, 184103 (2018).

    Article  ADS  Google Scholar 

  34. Tamblyn, I., Raty, J.-Y. & Bonev, S. A. Tetrahedral clustering in molten lithium under pressure. Phys. Rev. Lett. 101, 075703 (2008).

    Article  ADS  Google Scholar 

  35. Raty, J.-Y., Schwegler, E. & Bonev, S. A. Electronic and structural transitions in dense liquid sodium. Nature 449, 448–451 (2007).

    Article  ADS  Google Scholar 

  36. Bryk, T. et al. Dynamical crossover at the liquid-liquid transformation of a compressed molten alkali metal. Phys. Rev. Lett. 111, 077801 (2013).

    Article  ADS  Google Scholar 

  37. Falconi, S. & Ackland, G. J. Ab initio simulations in liquid caesium at high pressure and temperature. Phys. Rev. B 73, 184204 (2006).

    Article  ADS  Google Scholar 

  38. Boates, B. On the Stability of sp-Valent Materials at High Pressure. PhD thesis, Dalhousie Univ. (2013).

  39. Zhao, L., Zong, H., Ding, X., Sun, J. & Ackland, G. J. Commensurate-incommensurate phase transition of dense potassium simulated by machine-learned interatomic potential. Phys. Rev. B 100, 220101 (2019).

    Article  ADS  Google Scholar 

  40. Robinson, V. N., Zong, H., Ackland, G. J., Woolman, G. & Hermann, A. On the chain-melted phase of matter. Proc. Natl Acad. Sci. USA 116, 10297–10302 (2019).

    Article  Google Scholar 

  41. Rapoport, E. Model for melting-curve maxima at high pressure. J. Chem. Phys. 46, 2891–2895 (1967).

    Article  ADS  Google Scholar 

  42. Tanaka, H. Bond orientational order in liquids: towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization. Eur. Phys. J. E 35, 113 (2012).

    Article  Google Scholar 

  43. Holten, V. & Anisimov, M. A. Entropy-driven liquid–liquid separation in supercooled water. Sci. Rep. 2, 713 (2012).

    Article  ADS  Google Scholar 

  44. Brazhkin, V. V., Fomin, Y. D., Lyapin, A. G., Ryzhov, V. N. & Tsiok, E. N. Widom line for the liquid–gas transition in Lennard–Jones system. J. Phys. Chem. B 115, 14112–14115 (2011).

    Article  Google Scholar 

  45. Bastea, M. & Bastea, S. Electrical conductivity of lithium at megabar pressures. Phys. Rev. B 65, 193104 (2002).

    Article  ADS  Google Scholar 

  46. Kietzmann, A., Redmer, R., Desjarlais, M. P. & Mattsson, T. R. Complex behavior of fluid lithium under extreme conditions. Phys. Rev. Lett. 101, 070401 (2008).

    Article  ADS  Google Scholar 

  47. Bader, R. F. W. Atoms in Molecules: A Quantum Theory (Oxford Univ. Press, 1994).

    Google Scholar 

  48. Savin, A. et al. Electron localization in solid-state structures of the elements: the diamond structure. Angew. Chem. Int. Ed. 31, 187–188 (1992).

    Article  Google Scholar 

  49. Marqués, M. et al. Potassium under pressure: a pseudobinary ionic compound. Phys. Rev. Lett. 103, 115501 (2009).

    Article  ADS  Google Scholar 

  50. McBride, E. E. et al. One-dimensional chain melting in incommensurate potassium. Phys. Rev. B 91, 144111 (2015).

    Article  ADS  Google Scholar 

  51. Clark, S. J. et al. First principles methods using CASTEP. Z. Krist. 220, 567–570 (2005).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  53. Morris, A. J., Nicholls, R. J., Pickard, C. J. & Yates, J. R. OptaDOS: a tool for obtaining density of states, core-level and optical spectra from electronic structure codes. Comput. Phys. Commun. 185, 1477–1485 (2014).

    Article  ADS  MATH  Google Scholar 

  54. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).

    Article  Google Scholar 

  55. 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 

  56. Ackland, G. J. Temperature dependence in interatomic potentials and an improved potential for Ti. J. Phys. Conf. Ser. 402, 012001 (2012).

    Article  Google Scholar 

  57. Khakshouri, S., Alfè, D. & Duffy, D. M. Development of an electron-temperature-dependent interatomic potential for molecular dynamics simulation of tungsten under electronic excitation. Phys. Rev. B 78, 224304 (2008).

  58. Zhang, X., Grabowski, B., Körmann, F., Freysoldt, C. & Neugebauer, J. Accurate electronic free energies of the 3d, 4d, and 5d transition metals at high temperatures. Phys. Rev. B 95, 165126 (2017).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  60. Parrinello, M. & Rahman, A. Polymorphic transitions in single crystals: a new molecular dynamics method. J. Appl. Phys. 52, 7182 (1981).

    Article  ADS  Google Scholar 

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Acknowledgements

H.Z. and G.J.A. acknowledge the ERC project HECATE for funding. V.N.R. thanks the UK’s EPSRC for CM-CDT studentships. H.Z. and X.D. thank the National Natural Science Foundation of China (51931004 and 51871177) and the 111 project 2.0 (BP2018008). We are grateful for computational support from the UK national high performance computing service (ARCHER) and the UK Materials and Molecular Modelling Hub, which is partially funded by EPSRC (EP/P020194), access for both of which was obtained via the UKCP consortium and funded by EPSRC grant no. EP/P022561/1.

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Authors and Affiliations

  1. State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, China

    Hongxiang Zong, Long Zhao & Xiangdong Ding

  2. Centre for Science at Extreme Conditions and School of Physics and Astronomy, The University of Edinburgh, Edinburgh, UK

    Hongxiang Zong, Victor Naden Robinson, Andreas Hermann & Graeme J. Ackland

  3. The ‘Abdus Salam’ International Centre for Theoretical Physics, Trieste, Italy

    Victor Naden Robinson & Sandro Scandolo

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Contributions

H.Z., V.N.R., A.H. and G.J.A. conceived the research. H.Z., V.N.R., A.H. and L.Z. conducted the simulation. S.S. and G.J.A. created the two-state liquid model. All the authors participated in the analysis and interpretation of the results as well as writing of the manuscript.

Corresponding authors

Correspondence to Long Zhao or Graeme J. Ackland.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Takanori Hattori, Artem Oganov and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–20 and Notes 1–8.

Supplementary Video 1

Liquid potassium ELF at 22.8 GPa and 650 K. The ELF (0.70) for a liquid is challenging to summarize: here one snapshot is scanned over 100 ELF surfaces along the z direction.

Source data

Source Data Fig. 1

Plotted data points.

Source Data Fig. 2

Plotted data points.

Source Data Fig. 3

Plotted data points.

Source Data Fig. 4

Plotted data points.

Source Data Fig. 5

Plotted data points and single images for Fig. 5c–f.

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Zong, H., Robinson, V.N., Hermann, A. et al. Free electron to electride transition in dense liquid potassium. Nat. Phys. 17, 955–960 (2021). https://doi.org/10.1038/s41567-021-01244-w

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