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Structure of liquid mercury at high pressure

James W. E. Drewitt*, Francesco Turci, and Adrian C. Barnes

Benedict J. Heinen, Elena-Marie Rogmann, and Oliver T. Lord

Craig W. Wilson and Simon G. Macleod

Annette K. Kleppe

  • School of Physics, University of Bristol, H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom

  • School of Earth Sciences, University of Bristol, Wills Memorial Building, Queens Road, Bristol BS8 1RJ, United Kingdom

  • *Contact author: james.drewitt@bristol.ac.uk

Phys. Rev. B 113, 174201 – Published 14 May, 2026

DOI: https://doi.org/10.1103/nffz-z1g8

Abstract

The atomic-scale structure and melting curve of liquid mercury was measured using in situ synchrotron x-ray diffraction (SXRD) at pressure and temperature (p−T) conditions up to 9.44(2) GPa and 651(1) K. Ab initio molecular dynamics (AIMD) simulations were employed to obtain a detailed atomistic model of the liquid structure. The results reveal a pronounced flattening, and potential maximum, in the measured melting curve between 6 and 9 GPa. The structure factors SHgHg(Q) and pair distribution functions gHgHg(r) calculated from the AIMD simulations are in good overall agreement with the SXRD measurements under comparable reduced densities and temperatures, indicating that the atomistic structure of liquid Hg is well captured by AIMD. With increasing pressure, the principal peak in SHgHg(Q) shifts to higher Q, with the subsidiary peak at Q=2kF experiencing a concomitant shift consistent with the increased electron density. Considering the Evans t-matrix formulation of the Ziman theory of liquid metals, the structural S(2kF) term is expected to have only a weak influence on the electrical resistivity under compression. In contrast, the pressure-induced broadening and shift of the d-projected density of states towards the Fermi level is consistent with enhanced near-resonant d-electron scattering, and a corresponding increase in resistivity, analogous to the behavior of first-row transition metals. Analysis of the measured gHgHg(r) functions, and AIMD trajectories in real space, indicates that the liquid structure experiences a progressive development towards simple hard-sphere-like behavior at increasing p−T along the melting curve. However, topological cluster classification analysis shows that while the structural fingerprint of liquid Hg strongly resembles an effective hard-sphere system, even at the highest pressures investigated it contains more many-body motifs than expected for this simple model.

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Corrections

22 June, 2026

Correction: A redundant summation term has been removed from Eq. (3).

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Supplemental Material

References (48)

  1. Y. Waseda, The Structure of Non-Crystalline Materials. Liquids and Amorphous Solids (McGraw-Hill Inc, New York, 1980).
  2. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, 4th ed. (Academic Press, Elsevier Ltd., Amsterdam, 2013).
  3. J. W. E. Drewitt, Liquid structure under extreme conditions: High-pressure x-ray diffraction studies, J. Phys.: Condens. Matter 33, 503004 (2021).
  4. H. K. Onnes, Further experiments with liquid helium. G. On the electrical resistance of pure metals, etc. VI. On the sudden change in the rate at which the resistance of mercury disappears, in Through Measurement to Knowledge: The Selected Papers of Heike Kamerlingh Onnes 1853–1926, edited by K. Gavroglu and Y. Goudaroulis (Springer Netherlands, Dordrecht, 1991), pp. 267–272.
  5. F. Hensel and E. U. Franck, Metal-nonmetal transition in dense mercury vapor, Rev. Mod. Phys. 40, 697 (1968).
  6. J. R. Franz, Metal-nonmetal transition in expanded liquid mercury, Phys. Rev. Lett. 57, 889 (1986).
  7. G. Kresse and J. Hafner, Ab initio simulation of the metal/nonmetal transition in expanded fluid mercury, Phys. Rev. B 55, 7539 (1997).
  8. Y. Waseda and W. A. Miller, The structure of liquid mercury over a wide range of temperature (−30 to 290∘C), Phys. Status Solidi B 91, 141 (1979).
  9. M. Inui, X. Hong, and K. Tamura, Local structure of expanded fluid mercury using synchrotron radiation: From liquid to dense vapor, Phys. Rev. B 68, 094108 (2003).
  10. D. A. Young, Phase Diagrams of the Elements, Tech. Rep. UCRL-51902 (Lawrence Livermore National Lab. (LLNL), Livermore, CA (USA), 1975), OSTI ID: 4010212.
  11. P. J. Brown, A. G. Fox, E. N. Maslen, M. A. O'Keefe, and B. T. M. Willis, Intensity of diffracted intensities, in International Tables for Crystallography Volume C: Mathematical, Physical and Chemical Tables, edited by E. Prince (Springer, Dordrecht, 2006), pp. 554.
  12. J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, Atomic form factors, incoherent scattering functions, and photon scattering cross sections, J. Phys. Chem. Ref. Data 4, 471 (1975).
  13. G. W. Stinton, S. G. MacLeod, H. Cynn, D. Errandonea, W. J. Evans, J. E. Proctor, Y. Meng, and M. I. McMahon, Equation of state and high-pressure/high-temperature phase diagram of magnesium, Phys. Rev. B 90, 134105 (2014).
  14. C. Cazorla, S. G. MacLeod, D. Errandonea, K. A. Munro, M. I. McMahon, and C. Popescu, Thallium under extreme compression, J. Phys.: Condens. Matter 28, 445401 (2016).
  15. J. W. E. Drewitt, F. Turci, B. J. Heinen, S. G. Macleod, F. Qin, A. K. Kleppe, and O. T. Lord, Structural ordering in liquid gallium under extreme conditions, Phys. Rev. Lett. 124, 145501 (2020).
  16. P. I. Dorogokupets and A. Dewaele, Equations of state of MgO, Au, Pt, NaCl-B1, and NaCl-B2: Internally consistent high-temperature pressure scales, High Press. Res. 27, 431 (2007).
  17. See Supplemental Material at http://link.aps.org/supplemental/10.1103/nffz-z1g8 for further details of the data reduction and calibration and the Figs. S1–S5, which also contains Refs. [46, 47, 48].
  18. J. H. Eggert, G. Weck, P. Loubeyre, and M. Mezouar, Quantitative structure factor and density measurements of high-pressure fluids in diamond anvil cells by x-ray diffraction: Argon and water, Phys. Rev. B 65, 174105 (2002).
  19. B. J. Heinen and J. W. E. Drewitt, LiquidDiffract: Software for liquid total scattering analysis, Phys. Chem. Miner. 49, 9 (2022).
  20. G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  21. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  22. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  23. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  24. S. Nosé, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys. 81, 511 (1984).
  25. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  26. R. Armiento and A. E. Mattsson, Functional designed to include surface effects in self-consistent density functional theory, Phys. Rev. B 72, 085108 (2005).
  27. A. E. Mattsson, R. Armiento, J. Paier, G. Kresse, J. M. Wills, and T. R. Mattsson, The AM05 density functional applied to solids, J. Chem. Phys. 128, 084714 (2008).
  28. A. E. Mattsson and R. Armiento, Implementing and testing the AM05 spin density functional, Phys. Rev. B 79, 155101 (2009).
  29. S. Le Roux and P. Jund, Ring statistics analysis of topological networks: New approach and application to amorphous GeS2 and SiO2 systems, Comput. Mater. Sci. 49, 70 (2010).
  30. http://gw4.ac.uk/isambard/
  31. S. T. Cui, P. T. Cummings, and H. D. Cochran, The calculation of the viscosity from the autocorrelation function using molecular and atomic stress tensors, Mol. Phys. 88, 1657 (1996).
  32. W. Klement, A. Jayaraman, and G. C. Kennedy, Transformations in mercury at high pressures, Phys. Rev. 131, 1 (1963).
  33. F. Simon and G. Glatzel, Bemerkungen zur schmelzdruckkurve, Zeitschrift für Anorganische und Allgemeine Chemie 178, 309 (1929).
  34. V. V. Kechin, Melting curve equations at high pressure, Phys. Rev. B 65, 052102 (2001).
  35. U. Bafile, F. Barocchi, F. Cilloco, K. Hochgesand, R. Winter, and H. E. Fischer, The microscopic structure of liquid mercury from neutron and x-ray diffraction, Physica B 276-278, 452 (2000).
  36. O. Schulte and W. B. Holzapfel, Phase diagram for mercury up to 67 GPa and 500 K, Phys. Rev. B 48, 14009 (1993).
  37. R. Evans, The resistivity and thermopower of liquid mercury and its alloys, J. Phys. C 3, S137 (1970).
  38. V. G. Rivlin, R. M. Waghorne, and G. I. Williams, The structure of liquid mercury, Philos. Mag. 13, 1169 (1966).
  39. J. A. Cambell and J. H. Hildebrand, The structure of liquid mercury, J. Chem. Phys. 11, 330 (1943).
  40. D. R. Lide, Viscosity of liquids, in CRC Handbook of Chemistry and Physics, Internet Version 2005, edited by D. R. Lide (CRC Press, Boca Raton, FL, 2005), pp. 6, Sec. 6.
  41. R. Evans, D. Greenwood, P. Lloyd, and J. Ziman, The resistivity and thermopower of liquid mercury, Phys. Lett. A 30, 313 (1969).
  42. T. E. Faber, Introduction to the Theory of Liquid Metals (Cambridge University Press, Cambridge, 1972).
  43. R. Evans, D. A. Greenwood, and P. Lloyd, Calculations of the transport properties of liquid transition metals, Phys. Lett. A 35, 57 (1971).
  44. A. Malins, S. R. Williams, J. Eggers, and C. P. Royall, Identification of structure in condensed matter with the topological cluster classification, J. Chem. Phys. 139, 234506 (2013).
  45. J. W. E. Drewitt, (2026): Data from Drewitt, Phys. Rev. B 2026 https://doi.org/10.5523/bris.wrd53xwfyg9q1zhq0ao0dwovk.
  46. T. E. Faber and J. M. Ziman, A theory of the electrical properties of liquid metals: III. The resistivity of binary alloys, Philos. Mag. 11, 153 (1965).
  47. C. Carlile, Spectrum correction factors for sample holder and self-shielding effects for planar samples in thermal neutron scattering studies, Tech. Rep. RL-74-103 (Rutherford Appleton Laboratory, 1974).
  48. C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker, X-ray form factor, attenuation, and scattering tables (version 2.1), [Online] Available: http://physics.nist.gov/ffast. National Institute of Standards and Technology (2005).

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