- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Ab initio and embedded-atom-model simulation analysis of collective dynamics in liquid Fe at experimental high pressures

Taras Demchuk1, Anatoly B. Belonoshko2,3,4, and Taras Bryk1,5,*

  • *Contact author: bryk@icmp.lviv.ua
PDF

Phys. Rev. B 114, 154202 – Published 3 September, 2026

DOI: https://doi.org/10.1103/vzqb-lsq5

Abstract

We compare extensive ab initio simulations and embedded-atom-model molecular dynamics for analysis of collective dynamics in liquid Fe at several experimental pressures and temperatures of 2200 and 2700 K [Y. Kuwayama et al., Phys. Rev. Lett. 124, 165701 (2020)]. Dynamic eigenmodes of the generalized Langevin equation were calculated based on simulation data and analyzed in a wide range of wave numbers with a focus on dispersion of collective excitations. We analyze the origin of positive dispersion of sound excitations in connection with contributions from different types of hydrodynamic and nonhydrodynamic fluctuations to the corresponding eigenvectors. Dispersion of collective excitations and adiabatic speed of sound, estimated from the simulation data at three pressures, is compared to the values obtained from the inelastic x-ray scattering experiments.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (66)

  1. Y. Sun, M. Mendelev, F. Zhang, X. Liu, B. Da, C.-Zh Wang, and R. M. Wentzcovitch, Unveiling the effect of Ni on the formation and structure of Earth's inner core, Proc. Natl. Acad. Sci. USA 121, e2316477121 (2024).
  2. T. Liu and Z. Jing, Hydrogen and silicon are the preferred light elements in Earth's core, Commun. Earth. Environ. 5, 282 (2024).
  3. A. J. Wilson, D. Alfe, A. M. Walker, and C. J. Davies, Can homogeneous nucleation resolve the inner core nucleation paradox? Earth Planet. Sci. Lett. 614, 118176 (2023).
  4. X. Ma and H. Tkalcic, Seismic low-velocity equatorial torus in the Earth's outer core: Evidence from the late–coda correlation wavefield, Sci. Adv. 10, eadn5562 (2024).
  5. P. M. Nasch, M. H. Manghnani, and R. A. Secco, Sound velocity measurements in liquid iron by ultrasonic interferometry, J. Geophys. Res. 99, 4285 (1994).
  6. M. D. Rutter, R. A. Secco, H. Liu, T. Uchida, M. L. Rivers, S. R. Sutton, and Y. Wang, Viscosity of liquid Fe at high pressure, Phys. Rev. B 66, 060102(R) (2002).
  7. R. A. Secco, M. D. Rutter, S. P. Balog, H. Liu, D. C. Rubie, T. Uchida, D. Frost, Y. Wang, M. Rivers, and S. R. Sutton, Viscosity and density of Fe–S liquids at high pressures, J. Phys.: Condens. Matter 14, 11325 (2002).
  8. G. Shen, V. B. Prakapenka, M. L. Rivers, and S. R. Sutton, Structure of liquid iron at pressures up to 58 GPa, Phys. Rev. Lett. 92, 185701 (2004).
  9. S. Hosokawa, M. Inui, K. Matsuda, D. Ishikawa, and Alfred Q. R. Baron, Damping of the collective modes in liquid Fe, Phys. Rev. B 77, 174203 (2008).
  10. S. Hosokawa, M. Inui, K. Matsuda, D. Ishikawa, and A. Q. R. Baron, Collective dynamics of liquid Fe, J. Phys.: Conf. Ser. 98, 022004 (2008).
  11. G. A. de Wijs, G. Kresse, L. Vocadlo, D. Dobson, D. Alfe, M. J. Gillan, and G. D. Price, The viscosity of liquid iron at the physical conditions of the Earth's core, Nature (London) 392, 805 (1998).
  12. D. Alfe, M. J. Gillan, and G. D. Price, The melting curve of iron at the pressures of the Earth's core from ab initio calculations, Nature (London) 401, 462 (1999).
  13. D. Alfe, G. Kresse, and M. J. Gillan, Structure and dynamics of liquid iron under Earth's core conditions, Phys. Rev. B 61, 132 (2000).
  14. A. B. Belonoshko, R. Ahuja, and B. Johansson, Quasi–ab initio molecular dynamic study of Fe melting, Phys. Rev. Lett. 84, 3638 (2000).
  15. H. K. Mao, J. Xu, V. V. Struzhkin, J. Shu, R. J. Hemley, W. Sturhahn, M. Y. Hu, E. E. Alp, L. Vocadlo, D. Alfe, G. D. Price, M. J. Gillan, M. Schwoerer-Böhning, D. Häusermann, P. Eng, G. Shen, H. Giefers, R. Lübbers, and G. Wortmann, Phonon density of states of iron up to 153 gigapascals, Science 292, 914 (2001).
  16. L. Koči, A. B. Belonoshko, and R. Ahuja, Molecular dynamics study of liquid iron under high pressure and high temperature, Phys. Rev. B 73, 224113 (2006).
  17. C. Desgranges and J. Delhommelle, Viscosity of liquid iron under high pressure and high temperature: Equilibrium and nonequilibrium molecular dynamics simulation studies, Phys. Rev. B 76, 172102 (2007).
  18. W. Luo, B. Johansson, O. Eriksson, S. Arapan, P. Souvatzis, M. I. Katznelson, and R. Ahuja, Dynamical stability of body center cubic iron at the Earth's core conditions, Proc. Natl. Acad. Sci. USA 107, 9962 (2010).
  19. A. B. Belonoshko, T. Bryk, and A. Rosengren, Shear relaxation in iron under the conditions of Earth's inner core, Phys. Rev. Lett. 104, 245703 (2010).
  20. A. B. Belonoshko, S. Arapan, and A. Rosengren, An ab initio molecular dynamics study of iron phases at high pressure and temperature, J. Phys.: Condens. Matter 23, 485402 (2011).
  21. A. B. Belonoshko, N. V. Skorodumova, S. Davis, A. N. Osiptsov, A. Rosengren, and B. Johansson, Origin of the low rigidity of the Earth's inner core, Science 316, 1603 (2007).
  22. A. B. Belonoshko, N. V. Skorodumova, A. Rosengren, and B. Johansson, Elastic anisotropy of Earth's inner core, Science 319, 797 (2008).
  23. A. B. Belonoshko, Equation of state for ε-iron at high pressures and temperatures, Condens. Matter Phys. 13, 23605 (2010).
  24. T. Bryk and A. B. Belonoshko, Collective excitations in molten iron above the melting point: A generalized collective-mode analysis of simulations with embedded-atom potentials, Phys. Rev. B 86, 024202 (2012).
  25. M. Marques, L. E. Gonzalez, and D. J. Gonzalez, Ab initio study of the structure and dynamics of bulk liquid Fe, Phys. Rev. B 92, 134203 (2015).
  26. M. Marques, L. E. Gonzalez, and D. J. Gonzalez, Pressure-induced changes in structural and dynamic properties of liquid Fe close to the melting line. An ab initio study, J. Phys.: Condens. Matter 28, 075101 (2016).
  27. L. E. Gonzalez and D. J. Gonzalez, Structure and dynamics in liquid iron at high pressure and temperature. A first principles study, J. Geophys. Res.: Solid Earth 128, e2022JB025119 (2023).
  28. Y. Kuwayama, G. Morard, Y. Nakajima, K. Hirose, Alfred Q. R. Baron, S. I. Kawaguchi, T. Tsuchiya, D. Ishikawa, N. Hirao, and Y. Ohishi, Equation of state of liquid iron under extreme conditions, Phys. Rev. Lett. 124, 165701 (2020).
  29. M. I. Mendelev, S. Han, D. J. Srolovitz, G. J. Ackland, D. Y. Sun, and M. Asta, Development of new interatomic potentials appropriate for crystalline and liquid iron, Philos. Mag. 83, 3977 (2003).
  30. M. Pozzo, C. Davies, D. Gubbins, and D. Alfe, Thermal and electrical conductivity of iron at Earth's core conditions, Nature (London) 485, 355 (2012).
  31. D. Alfe, G. D. Price, and M. J. Gillan, Iron under Earth's core conditions: Liquid-state thermodynamics and high-pressure melting curve from ab initio calculations, Phys. Rev. B 65, 165118 (2002).
  32. P. Söderlind, J. A. Moriarty, and J. M. Wills, First-principles theory of iron up to Earth-core pressures: Structural, vibrational, and elastic properties, Phys. Rev. B 53, 14063 (1996).
  33. E. G. Moroni, G. Kresse, J. Hafner, and J. Furthmüller, Ultrasoft pseudopotentials applied to magnetic Fe, Co, and Ni: From atoms to solids, Phys. Rev. B 56, 15629 (1997).
  34. P. Ganesh and M. Widom, Ab initio simulations of geometrical frustration in supercooled liquid Fe and Fe-based metallic glass, Phys. Rev. B 77, 014205 (2008).
  35. J.-P. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill, New York, 1980).
  36. J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic, London, 1986).
  37. T. Scopigno, G. Ruocco, and F. Sette, Microscopic dynamics in liquid metals: The experimental point of view, Rev. Mod. Phys. 77, 881 (2005).
  38. T. Scopigno, U. Balucani, G. Ruocco, and F. Sette, Density fluctuations in molten lithium: Inelastic x-ray scattering study, J. Phys.: Condens. Matter 12, 8009 (2000).
  39. T. Scopigno, G. Ruocco, F. Sette, and G. Viliani, Evidence of short-time dynamical correlations in simple liquids, Phys. Rev. E 66, 031205 (2002).
  40. T. Scopigno, A. Filipponi, M. Krisch, G. Monaco, G. Ruocco, and F. Sette, High-frequency acoustic modes in liquid gallium at the melting point, Phys. Rev. Lett. 89, 255506 (2002).
  41. D. J. Gonzalez, L. E. Gonzalez, J. M. Lopez, and M. J. Stott, Microscopic dynamics in the liquid Li-Na alloy: An ab initio molecular dynamics study, Phys. Rev. E 69, 031205 (2004).
  42. D. J. Gonzalez, L. E. Gonzalez, J. M. Lopez, and M. J. Stott, Collective modes in liquid binary alloys. An ab initio molecular dynamics study of the LiMg and LiBa alloys, J. Phys.: Condens. Matter 17, 1429 (2005).
  43. W. Schirmacher and H. Sinn, Collective dynamics of simple liquids: A mode-coupling description, Condens. Matter Phys. 11, 127 (2008).
  44. B. Schmid and W. Schirmacher, Modified mode-coupling theory for the collective dynamics of simple liquids, J. Phys.: Condens. Matter 23, 254211 (2011).
  45. I. M. Mryglod, I. P. Omelyan, and M. V. Tokarchuk, Generalized collective modes for the Lennard-Jones fluid, Mol. Phys. 84, 235 (1995).
  46. T. Bryk, Non-hydrodynamic collective modes in liquid metals and alloys, Eur. Phys. J.: Spec. Top. 196, 65 (2011).
  47. T. Bryk, I. Mryglod, T. Scopigno, G. Ruocco, F. Gorelli, and M. Santoro, Collective excitations in supercritical fluids: Analytical and molecular dynamics study of “positive” and “negative” dispersion, J. Chem. Phys. 133, 024502 (2010).
  48. T. Bryk, G. Ruocco, and A. P. Seitsonen, Stress fluctuations and adiabatic speed of sound in liquids: A simple way to estimate it from ab initio simulations, Sci. Rep. 13, 18042 (2023).
  49. I. M Mrygold, I. M. Mryglod, and M. V. Tokarchuk, On the hydrodynamic theory of a magnetic liquid I. General description, Physica A 220, 325 (1995).
  50. I. M. Mryglod and R. Folk, On the hydrodynamic theory of a magnetic liquid II. Hydrodynamic modes in the Heisenberg fluid, Physica A 234, 129 (1996).
  51. I. Mryglod, R. Folk, S. Dubyk, and Y. Rudavskii, Hydrodynamic time-correlation functions of a Heisenberg ferrofluid, Physica A 277, 389 (2000).
  52. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  53. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  54. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  55. I. M. de Schepper, E. G. D. Cohen, C. Bruin, J. C. van Rijs, W. Montfrooij, and L. A. de Graaf, Hydrodynamic time correlation functions for a Lennard-Jones fluid, Phys. Rev. A 38, 271 (1988).
  56. T. Bryk and G. Ruocco, Generalised hydrodynamic description of the time correlation functions of liquid metals: Ab initio molecular dynamics study, Mol. Phys. 111, 3457 (2013).
  57. I. Tamblyn, J.-Y. Raty, and S. A. Bonev, Tetrahedral clustering in molten lithium under pressure, Phys. Rev. Lett. 101, 075703 (2008).
  58. T. Bryk, S. De Panfilis, F. A. Gorelli, E. Gregoryanz, M. Krisch, G. Ruocco, M. Santoro, T. Scopigno, and A. P. Seitsonen, Dynamical crossover at the liquid-liquid transformation of a compressed molten alkali metal, Phys. Rev. Lett. 111, 077801 (2013).
  59. L. Van Hove, Correlations in space and time and Born approximation scattering in systems of interacting particles, Phys. Rev. 95, 249 (1954).
  60. C. W. Ryu and T. Egami, Alpha-relaxation by scattering and medium-range atomic correlation in simple liquids, J. Chem. Phys. 163, 144506 (2025).
  61. T. Bryk, M. Kopcha, and G. Ruocco, Ab initio study of collective eigenmodes in dynamics of molten salts, J. Mol. Liq. 387, 122622 (2023).
  62. S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (2010).
  63. T. Bryk and A. P. Seitsonen, Ab initio molecular dynamics study of collective excitations in liquid HO and DO: Effect of dispersion corrections, Condens. Matter Phys. 19, 23604 (2016).
  64. A. P. Seitsonen and T. Bryk, Melting temperature of water: DFT-based molecular dynamics simulations with D3 dispersion correction, Phys. Rev. B 94, 184111 (2016).
  65. T. Bryk, W. Schirmacher, and G. Ruocco, Comment on "deformations, relaxation and broken symmetries in liquids, solids and glasses: A unified topological field theory”, Phys. Rev. E 106, 036601 (2022).
  66. Q. Niu, X. Wang, L. Kleinman, W.-M. Liu, D. M. C. Nicholson, and G. M. Stocks, Adiabatic dynamics of local spin moments in itinerant magnets, Phys. Rev. Lett. 83, 207 (1999).

Outline

Information

Phys. Rev. B 114, 154202– Published 3 September, 2026
  • Received 3 January 2025
  • Revised 20 May 2026
  • Accepted 7 August 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation