- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Materials

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Structure and viscosity of liquid uranium-zirconium mixtures from machine-learning-based molecular dynamics

Matteo Canducci1, Emeric Bourasseau1, Patrice Malfreyt2, Noël Jakse3, and Julien Tranchida1

PDF

Phys. Rev. Materials 10, 065601 – Published 4 June, 2026

DOI: https://doi.org/10.1103/3z69-s3d2

Abstract

The thermophysical properties of liquid uranium-zirconium (U,Zr) mixtures play a crucial role in understanding the early stages of nuclear accident scenarios in pressurized-water reactors, as well as in other reactor designs. In this study, atomistic modeling leveraging ab initio calculations and a machine-learning interatomic potential framework are employed to investigate the static and dynamic properties of liquid (U,Zr) mixtures. More specifically, a spectral neighbor analysis potential trained on ab initio configurations is used to model the system, and its predictions are systematically compared and analyzed with experimental data from the literature and ab initio results. The model is then used to analyze an increase of the viscosity predicted for intermediate liquid (U,Zr) compositions, and its relationship to the internal structure of the mixtures. These insights contribute to the refinement of nuclear fuel models, enhance the accuracy of in-vessel corium retention simulations related to the mitigation of severe accident scenarios, and emphasize the possibility of using a combined ab initio and machine-learning interatomic potential approach to compute properties of such complex mixtures.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (98)

  1. J. L. Rempe, K. Suh, F. Cheung, and S. Kim, In -vessel retention of molten corium: Lessons learned and outstanding issues, Nuclear Technol. 161, 210 (2008).
  2. C. Journeau, V. Bouyer, N. Cassiaut-Louis, P. Fouquart, P. Piluso, G. Ducros, S. Gossé, C. Guéneau, A. Quaini, B. Fluhrer, et al., Safest roadmap for corium experimental research in Europe, ASCE-ASME J. Risk Uncertainty Eng. Syst. B: Mech. Eng. 4, 030901 (2018).
  3. L. Carénini, F. Fichot, N. Bakouta, A. Filippov, R. Le Tellier, L. Viot, I. Melnikov, and P. Pandazis, Main outcomes from the IVR code benchmark performed in the European IVMR project, Ann. Nucl. Energy 146, 107612 (2020).
  4. R. Le Tellier, L. Saas, and S. Bajard, Transient stratification modelling of a corium pool in a LWR vessel lower head, Nucl. Eng. Des. 287, 68 (2015).
  5. C. Gueneau, N. Dupin, L. Kjellqvist, E. Geiger, M. Kurata, S. Gosse, E. Corcoran, A. Quaini, R. Hania, A. L. Smith, et al., TAF-ID: An international thermodynamic database for nuclear fuels applications, Calphad 72, 102212 (2021).
  6. S. Bakardjieva, M. Barrachin, S. Bechta, D. Bottomley, L. Brissoneau, B. Cheynet, E. Fischer, C. Journeau, M. Kiselova, L. Mezentseva, et al., Improvement of the European thermodynamic database NUCLEA, Prog. Nucl. Energy 52, 84 (2010).
  7. A. Quaini, C. Guéneau, S. Gossé, N. Dupin, B. Sundman, E. Brackx, R. Domenger, M. Kurata, and F. Hodaj, Contribution to the thermodynamic description of the corium–the U-Zr-O system, J. Nucl. Mater. 501, 104 (2018).
  8. S. U. Mun, G. Oh, J. H. Kim, S.-G. Park, and B. M. Weon, Solidification-induced nonuniformity in U–Zr–Re metallic nuclear fuel rods, Sci. Rep. 14, 19402 (2024).
  9. D. Chen, J. Burns, K. E. Wright, D. Salvato, T. Yao, and L. Capriotti, Transmission electron microscopy characterization of fuel-cladding chemical interaction between U-Pu-Zr fuel with added minor actinides and AIM1 cladding, J. Nucl. Mater. 607, 155667 (2025).
  10. M. Simnad, The U-ZrHx alloy: Its properties and use in TRIGA fuel, Nucl. Eng. Des. 64, 403 (1981).
  11. A. Pungerčič, D. Čalič, and L. Snoj, Computational burnup analysis of the TRIGA Mark II research reactor fuel, Prog. Nucl. Energy 130, 103536 (2020).
  12. M. W. Mallett, 7.4 Zirconium-uranium dioxide reaction, Uranium Dioxide: Properties and Nuclear Applications 4, 342 (1961).
  13. A. Brunel, A. Quaini, T. Alpettaz, C. Bonnet, R. Guillou, and L. Cormier, Experimental investigation of the phases transitions on O-rich side of the Zr–O system, Calphad 79, 102490 (2022).
  14. A. Quaini, C. Guéneau, S. Gossé, B. Sundman, D. Manara, A. Smith, D. Bottomley, P. Lajarge, M. Ernstberger, and F. Hodaj, High temperature investigation of the solid/liquid transition in the PuO2–UO2–ZrO2 system, J. Nucl. Mater. 467, 660 (2015).
  15. J. Delacroix, C. Journeau, N. Chikhi, P. Fouquart, and D. Zhan, Measurements of in-vessel and ex-vessel liquid corium surface tension and density in the VITI-MBP test bench within ALISA Euro-Chinese project, Mechanic. Eng. J. 7, 19-00611 (2020).
  16. J. Delacroix, C. Journeau, and P. Piluso, High-temperature characterization of melted nuclear core materials: Investigating corium properties through the case studies of in-vessel and ex-vessel retention, Front. Energy Res. 10, 883972 (2022).
  17. O. L. G. Alderman, L. B. Skinner, C. J. Benmore, A. Tamalonis, and J. K. R. Weber, Structure of molten titanium dioxide, Phys. Rev. B 90, 094204 (2014).
  18. L. Skinner, C. Benmore, J. Weber, M. Williamson, A. Tamalonis, A. Hebden, T. Wiencek, O. Alderman, M. Guthrie, L. Leibowitz, et al., Molten uranium dioxide structure and dynamics, Science 346, 984 (2014).
  19. O. Alderman, C. Benmore, J. Weber, L. Skinner, A. Tamalonis, S. Sendelbach, A. Hebden, and M. Williamson, Corium lavas: Structure and properties of molten UO2−ZrO2 under meltdown conditions, Sci. Rep. 8, 2434 (2018).
  20. W. K. Kim, J. H. Shim, and M. Kaviany, Thermophysical properties of liquid UO2, ZrO2 and corium by molecular dynamics and predictive models, J. Nucl. Mater. 491, 126 (2017).
  21. S. K. Wilke, C. J. Benmore, O. L. Alderman, G. Sivaraman, M. D. Ruehl, K. L. Hawthorne, A. Tamalonis, D. A. Andersson, M. A. Williamson, and R. Weber, Plutonium oxide melt structure and covalency, Nat. Mater., 23, 884 (2024).
  22. X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Côté, T. Deutsch, L. Genovese, P. Ghosez, M. Giantomassi, S. Goedecker, D. R. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, et al., ABINIT: First-principles approach to material and nanosystem properties, Comput. Phys. Commun. 180, 2582 (2009).
  23. A. H. Romero, D. C. Allan, B. Amadon, G. Antonius, T. Applencourt, L. Baguet, J. Bieder, F. Bottin, J. Bouchet, E. Bousquet, et al., ABINIT: Overview and focus on selected capabilities, J. Chem. Phys. 152, 124102 (2020).
  24. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  25. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  26. H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
  27. W. Xie, W. Xiong, C. A. Marianetti, and D. Morgan, Correlation and relativistic effects in U metal and U-Zr alloy: Validation of ab initio approaches, Phys. Rev. B 88, 235128 (2013).
  28. P. Söderlind, A. Landa, and P. E. A. Turchi, Comment on “correlation and relativistic effects in U metal and U-Zr alloy: Validation of ab initio approaches,” Phys. Rev. B 90, 157101 (2014).
  29. S. Zhou, R. Jacobs, W. Xie, E. Tea, C. Hin, and D. Morgan, Combined ab initio and empirical model of the thermal conductivity of uranium, uranium-zirconium, and uranium-molybdenum, Phys. Rev. Mater. 2, 083401 (2018).
  30. A. Aly, B. Beeler, and M. Avramova, Ab initio molecular dynamics investigation of γ-(U, Zr) structural and thermal properties as a function of temperature and composition, J. Nucl. Mater. 561, 153523 (2022).
  31. A. Castellano, F. Bottin, J. Bouchet, A. Levitt, and G. Stoltz, Ab initio canonical sampling based on variational inference, Phys. Rev. B 106, L161110, (2022).
  32. A. Castellano, R. Béjaud, P. Richard, O. Nadeau, C. Duval, G. Geneste, G. Antonius, J. Bouchet, A. Levitt, G. Stoltz, et al., Machine learning assisted canonical sampling (MLACS), Comput. Phys. Commun. 316, 109730 (2025).
  33. A. P. Thompson, L. P. Swiler, C. R. Trott, S. M. Foiles, and G. J. Tucker, Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials, J. Comput. Phys. 285, 316 (2015).
  34. Y. Zuo, C. Chen, X. Li, Z. Deng, Y. Chen, J. Behler, G. Csányi, A. V. Shapeev, A. P. Thompson, M. A. Wood, et al., Performance and cost assessment of machine learning interatomic potentials, J. Phys. Chem. A 124, 731 (2020).
  35. V. L. Deringer, M. A. Caro, and G. Csányi, Machine learning interatomic potentials as emerging tools for materials science, Adv. Mater. 31, 1902765 (2019).
  36. J. T. Willman, K. Nguyen-Cong, A. S. Williams, A. B. Belonoshko, S. G. Moore, A. P. Thompson, M. A. Wood, and I. I. Oleynik, Machine learning interatomic potential for simulations of carbon at extreme conditions, Phys. Rev. B 106, L180101 (2022).
  37. S. Kumar, H. Tahmasbi, K. Ramakrishna, M. Lokamani, S. Nikolov, J. Tranchida, M. A. Wood, and A. Cangi, Transferable interatomic potential for aluminum from ambient conditions to warm dense matter, Phys. Rev. Res. 5, 033162 (2023).
  38. S. Nikolov, K. Ramakrishna, A. Rohskopf, M. Lokamani, J. Tranchida, J. Carpenter, A. Cangi, and M. A. Wood, Probing iron in Earth's core with molecular-spin dynamics, Proc. Natl. Acad. Sci. USA 121, e2408897121 (2024).
  39. E. T. Dubois, J. Tranchida, J. Bouchet, and J.-B. Maillet, Atomistic simulations of nuclear fuel UO2 with machine learning interatomic potentials, Phys. Rev. Mater. 8, 025402 (2024).
  40. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford, 2017).
  41. U. Balucani and M. Zoppi, Dynamics of the Liquid State (Clarendon Press, Oxford, 1995), Vol. 10.
  42. J. Tranchida, F. Nicaud, B. W. Beeler, and E. Bourasseau, Thermophysical properties and unexpected viscosity of liquid (U, Zr): An atomistic investigation, J. Chem. Phys. 160, 214507 (2024).
  43. J. D. Honeycutt and H. C. Andersen, Molecular dynamics study of melting and freezing of small Lennard-Jones clusters, J. Phys. Chem. 91, 4950 (1987).
  44. D. Faken and H. Jónsson, Systematic analysis of local atomic structure combined with 3D computer graphics, Comput. Mater. Sci. 2, 279 (1994).
  45. Z. Xie, D. Chauraud, E. Bitzek, S. Korte-Kerzel, and J. Guénolé, Laves phase crystal analysis (LACA): Atomistic identification of lattice defects in C14 and C15 topologically close-packed phases, J. Mater. Res. 36, 2010 (2021).
  46. H. Zhang, M. A. Khan, T. Yan, and K. A. Fichthorn, Size and temperature dependent shapes of copper nanocrystals using parallel tempering molecular dynamics, Nanoscale 16, 11146 (2024).
  47. S. Xiao and W. Hu, Comparative study of microstructural evolution during melting and crystallization, J. Chem. Phys. 125, 014503 (2006).
  48. E. Urrutia Bañuelos, C. Contreras Aburto, and A. Maldonado Arce, A common neighbor analysis of crystallization kinetics and excess entropy of charged spherical colloids, J. Chem. Phys. 144, 094504 (2016).
  49. M. S. Green, The statistical mechanics of electrical conduction in fluids, J. Phys. Chem. 58, 714 (1954).
  50. R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn. 12, 570 (1957).
  51. W. Sutherland, LXXV. A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin, Lond. Edinb. Dubl. Philos. Mag. J. Sci. 9, 781 (1905).
  52. E. N. da C. Andrade, XLI. A theory of the viscosity of liquids—part I, Lond. Edinb. Dubl. Phil. Mag. 17, 497 (1934).
  53. E. N. d. C. Andrade, LVIII, A theory of the viscosity of liquids—part II, Lond. Edinb. Dubl. Philos. Mag. J. Sci. 17, 698 (1934).
  54. L. Pauling, Atomic radii and interatomic distances in metals, J. Am. Chem. Soc. 69, 542 (1947).
  55. V. Lubarda, On the effective lattice parameter of binary alloys, Mech. Mater. 35, 53 (2003).
  56. A. Landa, J. E. Klepeis, R. E. Rudd, K. J. Caspersen, and D. A. Young, Analytic binary alloy volume–concentration relations and the deviation from Zen's law, Appl. Sci. 11, 6231 (2021).
  57. C. C. Miller, The Stokes-Einstein law for diffusion in solution, Proc. Roy. Soc. Lond. Ser. A 106, 724 (1924).
  58. F. Sudreau and G. Cognet, Corium viscosity modelling above liquidus temperature, Nucl. Eng. Des. 178, 269 (1997).
  59. M. Ramacciotti, C. Journeau, F. Sudreau, and G. Cognet, Viscosity models for corium melts, Nucl. Eng. Des. 204, 377 (2001).
  60. A. P. Moore, B. Beeler, C. Deo, M. I. Baskes, and M. A. Okuniewski, Atomistic modeling of high temperature uranium–zirconium alloy structure and thermodynamics, J. Nucl. Mater. 467, 802 (2015).
  61. A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in 't Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, and S. J. Plimpton, LAMMPS—A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Comput. Phys. Commun. 271, 108171 (2022).
  62. L. Leibowitz, R. Blomquist, and A. Pelton, Thermodynamics of the uranium-zirconium system, J. Nucl. Mater. 167, 76 (1989).
  63. E. Sikorski, M. Cusentino, M. McCarthy, J. Tranchida, M. Wood, and A. Thompson, Machine learned interatomic potential for dispersion strengthened plasma facing components, J. Chem. Phys. 158, 114101 (2023).
  64. S. Nikolov, M. A. Wood, A. Cangi, J.-B. Maillet, M.-C. Marinica, A. P. Thompson, M. P. Desjarlais, and J. Tranchida, Data-driven magneto-elastic predictions with scalable classical spin-lattice dynamics, npj Comput Mater 7, 153 (2021).
  65. B. G. del Rio, L. E. González, and D. J. González, First principles study of liquid uranium at temperatures up to 2050 K, J. Phys.: Condens. Matter 32, 304001 (2020).
  66. T. Schenk, D. Holland-Moritz, V. Simonet, R. Bellissent, and D. M. Herlach, Icosahedral short-range order in deeply undercooled metallic melts, Phys. Rev. Lett. 89, 075507 (2002).
  67. M. C. Notarangelo, J. Tranchida, K. Goloviznina, M. Romanova, E. Bourasseau, and M. Salanne, Atomistic investigation of thermophysical properties of actinide chlorides-based molten salts via ab initio molecular dynamics and the polarizable ion model, J. Phys. Chem. B 130, 814 (2026).
  68. Y. Su, M. Mohr, R. K. Wunderlich, X. Wang, Q. Cao, D. Zhang, Y. Yang, H. J. Fecht, and J.-Z. Jiang, The relationship between viscosity and local structure in liquid zirconium via electromagnetic levitation and molecular dynamics simulations, J. Mol. Liq. 298, 111992 (2020).
  69. N. Jakse and A. Pasturel, Local order and dynamic properties of liquid and undercooled Cux Zr1−x alloys by ab initio molecular dynamics, Phys. Rev. B 78, 214204 (2008).
  70. M. A. Paramonov, D. V. Minakov, V. B. Fokin, D. V. Knyazev, G. S. Demyanov, and P. R. Levashov, Ab initio inspection of thermophysical experiments for zirconium near melting, J. Appl. Phys. 132, 065102 (2022).
  71. C. Lapointe, A. Zhong, T. D. Swinburne, F. Bruneval, M. Athènes, and M.-C. Marinica, Anomalous self-diffusion in tungsten and molybdenum: Exonerating the di-vacancy contribution and the key role of interatomic interaction, Phys. Rev. Mater. 9, 093801 (2025).
  72. S. Becker, E. Devijver, R. Molinier, and N. Jakse, Glass-forming ability of elemental zirconium, Phys. Rev. B 102, 104205 (2020).
  73. P.-F. Paradis, T. Ishikawa, and S. Yoda, Non-contact measurements of surface tension and viscosity of niobium, zirconium, and titanium using an electrostatic levitation furnace, Int. J. Thermophys. 23, 825 (2002).
  74. S. Xue, W. Dong, D. Chen, Q. Guo, H. He, and J. Yu, Analysis of electrostatic levitation control system and oscillation method for material properties measurement, Rev. Sci. Instrum. 92, 065111 (2021).
  75. Y. Ohishi, K. Kurokawa, Y. Sun, and H. Muta, Thermophysical properties of molten Zr1−xO (x=0.1, 0.2) measured by electrostatic levitation, J. Nucl. Mater. 528, 151873 (2020).
  76. A. D. Agaev, V. I. Kostikov, and V. N. Bobkovskii, Viscosity of liquid refractory metals, Izvest. Akad. Nauk SSSR Metally 3, 43 (1980).
  77. V. P. Elyutin, M. A. Maurakh, and V. D. Turov, Viscosity and electrical conductivity of liquid alloys of zirconium with aluminum, silicon, and niobium, Izv. Vyssh. Uchebn. Zaved. Chem. Metall. 8, 110 (1965); E. Ntonti, S. Sotiriadou, M. J. Assael, M. L. Huber, B. Wilthan, and M. Watanabe, Reference correlations for the density and thermal conductivity, and review of the viscosity measurements, of liquid titanium, zirconium, hafnium, vanadium, niobium, tantalum, chromium, molybdenum, and Tungsten, Int. J. Thermophys. 45, 18 (2024).
  78. International Atomic Energy Agency, Thermophysical Properties of Materials for Nuclear Engineering: A Tutorial and Collection of Data (International Atomic Energy Agency, Vienna, 2008).
  79. L. J. Wittenberg, D. Ofte, W. G. Rohr, and D. V. Rigney, Density and viscosity of liquid Pu-U alloys, Metall. Trans. 2, 287 (1971).
  80. A. Grosse, J. Cahill, and A. Kirshenbaum, Density of liquid uranium1, J. Am. Chem. Soc. 83, 4665 (1961).
  81. H. Wang, S. Yang, L. Hu, and B. Wei, Molecular dynamics prediction and experimental evidence for density of normal and metastable liquid zirconium, Chem. Phys. Lett. 653, 112 (2016).
  82. D. Steinberg, A simple relationship between the temperature dependence of the density of liquid metals and their boiling temperatures, Metall. Trans. 5, 1341 (1974).
  83. B. Allen, The surface tension of liquid transition metals at their melting points, Trans. AIME 227 (1963).
  84. Y. C. Hu, F. X. Li, M. Z. Li, H. Y. Bai, and W. H. Wang, Five-fold symmetry as indicator of dynamic arrest in metallic glass-forming liquids, Nat. Commun. 6, 8310 (2015).
  85. M. E. Blodgett, T. Egami, Z. Nussinov, and K. F. Kelton, Proposal for universality in the viscosity of metallic liquids, Sci. Rep. 5, 13837 (2015).
  86. N. Jakse and A. Pasturel, Local order of liquid and supercooled zirconium byab initiomolecular dynamics, Phys. Rev. Lett. 91, 195501 (2003).
  87. L. P. Kreuzer, F. Yang, A. Meyer, and N. Jakse, Impact of local structure on melt dynamics in Cu-Ti alloys: Insights from ab initio molecular dynamics simulations, Phys. Rev. B 111, 144107 (2025).
  88. M. Kramer and M. Li, Changes in short-and medium-range order in metallic liquids during undercooling, MRS Bull. 45, 943 (2020).
  89. A. Gangopadhyay, R. Bradshaw, T. Rathz, J. Rogers, and B. Sieve, Role of icosahedral short-range-order in undercooled liquids of Zr-Ti-Cu-Ni-Al alloys on bulk metallic glass formation, in APS March Meeting Abstracts (APS, New York, 2005), pp. H28–006.
  90. S. Shousha and B. Beeler, Magnetism and finite-temperature effects in UZr2: A density functional theory analysis, J. Nucl. Mater. 595, 155037 (2024).
  91. S. Starikov, L. Kolotova, A. Y. Kuksin, D. Smirnova, and V. Tseplyaev, Atomistic simulation of cubic and tetragonal phases of U-Mo alloy: Structure and thermodynamic properties, J. Nucl. Mater. 499, 451 (2018).
  92. H. E. Fischer, A. C. Barnes, and P. S. Salmon, Neutron and X-ray diffraction studies of liquids and glasses, Rep. Prog. Phys. 69, 233 (2006).
  93. D. A. Keen, Total scattering and the pair distribution function in crystallography, Crystallogr. Rev. 26, 143 (2020).
  94. P. Brown, A. Fox, E. Maslen, M. O'keefe, and B. Willis, 6.1. Intensity of diffracted intensities, in International Tables for Crystallography C (Wiley, New York, 2006), p. 554.
  95. V. G. Postovalov, E. P. Romanov, V. P. Kondrat'ev, and V. I. Kononenko, Theory of transport in liquid metals: Calculation of dynamic viscosity, High Temp. 41, 762 (2003).
  96. A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators, Phys. Rev. B 52, R5467 (1995).
  97. S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+ U study, Phys. Rev. B 57, 1505 (1998).
  98. S. L. Dudarev, P. Liu, D. A. Andersson, C. R. Stanek, T. Ozaki, and C. Franchini, Parametrization of LSDA+ U for noncollinear magnetic configurations: Multipolar magnetism in UO2, Phys. Rev. Mater. 3, 083802 (2019).

Outline

Information

Phys. Rev. Materials 10, 065601– Published 4 June, 2026
  • Received 2 December 2025
  • Revised 16 March 2026
  • Accepted 21 April 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation