- Open Access
Experimental and calculational equation of state and melting curve of
Phys. Rev. B 114, 144105 – Published 14 September, 2026
DOI: https://doi.org/10.1103/gglf-wx5w
Abstract
Diamond anvil cell synchrotron x-ray diffraction experiments, molecular dynamics, density functional theory, and Lindemann melting theory were used to investigate the compressibility and melting properties of . Ambient-temperature synchrotron x-ray diffraction measurements were made in diamond anvil cells up to a peak pressure of 20 GPa and show no indication of a first-order phase transition over this pressure range. Equation-of-state fits to the diamond anvil cell data constrain the isothermal bulk modulus, , to the range 76.7(51)–87.2(39) GPa. Molecular dynamics and density functional theory were employed to simulate compression curves to a peak pressure of GPa, and constrain to the range 71.6(12)–81.9(12) GPa. Using laser-heated diamond anvil cells, five melt points were measured at pressures between roughly 2 and 10 GPa. We report an experimentally determined zero-pressure melting temperature of 1737(75) K and K/GPa. A high-pressure melting curve generated from molecular dynamics simulations shows linear behavior between 0.5 GPa and the peak simulated pressure of 5 GPa, with a fit slope of K/GPa over this range. Calculations based on Lindemann melting theory yield a zero-pressure melting temperature of 1609 K and a slope of K/GPa for .
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (57)
- A. Rossi, Crystal structure of lanthanum, cerium and praseodymium hydrides, Nature (London) 133, 174 (1934).
- W. T. Buttler, R. K. Schulze, J. J. Charonko, J. C. Cooley, J. E. Hammerberg, J. D. Schwarzkopf, D. G. Sheppard, J. J. Goett III, M. Grover, B. M. La Lone, S. K. Lamoreaux, R. Manzanares, J. I. Martinez, J. D. Regele, M. M. Schauer, D. W. Schmidt, G. D. Stevens, W. D. Turley, and R. J. Valencia, Understanding the transport and break up of reactive ejecta, Physica D 415, 132787 (2021).
- T. M. Hartsfield et al., The temperatures of ejecta transporting in vacuum and gases, J. Appl. Phys. 131, 195104 (2022).
- X. Li et al., Polyhydride with an atomic-like hydrogen clathrate structure, Nat. Commun. 10, 3461 (2019).
- X. Li, X. Huang, W. Chen, D. Zhou, H. Xie, Q. Zhuang, D. Duan, and T. Cui, New cage-like cerium trihydride stabilized at ambient conditions, CCS Chem 4, 825 (2022).
- N. P. Salke et al., Synthesis of clathrate cerium superhydride at 80–100 GPa with atomic hydrogen sublattice, Nat. Commun. 10, 4453 (2019).
- W. Chen, D. V. Semenok, X. Huang, H. Shu, X. Li, D. Duan, T. Cui, and A. R. Oganov, High-temperature superconducting phases in cerium superhydride with a up to 115 K below a pressure of 1 megabar, Phys. Rev. Lett. 127, 117001 (2021).
- P. Vorderwisch, S. Hautecler, and B. Dorner, Phonon dispersion relations in , Solid State Commun. 34, 853 (1980).
- D. Avisar and T. Livneh, Raman scattering by phonons and crystal-field excitations in cerium hydrides, J. Alloys Compd. 494, 11 (2010).
- T. Livneh and D. Avisar, Raman scattering from cerium hydride growth centers overlayered by hydrogen-incorporated oxide, J. Phys. Chem. C 124, 28018 (2020).
- A. Fujimori, M. Ishii, and N. Tsuda, Infrared and raman spectra of non-stoichiometric cerium hydrides, Phys. Status Solidi B 99, 673 (1980).
- X. Ye, H. Li, and S. Li, New insights into phase separation of cerium hydrides under pressure, ACS Omega 7, 15681 (2022).
- T. Gürel and R. Eryiğit, Volume dependent vibrational properties of cerium hydrides from first principles, J. Alloys Compd. 477, 478 (2009).
- G. S. Priyanga, R. Rajeswarapalanichamy, and K. Iyakutti, First principles study of structural, electronic, elastic and magnetic properties of cerium and praseodymium hydrogen system REHx (RE: Ce, Pr and , 3), J. Rare Earths 33, 289 (2015).
- J. A. Bjorgaard, J. Hammerberg, and D. Sheppard, Density functional theory study of cerium deuterides, AIP Conf. Proc. 1979, 080002 (2018).
- W. L. Korst and J. C. Warf, Rare earth-hydrogen systems. i. structural and thermodynamic properties, Inorg. Chem. 5, 1719 (1966).
- G. G. Libowitz, J. G. Pack, and W. P. Binnie, Temperature-dependent electronic transition in cerium hydride, Phys. Rev. B 6, 4540 (1972).
- E. Boroch and E. Kaldis, Phase transitions in the system, Inorg. Chim. Acta 140, 89 (1987).
- M. Tellefsen, E. Kaldis, and E. Jilek, The phase diagram of the Ce- system and the solid solutions, J. Less Common Met. 110, 107 (1985).
- E. Kaldis, E. Boroch, and M. Tellefsen, Phase relationships and phase transitions in the homogeneity range of pure , J. Less-Common Met. 129, 57 (1987).
- E. Boroch and E. Kaldis, Progress in the T-X phase diagram of the solid solution , Z. Phys. Chem. 163, 117 (1989).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/gglf-wx5w for an overview of Lindemann melting theory and calculations used for the cerium hydride melting curve, a comparison of XRD patterns of Ce loaded in ammonia borane and cerium hydride (i.e., before and after laser heating), a stress strain plot for the high pressure EOS fit, and some high resolution XRD images.
- Y. Meng, R. Hrubiak, E. Rod, R. Boehler, and G. Shen, New developments in laser-heated diamond anvil cell with in situ synchrotron x-ray diffraction at High Pressure Collaborative Access Team, Rev. Sci. Instrum. 86, 072201 (2015).
- G. Shen et al., Toward an international practical pressure scale: A proposal for an IPPS ruby gauge (IPPS-Ruby2020), High Press. Res. 40, 299 (2020).
- A. Dewaele, P. Loubeyre, and M. Mezouar, Equations of state of six metals above 94 GPa, Phys. Rev. B 70, 094112 (2004).
- S. V. Sinogeikin, J. S. Smith, E. Rod, C. Lin, C. Kenney-Benson, and G. Shen, Online remote control systems for static and dynamic compression and decompression using diamond anvil cells, Rev. Sci. Instrum. 86, 072209 (2015).
- C. Prescher and V. B. Prakapenka, DIOPTAS: A program for reduction of two-dimensional X-ray diffraction data and data exploration, High Pressure Res. 35, 223 (2015).
- B. H. Toby and R. B. Von Dreele, GSAS-II: The genesis of a modern open-source all purpose crystallography software package, J. Appl. Crystallogr. 46, 544 (2013).
- P. Vinet, J. Ferrante, J. H. Rose, and J. R. Smith, Compressibility of solids, J. Geophys. Res. 92, 9319 (1987).
- 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).
- B. W. Hamilton, A. R. Muñoz, T. E. Jones, and B. T. Nebgen, Mott vs Kondo: Influence of various density functional based methods on the Ce isostructural phase transition mechanism, J. Appl. Phys. 139, 055101 (2026).
- B. W. Hamilton, T. E. Jones, T. C. Germann, and B. T. Nebgen, Stoichiometry dependent properties of cerium hydride: An active learning developed interatomic potential study, Phys. Rev. Mater. 10, 073603 (2026).
- N. Lubbers, J. S. Smith, and K. Barros, Hierarchical modeling of molecular energies using a deep neural network, J. Chem. Phys. 148, 241715 (2018).
- A. P. Thompson et al., LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Comput. Phys. Commun. 271, 108171 (2022).
- Y. Wang, Y. Ge, S. Yu, S. Ma, X. Huang, P. Zhu, S. Jiang, X. Li, and T. Cui, Synthesizing cerium hydrides with high hydrogen saturation under high temperature and pressure conditions, Solid State Commun. 404, 116084 (2025).
- S. Klotz, J.-C. Chervin, P. Munsch, and G. Le Marchand, Hydrostatic limits of 11 pressure transmitting media, J. Phys. D Appl. Phys. 42, 075413 (2009).
- I. Uts, K. Glazyrin, and K. K. M. Lee, Effect of laser annealing of pressure gradients in a diamond-anvil cell using common solid pressure media, Rev. Sci. Instrum. 84, 103904 (2013).
- Y. Akahama and H. Kawamura, Pressure calibration of diamond anvil Raman gauge to 310 GPa, J. Appl. Phys. 100, 043516 (2006).
- J. S. Olsen, L. Gerward, U. Benedict, and J. P. Itié, The crystal structure and the equation of state of cerium metal in the pressure range 0–46 GPa, Physica B+C 133, 129 (1985).
- C. Ma, Z.-Y. Dou, H.-Y. Zhu, G.-Y. Fu, X. Tan, B. Bai, P.-C. Zhang, and Q.-L. Cui, Structure phase transformation and equation of state of cerium metal under pressures up to 51 GPa, Chin. Phys. B 25, 046401 (2016).
- W. Chen, D. V. Semenok, I. A. Troyan, A. G. Ivanova, X. Huang, A. R. Oganov, and T. Cui, Superconductivity and equation of state of lanthanum at megabar pressures, Phys. Rev. B 102, 134510 (2020).
- A. Machida, T. Watanuki, D. Kawana, and K. Aoki, Phase separation of lanthanum hydride under high pressure, Phys. Rev. B 83, 054103 (2011).
- B. J. Baer, H. Cynn, V. Iota, C.-S. Yoo, and G. Shen, Phase diagram and equation of state of praseodymium at high pressures and temperatures, Phys. Rev. B 67, 134115 (2003).
- D. Zhou, D. V. Semenok, D. Duan, H. Xie, W. Chen, X. Huang, X. Li, B. Liu, A. R. Oganov, and T. Cui, Superconducting praseodymium superhydrides, Sci. Adv. 6, eaax6849 (2020).
- S. E. Finnegan, C. V. Storm, E. J. Pace, M. I. McMahon, S. G. MacLeod, E. Plekhanov, N. Bonini, and C. Weber, High-pressure structural systematics in neodymium up to 302 GPa, Phys. Rev. B 103, 134117 (2021).
- D. Zhou et al., High-pressure synthesis of magnetic neodymium polyhydrides, J. Am. Chem. Soc. 142, 2803 (2020).
- D. T. Sneed, P. Söderlind, E. F. O’Bannon, H. Cynn, D. Smith, J. S. Smith, C. Park, and Zs. Jenei, High-pressure structural systematics of dysprosium metal compressed in a neon pressure medium to 182 GPa, Phys. Rev. B 105, 214110 (2022).
- H. Meng, T. Palasyuk, V. Drozd, and M. Tkacz, Study of phase stability and isotope effect in dysprosium trihydride at high pressure, J. Alloys Compd. 722, 946 (2017).
- M. E. Kost, N. T. Kuznetsov, and A. L. Shilov, New hydride phases in the systems R-Mg-H (, La, Ce), Dokl. Chem. (Engl. Transl.) 292, 632 (1987).
- C. E. Yen, Q. Williams, and M. Kunz, Thermal pressure in the laser-heated diamond anvil cell: A quantitative study and implications for the density versus mineralogy correlation of the mantle, JGR Solid Earth 125, e2020JB020006 (2020).
- J. S. Pigott, N. Velisavljevic, E. K. Moss, N. Draganic, M. K. Jacobsen, Y. Meng, R. Hrubiak, and B. T. Sturtevant, Experimental melting curve of zirconium metal to 37 GPa, J. Phys.: Condens. Matter 32, 355402 (2020).
- A. Schiwek, F. Porsch, and W. B. Holzapfel, High temperature-high pressure structural studies of cerium, High Pressure Res. 22, 407 (2002).
- F. Lindemann, The calculation of molecular eigenfrequencies, Phys. Z. 11, 609 (1910).
- L. Burakovsky, C. W. Greeff, and D. L. Preston, Analytic model of the shear modulus at all temperatures and densities, Phys. Rev. B 67, 094107 (2003).
- P. Vorderwisch, S. Hautecler, and W. D. Teuchert, Phonon dispersion relations in , Solid State Commun. 25, 213 (1978).
- M. Guinan and D. Steinberg, Pressure and temperature derivatives of the isotropic polycrystalline shear modulus for 65 elements, J. Phys. Chem. Solids 35, 1501 (1974).
- https://doi.org/10.46936/APS-193059/60016244.