- 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

Crystal structure and temperature of tantalum dynamically compressed to hundreds of gigapascals

A. Krygier1,*, H. Sio1, S. Bonev1, A. L. Coleman1, N. Barton1, D. Braun1, F. Coppari1, J. H. Eggert1, D. Fratanduono1 et al.

A. Lazicki1, J. M. McNaney1, H.-S. Park1, R. E. Rudd1, J. R. Rygg2,3, S. Singh1, R. F. Smith1, S. Stoupin1, D. C. Swift1, and Y. Ping1

  • *Contact author: krygier1@llnl.gov
PDF

Phys. Rev. B 114, 214107 – Published 19 October, 2026

DOI: https://doi.org/10.1103/klbh-bmbl

Abstract

We determine the crystal structure and temperature of tantalum ramp and shock ramp compressed to hundreds of gigapascals at the National Ignition Facility. With x-ray diffraction, we find that tantalum remains in the body-centered-cubic structure with no evidence for the proposed Pnma phase up to ramp-compression stresses of 531.7−18.7+21.3GPa. In separate experiments measuring single-shot extended x-ray absorption fine structure (EXAFS) at the L3 edge, we find that tantalum's temperature agrees well with radiation-hydrodynamics calculations incorporating strength models for ramp and shock-ramp compression to ∼200GPa, but not ∼400GPa. The discrepancy at ∼400GPa can plausibly be explained by underestimated ablation-plasma x-ray heating, with the magnitude of this heating increasing with laser irradiance. These results constitute the highest‐stress structural determination for Ta, the first L-edge EXAFS thermometry in ramp and shock‐ramp experiments, and a stringent benchmark of hydrodynamic models. They validate L‐edge EXAFS as a robust platform for thermometry in dynamic compression and underscore the need for careful ablator design in future high‐pressure studies.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (68)

  1. R. G. Kraus, R. J. Hemley, S. J. Ali, J. L. Belof, L. X. Benedict, J. Bernier, D. Braun, R. E. Cohen, G. W. Collins, F. Coppari, M. P. Desjarlais, D. Fratanduono, S. Hamel, A. Krygier, A. Lazicki, J. Mcnaney, M. Millot, P. C. Myint, M. G. Newman, J. R. Rygg, et al., Measuring the melting curve of iron at super-Earth core conditions, Science 375, 202 (2022).
  2. A. Lazicki, D. McGonegle, J. R. Rygg, D. G. Braun, D. C. Swift, M. G. Gorman, R. F. Smith, P. G. Heighway, A. Higginbotham, M. J. Suggit, D. E. Fratanduono, F. Coppari, C. E. Wehrenberg, R. G. Kraus, D. Erskine, J. V. Bernier, J. M. McNaney, R. E. Rudd, G. W. Collins, J. H. Eggert, et al., Metastability of diamond ramp-compressed to 2 terapascals, Nature (London) 589, 532 (2021).
  3. R. F. Smith, D. E. Fratanduono, D. G. Braun, T. S. Duffy, J. K. Wicks, P. M. Celliers, S. J. Ali, A. Fernandez-Pañella, R. G. Kraus, D. C. Swift, G. W. Collins, and J. H. Eggert, Equation of state of iron under core conditions of large rocky exoplanets, Nat. Astron. 2, 452 (2018).
  4. M. G. Gorman, C. J. Wu, R. F. Smith, L. X. Benedict, C. J. Prisbrey, W. Schill, S. A. Bonev, Z. C. Long, P. Söderlind, D. Braun, D. C. Swift, R. Briggs, T. J. Volz, E. F. O'Bannon, P. M. Celliers, D. E. Fratanduono, J. H. Eggert, S. J. Ali, and J. M. McNaney, Ramp compression of tantalum to multiterapascal pressures: Constraints of the thermal equation of state to 2.3 TPa and 5000 K, Phys. Rev. B 107, 014109 (2023).
  5. A. Krygier, P. D. Powell, J. M. McNaney, C. M. Huntington, S. T. Prisbrey, B. A. Remington, R. E. Rudd, D. C. Swift, C. E. Wehrenberg, A. Arsenlis, H.-S. Park, P. Graham, E. Gumbrell, M. P. Hill, A. J. Comley, and S. D. Rothman, Extreme hardening of Pb at high pressure and strain rate, Phys. Rev. Lett. 123, 205701 (2019).
  6. H. Sio, A. Krygier, D. G. Braun, R. E. Rudd, S. A. Bonev, F. Coppari, M. Millot, D. E. Fratanduono, N. Bhandarkar, M. Bitter, D. K. Bradley, P. C. Efthimion, J. H. Eggert, L. Gao, K. W. Hill, R. Hood, W. Hsing, N. Izumi, G. Kemp, B. Kozioziemski, et al., Extended X-ray absorption fine structure of dynamically-compressed copper up to 1 terapascal, Nat. Commun. 14, 7046 (2023).
  7. J. C. Fernández, C. W. Barnes, M. J. Mocko, and L. Zavorka, Requirements and sensitivity analysis for temporally- and spatially-resolved thermometry using neutron resonance spectroscopy, Rev. Sci. Instrum. 90, 094901 (2019).
  8. D. C. Swift and J. M. McNaney, Comment on “Requirements and sensitivity analysis for temporally- and spatially-resolved thermometry using neutron resonance spectroscopy” [Rev. Sci. Instrum. 90, 094901 (2019)], Rev. Sci. Instrum. 92, 037101 (2021).
  9. V. W. Yuan, J. D. Bowman, D. J. Funk, G. L. Morgan, R. L. Rabie, C. E. Ragan, J. P. Quintana, and H. L. Stacy, Shock temperature measurement using neutron resonance spectroscopy, Phys. Rev. Lett. 94, 125504 (2005).
  10. A. Descamps, B. K. Ofori-Okai, K. Appel, V. Cerantola, A. Comley, J. H. Eggert, L. B. Fletcher, D. O. Gericke, S. Göde, O. Humphries, O. Karnbach, A. Lazicki, R. Loetzsch, D. McGonegle, C. A. J. Palmer, C. Plueckthun, T. R. Preston, R. Redmer, D. G. Senesky, C. Strohm, et al., An approach for the measurement of the bulk temperature of single crystal diamond using an X-ray free electron laser, Sci. Rep. 10, 14564 (2020).
  11. T. G. White, T. D. Griffin, D. Haden, H. J. Lee, E. Galtier, E. Cunningham, D. Khaghani, A. Descamps, L. Wollenweber, B. Armentrout, C. Convery, K. Appel, L. B. Fletcher, S. Goede, J. B. Hastings, J. Iratcabal, E. E. McBride, J. Molina, G. Monaco, L. Morrison, et al., Superheating gold beyond the predicted entropy catastrophe threshold, Nature (London) 643, 950 (2025).
  12. S. M. Sharma and Y. M. Gupta, Inherent issues regarding the use of in situ X-ray diffraction measurements to determine temperature in shock-compressed metals, Phys. Rev. B 104, 064113 (2021).
  13. J. S. Wark, D. J. Peake, T. Stevens, P. G. Heighway, Y. Ping, P. Sterne, B. Albertazzi, S. J. Ali, L. Antonelli, M. R. Armstrong, C. Baehtz, O. B. Ball, S. Banerjee, A. B. Belonoshko, C. A. Bolme, V. Bouffetier, R. Briggs, K. Buakor, T. Butcher, S. Di Dio Cafiso, et al., Femtosecond temperature measurements of laser-shocked copper deduced from the intensity of the X-ray thermal diffuse scattering, J. Appl. Phys. 137, 155904 (2025).
  14. Y. Ping, F. Coppari, D. G. Hicks, B. Yaakobi, D. E. Fratanduono, S. Hamel, J. H. Eggert, J. R. Rygg, R. F. Smith, D. C. Swift, D. G. Braun, T. R. Boehly, and G. W. Collins, Solid iron compressed up to 560 GPa, Phys. Rev. Lett. 111, 065501 (2013).
  15. S. J. Turneaure and P. Das, Vibrational response and temperature of shock-compressed Pt: In situ extended X-ray absorption fine structure measurements to 325 GPa, Phys. Rev. B 105, 174103 (2022).
  16. S. Balugani, J. A. Hernandez, N. Sévelin-Radiguet, O. Mathon, V. Recoules, J. J. Kas, D. E. Eakins, H. Doyle, A. Ravasio, and R. Torchio, New constraints on the melting temperature and phase stability of shocked iron up to 270 GPa probed by ultrafast X-ray absorption spectroscopy, Phys. Rev. Lett. 133, 254101 (2024).
  17. H. Cynn and C.-S. Yoo, Equation of state of tantalum to 174 GPa, Phys. Rev. B 59, 8526 (1999).
  18. K. C. Burrage, C. S. Perreault, E. K. Moss, J. S. Pigott, B. T. Sturtevant, J. S. Smith, N. Velisavljevic, and Y. K. Vohra, Ultrahigh pressure equation of state of tantalum to 310 GPa, High Press. Res. 39, 489 (2019).
  19. J. R. Rygg, J. H. Eggert, A. E. Lazicki, F. Coppari, J. A. Hawreliak, D. G. Hicks, R. F. Smith, C. M. Sorce, T. M. Uphaus, B. Yaakobi, and G. W. Collins, Powder diffraction from solids in the terapascal regime, Rev. Sci. Instrum. 83, 113904 (2012).
  20. R. G. Kraus, F. Coppari, D. E. Fratanduono, R. F. Smith, A. Lazicki, C. Wehrenberg, J. H. Eggert, J. R. Rygg, and G. W. Collins, Melting of tantalum at multimegabar pressures on the nanosecond timescale, Phys. Rev. Lett. 126, 255701 (2021).
  21. P. Söderlind and J. A. Moriarty, First-principles theory of Ta up to 10 Mbar pressure: Structural and mechanical properties, Phys. Rev. B 57, 10340 (1998).
  22. J. B. Haskins, J. A. Moriarty, and R. Q. Hood, Polymorphism and melt in high-pressure tantalum, Phys. Rev. B 86, 224104 (2012).
  23. J. B. Haskins and J. A. Moriarty, Polymorphism and melt in high-pressure tantalum. II. Orthorhombic phases, Phys. Rev. B 98, 144107 (2018).
  24. L. Burakovsky, S. P. Chen, D. L. Preston, and D. G. Sheppard, Z methodology for phase diagram studies: Platinum and tantalum as examples, J. Phys.: Conf. Ser. 500, 162001 (2014).
  25. Y. Yao and D. D. Klug, Stable structures of tantalum at high temperature and high pressure, Phys. Rev. B 88, 054102 (2013).
  26. S. Stoupin, D. B. Thorn, N. Ose, L. Gao, K. W. Hill, Y. Ping, F. Coppari, B. Kozioziemski, A. Krygier, H. Sio, J. Ayers, M. Bitter, B. Kraus, P. C. Efthimion, and M. B. Schneider, The multi-optics high-resolution absorption X-ray spectrometer (HiRAXS) for studies of materials under extreme conditions, Rev. Sci. Instrum. 92, 053102 (2021).
  27. A. Krygier, G. E. Kemp, F. Coppari, D. B. Thorn, D. Bradley, A. Do, J. H. Eggert, W. Hsing, S. F. Khan, C. Krauland, O. L. Landen, M. J. MacDonald, J. M. McNaney, H.-S. Park, B. A. Remington, M. Rubery, M. B. Schneider, H. Sio, and Y. Ping, Optimized continuum X-ray emission from laser-generated plasma, Appl. Phys. Lett. 117, 251106 (2020).
  28. A. Krygier, C. E. Wehrenberg, J. V. Bernier, S. Clarke, A. L. Coleman, F. Coppari, T. S. Duffy, M. G. Gorman, M. Hohenberger, D. Kalantar, G. E. Kemp, S. F. Khan, C. Krauland, R. G. Kraus, A. Lazicki, M. J. MacDonald, A. G. MacPhee, E. Marley, M. C. Marshall, M. May, et al., X-ray source characterization and sample heating on X-ray diffraction experiments at the National Ignition Facility, Phys. Plasmas 29, 103302 (2022).
  29. M. B. Prime, A. Arsenlis, R. A. Austin, N. R. Barton, C. C. Battaile, J. L. Brown, L. Burakovsky, W. T. Buttler, S.-R. Chen, D. M. Dattelbaum, S. J. Fensin, D. G. Flicker, G. T. Gray, C. Greeff, D. R. Jones, J. M. D. Lane, H. Lim, D. Luscher, T. R. Mattsson, J. M. McNaney, et al., A broad study of tantalum strength from ambient to extreme conditions, Acta Mater. 231, 117875 (2022).
  30. N. R. Barton, J. V. Bernier, R. Becker, A. Arsenlis, R. Cavallo, J. Marian, M. Rhee, H.-S. Park, B. A. Remington, and R. T. Olson, A multiscale strength model for extreme loading conditions, J. Appl. Phys. 109, 073501 (2011).
  31. N. R. Barton and M. Rhee, A multiscale strength model for tantalum over an extended range of strain rates, J. Appl. Phys. 114, 123507 (2013).
  32. J. R. Rygg, R. F. Smith, A. E. Lazicki, D. G. Braun, D. E. Fratanduono, R. G. Kraus, J. M. McNaney, D. C. Swift, C. E. Wehrenberg, F. Coppari, M. F. Ahmed, M. A. Barrios, K. J. M. Blobaum, G. W. Collins, A. L. Cook, P. Di Nicola, E. G. Dzenitis, S. Gonzales, B. F. Heidl, M. Hohenberger, et al., X-ray diffraction at the National Ignition Facility, Rev. Sci. Instrum. 91, 043902 (2020).
  33. H. Sio, A. Krygier, S. Stoupin, R. E. Rudd, S. A. Bonev, D. G. Braun, F. Coppari, A. L. Coleman, N. Bhandarkar, M. Bitter, D. K. Bradley, J. Buscho, J. Corbin, M. Dozieres, P. C. Efthimion, J. H. Eggert, L. Gao, K. W. Hill, S. Hamel, W. Hsing, et al., Measurements of K-edge and L-edge extended X-ray absorption fine structure at the National Ignition Facility (invited), Rev. Sci. Instrum. 95, 103523 (2024).
  34. M. Bitter, N. Pablant, K. W. Hill, L. Gao, B. Kraus, P. C. Efthimion, L. Delgado-Apericio, B. Stratton, M. Schneider, F. Coppari, R. Kauffman, M. J. MacDonald, A. MacPhee, Y. Ping, S. Stoupin, and D. Thorn, A new class of focusing crystal shapes for Bragg spectroscopy of small, point-like, X-ray sources in laser produced plasmas, Rev. Sci. Instrum. 92, 043531 (2021).
  35. See Supplemental Material at http://link.aps.org/supplemental/10.1103/klbh-bmbl for additional details on the experimental methods, data analysis, and numerical modeling used in this work. It includes supporting information for the EXAFS and XRD analyses, validation measurements, and the treatment of experimental uncertainties. Additional details of the hydrodynamic calculations and heating estimates are also provided, which includes Refs. [58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68].
  36. R. S. McWilliams, J. H. Eggert, D. G. Hicks, D. K. Bradley, P. M. Celliers, D. K. Spaulding, T. R. Boehly, G. W. Collins, and R. Jeanloz, Strength effects in diamond under shock compression from 0.1 to 1 TPa, Phys. Rev. B 81, 014111 (2010).
  37. S. Ayers, P. Bell, D. Bradley, R. Feldman, W. Marlin, M. Schneider, and J. Seely, Design of survey X-ray spectrometer for NIF, NSS, Technical Report, Lawrence Livermore National Laboratory (LLNL), Livermore, CA, 2013, https://www.osti.gov/biblio/1092524.
  38. J. Maw, A characteristics code for analysis of isentropic compression experiments, AIP Conf. Proc. 706, 1217 (2004).
  39. S. D. Rothman and J. Maw, Characteristics analysis of isentropic compression experiments (ICE), J. Phys. IV France 134, 745 (2006).
  40. P. M. Celliers and M. Millot, Imaging velocity interferometer system for any reflector(VISAR) diagnostics for high energy density sciences, Rev. Sci. Instrum. 94, 011101 (2023).
  41. F. Coppari, D. E. Fratanduono, M. Millot, R. G. Kraus, A. Lazicki, J. R. Rygg, R. F. Smith, and J. H. Eggert, X-ray diffraction measurements and pressure determination in nanosecond compression of solids up to 600 GPa, Phys. Rev. B 106, 134105 (2022).
  42. D. K. Bradley, J. H. Eggert, R. F. Smith, S. T. Prisbrey, D. G. Hicks, D. G. Braun, J. Biener, A. V. Hamza, R. E. Rudd, and G. W. Collins, Diamond at 800 GPa, Phys. Rev. Lett. 102, 075503 (2009).
  43. A. C. Mitchell and W. J. Nellis, Shock compression of aluminum, copper, and tantalum, J. Appl. Phys. 52, 3363 (1981).
  44. S. P. Marsh, LASL Shock Hugoniot Data (University of California Press, Berkeley, 1980), Vol. 5.
  45. P. A. Rigg, M. D. Knudson, R. J. Scharff, and R. S. Hixson, Determining the refractive index of shocked [100] lithium fluoride to the limit of transmissibility, J. Appl. Phys. 116, 033515 (2014).
  46. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
  47. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
  48. N. D. Mermin, Thermal properties of the inhomogeneous electron gas, Phys. Rev. 137, A1441 (1965).
  49. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008).
  50. J. J. Kas, F. D. Vila, C. D. Pemmaraju, T. S. Tan, and J. J. Rehr, Advanced calculations of X-ray spectroscopies with FEFF10 and Corvus, J. Synchrotron Rad. 28, 1801 (2021).
  51. M. Newville, Larch: An analysis package for XAFS and related spectroscopies, J. Phys.: Conf. Ser. 430, 012007 (2013).
  52. M. G. Gorman, S. Elatresh, A. Lazicki, M. M. E. Cormier, S. A. Bonev, D. McGonegle, R. Briggs, A. L. Coleman, S. D. Rothman, L. Peacock, J. V. Bernier, F. Coppari, D. G. Braun, J. R. Rygg, D. E. Fratanduono, R. Hoffmann, G. W. Collins, J. S. Wark, R. F. Smith, J. H. Eggert, et al., Experimental observation of open structures in elemental magnesium at terapascal pressures, Nat. Phys. 18, 1307 (2022).
  53. D. J. Steinberg, S. G. Cochran, and M. W. Guinan, A constitutive model for metals applicable at high‐strain rate, J. Appl. Phys. 51, 1498 (1980).
  54. D. B. Thorn, F. Coppari, T. Döppner, M. J. MacDonald, S. P. Regan, and M. B. Schneider, X-ray spectrometer throughput model for (selected) flat Bragg crystal spectrometers on laser plasma facilities, Rev. Sci. Instrum. 89, 10F119 (2018).
  55. K. W. Hill, M. Bitter, L. Delgado-Aparicio, P. C. Efthimion, R. Ellis, L. Gao, J. Maddox, N. A. Pablant, M. B. Schneider, H. Chen, S. Ayers, R. L. Kauffman, A. G. MacPhee, P. Beiersdorfer, R. Bettencourt, T. Ma, R. C. Nora, H. A. Scott, D. B. Thorn, J. D. Kilkenny, et al., Development of a high resolution X-ray spectrometer for the National Ignition Facility (NIF), Rev. Sci. Instrum. 87, 11E344 (2016).
  56. P. Mora, Theoretical model of absorption of laser light by a plasma, Phys. Fluids 25, 1051 (1982).
  57. A. Krygier, Replication data for: The crystal structure and temperature of tantalum dynamically compressed to hundreds of gigapascals, Harvard Dataverse, 2026, https://doi.org/10.7910/DVN/EKLE0G.
  58. A. W. Joseph, The Whittaker-Henderson method of graduation, J. Instit. Actuaries 78, 99 (1952).
  59. M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, XCOM: Photon Cross Sections Database, National Institute of Standards and Technology, Gaithersburg, MD, 2010, https://www.nist.gov/pml/xcom-photon-cross-sections-database.
  60. M. Newville, P. Līviņš, Y. Yacoby, J. J. Rehr, and E. A. Stern, Near-edge X-ray-absorption fine structure of Pb: A comparison of theory and experiment, Phys. Rev. B 47, 14126 (1993).
  61. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  62. D. J. Benson, Computational methods in Lagrangian and Eulerian hydrocodes, Comput. Methods Appl. Mech. Eng. 99, 235 (1992).
  63. L. Brookshaw, B. I. Cohen, J. Hittinger, M. Marinak, R. Rieben, D. Sharp, and D. Wallace, in Proceedings of the 2006 American Physical Society Topical Conference on Shock Compression of Condensed Matter (AIP, Melville, NY, 2006).
  64. International X-ray Absorption Society XAFS database, http://ixs.iit.edu/database/.
  65. Y. T. Lee and R. M. More, An electron conductivity model for dense plasmas, Phys. Fluids 27, 1273 (1984).
  66. M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, Three-dimensional HYDRA simulations of National Ignition Facility targets, Phys. Plasmas 8, 2275 (2001).
  67. O. K. Andersen, O. Jepsen, and D. Glötzel, in Highlights of Condensed-Matter Theory, Proceedings of the International School of Physics “Enrico Fermi”, Course LXXXIX, edited by F. Bassani, F. Fumi, and M. P. Tosi (North-Holland, Amsterdam, 1985), pp. 59–176.
  68. P. Haas, F. Tran, and P. Blaha, Calculation of the lattice constant of solids with semilocal functionals, Phys. Rev. B 79, 085104 (2009).

Outline

Information

Phys. Rev. B 114, 214107– Published 19 October, 2026
  • Received 22 August 2025
  • Revised 11 September 2026
  • Accepted 16 September 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