- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Phase transition lowering under shock compression: The case of lead

Charles M. Pépin1,2,*, Mikhail A. Kozhaev3,†, Matteo Levantino3, and Arnaud Sollier1,2

  • *Contact author: charles.pepin@cea.fr
  • †Present address: Fibercryst S.A.S., 31 rue Wilson, 69150 Décines-Charpieu, France.
PDF

Phys. Rev. Research 8, 033294 – Published 10 September, 2026

DOI: https://doi.org/10.1103/6qmk-qs9l

Abstract

We report time-resolved x-ray diffraction measurements of lead (Pb) subjected to laser-driven shock compression up to the melt on nanosecond timescales. Along its Hugoniot, Pb exhibits a sequence of structural transitions markedly different from those observed under static compression. The conventional fcc-to-hcp transition is suppressed. Instead, the stacking fault probability in the fcc phase increases with compression up to ∼20GPa, and the high-pressure bcc phase appears at 27 GPa, i.e., ∼60GPa below the static hcp-bcc boundary at the same temperature. At 45.4 (±2.1) GPa and a calculated temperature of 2695 K, partial melting is evidenced by diffuse scattering, in excellent agreement with previous diamond anvil cell (DAC) melting data. Our results demonstrate that the dynamical response of Pb involves a distinct solid-state pathway, likely associated with stacking faults probability increase. These findings highlight the need to revisit phase diagrams under shock compression, particularly when coupled with time-resolved in situ microscopic diagnostics.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (50)

  1. S. Pascarelli, M. McMahon, C. Pépin, O. Mathon, R. F. Smith, W. L. Mao, H.-P. Liermann, and P. Loubeyre, Materials under extreme conditions using large x-ray facilities, Nat. Rev. Methods Primers 3, 82 (2023).
  2. J. S. Wark, M. I. McMahon, and J. H. Eggert, Femtosecond diffraction and dynamic high pressure science, J. Appl. Phys. 132, 080902 (2022).
  3. S. M. Sharma, S. J. Turneaure, J. M. Winey, Y. Li, P. Rigg, A. Schuman, N. Sinclair, Y. Toyoda, X. Wang, N. Weir, J. Zhang, and Y. M. Gupta, Structural transformation and melting in gold shock compressed to 355 GPa, Phys. Rev. Lett. 123, 045702 (2019).
  4. R. Briggs, F. Coppari, M. G. Gorman, R. F. Smith, S. J. Tracy, A. L. Coleman, A. Fernandez-Pañella, M. Millot, J. H. Eggert, and D. E. Fratanduono, Measurement of body-centered cubic gold and melting under shock compression, Phys. Rev. Lett. 123, 045701 (2019).
  5. M. G. Gorman, S. Elatresh, A. Lazicki, J. R. Rygg, J. H. Eggert, S. Hamel, A. F. Goncharov, L. R. Benedetti, and J. M. McMahon, Experimental observation of open structures in elemental magnesium at terapascal pressures, Nat. Phys. 18, 1307 (2022).
  6. S. Singh, M. G. Gorman, P. G. Heighway, J. V. Bernier, D. McGonegle, H. J. Lee, B. Nagler, J. H. Eggert, and R. F. Smith, Unexpected observation of disorder and multiple phase-transition pathways in shock-compressed Zr, Phys. Rev. Lett. 133, 096101 (2024).
  7. R. Briggs, M. G. Gorman, A. L. Coleman, R. S. McWilliams, E. E. McBride, D. McGonegle, J. S. Wark, L. Peacock, S. Rothman, S. G. Macleod, et al., Ultrafast x-ray diffraction studies of the phase transitions and equation of state of scandium shock compressed to 82 GPa, Phys. Rev. Lett. 118, 025501 (2017).
  8. E. E. McBride, A. Krygier, A. Ehnes, E. Galtier, M. Harmand, Z. Konôpková, H. J. Lee, H.-P. Liermann, B. Nagler, A. Pelka, M. Rödel, A. Schropp, R. F. Smith, C. Spindloe, D. C. Swift, F. Tavella, S. Toleikis, T. Tschentscher, J. S. Wark, and A. Higginbotham, Phase transition lowering in dynamically compressed silicon, Nat. Phys. 15, 89 (2019).
  9. C. M. Pépin, A. Sollier, A. Marizy, F. Occelli, M. Sander, R. Torchio, and P. Loubeyre, Kinetics and structural changes in dynamically compressed bismuth, Phys. Rev. B 100, 060101(R) (2019).
  10. A. Sollier, C. Pépin, M. Kozhaev, C. Mariette, W. Reichenbach, and M. Levantino, Development of a laser-driven shock compression platform for time-resolved XRD experiments at the ID09 beamline of the European Synchrotron Radiation Facility, High Press. Res. 44, 418 (2024).
  11. A. Kuznetsov, V. Dmitriev, L. Dubrovinsky, V. Prakapenka, and H. P. Weber, FCC–HCP phase boundary in lead, Solid State Commun. 122, 125 (2002).
  12. H. K. Mao, Y. Wu, J. F. Shu, J. Z. Hu, R. J. Hemley, and D. E. Cox, High-pressure phase transition and equation of state of lead to 238 GPa, Solid State Commun. 74, 1027 (1990).
  13. B. K. Godwal, C. Meade, R. Jeanloz, A. Garcia, A. Y. Liu, and M. L. Cohen, Ultrahigh-pressure melting of lead: A multidisciplinary study, Science 248, 462 (1990).
  14. D. Partouche-Sebban, J. L. Pélissier, F. G. Abeyta, W. W. Anderson, M. E. Byers, D. Dennis-Koller, J. S. Esparza, R. S. Hixson, D. B. Holtkamp, B. J. Jensen, J. C. King, P. A. Rigg, P. Rodriguez, D. L. Shampine, J. B. Stone, D. T. Westley, S. D. Borror, and C. A. Kruschwitz, Measurement of the shock-heated melt curve of lead using pyrometry and reflectometry, J. Appl. Phys. 97, 043521 (2005).
  15. A. Dewaele, M. Mezouar, N. Guignot, and P. Loubeyre, Melting of lead under high pressure studied using second-scale time-resolved x-ray diffraction, Phys. Rev. B 76, 144106 (2007).
  16. G. E. Duvall and R. A. Graham, Phase transitions under shock-wave loading, Rev. Mod. Phys. 49, 523 (1977).
  17. Yu. V. Bat'kov, V. N. German, R. S. Osipov, S. A. Novikov, and V. A. Tsyganov, Melting of lead in shock compression, J. Appl. Mech. Tech. Phys. 29, 139 (1988).
  18. W. J. Carter, Metallurgical effects at high strain rates, in Metallurgical Effects at High Strain Rates, edited by R. W. Rohde, B. M. Butcher, J. R. Holland, and C. H. Karnes (Plenum Press, New York, 1973), p. 171.
  19. J. P. Colombier, P. Combis, F. Bonneau, R. Le Harzic, and E. Audouard, Hydrodynamic simulations of metal ablation by femtosecond laser irradiation, Phys. Rev. B 71, 165406 (2005).
  20. J. Johnson and S. Lyon, SESAME: The Los Alamos National Laboratory Equation of State Database, Technical Report LA-UR 92-3407, Los Alamos National Laboratory (1992), https://cdn.lanl.gov/files/laur-92-3407_a0e99.pdf.
  21. C. Dai, H. Tan, and H. Geng, Model for assessing the melting on Hugoniots of metals: Al, Pb, Cu, Mo, Fe, and U, J. Appl. Phys. 92, 5019 (2002).
  22. See Supplemental Material at http://link.aps.org/supplemental/10.1103/6qmk-qs9l for additional experimental data and simulation details.
  23. A. V. Bushman and V. E. Fortov, Model equations of state, Sov. Phys. Usp. 26, 465 (1983).
  24. I. V. Lomonosov, A. V. Bushman, and V. E. Fortov, Equations of state for metals at high energy densities, AIP Conf. Proc. 309, 117 (1994).
  25. D. A. Boness, J. M. Brown, and J. W. Shaner, Shock waves in condensed matter, in Shock Waves in Condensed Matter, edited by S. C. Schmidt and N. C. Holmes (Elsevier, New York, 1988), p. 115.
  26. B. E. Warren, X-ray Diffraction (Addison-Wesley, Reading, MA, 1969).
  27. L. Velterop, R. Delhez, T. H. de Keijser, E. J. Mittemeijer, and D. Reefman, X-ray diffraction analysis of stacking and twin faults in f.c.c. metals: A revision and allowance for texture and non-uniform fault probabilities, J. Appl. Cryst. 33, 296 (2000).
  28. S. M. Sharma, S. J. Turneaure, J. M. Winey, and Y. M. Gupta, Transformation of shock-compressed copper to the body-centered-cubic structure at 180 GPa, Phys. Rev. B 102, 020103 (2020).
  29. S. M. Sharma, S. J. Turneaure, J. M. Winey, and Y. M. Gupta, What determines the fcc-bcc structural transformation in shock compressed noble metals? Phys. Rev. Lett. 124, 235701 (2020).
  30. S. M. Sharma, S. J. Turneaure, J. M. Winey, P. A. Rigg, N. Sinclair, X. Wang, Y. Toyoda, and Y. M. Gupta, Real-time observation of stacking faults in gold shock compressed to 150 GPa, Phys. Rev. X 10, 011010 (2020).
  31. B. L. Holian and P. S. Lomdahl, Plasticity induced by shock waves in nonequilibrium molecular-dynamics simulations, Science 280, 2085 (1998).
  32. S. P. Marsh, LASL Shock Hugoniot Data (University of California Press, Berkeley, 1980).
  33. S. Anzellini, A. K. Kleppe, D. Daisenberger, M. T. Wharmby, R. Giampaoli, S. Boccato, M. A. Baron, F. Miozzi, D. S. Keeble, A. Ross, S. Gurney, J. Thompson, G. Knap, M. Booth, L. Hudson, D. Hawkins, M. J. Walter, and H. Wilhelm, Laser-heating system for high-pressure X-ray diffraction at the Extreme Conditions beamline I15 at Diamond Light Source, J. Synchrotron Radiat. 25, 1860 (2018).
  34. A. Dewaele, Equations of state of simple solids (including Pb, NaCl and LiF) compressed in helium or neon in the Mbar range, Minerals 9, 684 (2019).
  35. D. McGonegle, P. G. Heighway, M. Sliwa, C. A. Bolme, A. J. Comley, L. E. Dresselhaus-Marais, A. Higginbotham, A. J. Poole, E. E. McBride, B. Nagler, I. Nam, M. H. Seaberg, B. A. Remington, R. E. Rudd, C. E. Wehrenberg, and J. S. Wark, Investigating off-Hugoniot states using multi-layer ring-up targets, Sci. Rep. 10, 13172 (2020).
  36. E. C. Bain and N. Dunkirk, The nature of martensite, AIME Trans. 70, 25 (1924).
  37. Z. Nishiyama, Martensitic transformation, in Martensitic Transformation, edited by M. E. Fine, M. Meshii, and C. M. Wayman (Academic Press, New York, 1978), pp. 344–411.
  38. A. J. Bogers and W. G. Burgers, Partial dislocations on the 110 planes in the b.c.c. lattice and the transition of the f.c.c. into the b.c.c. lattice, Acta Metall. 12, 255 (1964).
  39. C. Cayron, One-step model of the face-centred-cubic to body-centred-cubic martensitic transformation, Acta Cryst. A 69, 498 (2013).
  40. M. Sims, R. Briggs, T. J. Volz, S. Singh, S. Hamel, A. L. Coleman, F. Coppari, D. J. Erskine, M. G. Gorman, B. Sadigh, J. Belof, J. H. Eggert, R. F. Smith, and J. K. Wicks, Experimental and theoretical examination of shock‐compressed copper through the fcc to bcc to melt phase transitions, J. Appl. Phys. 132, 075902 (2022).
  41. Th. Strässle, S. Klotz, K. Kunc, V. Pomjakushin, and J. S. White, Equation of state of lead from high-pressure neutron diffraction up to 8.9 GPa and its implication for the NaCl pressure scale, Phys. Rev. B 90, 014101 (2014).
  42. 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).
  43. R. E. Rudd, L. H. Yang, P. D. Powell, P. Graham, A. Arsenlis, R. M. Cavallo, A. G. Krygier, J. M. McNaney, S. T. Prisbrey, B. A. Remington, D. C. Swift, C. E. Wehrenberg, and H.-S. Park, Modeling laser-driven high-rate plasticity in BCC lead, AIP Conf. Proc. 1979, 070027 (2018).
  44. W. Ling, B. Chen, Q. Zeng, X. Yu, S. Zhang, Z. Zhao, and J. Dai, Atomic insight into phase transition lowering in shock compressed copper, Front. Phys. 10, 838316 (2022).
  45. G. Bolling, L. Hays, and H. Wiedersich, The plasticity of lead single crystals and the determination of stack-fault energy, Acta Metall. 10, 185 (1962).
  46. N. M. Rosengaard and H. L. Skriver, Calculated stacking-fault energies of elemental metals, Phys. Rev. B 47, 12865 (1993).
  47. A. L. Coleman, M. G. Gorman, R. Briggs, R. S. McWilliams, D. McGonegle, C. A. Bolme, A. E. Gleason, D. E. Fratanduono, R. F. Smith, E. Galtier, H. J. Lee, B. Nagler, E. Granados, G. W. Collins, J. H. Eggert, J. S. Wark, and M. I. McMahon, Identification of phase transitions and metastability in dynamically compressed antimony using ultrafast x-ray diffraction, Phys. Rev. Lett. 122, 255704 (2019).
  48. I. K. Ocampo, R. F. Smith, D. Kim, V. Prakapenka, S. Speziale, M. Schoelmerich, K. Appel, D. N. Polsin, M. Marshall, S. J. Tracy, F. Miozzi, H. J. Lee, E. Galtier, E. Cunningham, C. McGuire, C. Vennari, A. E. Gleason, and T. S. Duffy, Ultrafast x-ray diffraction of high-pressure phases in dynamically compressed TiO2, Phys. Rev. B 112, 104103 (2025).
  49. M. Y. Chou, M. L. Cohen, and S. G. Louie, Theoretical study of stacking faults in silicon, Phys. Rev. B 32, 7979 (1985).
  50. 10.15151/ESRF-ES-1710755704

Outline

Information

Phys. Rev. Research 8, 033294– Published 10 September, 2026
  • Received 6 June 2025
  • Accepted 10 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