- 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

Direct sound speed measurements of MgO along planetary adiabats up to 400 GPa using shock-ramp compression

Hannah J. Bausch1,2,*, Joshua P. Townsend2,*, Jean-Paul Davis2, Sakun Duwal2, Christopher T. Seagle2, Tirzah M. Abbott1,3, Alisha N. Clark4, and Steven D. Jacobsen4,†

  • *These authors contributed equally to this work.
  • †Contact author: steven.jacobsen@colorado.edu
PDF

Phys. Rev. B 114, 274108 – Published 12 November, 2026

DOI: https://doi.org/10.1103/x7x6-16cs

Abstract

Accurate models of planetary formation and evolution rely on equation-of-state (EOS) models for their constituent materials across wide ranges of pressure, temperature, and density. Currently, estimates of thermoelastic properties along Earth-like pressure and temperature adiabats (the geotherm) require extrapolation of laboratory data, which confounds clear interpretation of the physical and chemical states of planetary interiors. We designed experiments on the Z Machine at Sandia National Laboratories to directly measure the EOS and sound speeds in dense oxides along quasi-isentropes close to the geotherm using shock-ramp compression. Here we demonstrate the method on magnesium oxide, representing the major nonsilicate mineral in the mantle, to pressures exceeding Earth's core. Our observations up to 400 GPa are confirmed by independent density functional theory and quantum Monte Carlo predictions and indicate the experimental compression path is close to a 1900 K geotherm. The results show excellent agreement with the preliminary reference Earth model (PREM), suggesting the technique can produce highly accurate thermoelastic data useful for interpreting the internal structure of terrestrial planets.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (70)

  1. W. Lowrie and A. Fichtner, Fundamentals of Geophysics, 2nd ed. (Cambridge University Press, Cambridge, 2020).
  2. D. Valencia, R. J. O'Connell, and D. Sasselov, Internal structure of massive terrestrial planets, Icarus 181, 545 (2006).
  3. A. M. Dziewonski and D. L. Anderson, Preliminary reference Earth model, Phys. Earth Planet. Inter. 25, 297 (1981).
  4. W. Xu, C. Lithgow-Bertelloni, L. Stixrude, and J. Ritsema, The effect of bulk composition and temperature on mantle seismic structure, Earth Planet. Sci. Lett. 275, 70 (2008).
  5. F. Wang, M. Barklage, X. Lou, S. van der Lee, C. R. Bina, and S. D. Jacobsen, HyMaTZ: A python program for modeling seismic velocities in hydrous regions of the mantle transition zone, Geochem. Geophys. Geosyst. 19, 2308 (2018).
  6. S. D. Jacobsen, C. M. Holl, K. A. Adams, R. A. Fischer, E. S. Martin, C. R. Bina, J.-F. Lin, V. B. Prakapenka, A. Kubo, and P. Dera, Compression of single-crystal magnesium oxide to 118 GPa and a ruby pressure gauge for helium pressure media, Am. Mineral. 93, 1823 (2008).
  7. F. V. Kaminsky, The Earth's Lower Mantle (Springer International Publishing, Cham, 2017).
  8. O. V. Fat'yanov, P. D. Asimow, and T. J. Ahrens, Thermodynamically complete equation of state of MgO from true radiative shock temperature measurements on samples preheated to 1850 K, Phys. Rev. B 97, 024106 (2018).
  9. T. S. Duffy, R. J. Hemley, and H. Mao, Equation of state and shear strength at multimegabar pressures: Magnesium oxide to 227 GPa, Phys. Rev. Lett. 74, 1371 (1995).
  10. S. V. Sinogeikin and J. D. Bass, Single-crystal elasticity of pyrope and MgO to 20 GPa by Brillouin scattering in the diamond cell, Phys. Earth Planet. Inter. 120, 43 (2000).
  11. S. Speziale, C. Zha, T. S. Duffy, R. J. Hemley, and H. Mao, Quasi‐hydrostatic compression of magnesium oxide to 52 GPa: Implications for the pressure‐volume‐temperature equation of state, J. Geophys. Res. 106, 515 (2001).
  12. A. E. Gleason, H. Marquardt, B. Chen, S. Speziale, J. Wu, and R. Jeanloz, Anomalous sound velocities in polycrystalline MgO under non-hydrostatic compression, Geophys. Res. Lett. 38, L03304 (2011).
  13. O. V. Fat'yanov and P. D. Asimow, MgO melting curve constraints from shock temperature and rarefaction overtake measurements in samples preheated to 2300 K, J. Phys.: Conf. Ser. 500, 062003 (2014).
  14. O. V. Fat'yanov and P. D. Asimow, Melting of B1‐phase MgO from simultaneous true radiative shock temperature and sound speed measurements to 250 GPa on samples preheated to 2300 K, J. Geophys. Res. 129, e2024JB029137 (2024).
  15. J. M. Brown and T. J. Shankland, Thermodynamic parameters in the Earth as determined from seismic profiles, Geophys. J. Int. 66, 579 (1981).
  16. Edited by J. R. Asay and M. Shahinpoor, High-Pressure Shock Compression of Solids (Springer, New York, NY, 1993).
  17. T. S. Duffy and T. J. Ahrens, Compressional sound velocity, equation of state, and constitutive response of shock‐compressed magnesium oxide, J. Geophys. Res. 100, 529 (1995).
  18. C. T. Seagle and A. J. Porwitzky, Shock-ramp compression of tin near the melt line, AIP Conf. Proc. 1979, 040005 (2018).
  19. C. T. Seagle, J.-P. Davis, and M. D. Knudson, Mechanical response of lithium fluoride under off-principal dynamic shock-ramp loading, J. Appl. Phys. 120, 165902 (2016).
  20. D. E. Fratanduono, M. Millot, D. G. Braun, S. J. Ali, A. Fernandez-Pañella, C. T. Seagle, J.-P. Davis, J. L. Brown, Y. Akahama, R. G. Kraus, M. C. Marshall, R. F. Smith, E. F. O'Bannon, J. M. McNaney, and J. H. Eggert, Establishing gold and platinum standards to 1 terapascal using shockless compression, Science 372, 1063 (2021).
  21. J.-P. Davis, M. D. Knudson, L. Shulenburger, and S. D. Crockett, Mechanical and optical response of [100] lithium fluoride to multi-megabar dynamic pressures, J. Appl. Phys. 120, 165901 (2016).
  22. J.-P. Davis, J. L. Brown, M. D. Knudson, and R. W. Lemke, Analysis of shockless dynamic compression data on solids to multi-megabar pressures: Application to tantalum, J. Appl. Phys. 116, 204903 (2014).
  23. R. G. Kraus, J.-P. Davis, C. T. Seagle, D. E. Fratanduono, D. C. Swift, J. L. Brown, and J. H. Eggert, Dynamic compression of copper to over 450 GPa: A high-pressure standard, Phys. Rev. B 93, 134105 (2016).
  24. S. Root, J. P. Townsend, and M. D. Knudson, Shock compression of fused silica: An impedance matching standard, J. Appl. Phys. 126, 165901 (2019).
  25. F. Coppari, R. F. Smith, J. H. Eggert, J. Wang, J. R. Rygg, A. Lazicki, J. A. Hawreliak, G. W. Collins, and T. S. Duffy, Experimental evidence for a phase transition in magnesium oxide at exoplanet pressures, Nat. Geosci. 6, 926 (2013).
  26. J. Wang, R. F. Smith, F. Coppari, J. H. Eggert, T. R. Boehly, G. W. Collins, and T. S. Duffy, Ramp compression of magnesium oxide to 234 GPa, J. Phys.: Conf. Ser. 500, 062002 (2014).
  27. F. González-Cataldo, B. K. Godwal, K. Driver, R. Jeanloz, and B. Militzer, Model of ramp compression of diamond from ab initio simulations, Phys. Rev. B 104, 134104 (2021).
  28. S. C. Grant, T. Ao, C. T. Seagle, A. J. Porwitzky, J.-P. Davis, K. R. Cochrane, D. H. Dolan, J.-F. Lin, T. Ditmire, and A. C. Bernstein, Equation of state measurements on iron near the melting curve at planetary core conditions by shock and ramp compressions, J. Geophys. Res. 126, e2020JB020008 (2021).
  29. B.   T. Hutsel, P.   A. Corcoran, M.   E. Cuneo, M.   R. Gomez, M.   H. Hess, D.   D. Hinshelwood, C.   A. Jennings, G.   R. Laity, D.   C. Lamppa, R.   D. McBride, J.   K. Moore, A. Myers, D.   V. Rose, S.   A. Slutz, W.   A. Stygar, E.   M. Waisman, D.   R. Welch, and B.   A. Whitney, Transmission-line-circuit model of an 85-TW, 25-MA pulsed-power accelerator, Phys. Rev. Accel. Beams 21, 030401 (2018).
  30. R. W. Lemke, M. D. Knudson, and J.-P. Davis, Magnetically driven hyper-velocity launch capability at the Sandia Z accelerator, Int. J. Impact Eng. 38, 480 (2011).
  31. M. Li and A. K. McNamara, The influence of deep mantle compositional heterogeneity on Earth's thermal evolution, Earth Planet. Sci. Lett. 500, 86 (2018).
  32. B. A. Buffett, The thermal state of Earth's core, Science 299, 1675 (2003).
  33. K. Hirose, G. Morard, R. Sinmyo, K. Umemoto, J. Hernlund, G. Helffrich, and S. Labrosse, Crystallization of silicon dioxide and compositional evolution of the Earth's core, Nature (London) 543, 99 (2017).
  34. S. Root, L. Shulenburger, R. W. Lemke, D. H. Dolan, T. R. Mattsson, and M. P. Desjarlais, Shock response and phase transitions of MgO at planetary impact conditions, Phys. Rev. Lett. 115, 198501 (2015).
  35. The temperature of the geotherm is conventionally defined as the temperature at 23 GPa (approximately 660 km depth on Earth). So a “1900 K” geotherm is the adiabat for which T=1900 K where P=23 GPa.
  36. See Supplemental Material at http://link.aps.org/supplemental/10.1103/x7x6-16cs for further descriptions of experimental and theory details, which includes Refs. [68, 69].
  37. L. M. Barker and R. E. Hollenbach, Laser interferometer for measuring high velocities of any reflecting surface, J. Appl. Phys. 43, 4669 (1972).
  38. O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, Compact system for high-speed velocimetry using heterodyne techniques, Rev. Sci. Instrum. 77, 083108 (2006).
  39. J.-P. Davis and J. L. Brown, Quantifying uncertainty in analysis of shockless dynamic compression experiments on platinum. I. Inverse Lagrangian analysis, J. Appl. Phys. 134, 235901 (2023).
  40. S. D. Rothman, S. J. Ali, J. L. Brown, J. H. Eggert, and C. T. Seagle, Shock-ramp analysis test problem, J. Appl. Phys. 129, 185901 (2021).
  41. J. L. Brown, J.-P. Davis, J. D. Tucker, G. Huerta, and K. W. Shuler, Quantifying uncertainty in analysis of shockless dynamic compression experiments on platinum. II. Bayesian model calibration, J. Appl. Phys. 134, 235902 (2023).
  42. G. Kresse and J. Hafner, Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium, Phys. Rev. B 49, 14251 (1994).
  43. G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  44. 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).
  45. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  46. G. Prandini, A. Marrazzo, I. E. Castelli, N. Mounet, and N. Marzari, Precision and efficiency in solid-state pseudopotential calculations, npj Comput. Mater. 4, 72 (2018).
  47. G. Kresse and J. Hafner, Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements, J. Phys. Condens. Matter 6, 8245 (1994).
  48. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  49. N. D. Mermin, Thermal properties of the inhomogeneous electron gas, Phys. Rev. 137, A1441 (1965).
  50. Y. Fei, Effects of temperature and composition on the bulk modulus of (Mg,Fe)O, Am. Mineral. 84, 272 (1999).
  51. J. Kim et al., qmcpack: An open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids, J. Phys. Condens. Matter 30, 195901 (2018).
  52. J. P. Townsend, S. D. Pineda Flores, R. C. Clay, T. R. Mattsson, E. Neuscamman, L. Zhao, R. E. Cohen, and L. Shulenburger, Starting-point-independent quantum Monte Carlo calculations of iron oxide, Phys. Rev. B 102, 155151 (2020).
  53. P. Giannozzi et al., quantum espresso: A modular and open-source software project for quantum simulations of materials, J. Phys. Condens. Matter 21, 395502 (2009).
  54. P. Giannozzi et al., Advanced capabilities for materials modelling with Quantum espresso, J. Phys. Condens. Matter 29, 465901 (2017).
  55. M. C. Bennett, C. A. Melton, A. Annaberdiyev, G. Wang, L. Shulenburger, and L. Mitas, A new generation of effective core potentials for correlated calculations, J. Chem. Phys. 147, 224106 (2017).
  56. M. C. Bennett, G. Wang, A. Annaberdiyev, C. A. Melton, L. Shulenburger, and L. Mitas, A new generation of effective core potentials from correlated calculations: 2nd row elements, J. Chem. Phys. 149, 104108 (2018).
  57. M. Casula, S. Moroni, S. Sorella, and C. Filippi, Size-consistent variational approaches to nonlocal pseudopotentials: Standard and lattice regularized diffusion Monte Carlo methods revisited, J. Chem. Phys. 132, 154113 (2010).
  58. Y. Fei, C. T. Seagle, J. P. Townsend, C. A. McCoy, A. Boujibar, P. Driscoll, L. Shulenburger, and M. D. Furnish, Melting and density of MgSiO3 determined by shock compression of bridgmanite to 1254 GPa, Nat. Commun. 12, 876 (2021).
  59. S. Root, J. P. Townsend, E. Davies, R. W. Lemke, D. E. Bliss, D. E. Fratanduono, R. G. Kraus, M. Millot, D. K. Spaulding, L. Shulenburger, S. T. Stewart, and S. B. Jacobsen, The principal Hugoniot of forsterite to 950 GPa, Geophys. Res. Lett. 45, 3865 (2018).
  60. P. F. Weck, J. P. Townsend, K. R. Cochrane, S. D. Crockett, and N. W. Moore, Shock compression of niobium from first-principles, J. Appl. Phys. 125, 245905 (2019).
  61. P. F. Weck, K. R. Cochrane, S. Root, J. M. D. Lane, L. Shulenburger, J. H. Carpenter, T. Sjostrom, T. R. Mattsson, and T. J. Vogler, Shock compression of strongly correlated oxides: A liquid-regime equation of state for cerium (IV) oxide, Phys. Rev. B 97, 125106 (2018).
  62. C. Meade and R. Jeanloz, Yield strength of MgO to 40 GPa, J. Geophys. Res. 93, 3261 (1988).
  63. M. B. Prime, S. J. Fensin, D. R. Jones, J. W. Dyer, and D. T. Martinez, Multiscale Richtmyer-Meshkov instability experiments to isolate the strain rate dependence of strength, Phys. Rev. E 109, 015002 (2024).
  64. M. S. Vassiliou and T. J. Ahrens, Hugoniot equation of state of periclase to 200 GPa, Geophys. Res. Lett. 8, 729 (1981).
  65. S. P. Marsh, LASL Shock Hugoniot Data (University of California Press, Berkeley, CA, 1980).
  66. G. F. Davies and T. J. Ahrens, Measurement of elastic velocities of MgO under shock compression to 500 kilobars, J. Geophys. Res. 78, 7596 (1973).
  67. H. J. Bausch, J. P. Townsend, J.-P. Davis, S. Duwal, C. T. Seagle, T. M. Abbott, A. N. Clark, and S. D. Jacobsen, Direct sound speed measurements of MgO along planetary adiabats up to 400 GPa using shock-ramp compression [Dataset], Zenodo, 2026, doi: 10.5281/zenodo.23404812.
  68. K. Tomlinson, C. T. Seagle, H. Huang, G. E. Smith, J. L. Taylor, and R. R. Paguio, Enhanced dual confocal measurement system, Fusion Sci. Technol. 73, 139 (2018).
  69. Y. Tange, Y. Nishihara, and T. Tsuchiya, Unified analyses for P−V−T equation of state of MgO: A solution for pressure‐scale problems in high P−T experiments, J. Geophys. Res. 114, B03208 (2009).
  70. C.-S. Zha, H.-k. Mao, and R. J. Hemley, Elasticity of MgO and a primary pressure scale to 55 GPa, Proc. Natl. Acad. Sci. USA 97, 13494 (2000).

Outline

Information

Phys. Rev. B 114, 274108– Published 12 November, 2026
  • Received 6 February 2026
  • Revised 2 September 2026
  • Accepted 14 October 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