- Open Access
Identification of distortions to the Ni atomic potential at 100 GPa with temperature measurements
Phys. Rev. Research 8, 033372 – Published 28 September, 2026
DOI: https://doi.org/10.1103/qzck-1qpn
Abstract
Characterizing the temperature of materials in high-energy-density (HED) experiments is a major gap in the benchmarking of HED matter, such as matter in the deep interiors of planets and low-mass stars. Extended x-ray absorption fine structure (EXAFS) spectroscopy is one of the few techniques capable of determining temperature at HED conditions, but the inferred EXAFS temperature depends upon the atomic potential, which itself is not measured. This work compares simultaneous EXAFS and self-emission temperature measurements [S. Boccato et al., J. Geophys. Res.: Solid Earth, 122, 9921 (2017)], to quantify the impact of atomic potentials implicit in the EXAFS temperature analysis. Traditional EXAFS analysis employing a harmonic potential produces systematically lower temperatures than from self-emission ( at 100 GPa and 3000 K), while a sixth-order distortion to the pair potential recovers agreement between the two measurements. These results highlight and quantify the need and complexity of distortions or anharmonic corrections to atomic potentials at HED conditions.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (59)
- B. Yaakobi, D. D. Meyerhofer, T. R. Boehly, J. J. Rehr, B. A. Remington, P. G. Allen, S. M. Pollaine, and R. C. Albers, Extended x-ray absorption fine structure measurements of laser-shocked V and Ti and crystal phase transformation in Ti, Phys. Rev. Lett. 92, 095504 (2004).
- B. Yaakobi, T. R. Boehly, D. D. Meyerhofer, T. J. B. Collins, B. A. Remington, P. G. Allen, S. M. Pollaine, H. E. Lorenzana, and J. H. Eggert, EXAFS measurement of iron bcc-to-hcp phase transformation in nanosecond-laser shocks, Phys. Rev. Lett. 95, 075501 (2005).
- 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).
- R. Torchio, F. Occelli, O. Mathon, A. Sollier, E. Lescoute, L. Videau, T. Vinci, A. Benuzzi-Mounaix, J. Headspith, W. Helsby, S. Bland, D. Eakins, D. Chapman, S. Pascarelli, and P. Loubeyre, Probing local and electronic structure in warm dense matter: Single pulse synchrotron x-ray absorption spectroscopy on shocked Fe, Sci. Rep. 6, 26402 (2016).
- H. Sio, A. Krygier, D. G. Braun, R. E. Rudd, S. A. Bonev, F. Coppari, M. Millot, D. E. Fratanduono, N. Bhandarkar, et al., Extended X-ray absorption fine structure of dynamically-compressed copper up to 1 terapascal, Nat. Commun. 14, 7046 (2023).
- D. A. Chin, P. M. Nilson, J. J. Ruby, G. Bunker, M. Ghosh, M. E. Signor, D. T. Bishel, E. A. Smith, F. Coppari, Y. Ping, J. R. Rygg, and G. W. Collins, Parametrized ion-distribution model for extended x-ray absorption fine-structure analysis at high-energy-density conditions, Phys. Plasmas 31, 042708 (2024).
- H. Sio, A. Krygier, S. Stoupin, R. E. Rudd, S. A. Bonev, D. G. Braun, F. Coppari, A. L. Coleman, N. Bhandarkar, M. Bitter, 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).
- J.-A. Hernandez, N. Sévelin-Radiguet, R. Torchio, S. Balugani, A. Dwivedi, G. Berruyer, D. Bugnazet, S. Chazalette, C. Clavel, D. Lorphévret, S. Pasternak, F. Perrin, F. Villar, W. Helsby, M. Borri, F. Mollica, S. Branly, L. Meignien, P. Audebert, and O. Mathon, The high power laser facility at beamline ID24-ED at the ESRF, High Pressure Res. 44, 372 (2024).
- A. Descamps, B. K. Ofori-Okai, K. Appel, V. Cerantola, A. Comley, J. H. Eggert, L. B. Fletcher, D. O. Gericke, S. Göde, 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).
- M. C. Gregor, R. Boni, A. Sorce, J. Kendrick, C. A. McCoy, D. N. Polsin, T. R. Boehly, P. M. Celliers, G. W. Collins, D. E. Fratanduono, J. H. Eggert, and M. Millot, Absolute calibration of the OMEGA streaked optical pyrometer for temperature measurements of compressed materials, Rev. Sci. Instrum. 87, 114903 (2016).
- D. C. Koningsberger, B. L. Mojet, G. E. Van Dorssen, and D. E. Ramaker, XAFS spectroscopy; fundamental principles and data analysis, Top. Catal. 10, 143 (2000).
- G. Bunker, Introduction to XAFS: A Practical Guide to X-ray Absorption Fine Structure Spectroscopy (Cambridge University Press, Cambridge, 2010).
- S. Calvin, XAFS for Everyone (CRC Press, Boca Raton, FL, 2013).
- 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).
- 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).
- I. Kantor, C. Marini, O. Mathon, and S. Pascarelli, A laser heating facility for energy-dispersive x-ray absorption spectroscopy, Rev. Sci. Instrum. 89, 013111 (2018).
- S. Boccato, R. Torchio, I. Kantor, G. Morard, S. Anzellini, R. Giampaoli, R. Briggs, A. Smareglia, T. Irifune, and S. Pascarelli, The melting curve of nickel up to 100 GPa explored by XAS, J. Geophys. Res.: Solid Earth 122, 9921 (2017).
- R. Giampaoli, I. Kantor, M. Mezouar, S. Boccato, A. D. Rosa, R. Torchio, G. Garbarino, O. Mathon, and S. P. and, Measurement of temperature in the laser heated diamond anvil cell: Comparison between reflective and refractive optics, High Pressure Res. 38, 250 (2018).
- D. N. Polsin, D. A. Chin, T. S. Duffy, M. Ginnane, X. Gong, L. E. Hansen, A. J. LaPierre, M. C. Marshall, G. W. Collins, and J. R. Rygg, Atomic structure and melting of Ni and up to 400 GPa, Phys. Rev. B 109, 214112 (2024).
- K. A. Pereira, S. M. Clarke, S. Singh, R. Briggs, C. P. McGuire, H. J. Lee, D. Khaghani, B. Nagler, E. Galtier, E. Cunningham et al., Stability of the fcc phase in shocked nickel up to 332 GPa, Nat. Commun. 16, 4385 (2025).
- E. Sevillano, H. Meuth, and J. J. Rehr, Extended x-ray absorption fine structure Debye-Waller factors. I. Monatomic crystals, Phys. Rev. B 20, 4908 (1979).
- S. Boccato, Local structure of liquid 3d metals under extreme conditions of pressure and temperature, Ph.D. thesis, Université Grenoble Alpes, 2016.
- G. Smith, Numerical Solutions of Partial Differential Equations (Oxford Universtiy Press, Oxford, 1985).
- K. Arendt and W. Urban, Partial Differential Equations: An Introduction to Analytical and Numerical Methods (Springer Nature, Switzerland, 2023), Vol. 294.
- K. M. Razeeb and S. Roy, Thermal diffusivity of nonfractal and fractal nickel nanowires, J. Appl. Phys. 103, 084302 (2008).
- M. W. Chase, Jr., NIST-JANAF Thermochemical Tables, 4th ed., Monograph 9 (Part I and Part II) J. Phys. Chem. Ref. Data, 1998, p. 1698.
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/qzck-1qpn for additional information about the EXAFS analysis, Debye temperature calculations, and AIMD calculations, which includes Refs. [37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59].
- G. Bunker, Application of the ratio method of EXAFS analysis to disordered systems, Nucl. Instrum. Methods Phys. Res. 207, 437 (1983).
- F. W. Lytle, D. E. Sayers, and E. A. Stern, Extended x-ray-absorption fine-structure technique. II. Experimental practice and selected results, Phys. Rev. B 11, 4825 (1975).
- E. A. Stern, D. E. Sayers, and F. W. Lytle, Extended x-ray-absorption fine-structure technique. III. Determination of physical parameters, Phys. Rev. B 11, 4836 (1975).
- J. J. Rehr and R. C. Albers, Theoretical approaches to x-ray absorption fine structure, Rev. Mod. Phys. 72, 621 (2000).
- E. A. Stern, P. Līvņš, and Z. Zhang, Thermal vibration and melting from a local perspective, Phys. Rev. B 43, 8850 (1991).
- P. Fornasini, Thermal effects on EXAFS, International Tables for Crystallography, edited by C. T. Chantler, F. Boscherini, and B. Bunker (International Union of Crystallography, 2024), Vol. I, Chap. 2.14, p. 139.
- G. Bunker, The Phase Method for Numerical Solution of the Schrodinger Equation (Grant Byrd Bunker, Chicago, IL, 2024).
- R. K. Pathria and P. D. Beale, Statistical Mechanics, 3rd ed. (Elsevier Ltd., Amsterdam, 2011).
- J. J. Rehr, J. J. Kas, F. D. Vila, M. P. Prange, and K. Jorissen, Parameter-free calculations of X-ray spectra with FEFF9, Phys. Chem. Chem. Phys. 12, 5503 (2010).
- M. Newville, Fundamentals of XAFS, Rev. Mineral. Geochem. 78, 33 (2014).
- 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).
- W. J. Murphy, A. Higginbotham, J. S. Wark, and N. Park, Molecular dynamics simulations of the Debye-Waller effect in shocked copper, Phys. Rev. B 78, 014109 (2008).
- B. Onat and S. Durukanoğlu, An optimized interatomic potential for Cu–Ni alloys with the embedded-atom method, J. Phys.: Condens. Matter 26, 035404 (2014).
- S. P. Coleman, D. E. Spearot, and L. Capolungo, Virtual diffraction analysis of Ni [010] symmetric tilt grain boundaries, Modell. Simul. Mater. Sci. Eng. 21, 055020 (2013).
- C. Kittel, Introduction to Solid State Physics (Wiley, New Jersey, 2005).
- 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).
- B. E. Warren, X-ray Diffraction (Dover, New York, 1990).
- B. Willis and A. Pryor, Thermal Vibrations in Crystallography (Cambridge University Press, London, 1975).
- R. Kumar, C. Carroll, A. Hartikainen, and O. Martin, ArviZ a unified library for exploratory analysis of Bayesian models in Python, J. Open Source Software 4, 1143 (2019).
- Y. Mishin, D. Farkas, M. J. Mehl, and D. A. Papaconstantopoulos, Interatomic potentials for monoatomic metals from experimental data and ab initio calculations, Phys. Rev. B 59, 3393 (1999).
- R. M. More, K. H. Warren, D. A. Young, and G. B. Zimmerman, A new quotidian equation of state (QEOS) for hot dense matter, Phys. Fluids 31, 3059 (1988).
- N. W. Ashcroft and N. D. Mermin, Solid State Physics (Brooks/Cole, Pacific Grove, CA, 1976), 1st ed.
- J. S. Pigott, D. A. Ditmer, R. A. Fischer, D. M. Reaman, R. Hrubiak, Y. Meng, R. J. Davis, and W. R. Panero, High-pressure, high-temperature equations of state using nanofabricated controlled-geometry Ni//Ni double hot-plate samples, Geophys. Res. Lett. 42, 10239 (2015).
- L. S. Dubrovinsky, S. K. Saxena, N. A. Dubrovinskaia, S. Rekhi, and T. Le Bihan, Gruneisen parameter of -iron up to 300 GPa from in-situ X-ray study, Am. Mineral. 85, 386 (2000).
- D. Phan, N. Pradhan, and M. Jankowiak, Composable effects for flexible and accelerated probabilistic programming in NumPyro, arXiv:1912.11554.
- E. Bingham, J. P. Chen, M. Jankowiak, F. Obermeyer, N. Pradhan, T. Karaletsos, R. Singh, P. A. Szerlip, P. Horsfall, and N. D. Goodman, Pyro: Deep universal probabilistic programming, J. Mach. Learn. Res. 20, 973 (2019).
- J. J. Ruby, J. R. Rygg, D. A. Chin, J. A. Gaffney, P. J. Adrian, D. Bishel, C. J. Forrest, V. Y. Glebov, N. V. Kabadi, P. M. Nilson, Y. Ping, C. Stoeckl, and G. W. Collins, Constraining physical models at gigabar pressures, Phys. Rev. E 102, 053210 (2020).
- W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
- N. D. Mermin, Thermal properties of the inhomogeneous electron gas, Phys. Rev. 137, A1441 (1965).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple [Phys. Rev. Lett. 77, 3865 (1996)], Phys. Rev. Lett. 78, 1396(E) (1997).
- G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558(R) (1993).