Femtosecond temperature measurements of laser-shocked copper deduced from the intensity of the x-ray thermal diffuse scattering

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; V. Cerantola; J. Chantel; A. Di Cicco; A. L. Coleman; J. Collier; G. Collins; A. J. Comley; F. Coppari; T. E. Cowan; G. Cristoforetti; H. Cynn; A. Descamps; F. Dorchies; M. J. Duff; A. Dwivedi; C. Edwards; J. H. Eggert; D. Errandonea; G. Fiquet; E. Galtier; A. Laso Garcia; H. Ginestet; L. Gizzi; A. Gleason; S. Goede; J. M. Gonzalez; M. G. Gorman; M. Harmand; N. Hartley; C. Hernandez-Gomez; A. Higginbotham; H. Höppner; O. S. Humphries; R. J. Husband; T. M. Hutchinson; H. Hwang; D. A. Keen; J. Kim; P. Koester; Z. Konopkova; D. Kraus; A. Krygier; L. Labate; A. E. Lazicki; Y. Lee; H.-P. Liermann; P. Mason; M. Masruri; B. Massani; E. E. McBride; C. McGuire; J. D. McHardy; D. McGonegle; R. S. McWilliams; S. Merkel; G. Morard; B. Nagler; M. Nakatsutsumi; K. Nguyen-Cong; A.-M. Norton; I. I. Oleynik; C. Otzen; N. Ozaki; S. Pandolfi; A. Pelka; K. A. Pereira; J. P. Phillips; C. Prescher; T. R. Preston; L. Randolph; D. Ranjan; A. Ravasio; R. Redmer; J. Rips; D. Santamaria-Perez; D. J. Savage; M. Schoelmerich; J.-P. Schwinkendorf; S. Singh; J. Smith; R. F. Smith; A. Sollier; J. Spear; C. Spindloe; M. Stevenson; C. Strohm; T.-A. Suer; M. Tang; M. Toncian; T. Toncian; S. J. Tracy; A. Trapananti; T. Tschentscher; M. Tyldesley; C. E. Vennari; T. Vinci; S. C. Vogel; T. J. Volz; J. Vorberger; J. T. Willman; L. Wollenweber; U. Zastrau; E. Brambrink; K. Appel; M. I. McMahon

doi:10.1063/5.0256844

Femtosecond temperature measurements of laser-shocked copper deduced from the intensity of the x-ray thermal diffuse scattering

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 CafisoV. Cerantola, J. Chantel, A. Di Cicco, A. L. Coleman, J. Collier, G. Collins, A. J. Comley, F. Coppari, T. E. Cowan, G. Cristoforetti, H. Cynn, A. Descamps, F. Dorchies, M. J. Duff, A. Dwivedi, C. Edwards, J. H. Eggert, D. Errandonea, G. Fiquet, E. Galtier, A. Laso Garcia, H. Ginestet, L. Gizzi, A. Gleason, S. Goede, J. M. Gonzalez, M. G. Gorman, M. Harmand, N. Hartley, C. Hernandez-Gomez, A. Higginbotham, H. Höppner, O. S. Humphries, R. J. Husband, T. M. Hutchinson, H. Hwang, D. A. Keen, J. Kim, P. Koester, Z. Konopkova, D. Kraus, A. Krygier, L. Labate, A. E. Lazicki, Y. Lee, H.-P. Liermann, P. Mason, M. Masruri, B. Massani, E. E. McBride, C. McGuire, J. D. McHardy, D. McGonegle, R. S. McWilliams, S. Merkel, G. Morard, B. Nagler, M. Nakatsutsumi, K. Nguyen-Cong, A.-M. Norton, I. I. Oleynik, C. Otzen, N. Ozaki, S. Pandolfi, A. Pelka, K. A. Pereira, J. P. Phillips, C. Prescher, T. R. Preston, L. Randolph, D. Ranjan, A. Ravasio, R. Redmer, J. Rips, D. Santamaria-Perez, D. J. Savage, M. Schoelmerich, J.-P. Schwinkendorf, S. Singh, J. Smith, R. F. Smith, A. Sollier, J. Spear, C. Spindloe, M. Stevenson, C. Strohm, T.-A. Suer, M. Tang, M. Toncian, T. Toncian, S. J. Tracy, A. Trapananti, T. Tschentscher, M. Tyldesley, C. E. Vennari, T. Vinci, S. C. Vogel, T. J. Volz, J. Vorberger, J. T. Willman, L. Wollenweber, U. Zastrau, E. Brambrink, K. Appel, M. I. McMahon

Research output: Contribution to journal › Article › peer-review

Abstract

We present 50-fs, single-shot measurements of the x-ray thermal diffuse scattering (TDS) from copper foils that have been shocked via nanosecond laser ablation up to pressures above ∼ 135 GPa. We hence deduce the x-ray Debye–Waller factor, providing a temperature measurement. The targets were laser-shocked with the DiPOLE 100-X laser at the High Energy Density endstation of the European X-ray Free-Electron Laser. Single x-ray pulses, with a photon energy of 18 keV, were scattered from the samples and recorded on Varex detectors. Despite the targets being highly textured (as evinced by large variations in the elastic scattering) and with such texture changing upon compression, the absolute intensity of the azimuthally averaged inelastic TDS between the Bragg peaks is largely insensitive to these changes, and allowing for both Compton scattering and the low-level scattering from a sacrificial ablator layer provides a reliable measurement of T / Θ D 2, where Θ D is the Debye temperature. We compare our results with the predictions of the SESAME 3336 and LEOS 290 equations of state for copper and find good agreement within experimental errors. We, thus, demonstrate that single-shot temperature measurements of dynamically compressed materials can be made via thermal diffuse scattering of XFEL radiation.

Original language	English
Article number	155904
Number of pages	18
Journal	Journal of Applied Physics
Volume	137
Issue number	15
DOIs	https://doi.org/10.1063/5.0256844
Publication status	Published - 21 Apr 2025

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10.1063/5.0256844Licence: CC BY-NC-ND

Femtosecond temperature measurements of laser-shocked copper deduced from the intensity of the x-ray thermal diffuse scattering
© Author(s) 2025
Final published version, 6.37 MBLicence: CC BY-NC-ND

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Wark, J. S., Peake, D. J., Stevens, T., Heighway, P. G., Ping, Y., Sterne, P., Albertazzi, B., Ali, S. J., Antonelli, L., Armstrong, M. R., Baehtz, C., Ball, O. B., Banerjee, S., Belonoshko, A. B., Bolme, C. A., Bouffetier, V., Briggs, R., Buakor, K., Butcher, T., ... McMahon, M. I. (2025). Femtosecond temperature measurements of laser-shocked copper deduced from the intensity of the x-ray thermal diffuse scattering. Journal of Applied Physics, 137(15), Article 155904. https://doi.org/10.1063/5.0256844

@article{8a47537380e249ebb161b73db07bbd09,

title = "Femtosecond temperature measurements of laser-shocked copper deduced from the intensity of the x-ray thermal diffuse scattering",

abstract = "We present 50-fs, single-shot measurements of the x-ray thermal diffuse scattering (TDS) from copper foils that have been shocked via nanosecond laser ablation up to pressures above ∼ 135 GPa. We hence deduce the x-ray Debye–Waller factor, providing a temperature measurement. The targets were laser-shocked with the DiPOLE 100-X laser at the High Energy Density endstation of the European X-ray Free-Electron Laser. Single x-ray pulses, with a photon energy of 18 keV, were scattered from the samples and recorded on Varex detectors. Despite the targets being highly textured (as evinced by large variations in the elastic scattering) and with such texture changing upon compression, the absolute intensity of the azimuthally averaged inelastic TDS between the Bragg peaks is largely insensitive to these changes, and allowing for both Compton scattering and the low-level scattering from a sacrificial ablator layer provides a reliable measurement of T / Θ D 2, where Θ D is the Debye temperature. We compare our results with the predictions of the SESAME 3336 and LEOS 290 equations of state for copper and find good agreement within experimental errors. We, thus, demonstrate that single-shot temperature measurements of dynamically compressed materials can be made via thermal diffuse scattering of XFEL radiation.",

author = "Wark, {J. S.} and Peake, {D. J.} and T. Stevens and Heighway, {P. G.} and Y. Ping and P. Sterne and B. Albertazzi and Ali, {S. J.} and L. Antonelli and Armstrong, {M. R.} and C. Baehtz and Ball, {O. B.} and S. Banerjee and Belonoshko, {A. B.} and Bolme, {C. A.} and V. Bouffetier and R. Briggs and K. Buakor and T. Butcher and {Di Dio Cafiso}, S. and V. Cerantola and J. Chantel and {Di Cicco}, A. and Coleman, {A. L.} and J. Collier and G. Collins and Comley, {A. J.} and F. Coppari and Cowan, {T. E.} and G. Cristoforetti and H. Cynn and A. Descamps and F. Dorchies and Duff, {M. J.} and A. Dwivedi and C. Edwards and Eggert, {J. H.} and D. Errandonea and G. Fiquet and E. Galtier and {Laso Garcia}, A. and H. Ginestet and L. Gizzi and A. Gleason and S. Goede and Gonzalez, {J. M.} and Gorman, {M. G.} and M. Harmand and N. Hartley and C. Hernandez-Gomez and A. Higginbotham and H. H{\"o}ppner and Humphries, {O. S.} and Husband, {R. J.} and Hutchinson, {T. M.} and H. Hwang and Keen, {D. A.} and J. Kim and P. Koester and Z. Konopkova and D. Kraus and A. Krygier and L. Labate and Lazicki, {A. E.} and Y. Lee and H.-P. Liermann and P. Mason and M. Masruri and B. Massani and McBride, {E. E.} and C. McGuire and McHardy, {J. D.} and D. McGonegle and McWilliams, {R. S.} and S. Merkel and G. Morard and B. Nagler and M. Nakatsutsumi and K. Nguyen-Cong and A.-M. Norton and Oleynik, {I. I.} and C. Otzen and N. Ozaki and S. Pandolfi and A. Pelka and Pereira, {K. A.} and Phillips, {J. P.} and C. Prescher and Preston, {T. R.} and L. Randolph and D. Ranjan and A. Ravasio and R. Redmer and J. Rips and D. Santamaria-Perez and Savage, {D. J.} and M. Schoelmerich and J.-P. Schwinkendorf and S. Singh and J. Smith and Smith, {R. F.} and A. Sollier and J. Spear and C. Spindloe and M. Stevenson and C. Strohm and T.-A. Suer and M. Tang and M. Toncian and T. Toncian and Tracy, {S. J.} and A. Trapananti and T. Tschentscher and M. Tyldesley and Vennari, {C. E.} and T. Vinci and Vogel, {S. C.} and Volz, {T. J.} and J. Vorberger and Willman, {J. T.} and L. Wollenweber and U. Zastrau and E. Brambrink and K. Appel and McMahon, {M. I.}",

note = "{\textcopyright} Author(s) 2025",

year = "2025",

month = apr,

day = "21",

doi = "10.1063/5.0256844",

language = "English",

volume = "137",

journal = "Journal of Applied Physics",

issn = "0021-8979",

publisher = "American Institute of Physics",

number = "15",

}

Wark, JS, Peake, DJ, Stevens, T, Heighway, PG, Ping, Y, Sterne, P, Albertazzi, B, Ali, SJ, Antonelli, L, Armstrong, MR, Baehtz, C, Ball, OB, Banerjee, S, Belonoshko, AB, Bolme, CA, Bouffetier, V, Briggs, R, Buakor, K, Butcher, T, Di Dio Cafiso, S, Cerantola, V, Chantel, J, Di Cicco, A, Coleman, AL, Collier, J, Collins, G, Comley, AJ, Coppari, F, Cowan, TE, Cristoforetti, G, Cynn, H, Descamps, A, Dorchies, F, Duff, MJ, Dwivedi, A, Edwards, C, Eggert, JH, Errandonea, D, Fiquet, G, Galtier, E, Laso Garcia, A, Ginestet, H, Gizzi, L, Gleason, A, Goede, S, Gonzalez, JM, Gorman, MG, Harmand, M, Hartley, N, Hernandez-Gomez, C, Higginbotham, A, Höppner, H, Humphries, OS, Husband, RJ, Hutchinson, TM, Hwang, H, Keen, DA, Kim, J, Koester, P, Konopkova, Z, Kraus, D, Krygier, A, Labate, L, Lazicki, AE, Lee, Y, Liermann, H-P, Mason, P, Masruri, M, Massani, B, McBride, EE, McGuire, C, McHardy, JD, McGonegle, D, McWilliams, RS, Merkel, S, Morard, G, Nagler, B, Nakatsutsumi, M, Nguyen-Cong, K, Norton, A-M, Oleynik, II, Otzen, C, Ozaki, N, Pandolfi, S, Pelka, A, Pereira, KA, Phillips, JP, Prescher, C, Preston, TR, Randolph, L, Ranjan, D, Ravasio, A, Redmer, R, Rips, J, Santamaria-Perez, D, Savage, DJ, Schoelmerich, M, Schwinkendorf, J-P, Singh, S, Smith, J, Smith, RF, Sollier, A, Spear, J, Spindloe, C, Stevenson, M, Strohm, C, Suer, T-A, Tang, M, Toncian, M, Toncian, T, Tracy, SJ, Trapananti, A, Tschentscher, T, Tyldesley, M, Vennari, CE, Vinci, T, Vogel, SC, Volz, TJ, Vorberger, J, Willman, JT, Wollenweber, L, Zastrau, U, Brambrink, E, Appel, K & McMahon, MI 2025, 'Femtosecond temperature measurements of laser-shocked copper deduced from the intensity of the x-ray thermal diffuse scattering', Journal of Applied Physics, vol. 137, no. 15, 155904. https://doi.org/10.1063/5.0256844

TY - JOUR

T1 - Femtosecond temperature measurements of laser-shocked copper deduced from the intensity of the x-ray thermal diffuse scattering

AU - Wark, J. S.

AU - Peake, D. J.

AU - Stevens, T.

AU - Heighway, P. G.

AU - Ping, Y.

AU - Sterne, P.

AU - Albertazzi, B.

AU - Ali, S. J.

AU - Antonelli, L.

AU - Armstrong, M. R.

AU - Baehtz, C.

AU - Ball, O. B.

AU - Banerjee, S.

AU - Belonoshko, A. B.

AU - Bolme, C. A.

AU - Bouffetier, V.

AU - Briggs, R.

AU - Buakor, K.

AU - Butcher, T.

AU - Di Dio Cafiso, S.

AU - Cerantola, V.

AU - Chantel, J.

AU - Di Cicco, A.

AU - Coleman, A. L.

AU - Collier, J.

AU - Collins, G.

AU - Comley, A. J.

AU - Coppari, F.

AU - Cowan, T. E.

AU - Cristoforetti, G.

AU - Cynn, H.

AU - Descamps, A.

AU - Dorchies, F.

AU - Duff, M. J.

AU - Dwivedi, A.

AU - Edwards, C.

AU - Eggert, J. H.

AU - Errandonea, D.

AU - Fiquet, G.

AU - Galtier, E.

AU - Laso Garcia, A.

AU - Ginestet, H.

AU - Gizzi, L.

AU - Gleason, A.

AU - Goede, S.

AU - Gonzalez, J. M.

AU - Gorman, M. G.

AU - Harmand, M.

AU - Hartley, N.

AU - Hernandez-Gomez, C.

AU - Higginbotham, A.

AU - Höppner, H.

AU - Humphries, O. S.

AU - Husband, R. J.

AU - Hutchinson, T. M.

AU - Hwang, H.

AU - Keen, D. A.

AU - Kim, J.

AU - Koester, P.

AU - Konopkova, Z.

AU - Kraus, D.

AU - Krygier, A.

AU - Labate, L.

AU - Lazicki, A. E.

AU - Lee, Y.

AU - Liermann, H.-P.

AU - Mason, P.

AU - Masruri, M.

AU - Massani, B.

AU - McBride, E. E.

AU - McGuire, C.

AU - McHardy, J. D.

AU - McGonegle, D.

AU - McWilliams, R. S.

AU - Merkel, S.

AU - Morard, G.

AU - Nagler, B.

AU - Nakatsutsumi, M.

AU - Nguyen-Cong, K.

AU - Norton, A.-M.

AU - Oleynik, I. I.

AU - Otzen, C.

AU - Ozaki, N.

AU - Pandolfi, S.

AU - Pelka, A.

AU - Pereira, K. A.

AU - Phillips, J. P.

AU - Prescher, C.

AU - Preston, T. R.

AU - Randolph, L.

AU - Ranjan, D.

AU - Ravasio, A.

AU - Redmer, R.

AU - Rips, J.

AU - Santamaria-Perez, D.

AU - Savage, D. J.

AU - Schoelmerich, M.

AU - Schwinkendorf, J.-P.

AU - Singh, S.

AU - Smith, J.

AU - Smith, R. F.

AU - Sollier, A.

AU - Spear, J.

AU - Spindloe, C.

AU - Stevenson, M.

AU - Strohm, C.

AU - Suer, T.-A.

AU - Tang, M.

AU - Toncian, M.

AU - Toncian, T.

AU - Tracy, S. J.

AU - Trapananti, A.

AU - Tschentscher, T.

AU - Tyldesley, M.

AU - Vennari, C. E.

AU - Vinci, T.

AU - Vogel, S. C.

AU - Volz, T. J.

AU - Vorberger, J.

AU - Willman, J. T.

AU - Wollenweber, L.

AU - Zastrau, U.

AU - Brambrink, E.

AU - Appel, K.

AU - McMahon, M. I.

PY - 2025/4/21

Y1 - 2025/4/21

N2 - We present 50-fs, single-shot measurements of the x-ray thermal diffuse scattering (TDS) from copper foils that have been shocked via nanosecond laser ablation up to pressures above ∼ 135 GPa. We hence deduce the x-ray Debye–Waller factor, providing a temperature measurement. The targets were laser-shocked with the DiPOLE 100-X laser at the High Energy Density endstation of the European X-ray Free-Electron Laser. Single x-ray pulses, with a photon energy of 18 keV, were scattered from the samples and recorded on Varex detectors. Despite the targets being highly textured (as evinced by large variations in the elastic scattering) and with such texture changing upon compression, the absolute intensity of the azimuthally averaged inelastic TDS between the Bragg peaks is largely insensitive to these changes, and allowing for both Compton scattering and the low-level scattering from a sacrificial ablator layer provides a reliable measurement of T / Θ D 2, where Θ D is the Debye temperature. We compare our results with the predictions of the SESAME 3336 and LEOS 290 equations of state for copper and find good agreement within experimental errors. We, thus, demonstrate that single-shot temperature measurements of dynamically compressed materials can be made via thermal diffuse scattering of XFEL radiation.

AB - We present 50-fs, single-shot measurements of the x-ray thermal diffuse scattering (TDS) from copper foils that have been shocked via nanosecond laser ablation up to pressures above ∼ 135 GPa. We hence deduce the x-ray Debye–Waller factor, providing a temperature measurement. The targets were laser-shocked with the DiPOLE 100-X laser at the High Energy Density endstation of the European X-ray Free-Electron Laser. Single x-ray pulses, with a photon energy of 18 keV, were scattered from the samples and recorded on Varex detectors. Despite the targets being highly textured (as evinced by large variations in the elastic scattering) and with such texture changing upon compression, the absolute intensity of the azimuthally averaged inelastic TDS between the Bragg peaks is largely insensitive to these changes, and allowing for both Compton scattering and the low-level scattering from a sacrificial ablator layer provides a reliable measurement of T / Θ D 2, where Θ D is the Debye temperature. We compare our results with the predictions of the SESAME 3336 and LEOS 290 equations of state for copper and find good agreement within experimental errors. We, thus, demonstrate that single-shot temperature measurements of dynamically compressed materials can be made via thermal diffuse scattering of XFEL radiation.

U2 - 10.1063/5.0256844

DO - 10.1063/5.0256844

M3 - Article

SN - 0021-8979

VL - 137

JO - Journal of Applied Physics

JF - Journal of Applied Physics

IS - 15

M1 - 155904

ER -