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Shock compression of diamond single crystals to 120 GPa: Refractive index and nonlinear photoelasticity

P. Renganathan1, J. M. Lang, Jr.2, Y. Toyoda1, J. M. Winey3,*, and Y. M. Gupta3,4

  • *Contact author: mwiney@wsu.edu

Phys. Rev. B 113, 134103 – Published 2 April, 2026

DOI: https://doi.org/10.1103/ymz4-tyml

Abstract

The optical response of transparent solids at extreme conditions is important for both fundamental science and many applications. Strong transparent solids are of particular interest for use as optical windows in dynamic compression experiments. Due to diamond's exceptional strength and optical properties, laser-driven shock experiments and plate impact experiments were carried out to examine the diamond optical response for shock wave compression along two different crystal orientations. Using laser interferometry at 532 and 1550 nm wavelengths, optical transparency was observed and refractive indices were determined for [100] diamond at stresses up to 119 GPa and for [111] diamond at stresses up to 87 GPa. From these results, the nonlinear photoelastic response for [100] and [111] diamond was determined, revealing significant dependence on both crystal orientation and laser wavelength. To enable [100] diamond as an interferometry window in dynamic compression experiments, the requisite window corrections were determined for 532 and 1550 nm wavelengths. Because of diamond's excellent x-ray transparency, the present findings will be particularly useful for incorporating [100] diamonds as windows in dynamic compression experiments involving x-ray diffraction or other x-ray diagnostics.

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References (42)

  1. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  2. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 2005).
  3. K. Vedam and E. D. D. Schmidt, Variation of refractive index of MgO with pressure to 7 kbar, Phys. Rev. 146, 548 (1966).
  4. N. M. Balzaretti and J. A. H. Da Jornada, Pressure dependence of the refractive index and electronic polarizability of LiF, MgF2 and CaF2, J. Phys. Chem. Solids 57, 179 (1996).
  5. P. Rigg, M. Knudson, R. Scharff, and R. Hixson, Determining the refractive index of shocked [100] lithium fluoride to the limit of transmissibility, J. Appl. Phys. 116, 033515 (2014).
  6. J. A. Hawreliak, J. M. Winey, and Y. M. Gupta, Refractive index of lithium fluoride at high dynamic stresses, Phys. Rev. B 110, 134106 (2024).
  7. K. Vedam and T. A. Davis, Nonlinear variation of the refractive indices of α-quartz with pressure, J. Opt. Soc. Am. 57, 1140 (1967).
  8. N. M. Balzaretti, J. P. Denis,, and J. A. H. da Jornada, Variation of the refractive index and polarizability of sapphire under high pressures, J. Appl. Phys. 73, 1426 (1993).
  9. S. C. Jones and Y. M. Gupta, Refractive index and elastic properties of z-cut quartz shocked to 60 kbar, J. Appl. Phys. 88, 5671 (2000).
  10. R. E. Setchell, Refractive index of sapphire at 532 nm under shock compression and release, J. Appl. Phys. 91, 2833 (2002).
  11. S. C. Jones, M. C. Robinson, and Y. M. Gupta, Ordinary refractive index of sapphire in uniaxial tension and compression along the c axis, J. Appl. Phys. 93, 1023 (2003).
  12. L. M. Barker and R. E. Hollenbach, Shock-wave studies of PMMA, fused silica, and sapphire, J. Appl. Phys. 41, 4208 (1970).
  13. L. M. Barker and R. E. Hollenbach, Laser interferometer for measuring high velocities of any reflecting surface, J. Appl. Phys. 43, 4669 (1972).
  14. 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).
  15. K. M. Ogilvie and G. E. Duvall, Shock-induced changes in the electronic spectra of liquid CS2, J. Chem. Phys. 78, 1077 (1983).
  16. G. I. Pangilinan and Y. M. Gupta, Use of time-resolved Raman scattering to determine temperatures in shocked carbon tetrachloride, J. Appl. Phys. 81, 6662 (1997).
  17. Q. Williams, R. Jeanloz, J. Bass, B. Svendsen, and T. J. Ahrens, The melting curve of iron to 250 gigapascals: A constraint on the temperature at earth's center, Science 236, 181 (1987).
  18. C. S. Yoo, N. C. Holmes, M. Ross, D. J. Webb, and C. Pike, Shock temperatures and melting of iron at earth core conditions, Phys. Rev. Lett. 70, 3931 (1993).
  19. W. J. Carter, Hugoniot equation of state of some alkali halides, High Temp.-High Press. 5, 313 (1973).
  20. J. L. Wise and L. C. Chhabildas, Laser interferometer measurements of refractive index in shock-compressed materials, in Shock Waves in Condensed Matter, edited by Y. M. Gupta (Plenum, New York, 1986), pp. 441–454.
  21. J. A. Hawreliak, J. M. Winey, Y. Toyoda, M. Wallace, and Y. M. Gupta, Shock-induced melting of [100] lithium fluoride: Sound speed and Hugoniot measurements to 230 GPa, Phys. Rev. B 107, 014104 (2023).
  22. S. C. Jones, B. A. M. Vaughan, and Y. M. Gupta, Refractive indices of sapphire under elastic, uniaxial strain compression along the a axis, J. Appl. Phys. 90, 4990 (2001).
  23. H. J. McSkimin and P. Andreatch Jr., Elastic moduli of diamond as a function of pressure and temperature, J. Appl. Phys. 43, 2944 (1972).
  24. J. M. Lang Jr. and Y. M. Gupta, Strength and elastic deformation of natural and synthetic diamond crystals shock compressed along [100], J. Appl. Phys. 107, 113538 (2010).
  25. J. M. Lang, J. M. Winey, and Y. M. Gupta, Strength and deformation of shocked diamond single crystals: Orientation dependence, Phys. Rev. B 97, 104106 (2018).
  26. J. M. Lang Jr., Mechanical and optical response of diamond crystals shock compressed along dfferent orientations, Ph.D. dissertation, Washington State University, 2013.
  27. J. M. Lang Jr. and Y. M. Gupta, Experimental determination of third-order elastic constants of diamond, Phys. Rev. Lett. 106, 125502 (2011).
  28. J. M. Winey, A. Hmiel, and Y. M. Gupta, Third-order elastic constants of diamond determined from experimental data, J. Phys. Chem. Solids 93, 118 (2016).
  29. D. H. Dolan, Dynamic compression of synthetic diamond windows, Sandia National Laboratories Technical Report No. SAND2008-6284 (Sandia National Laboratories, Albuquerque, NM, 2008).
  30. K. Katagiri, N. Ozaki, K. Miyanishi, N. Kamimura, Y. Umeda, T. Sano, T. Sekine, and R. Kodama, Optical properties of shock-compressed diamond up to 550 GPa, Phys. Rev. B 101, 184106 (2020).
  31. J. M. Winey and Y. M. Gupta, Nonlinear anisotropic description for shocked single crystals: Thermoelastic response and pure mode wave propagation, J. Appl. Phys. 96, 1993 (2004).
  32. Laue x-ray diffraction measurements were carried out on all the plate impact samples and 5 of the 11 laser shock samples. The remaining 6 laser shock samples are assumed to have similar orientation tolerances because they were obtained as part of the same order from the same vendor. We note that small (2 to 3 degree) variations in crystal orientation do not have a significant effect on the response of diamond single crystals. For example, using the published diamond elastic constants [23] to calculate sound speeds along directions that vary by 3 degrees from [100] and [111], the longitudinal sound speeds vary by less than 0.07%.
  33. X. Wang, P. Rigg, J. Sethian, N. Sinclair, N. Weir, B. Williams, J. Zhang, J. Hawreliak, Y. Toyoda, Y. M. Gupta, Y. Li, D. Broege, J. Bromage, R. Earley, D. Guy, and J. Zuegel, The laser shock station in the dynamic compression sector, Rev. Sci. Instrum. 90, 053901 (2019).
  34. P. A. Rigg, P. Renganathan, N. W. Sinclair, Y. Toyoda, X. Wang, and Y. M. Gupta, Optimizing ablator thickness for laser shock experiments, Rev. Sci. Instrum. 96, 103904 (2025).
  35. P. M. Celliers, D. K. Bradley, G. W. Collins, D. G. Hicks, T. R. Boehly, and W. J. Armstrong, Line-imaging velocimeter for shock diagnostics at the OMEGA laser facility, Rev. Sci. Instrum. 75, 4916 (2004).
  36. A. M. Zaitsev, Optical Properties of Diamond (Springer, New York, 2001).
  37. E. D. D. Schmidt, J. L. Kirk, and K. Vedam, Variation of the refractive index of diamond with hydrostatic pressure to 7 kilobars, Amer. Mineral. 53, 1404 (1968).
  38. J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, 1985).
  39. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  40. K. Vedam and R. Srinivasan, Nonlinear piezo-optics, Acta Cryst. 22, 630 (1967).
  41. R. M. Denning, A. A. Giardini, E. Poindexter, and C. B. Slawson, Piezobirefringence in diamond: Further results, Amer. Mineral. 42, 556 (1957).
  42. M. H. Grimsditch and A. K. Ramdas, Brillouin scattering in diamond, Phys. Rev. B 11, 3139 (1975).

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