Skip to main content

Radial Diffraction in the Diamond Anvil Cell: Methods and Applications

  • Conference paper
  • First Online:

Abstract

Radial diffraction in the diamond anvil cell is a relevant technique for the study of plastic behavior of materials under high pressure. In this geometry, incident x-rays are perpendicular to the compression direction and we study the distortion of the diffraction rings, as well as variations of diffraction intensities with orientation. Plastic deformation induces local stress heterogeneities that are not properly accounted for in theories relying on elasticity only. Here, I show how those experiments coupled to numerical plasticity models can be used to extract important information, such as the identification of microscopic deformation mechanisms, a measure of the average stress supported by the sample, and a quantification of local stresses.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Antonangeli, D., M. Krisch, G. Fiquet, D. L. Farber, C. M. Aracne, J. Badro, F. Occelli, and H. Requardt, 2004, Elasticity of Cobalt at High pressure studied by inelastic x-ray scattering, Phys. Rev. Lett. 93, 215505

    Article  ADS  Google Scholar 

  • Antonangeli, D., S. Merkel, and D. L. Farber, 2006, Elastic anisotropy in hcp metals at high pressure and the sound wave anisotropy of the Earth’s inner core, Geophys. Res. Lett. 33, L24303

    Article  ADS  Google Scholar 

  • Burnley, P. C., and D. Zhang, 2008, Interpreting in situ x-ray diffraction data from high pressure deformation experiments using elastic-plastic self-consistent models: an example using quartz, J. Phys. : Condens. Matter 20, 285201

    Article  Google Scholar 

  • Duffy, T. S., G. Shen, D. L. Heinz, J. Shu, Y. Ma, H. K. Mao, R. J. Hemley, and A. K. Singh 1999, Lattice strains in gold and rhenium under non-hydrostatic compression to 37 GPa, Phys. Rev. B 60, 15063–15073

    Article  ADS  Google Scholar 

  • Hemley, R. J., H. K. Mao, G. Shen, J. Badro, P. Gillet, M. Hanfland, and D. Häusermann, 1997, X-Ray imaging of stress and strain of diamond, iron, and tungsten at megabar pressures, Science 276, 1242–1245

    Article  Google Scholar 

  • Kavner, A., 2007, Garnet yield strength at high pressures and implications for upper mantle and transition zone rheology, J. Geophys. Res. 112, B12207

    Article  ADS  Google Scholar 

  • Kinsland, G. L., and W. A. Bassett, 1976, Modification of the diamond anvil cell for the measuring strain and the strength of materials at pressures up to 300 kilobar, Rev. Sci. Instrum. 47, 130–132

    Article  ADS  Google Scholar 

  • Kocks, U. F., C. Tomé, and H. R. Wenk, 1998, Texture and Anisotropy: Preferred Orientations and their Effects on Material Properties, Cambridge University Press, Cambridge

    Google Scholar 

  • Lebensohn, R. A., and C. N. Tomé, 1994, A self-consistent visco-plastic model: calculation of rolling textures of anisotropic materials, Mater. Sci. Eng. A 175, 71–82

    Article  Google Scholar 

  • Li, L., D. J. Weidner, J. Chen, M. T. Vaughan, M. Davis, and W. B. Durham (2004), X-ray strain analysis at high pressure: Effect of plastic deformation in MgO, J. Appl. Phys. 95, 8357–8365

    Article  ADS  Google Scholar 

  • Lutterotti, L., S. Matthies, and H. R. Wenk, 1999, MAUD: a friendly Java program for materials analysis using diffraction, IUCr: Newslett. CPD 21, 14–15

    Google Scholar 

  • Mao, H. K., J. Shu, Y. Fei, J. Hu, and R. J. Hemley, 1996, The wüstite enigma, Phys. Earth Planet. Int. 96, 135–145

    Article  ADS  Google Scholar 

  • Mao, H. K., J. Shu, G. Shen, R. J. Hemley, B. Li, and A. K. Singh, 1998, Elasticity and rheology of iron above 220 GPa and the nature of the Earth’s inner core, Nature 396, 741–743

    Article  ADS  Google Scholar 

  • Mao, W. L., V. V. Struzhkin, A. Q. R. Baron, S. Tsutsui, C. E. Tommaseo, H.-R. Wenk, M. Y. Hu, P. Chow, W. Sturhahn, J. Shu, R. J. Hemley, D. L. Heinz, and H. K. Mao, 2008, Experimental determination of the elasticity of iron at high pressure, J. Geophys. Res. 113, B09213

    Article  ADS  Google Scholar 

  • Matthies, S., H. G. Priesmeyer, and M. R. Daymond, 2001, On the diffractive determination of single-crystal elastic constants using polycrystalline samples, J. Appl. Cryst. 34, 585–601

    Article  Google Scholar 

  • Merkel, S., H. R. Wenk, J. Shu, G. Shen, P. Gillet, H. K. Mao, and R. J. Hemley, 2002, Deformation of polycrystalline MgO at pressures of the lower mantle, J. Geophys. Res. 107, 2271

    Article  ADS  Google Scholar 

  • Merkel, S., and T. Yagi, 2005, X-ray transparent gasket for diamond anvil cell high pressure experiments, Rev. Sci. Instrum. 76, 046109

    Article  ADS  Google Scholar 

  • Merkel, S., J. Shu, P. Gillet, H. Mao, and R. Hemley, 2005, X-ray diffraction study of the single crystal elastic moduli of ε-Fe up to 30 GPa, J. Geophys. Res. 110, B05201

    Article  ADS  Google Scholar 

  • Merkel, S., 2006, X-ray diffraction evaluation of stress in high pressure deformation experiments, J. Phys: Condens. Matter 18, S949–S962

    Article  ADS  Google Scholar 

  • Merkel, S., A. Kubo, L. Miyagi, S. Speziale, T. S. Duffy, H.-K. Mao, and H.-R. Wenk, 2006a, Plastic deformation of MgGeO3 post-perovskite at lower mantle pressures, Science 311, 644–646

    Article  ADS  Google Scholar 

  • Merkel, S., N. Miyajima, D. Antonangeli, G. Fiquet, and T. Yagi, 2006, Lattice preferred orientation and stress in polycrystalline hcp-Co plastically deformed under high pressure, J. Appl. Phys. 100, 023510

    Article  ADS  Google Scholar 

  • Merkel, S., C. Tomé, and H.-R. Wenk, 2009, A modeling analysis of the influence of plasticity on high pressure deformation of hcp-Co, Phys. Rev. B 79, 064110

    Article  ADS  Google Scholar 

  • Miyagi, L., S. Merkel, T. Yagi, N. Sata, Y. Ohishi, and H. R. Wenk, 2006, Quantitative Rietveld texture analysis of CaSiO3 perovskite deformed in a diamond anvil cell, J. Phys.: Condens. Matter 18, S995–S1005

    Article  ADS  Google Scholar 

  • Singh, A. K., C. Balasingh, H. K. Mao, R. J. Hemley, and J. Shu, 1998, Analysis of lattice strains measured under non-hydrostatic pressure, J. Appl. Phys. 83, 7567–7575

    Article  ADS  Google Scholar 

  • Speziale, S., I. Lonardelli, L. Miyagi, J. Pehl, C. E. Tommaseo, and H. R. Wenk, 2006, Deformation experiments in the diamond-anvil cell: texture in copper to 30 GPa, J. Phys.: Condens. Matter 18, S1007–S1020

    Article  ADS  Google Scholar 

  • Weidner, D. J., L. Li, M. Davis, and J. Chen, 2004, Effect of plasticity on elastic modulus measurements, Geophys. Res. Lett. 31, L06621

    Article  ADS  Google Scholar 

  • Weinberger, M. B., S. H. Tolbert, and A. Kavner, 2008, Osmium metal studied under high pressure and nonhydrostatic Stress, Phys. Rev. Lett. 100, 045506

    Article  ADS  Google Scholar 

  • Wenk, H. R., S. Matthies, J. Donovan, and D. Chateigner, 1998, BEARTEX : a Windows-based program system for quantitative texture analysis, J. Appl. Cryst. 31, 262–269

    Article  Google Scholar 

  • Wenk, H. R., S. Matthies, R. J. Hemley, H. K. Mao, and J. Shu, 2000, The plastic deformation of iron at pressures of the Earth’s inner core, Nature 405, 1044–1047

    Article  ADS  Google Scholar 

  • Wenk, H. R., I. Lonardelli, S. Merkel, L. Miyagi, J. Pehl, S. Speziale, and C. E. Tommaseo, 2006, Deformation textures produced in diamond anvil experiments, analyzed in radial diffraction geometry, J. Phys: Condens. Matter 18, S933–S947

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sebastien Merkel .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media B.V.

About this paper

Cite this paper

Merkel, S. (2010). Radial Diffraction in the Diamond Anvil Cell: Methods and Applications. In: Boldyreva, E., Dera, P. (eds) High-Pressure Crystallography. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9258-8_10

Download citation

Publish with us

Policies and ethics