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Quadrupole transitions revealed by Borrmann spectroscopy


The Borrmann effect1,2—a dramatic increase in transparency to X-ray beams—is observed when X-rays satisfying Bragg’s law diffract through a perfect crystal. The minimization of absorption seen in the Borrmann effect has been explained by noting that the electric field of the X-ray beam approaches zero amplitude at the crystal planes, thus avoiding the atoms. Here we show experimentally that under conditions of absorption suppression, the weaker electric quadrupole absorption transitions are effectively enhanced to such a degree that they can dominate the absorption spectrum. This effect can be exploited as an atomic spectroscopy technique; we show that quadrupole transitions give rise to additional structure at the L1, L2 and L3 absorption edges of gadolinium in gadolinium gallium garnet, which mark the onset of excitations from 2s, 2p1/2 and 2p3/2 atomic core levels, respectively. Although the Borrmann effect served to underpin the development of the theory of X-ray diffraction3,4,5,6, this is potentially the most important experimental application of the phenomenon since its first observation seven decades ago. Identifying quadrupole features in X-ray absorption spectroscopy is central to the interpretation of ‘pre-edge’ spectra, which are often taken to be indicators of local symmetry, valence and atomic environment7. Quadrupolar absorption isolates states of different symmetries to that of the dominant dipole spectrum, and typically reveals orbitals that dominate the electronic ground-state properties of lanthanides and 3d transition metals, including magnetism. Results from our Borrmann spectroscopy technique feed into contemporary discussions regarding resonant X-ray diffraction8 and the nature of pre-edge lines identified by inelastic X-ray scattering7. Furthermore, because the Borrmann effect has been observed in photonic materials, it seems likely that the quadrupole enhancement reported here will play an important role in modern optics.

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Figure 1: The Borrmann effect in a gadolinium gallium garnet crystal.
Figure 2: Comparison of gadolinium absorption spectra in the Borrmann case (red) and the conventional case (black).


  1. Borrmann, G. The absorbance diagram of quartz. Phys. Z. 42, 157–162 (1941)

    CAS  Google Scholar 

  2. Borrmann, G. Der kleinste Absorptionskoeffizient interferierender Rontgenstrahlung. Z. Kristallogr. Kristallgeom. Kristallphys. Kristallchem. 106, 109–121 (1954)

    Article  ADS  CAS  Google Scholar 

  3. Darwin, C. G. The theory of X-ray reflexion. Phil. Mag. 27, 315–333 (1914)

    Article  CAS  Google Scholar 

  4. Darwin, C. G. The theory of X-ray reflexion. Part 2. Phil. Mag. 27, 675–690 (1914)

    Article  CAS  Google Scholar 

  5. Ewald, P. P. Zur Begrundung der Kristalloptik. Teil II. Ann. Phys. 49, 117–143 (1916)

    Article  Google Scholar 

  6. Ewald, P. P. Crystal optics for visible light and X rays. Rev. Mod. Phys. 37, 46–56 (1965)

    Article  ADS  Google Scholar 

  7. De Groot, F. High-resolution X-ray emission and X-ray absorption spectroscopy. Chem. Rev. 101, 1779–1808 (2001)

    Article  CAS  Google Scholar 

  8. Dmitrienko, V. E., Ishida, K., Kirfel, A. & Ovchinnikova, E. N. Polarization anisotropy of X-ray atomic factors and ‘forbidden’ resonant reflections. Acta Crystallogr. A61, 481–493 (2005)

    Article  ADS  CAS  Google Scholar 

  9. Von Laue, M. Röntgenstrahl-Interferenzen (Academische, Frankfurt, 1960)

    MATH  Google Scholar 

  10. Batterman, B. W. & Cole, H. Dynamical diffraction of X-rays by perfect crystals. Rev. Mod. Phys. 36, 681–717 (1964)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  11. Borie, B. The theory of the Borrmann effect in terms of difference equations. Acta Crystallogr. 12, 470–472 (1966)

    Article  Google Scholar 

  12. Feynman, R. P., Leighton, R. B. & Sands, M. The Feynman Lectures on Physics Vol. 2., Ch. 24-10–12 (Addison-Wesley, Reading, Massachusetts, 1964)

    Book  Google Scholar 

  13. Brouder, C. Angular dependence of X-ray absorption spectra. J. Phys. Condens. Matter 2, 701–738 (1990)

    Article  ADS  CAS  Google Scholar 

  14. Lovesey, S. W. & Collins, S. P. X-ray Scattering and Absorption by Magnetic Materials (Clarendon, Oxford, UK, 1996)

    Google Scholar 

  15. Vatanyants, I. A. & Zegenhagen, J. Photoelectric scattering from an X-ray interference field. Solid State Commun. 113, 299–320 (2000)

    Article  ADS  Google Scholar 

  16. Schülke, W. & Mourikis, S. Nondiagonal momentum density of Si by coherent inelastic X-ray scattering. Acta Crystallogr. A 42, 86–98 (1986)

    Article  Google Scholar 

  17. Batson, P. E. Symmetry-selected electron-energy-loss scattering in diamond. Phys. Rev. Lett. 70, 1822–1825 (1993)

    Article  ADS  CAS  Google Scholar 

  18. Gordon, R. A. et al. High multipole transitions in NIXS: Valence and hybridization in 4f systems. Europhys. Lett. 81, 26004 (2008)

    Article  ADS  Google Scholar 

  19. Wagenfeld, H. Normal and anomolous photoelectric absorption of X rays in crystals. Phys. Rev. 144, 216–224 (1966)

    Article  ADS  CAS  Google Scholar 

  20. Loeffen, P. W. et al. Deconvolution of lifetime broadening at rare-earth LIII edges compared to resonant inelastic X-ray scattering measurements. Phys. Rev. B 54, 14877–14880 (1996)

    Article  ADS  CAS  Google Scholar 

  21. Sawada, H. Electron density study of garnets: Z3Ga5O12; Z = Nd, Sm, GD, Tb. J. Solid State Chem. 132, 300–307 (1997)

    Article  ADS  CAS  Google Scholar 

  22. Collins, S. P. et al. Station 16.3: a high-resolution single-crystal diffraction facility at the SRS, Daresbury. J. Synchotron Rad. 5, 1263–1269 (1998)

    Article  CAS  Google Scholar 

  23. Krisch, M. H. et al. Evidence for a quadrupolar excitation channel at the LIII edge of gadolinium by resonant inelastic X-ray scattering. Phys. Rev. Lett. 74, 4931–4934 (1995)

    Article  ADS  CAS  Google Scholar 

  24. Materlik, G., Müller, J. E. & Wilkins, J. W. L-edge absorption spectra of the rare earths: assessment of the single particle picture. Phys. Rev. Lett. 50, 267–270 (1983)

    Article  ADS  CAS  Google Scholar 

  25. Chen, M. H., Crasemann, B. & Kostroun, V. O. Theoretical L2- and L3-subshell fluorescence yields and L2-L3X Coster-Kronig transition probabilities. Phys. Rev. A 4, 1–7 (1971)

    Article  ADS  Google Scholar 

  26. Thole, B. T. et al. 3d x-ray-absorption lines and the 3d94fn+1 multiplets of lanthanides. Phys. Rev. B 32, 5107–5118 (1985)

    Article  ADS  CAS  Google Scholar 

  27. Fabrizio, M., Altarelli, M. & Benfatto, M. X-Ray resonant scattering as a direct probe of orbital ordering in transition-metal oxides. Phys. Rev. Lett. 80, 3400–3403 (1998)

    Article  ADS  CAS  Google Scholar 

  28. Brown, S. D. et al. Dipolar excitations at the LIII X-ray absorption edges of the heavy rare-earth metals. Phys. Rev. Lett. 99, 247401 (2007)

    Article  ADS  CAS  Google Scholar 

  29. Zhang, Z. & Satpathy, S. Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations. Phys. Rev. Lett. 65, 2650–2653 (1990)

    Article  ADS  CAS  Google Scholar 

  30. Ward, A. J., Pendry, J. B. & Stewart, W. J. Photonic dispersion surfaces. J. Phys. Condens. Matter 7, 2217–2224 (1995)

    Article  ADS  CAS  Google Scholar 

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This paper is dedicated to R. F. Pettifer, who died on 5 March 2008, and whose numerous contributions to the field of synchrotron radiation included the original proposal of Borrmann spectroscopy. The authors are grateful to C. Nave and V. E. Dmitrienko for their comments on the manuscript.

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Correspondence to Stephen P. Collins.

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Pettifer, R., Collins, S. & Laundy, D. Quadrupole transitions revealed by Borrmann spectroscopy. Nature 454, 196–199 (2008).

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