Advertisement

Extinction correction and synchrotron radiation

  • P. Suortti
Crystallography
  • 27 Downloads

Abstract

The primary extinction factor yp is defined as the ratio of the integrated reflection from a coherently diffracting domain to the integrated kinematical reflection from the same domain. When yp is larger than 0.5 it may be approximated by yp = exp{−(αδ)2}, where α is about 0.5 andδ the average size of the coherent domain when measured in units of the extinction length A,δ = D/λ.

Transfer equations are applied to symmetrical Laue diffraction, and the reflectivity per unit length, Σ(ε) is solved from the measured reflecting ratio as a function of the rocking angleε =θ− θB.

Measurements with conventional x-ray sources are made on single crystal slabs of Be and Si using AgKΒ, MoKα1 and CuKα radiation. The primary extinction factor yp(ε) is solved from a point-by-point comparison of two measurements where the extinction length λ is changed by varying the polarization and/or wavelength of the x-ray beam. The results show that primary and secondary extinction are strongly correlated, and that the customary assumption of independent size and orientation distributions of crystal mosaics is unjustified. The structure factors for Be and Si show close agreement with other recent measurements and calculations.

The limitations of the method are discussed in length, particularly the effects of beam divergences and incoherence of the rays in the crystal. It is concluded that under typical experimental conditions the requirements of the theory are met. Practical limitations arising from the use of characteristic wavelengths and unpolarized radiation prohibit the use of the full potential of the method.

The properties of a synchrotron radiation source are compared with a conventional x-ray source, and it is demonstrated that the experimental limitations can be removed by the use of synchrotron radiation. A diffraction experiment with synchrotron radiation is outlined, as well as generalization of the method to small spherical crystals.

Keywords

Extinction synchrotron radiation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aldred P J E and Hart M 1973Proc. R. Soc. London A332 223Google Scholar
  2. Becker P J and Coppens P 1974aActa Crystallogr. A30 129Google Scholar
  3. Becker P J and Coppens P 1974bActa Crystallogr. A30 148Google Scholar
  4. Becker P J and Coppens P 1975Acta Crystallogr. A31 417Google Scholar
  5. Bragg W L, James R W and Bosanquet C H 1921Philos. Mag. 42 1Google Scholar
  6. Cooper M J and Rouse K D 1970Acta Crystallogr. A26 214Google Scholar
  7. Coppens P and Hamilton W CActa Crystallogr.A26 71Google Scholar
  8. Darwin C G 1922Philos. Mag. 43 800Google Scholar
  9. Dovesi R, Pisani C, Ricca F and Roetti C 1982Phys. Rev. B25 3731Google Scholar
  10. Hamilton W C 1957Acta Crystallogr. 10 629CrossRefGoogle Scholar
  11. Hansen N K, Schneider J R and Larsen F K 1983Phys. Rev. B, to be publishedGoogle Scholar
  12. Hastings J B, Suortti P, Thomlinson W, Kvick å and Koetzle T F 1983Nucl. Instrum. Methods 208 55CrossRefGoogle Scholar
  13. James R W 1962The optical principles of the diffraction of x-rays (London: Bell)Google Scholar
  14. Kato N 1980aActa Crystallogr. A36 171Google Scholar
  15. Kato N 1980bActa Crystallogr. A36 763Google Scholar
  16. Kawamura T and Kato N 1983Acta Crystallogr. A39 305Google Scholar
  17. Larsen F K and Hansen N K 1983 Univ. Aarhus unpublished reportGoogle Scholar
  18. Materlik G and Suortti P 1983J. Appl. Crystallogr. to be publishedGoogle Scholar
  19. Mathieson A McL 1979Acta Crystallogr. A35 50Google Scholar
  20. Olekhnovich N M, Markovich V L and Olekhnovich A I 1980Acta Crystallogr. A36 989Google Scholar
  21. Olekhnovich N M and Olekhnovich A I 1978Acta Crystallogr. A34 321Google Scholar
  22. Olekhnovich N M and Olekhnovich A I 1980Acta Crystallogr. A36 22Google Scholar
  23. Suortti P 1982aActa Crystallogr. A38 642Google Scholar
  24. Suortti P 1982bActa Crystallogr. A38 648Google Scholar
  25. Takagi S 1962Acta Crystallogr. 15 1311CrossRefGoogle Scholar
  26. Takagi S 1969J. Phys. Soc. Jpn 26 1239CrossRefGoogle Scholar
  27. Taupin D 1964Bull. Soc. Fr. Minéral. Cristallogr.87 469Google Scholar
  28. Werner S A 1974J. Appl. Phys. 45 3246CrossRefGoogle Scholar
  29. Zachariasen W H 1967Acta Crystallogr. 23 558CrossRefGoogle Scholar

Copyright information

© Printed in India 1983

Authors and Affiliations

  • P. Suortti
    • 1
  1. 1.Department of PhysicsUniversity of HelsinkiHelsinki 17Finland

Personalised recommendations