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Fourier transform (see Cowley Sect. 2.2)

Diving into the principles of X-ray scattering by single electrons and atoms, covering Fourier transforms, atomic scattering factors, dispersion, and correct scattering factors. This includes investigating scattering by atom assemblies and periodic arrays of slits.

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Fourier transform (see Cowley Sect. 2.2)

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  1. Fourier transform (see Cowley Sect. 2.2)

  2. Fourier transform (see Cowley Sect. 2.2)

  3. Fourier transform (see Cowley Sect. 2.2)

  4. Fourier transform (see Cowley Sect. 2.2)

  5. Fourier transform

  6. Fourier transform

  7. Fourier transform

  8. Fourier transform

  9. Scattering of x-rays by single electron (Thomson) (see Cowley sect. 4.1)

  10. Scattering of x-rays by single electron (Thomson) (see Cowley sect. 4.1)

  11. Scattering of x-rays by single electron (Thomson)

  12. Scattering of x-rays by single electron (Thomson)

  13. Scattering of x-rays by single atom For n electrons in an atom, time-averaged electron density is

  14. Scattering of x-rays by single atom For n electrons in an atom, time-averaged electron density is Can define an atomic scattering factor

  15. Scattering of x-rays by single atom For n electrons in an atom, time-averaged electron density is Can define an atomic scattering factor For spherical atoms

  16. Scattering of x-rays by single atom Need to find (r) …. A QM problem But soln for f() looks like this (in electron scattering units)

  17. Dispersion - anomalous scattering Have assumed radiation frequency >> resonant frequency of electrons in atom … frequently not true

  18. Dispersion - anomalous scattering Have assumed radiation frequency >> resonant frequency of electrons in atom … frequently not true Need to correct scattering factors f = fo + f' + i f"

  19. Dispersion - anomalous scattering Need to correct scattering factors f = fo + f' + i f" 5 f" 1 2 K f'

  20. Atom assemblies (see Cowley sect. 5.1)

  21. Atom assemblies (see Cowley sect. 5.1) For this electron density, there is a Fourier transform F(u) is a fcn in reciprocal space

  22. Atom assemblies (see Cowley sect. 5.1)

  23. Atom assemblies

  24. Atom assemblies For single slit, width a & g(x) = 1 If scatterer is a box a, b, c

  25. Atom assemblies For single slit, width a & g(x) = 1 If scatterer is a box a, b, c For periodic array of zero-wiidth slits

  26. Atom assemblies This requires ua = h, an integer. Then Finally

  27. Atom assemblies This requires ua = h, an integer. Then Finally

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