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X-rays

X-rays. The electric field E(r,t) is given as a cosine function. X-rays. In formal derivations the vector potential A is used. The electric field E(r,t) is directly related to the vector potential A(r,t). Interaction of x-rays with matter 1. The photon moves towards the atom.

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X-rays

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  1. X-rays The electric field E(r,t) is given as a cosine function.

  2. X-rays In formal derivations the vector potential A is used. The electric field E(r,t) is directly related to the vector potential A(r,t).

  3. Interaction of x-rays with matter 1 The photon moves towards the atom

  4. Interaction of x-rays with matter 1 The photon meets an electron and is annihilated

  5. Interaction of x-rays with matter 1 The electron gains the energy of the photon and is turned into a blue electron.

  6. Interaction of x-rays with matter 1 The blue electron (feeling lonely) leaves the atomand scatters of neighbors (cf. EXAFS) or escapes from the sample (cf. XPS)

  7. Interaction of x-rays with matter 1 The probability of photon annihilation determines the intensity of the transmitted photon beam I I0 Ek

  8. Interaction of x-rays with matter 2 The photon moves towards the atom

  9. Interaction of x-rays with matter 2 The photon meets an electron and is scattered

  10. Interaction of x-rays with matter 2 The photon leaves the atom under a different angle.(Interference between scattering events yields XRD)

  11. Interaction of x-rays with matter Energy  Spectroscopy Direction  Structure Polarization  Magnetism I’(’,k’,q’) I(,k,q) I”(Ek,k”,)

  12. Interaction of x-rays with matter HINT(1) describes the interaction of the vector field A on the momentum operator p of an electron, or in other words the electric field E acting on the electron moments. The momentum operator p is given as the electron charge q times the displacement operator r.

  13. Interaction of x-rays with matter 1 The photon meets the electron and is annihilated p=q•r A

  14. Interaction of x-rays with matter HINT(1) describes the interaction of the vector field A on the momentum operator p of an electron, or in other words the electric field E acting on the electron moments. The momentum operator p is given as the electron charge q times the displacement operator r.

  15. Interaction of x-rays with matter HINT(2) describes the second order interaction of the vector field A. This gives rise to the elastic scattering of the x-rays by the electrons. This is the basis for x-ray diffraction (XRD) and small angle x-ray scattering (SAXS)

  16. Interaction of x-rays with matter Mn • XAFS studies photoelectric absorption • Elastic scattering (Thompson) • Inelastic scattering • (Compton)

  17. X-ray absorption and X-ray photoemission • Excitation of core electrons to empty states. • Spectrum given by the Fermi Golden Rule

  18. X-ray absorption and X-ray photoemission I(FIXED)

  19. X-ray absorption and X-ray photoemission

  20. X-ray emission: core hole decay Basis for X-ray Fluorescence (XRF) and Energy Dispersive X-ray analysis (EDX)

  21. Interaction of x-rays with matter Photoelectric effect: (annihilation of photon) XAS, XPS XES, XRF, EDX X-ray scattering: (photon-in photon-out) XRD, SAXS

  22. Interaction of x-rays with matter • X-ray scattering: • with Hint(2) • with Hint(1) via a (virtual) intermediate state • = Resonant X-ray scattering

  23. Interaction of x-rays with matter 3 The photon moves towards the atom

  24. Interaction of x-rays with matter 3 The photon meets an electron and is annihilated

  25. Interaction of x-rays with matter 3 The electron gains the energy of the photon and is turned into a virtual blue electron.

  26. Interaction of x-rays with matter 3 The virtual blue electron loses a photon with exactly the same energy as gained

  27. Interaction of x-rays with matter 3 The photon leaves the atom

  28. Resonant X-ray scattering • Combination of XAS and XES [only Hint(1)] • - RXES • Resonant Inelastic X-ray Scattering (RIXS) • (also called Resonant X-ray Raman Spectroscopy) • Combination of Hint(1) and Hint(2) • Resonant XRD (also called: anomalous) • Multi-wavelength anomalous Diffraction (MAD) • Resonant SAXS (ASAXS) • TEDDI

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