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X-rays The electric field E(r,t) is given as a cosine function. E (r , t ) cos( kr t ) 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). E (r , t ) t A(r , t ) Interaction of x-rays with matter 1 The photon moves towards the atom Interaction of x-rays with matter 1 The photon meets an electron and is annihilated Interaction of x-rays with matter 1 The electron gains the energy of the photon and is turned into a blue electron. Interaction of x-rays with matter 1 The blue electron (feeling lonely) leaves the atom and scatters of neighbors (cf. EXAFS) or escapes from the sample (cf. XPS) Interaction of x-rays with matter 1 The probability of photon annihilation determines the intensity of the transmitted photon beam I I0 Ek Interaction of x-rays with matter 2 The photon moves towards the atom Interaction of x-rays with matter 2 The photon meets an electron and is scattered Interaction of x-rays with matter 2 The photon leaves the atom under a different angle. (Interference between scattering events yields XRD) Interaction of x-rays with matter Energy Spectroscopy Direction Structure Polarization Magnetism I’(’,k’,q’) I(,k,q) I”(Ek,k”,) 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. T1 H INT (1) e mc p A Interaction of x-rays with matter 1 The photon meets the electron and is annihilated p=q•r A 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. T1 H INT (1) e mc p A 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) H INT ( 2) 2 e 2 2 mc A 2 Interaction of x-rays with matter • Elastic scattering (Thompson) • Inelastic scattering • (Compton) Intensity (log) • XAFS studies photoelectric absorption 100 Mn Photoelectric 10 Thompson Compton 1 100 1k 10k Energy (eV) 100k X-ray absorption and X-ray photoemission Excitation of core electrons to empty states. Spectrum given by the Fermi Golden Rule I XAS ~ f f T1 i 2 E f Ei X-ray absorption and X-ray photoemission I(FIXED) X-ray absorption and X-ray photoemission X-ray emission: core hole decay Basis for X-ray Fluorescence (XRF) and Energy Dispersive X-ray analysis (EDX) Interaction of x-rays with matter H INT (1) e mc H INT ( 2) p A 2 e 2 mc 2 A 2 Photoelectric effect: (annihilation of photon) XAS, XPS XES, XRF, EDX X-ray scattering: (photon-in photon-out) XRD, SAXS Interaction of x-rays with matter T2 H INT ( 2) H 1 INT (1) Ei H i / 2 H INT (1) X-ray scattering: - with Hint(2) - with Hint(1) via a (virtual) intermediate state = Resonant X-ray scattering Interaction of x-rays with matter 3 The photon moves towards the atom Interaction of x-rays with matter 3 The photon meets an electron and is annihilated Interaction of x-rays with matter 3 The electron gains the energy of the photon and is turned into a virtual blue electron. Interaction of x-rays with matter 3 The virtual blue electron loses a photon with exactly the same energy as gained Interaction of x-rays with matter 3 The photon leaves the atom 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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