X-rays

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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).
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Interaction of x-rays with matter 1
The photon moves towards the atom
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Interaction of x-rays with matter 1
The photon meets an electron and is annihilated
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Interaction of x-rays with matter 1
The electron gains the energy of the photon and
is turned into a blue electron.
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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)
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Interaction of x-rays with matter 1
The probability of photon annihilation determines
the intensity of the transmitted photon beam
I
I0
Ek
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Interaction of x-rays with matter 2
The photon moves towards the atom
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Interaction of x-rays with matter 2
The photon meets an electron and is scattered
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Interaction of x-rays with matter 2
The photon leaves the atom under a different
angle.(Interference between scattering events
yields XRD)
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Interaction of x-rays with matter
Energy ? Spectroscopy Direction ?
Structure Polarization ? Magnetism
I(?,k,q)
I(?,k,q)
I(Ek,k,?)
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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.
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Interaction of x-rays with matter 1
The photon meets the electron and is annihilated
pqr
A
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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.
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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)
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Interaction of x-rays with matter

• XAFS studies photoelectric absorption
• Elastic scattering (Thompson)
• Inelastic scattering
• (Compton)

Mn
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X-ray absorption and X-ray photoemission

• Excitation of core electrons to empty states.
• Spectrum given by the Fermi Golden Rule

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X-ray absorption and X-ray photoemission
I(?FIXED)
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X-ray absorption and X-ray photoemission
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X-ray emission core hole decay
Basis for X-ray Fluorescence (XRF) and Energy
Dispersive X-ray analysis (EDX)
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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
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Interaction of x-rays with matter

• X-ray scattering
• with Hint(2)
• with Hint(1) via a (virtual) intermediate state
• Resonant X-ray scattering

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Interaction of x-rays with matter 3
The photon moves towards the atom
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Interaction of x-rays with matter 3
The photon meets an electron and is annihilated
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Interaction of x-rays with matter 3
The electron gains the energy of the photon and
is turned into a virtual blue electron.
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Interaction of x-rays with matter 3
The virtual blue electron loses a photon with
exactly the same energy as gained
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Interaction of x-rays with matter 3
The photon leaves the atom
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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