x-rays the electric field e(r,t) is given as a cosine function
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X-rays X-rays
)cos(),( tkrtrE
The electric field E(r,t) is given as a cosine function.
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X-rays 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).
),(),( trAtrE t
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Interaction of x-rays with matter 1Interaction of x-rays with matter 1
The photon moves towards the atom
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Interaction of x-rays with matter 1Interaction of x-rays with matter 1
The photon meets an electron and is annihilated
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Interaction of x-rays with matter 1Interaction 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 1Interaction 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 1Interaction of x-rays with matter 1
The probability of photon annihilation determines the intensity of the transmitted photon beam
I0I
Ek
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Interaction of x-rays with matter 2Interaction of x-rays with matter 2
The photon moves towards the atom
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Interaction of x-rays with matter 2Interaction of x-rays with matter 2
The photon meets an electron and is scattered
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Interaction of x-rays with matter 2Interaction 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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I(,k,q)
I’(’,k’,q’)
I”(Ek,k”,)
Energy Spectroscopy
Direction Structure
Polarization Magnetism
Interaction of x-rays with matterInteraction of x-rays with matter
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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.
Interaction of x-rays with matterInteraction of x-rays with matter
ApHT mce
INT )1(1
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Interaction of x-rays with matter 1Interaction of x-rays with matter 1
The photon meets the electron and is annihilated
A
p=q•r
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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.
Interaction of x-rays with matterInteraction of x-rays with matter
ApHT mce
INT )1(1
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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)
Interaction of x-rays with matterInteraction of x-rays with matter
2
2)2( 2
2AH
mce
INT
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Interaction of x-rays with matterInteraction of x-rays with matter
• XAFS studies photoelectric absorption
• Elastic scattering (Thompson)
• Inelastic scattering
• (Compton)100 1k 10k 100k 1M
1
10
100
Photonuclear
Electron-
positron
Photoelectric
Thompson
Compton
Inte
nsi
ty (
log
)
Energy (eV)
Mn
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if EEiffXAS TI
2
1~
Excitation of core electrons to empty states.
Spectrum given by the Fermi Golden RuleFermi Golden Rule
X-ray absorption and X-ray photoemissionX-ray absorption and X-ray photoemission
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I(FIXED)
X-ray absorption and X-ray photoemissionX-ray absorption and X-ray photoemission
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X-ray absorption and X-ray photoemissionX-ray absorption and X-ray photoemission
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X-ray emission: core hole decayX-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 matterInteraction of x-rays with matter
ApH mce
INT )1(
2
2)2( 2
2AH
mce
INT
Photoelectric effect:(annihilation of photon)XAS, XPSXES, XRF, EDX
X-ray scattering:(photon-in photon-out)XRD, SAXS
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Interaction of x-rays with matterInteraction of x-rays with matter
X-ray scattering:- with Hint(2)
- with Hint(1) via a (virtual) intermediate state
= Resonant X-ray scattering
)1(2/1
)1()2(2 INTiHEINTINT HHHTi
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Interaction of x-rays with matter 3Interaction of x-rays with matter 3
The photon moves towards the atom
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Interaction of x-rays with matter 3Interaction of x-rays with matter 3
The photon meets an electron and is annihilated
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Interaction of x-rays with matter 3Interaction 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 3Interaction 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 3Interaction of x-rays with matter 3
The photon leaves the atom
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Resonant X-ray scatteringResonant 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