analisi exafs

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Interaction X-rays - Matter
Pair production
Photoelectric absorption
Transmission
MATTER
X-rays
Scattering
Compton
Thomson
Decay processes
Auger electrons
Fluorescence
Primary competing processes and some radiative
and non-radiative decay processes
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X-ray attenuation atomic cross section
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Photoelectric absorption coefficient
m
m
m - mK
L3, L2, L1 edges
m - mK - mL1
(cm2/g)
m - mK - mL1- mL2
m - mK - mL1- mL2 - mL3
K edge
Z57 Lanthanum
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X-ray absorption spectroscopy
K 1s p L1 2s p L2 2p1/2
s, d L3 2p3/2 s, d
Z dependence Þ atomic selectivity
x
Photon flux
hn
hn
sample
X-ray energy range 1 - 30 KeV
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EXAFS analysis
Detectors
Sample
Double - crystal monochromator
Storage ring
I0
I
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XAFS measurements
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Always transmission, if possible Most accurate
method, best overall S/N counting statistics of
about 10-4 from beamlines with more than 108
photons/s)
Fluorescence for very diluted samples A specific
signal reduces the large background (but maximum
tolerable detector count-rate can result in very
long measuring times).
Total electron yield (TEY) for surface
sensitivity and surface XAFS (adsorbates on
surfaces) TEY for thick samples that cannot be
made uniform.
XEOL X-ray excited optical luminescence VIS/UV
detection from luminescent samples
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Measurement sensitivity in transmission mode
Sample Species (A B)
A solute, B Solvent
By changing the solute absorption coefficient
For
and
Statistically
so that
Assuming that the solute X-ray cross section is
almost equal to that of the solvent
R Dilution Ratio
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Evaluation of the absorption coefficient
Transition probability Gif
INITIAL STATE
INTERACTION
FINAL STATE
Core hole excitation or ionization
Ground state
GOLDEN RULE (weak interaction, time dependent
perturbation theory (1st order))
is the density of the final states compatible
with the energy conservation principle
atomic initial and final states
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Interaction Hamiltonian
j electrons polarization unit vector
radiation wavevector
An equivalent expression often used is
Electric dipole approximation
i.e. for the K edges for energies up to 25 - 30 K
eV and for the L edges
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The direct and inverse problem
Direct problem
Inverse problem

• Many bodies interactions
• The final state is influenced by the environment
  around the absorption atom

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One electron approximation
1 active electron
N-1 electrons
mTOT(w) if So2 1
So2 _at_ 0.7 0.9
Evaluation of the final state!
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X-ray Absorption Fine Structure (XAFS)
m
x
a-Ge
XAFS XANES EXAFS
EXAFS
XANES
XANES X-ray absorption Near Edge
Structure EXAFS Extended X-ray Absorption
Fine Structure
X-ray photon energy (keV)
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XANES pre edge structure
E
Fermi Golden rule
½f gt
½i gt
E
m
Arctangent curve
½f gt
Inflection point

E
½i gt
E
m
½i gt
E
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XANES
WL
Ar K
m x
1snp, ngt3
Arctangent curve
0.58 eV
2
4
6
8
Energy eV
1s2p
m x
Ne K
4p
5p
866
868
eV
870
Energy eV
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XANES Chemical information oxidation state
Oxidation Numbers (formal valences) I Cu2O II
CuO III KCuO2 Higher transitions energy
are expected for higher valence states.
(J.B. Boyce et al. Phys. Rev. B 1987)
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XANES projected density of state
E
2s p
0
X-rays
2p p, d
DOS
(G. Dalba et al., J.of Condensed Matter, 1983)
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Autointerference phenomenon of the outgoing
photoelectron with its parts that are
backscattered by the neighboring atoms
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Atoms
e-
A
Outgoing wave
Molecules
Positive interference
Negative interference
A
B
B
A
rf smoothly varying in the EXAFS region
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Scattering phases of the photoelectron
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XAFS formula
Approximations
1) Inelastic scattering effect
2) Thermal disorder
Standard EXAFS formula
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EXAFS formula
For several coordination shells
From ab-initio calculations or from reference
compounds
Interatomic distance
Coordination number
Debye Waller factor
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Multiple scattering
EXAFS single scattering processes
XANES multiple scattering processes
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RAB
Single scattering
C
Double scattering
Double scattering
Triple scattering
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Multiple scattering
Si
K
-edge in c-Si

Experiment
8
7
6
5
4
Absorption

3
2
1
0
50
100
150
Energy E-E
(eV)
F
Comparison between the experimental Si K-edge
XAFS for c-Si and calculations carried out with
the FEFF code. The total multiple scattering in
the first 8 shells around the absorption atom
have been considered. m0 is the atomic
absorption coefficient.