1. Interaction X-rays - Matter
Pair production
> 1M eV
Photoelectric absorption
Transmission
MATTER
X-rays
Scattering
Compton
Thomson
Decay processes
Fluorescence
Auger electrons
Primary competing processes and some radiative and non-radiative decay processes

2. X-ray attenuation: atomic cross section:hn
sample
X-ray attenuation: atomic cross section:
Thomson
Observed data
Electron positron pairs
Compton
Photoelectric absorption
Photonuclear
absorption
Cross section (barns/atom) 1
103
106
10 eV
1 KeV
1 GeV
1 MeV
Cu Z=29
Energy
Li Z=3
Ge Z=32
Gd Z=64
Energy (KeV)
100
102
104
s (Barns/atom)

3. Photoelectric absorption coefficientm m
L3, L2, L1 edges
m - mK
m - mK - mL1
(cm2/g)
m - mK - mL1- mL2
m - mK - mL1- mL2 - mL3
K edge
Z=57 Lanthanum

4. X-ray absorption spectroscopy10 2 4 6 1
100
Cross section (cm2g)
Photon energy (keV)
K edge
L3, L2, L1 edges Ge
Compton
Thomson
K s ® p
L s ® p
L p1/2 ® s, d
L p3/2 ® s, d
Z dependence Þ
atomic selectivity x
Photon flux hn
Fig. 1 – Photoelectric absorption coefficient of Germanium (continuous red line) as a function of photon energy; clearly visible are the L and K absorption edges. Also shown for comparison are the cross sections for scattering, both elastic (Rayleigh, dashed green line) and inelastic (Compton, dotted brown line).
Fig 2 – X-ray absorption coefficient at the K edge of amorphous germanium. EXAFS is clearly visible as a sinusoidal oscillation above the edge energy. hn
sample
X-ray energy range KeV

5. EXAFS analysis
Detectors
Storage ring
Double - crystal
monochromator
Sample I0 I
photon fluxes; x sample thickness, C depends on the detectors efficiency.
8800
9200
9600
10000
-2.0
-1.0
0.0
1.0
Ln ( I / I0 )
E (eV)

6. XAFS measurements  h e- Fluorescence X-rays TEY SAMPLE
Incident X-rays
Transmitted X-rays
Visible light
XEOL h e-
X-ray energy 
XAFS spectrum

7. Which method for which application?
The most important criterion:
The best signal to noise ratio for the
element of interest e-
Ie-
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

8. Measurement sensitivity in transmission mode
Sample = Species (A + B)
A = solute, B = Solvent x
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

9. Evaluation of the absorption coefficient
n = atomic density
A0 = vector potential amplitude
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

10. Interaction Hamiltonian
j = electrons; = polarization unit vector; = radiation wavevector
An equivalent expression often used is:
Electric dipole approximation
This approximation is valid if:
i.e. for the K edges for energies up to K eV and for the L edges
Selection rules:

11. The direct and inverse problem
Direct problem:
Inverse problem
In practice one is interested to the inverse problem.
Given: m, experimentally determined, one wants to know from XAFS, the
final state
But also in this case one needs to know the initial and final states or, at least , to express in parametric form the interesting structural properties.
is known because it is the fundamental state of the atom.
The calculation of
is complicated because the absorption process because:
Many bodies interactions
The final state is influenced by the environment around the absorption atom

12. One electron approximation
Elastic transitions:
1 core electron excited
N-1 passive electrons (relaxed)
Anelastic transitions:
1 core electron excited
Other electrons excited; shake up and shake off
High photoelectron energy ® sudden approximation
1 active electron
N-1 electrons
= mTOT(w) if So2 = 1
= 0.7 ¸ 0.9
Evaluation of the final state!

13. X-ray Absorption Fine Structure (XAFS)10 2 4 6 1
100
Cross section (cm2g)
Photon energy (keV)
K edge
L3, L2, L1 edges Ge
Compton
Thomson m x
0.0
0.4
0.8
1.2 11
11.5 12
a-Ge
XAFS =
XANES + EXAFS
XANES
EXAFS
XANES = X-ray absorption
Near Edge Structure
EXAFS = Extended X-ray Absorption Fine Structure
X-ray photon energy (keV)

14. XANES: pre edge structure
Fermi Golden rule E m
½f >
½i > E m
Arctangent curve
½f > }
Inflection
point
½i > E E m
½i > E

15. m Energy Experimental K- edge of metallic Iridium and its simulation
Ir metal (Experimental signal)
Experimental K- edge of metallic Iridium and its simulation
obtained by the superposition of an arctang function and a Lorentian 2
Energy
1160
0.5 1
1.5 m
Theoretical edge
Lorentian
Arctangent

16. Single particle binding energy (eV)
XANES WL
m x
Ar K
1s®np, n>3
Single particle binding energy (eV) 1s 2s 2p s p d 50
100
EXAFS
XANES
EDGE
X-ray edges
Visible UV
Arctangent
curve
0.58 eV 2 4 6 8
Energy eV
m x
1s®2p
Ne K
The solid curve represents the K absorption spectrum (uncorrected)
of gaseous Ar. The resonance lines and the main absorption edge (arctangent
curve) at the series limit are shown by dashed curves. 4p 5p
866
868
870 eV
Energy eV

17. K-shell photoabsorption of N2 molecule
C.T. Chen and F. Sette, Phys. Rev. A 40 (1989)
K-shell photoabsorption of gas-phase N2
Absorption Intensity (arb.units)
N 1s® 1pg*
N 1s ®
Rydberg series
Double
excitations
Shape
resonance
x10
400
405
410
415
420
Photon energy (eV)
(a)
400
401
402
N 1s®1pg*
(a) 8 vibrational levels observed in the absorpttion spectrum: N 1s®1pg*
414
415
Double excitations
(c)
(c) Double excitations in the N2 spectrum Rydberg associated to the N 1s®1pg* transition.
Absorption Intensity (arb. Units)
406
407
408
409
410
Photon Energy (eV)
(b)
N 1s®Rydberg series 1 3 2 4 5 6 7 8 9 10 11 12 13
(b) N 1s®Rydberg series

18. m XANES Chemical information: oxidation state CuO Cu2O KCuO2 Cu E (eV)
8970
8990
0.5 1
Y-Ba-Cu-O
Oxidation Numbers (formal valences)
I Cu2O
II CuO
III KCuO2
Higher transitions energy are expected for higher valence states.
X-ray absorption near-edge structure in the vicinity of the Cu K edge for Cu2O, CuO and KCuO2 and for Y-Ba-Cu-O (dotted line). The energy scale is referenced to the Cu K edge energy, E0=8980 eV. The near-edge spectra are the same for each of the threee samples studied and are independent of temperature from 4.2 to 688 K.
(J.B. Boyce et al. Phys. Rev. B 1987)

19. SbSI XANES: projected density of state X-rays Sb L1 I L1
Absorbance (a.u.)
E - E0 (eV)
Total DOS (a.u.) -5 5 15 10 20
Sb L3
I L3 E
2s ® p
X-rays
2p ® p, d
Fine structure al the L1 edges of antimony and Iodine in SbSI and total DOS of the conduction band calculated by Nakao and Balkanski (blu line).
Fine structures at the L3 edges od Antimony and Iodine in SbSI and total DOS of the conduction band calculated by Nakao and Balkanski (blu line). The vertical bars show the positions of the first two maxima of the first derivative of the experimental spectra.
DOS
(G. Dalba et al., J.of Condensed Matter, 1983)

20. phenomenological interpretation
EXAFS:
phenomenological interpretation e- A B A B
Autointerference phenomenon of
the outgoing photoelectron with its parts that are
backscattered by the neighboring atoms

21. phenomenological interpretation
EXAFS:
phenomenological interpretation
Atoms Kr mx
14.2
15.0
14.6
E (KeV) e- A
Outgoing wave:
Molecules
Positive
interference
Negative
interference 50
-50 1 2 3 4
Br2
XANES
Photon energy (eV)
13400
13800 mx
14200
14600 kr A B A B
Schematic explanation of the origin of EXAFS oscillations. A x-ray photon is absorbed by atom A (left). A photoelectron is emitted by atom A as an outgoing spherical wave (centre). The photoelectron can be back-scattered by atom B, generating a new incoming spherical wave (right), which interferes with the original outgoing wave.
rf smoothly varying in the EXAFS region

22. Scattering phases of the photoelectronB B A B A B A x B A R

23. Standard EXAFS formula
Approximations
1) Inelastic scattering effect:
Electron mean free path
2) Thermal disorder:
Standard EXAFS formula

24. EXAFS formula For several coordination shells: 1 st 2 nd 3 rd
1 st
2 nd
3 rd
Coordination shells R
From ab-initio calculations or from reference compounds
Coordination
number
Debye Waller
factor
Interatomic distance

25. Multiple scattering EXAFS: single scattering processes R
XANES: multiple scattering processes

26. RAB Single scattering Double scattering Double scattering
Triple scattering

27. Multiple scattering 8 7 6 5 Absorption 4 3 2 1 50 100 150 Energy E-ESi K
-edge in c-Si
Experiment 8 7 6 5
Absorption 4 3 2 1 m 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.