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EXAFS
Santiago J. A. FigueroaResearcherBeamline coordinator [email protected]
Extended X-Ray Absorption Fine Structure
EXAFS
Campinas, 23 de Agosto de 2016
5th School on X-Ray Spectroscopy Methods
1.Interaction of X-rays with matter
2.Basics aspects about XAFS
3.Understanding the EXAFS equation
Overview
hTransmissionMATTER
h
Scattering
Compton
h h '
Thomson
Photoelectric absorption
Pair productionh > 1M eV
X-rays
Interaction of X-rays with matter
h
Decay processes
Fluorescence Auger electrons
h f
Primary competing processes and some radiative and non-radiative decay processes
Thomson Observed data
Pair production
Compton
Absorption
Photonuclear absorption
Cro
ss s
ecti
on
(b
arn
s/at
om
)
1
103
106
10 eV 1 KeV 1 GeV1 MeV
Cu Z=29
Energy
X-ray attenuation :
Photoelectric effect is thedominating process at the x-rayenergy range (200-100 keV)
Interaction of X-rays with matter
• What is XAFS?
– XAFS studies the details of the x-ray absorptioncoefficient around an absorption edge.
– It reveals a wealth of information regarding thegeometric and electronic structure of materials.
11.2 11.6 12.0 12.4-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
mt
Energia(keV)
Basics aspects about XAFS
Basics aspects about XAFS
103
104
10
102
103
104
K
LI
LII
Co
eficie
nte
de
ate
nu
açã
o (
cm
2/g
)
Energia (eV)
Ge (Z=32)
LIII
XAFS: Study the details of the variation on the absorption
coefficient (fine structure) after the edge.
K 1s p
L1 2s p
L2 2p1/2 s, d
L3 2p3/2 s, d
Absorption edges
11.2 11.6 12.0 12.4-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
mt
Energia(keV)
Basics aspects about XAFS
X-ray attenuationAbsorption coefficient:
tII dd m
Mass absorpion coefficient:
jj
jg
m
m
Mass fraction of el. j
Atomic absorption coefficient:
N
Aj
j
a
j
mm
units (cm2/g)
Units: 10-24cm2 (1 barn)
h h
amostra
I0I1
t
µ : linear absorptioncoefficient
t : thickness
µt: absorbance
)exp(01 tII mIncludes contributions from allscattering and absorption precesses
Basics aspects about XAFS
Basic XAFS experiment – sequential mode
Radiation source
monochromatorIo I
sample
detectors
1
0logI
Itm
Basics aspects about XAFS
X-ray energy
m
EXAFS spectrum
Fluorescence X-rays
TEY
SAMPLE
Incident X-rays Transmitted X-rays
Visible light
XEOL
h
h
e-
Basics aspects about EXAFS
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)
Which method for which application?
The most important criterion:
The best signal to noise ratio for the
element of interest
hh fluor .
e-h lu min.
h
Ie-
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
Basics aspects about XAFS
XAFS = XANES + EXAFS
12.0 12.5 13.00.1
0.2
0.3
0.4
0.5
0.6
E0=11.867 keV
InAs - As K-Edge mt
Photon Energy (keV)
XANES EXAFS
X-ray Absorption NearEdge Strucuture
Extended X-ray AbsorptionFine Strucuture
Near Edge X-rayAbsorption Fine Strucuture
NEXAFS
high Z elements
low Z elements
XANES is the region ~50 eV around the edge
Basics aspects about XAFS
Information content
•Fermi energy•Projected density of unoccupied states•Oxidation states •Coordination symmetry
Information content
•interatomic distances•disorder•coordination numbes•Bond-angle distributions•Partial pair distribution•Vibrational properties.
XANES : transitions to unoccupied states (localized and continuum)
low energy photoelectron multiple scattering (MS)
EXAFS: high energy photoelectron single scattering + some important MS
Basics aspects about XAFS
K
L
M
Fermi Energy
Continuum
1s
2s, 2pfóton
Bin
din
g En
erg
y
N
3s, 3p, 3d
4s, 4p, 4d, 4f
0
Ocupped states
Unnocuped statesXANES
Basics aspects about XAFS
E
m
E
m
i >
E
f >
i >
E
Fermi Golden rule
i >
E
f >
f
Arctangent curve
Inflectionpoint
XANES: pre edge structure
E
ma
b
0
0
0
0
0
K
L
M
Fermi Energy
Continuum
1s
2s, 2pfóton
Bin
din
g En
erg
y
N
3s, 3p, 3d
4s, 4p, 4d, 4f
0
Ocupped states
Unnocuppied statesEXAFS
Information obtained:•Coordination number•Interactomic distances•Disorder
Basics aspects about XAFS
Basics aspects about XAFS
XAFS = XANES + EXAFS
12.0 12.5 13.00.1
0.2
0.3
0.4
0.5
0.6
E0=11.867 keV
InAs - As K-Edge mt
Photon Energy (keV)
EXAFS
Extended X-ray AbsorptionFine Strucuture
EXAFS is the region from 50 – 1200 eV after the edge
Fine Strucuture
Basics aspects about XAFS
R
•Interference in between propagating waves and retrodispersed ones. Thismoduls the absorption coefficient.
•Photon energy (E) > Binding Energy (El): Photoelectric effect.
•Kinetic energy of the photoelectron (Ec)= E - EL
•Wave-Particle duality: The photoelectron travel as a esferic wave: Ec = h
2
)(2
Le EEmk
•Wavevector of the photoelectron: K
•Phase difference of the incoming and outgoing waves: Δ
kR2
•Quantical state of the photoelectron: superposition of thepropagating wave with the retrodispersed waves on theneightbourgs
•Oscilation frequence: 2R•Oscilation amplitudes: number of neightbourgs and disorder
Understanding the XAFS equation
7000 7200 7400 7600 7800 8000 8200
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
mx
Energia(eV)
Here we add (superpose) oscilations ofdifferent frequencies (radial distances), one for each coordination shell
-2 0 2 4 6 8 10 12 14 16 18-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
(k
)
Vetor de onda do fotoelétron: k(Å-1)
•Coordination shell: Refers to the aggrupation's of atoms at the same distance to the absorber atom.
•Coordination Number: amount of atoms in a coordination shell
m
0mm
mm
0
Understanding the XAFS equation
)](2sin[ kkR ii
i
R
i
i
i
i
ik
eekFSkR
N
2
2
02
222
)()(k
iR
iN
i2
2
0S)(kF
)(k
Estructural parameters
ab initio
Atomic parameters: Absoption and dispersion of thePhotoelectron
Understanding the XAFS equation
Principal hypothesis:•Final states are plane waves•Gaussian disorder•Dipolares transitions•One active electron•Photoelectron dispersion is single
Sayers et al.,PRL 27, 1204 (1971)
)(ê)(2
f
EE
f
EirfEFf
m
max
min
2e)(2
1)(
k
k
Rki dkkRTF
Understanding the XAFS equation
max
min
2e)(2
1)(
k
k
Rki dkkRTF
Understanding the XAFS equation
max
min
2e)(2
1)(
k
k
Rki dkkRTF
-5 0 5 10 15 20 25 30 35
0
2
4
6
8
R=1
R=2
R=2.5
sin(2*R*k)
(k
)
k(Å-1)
R=3
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
0
4
8
12
16
20
24
28
32
36
Módulo
da T
F
R(Å)
Understanding the XAFS equation
max
min
2e)(2
1)(
k
k
Rki dkkRTF
0 5 10 15 20 25 30
-1.0
-0.5
0.0
0.5
1.0
(k
)
k(Å-1)
i*sin(2*R
i*k)
1=6
2=4
3=5
4=12
0 1 2 3 4 50
2
4
6
8
10
12
Módulo
da T
F
R(Å)
)](2sin[ kkR ii
i
R
i
i
i
i
ik
eekFSkR
N
2
2
02
222
)()(k
Understanding the XAFS equation
0 5 10 15 20-8
-6
-4
-2
0
2
4
6
(k
) x k
2
k(Å-1)
0 1 2 3 4 5 60
2
4
6
8
10
Módulo
da T
F
R(Å)
Signal at Ge-K edge
1a shell: R =2.45 Å N=4
2a shell: R = 4.00 ÅN=12
3a shell: R = 4.69 Å N=12
4a shell: R = 5.66N=4
Fourier Transform (FT)
FT: is not a Radial Distribution function buthave some resemblance
)](2sin[ kkR ii
i
R
i
i
i
i
ik
eekFSkR
N
2
2
02
222
)()(k
oK
Understanding the XAFS equation
0 5 10 15 20
-3
-2
-1
0
1
2
3
x
k2
k(Å-1)
N=4
N=3
N=2
N=1
0 5 10 15 20
-3
-2
-1
0
1
2
3
x
k2
k(Å-1)
N=4
N=3
N=2
N=1
0 5 10 15 20
-3
-2
-1
0
1
2
3
x
k2
k(Å-1)
N=4
N=3
N=2
N=1
0 5 10 15 20
-3
-2
-1
0
1
2
3
x
k2
k(Å-1)
N=4
N=3
N=2
N=1
0 1 2 3 40
2
4
6
8
10
Módulo
da T
F
R(Å)
N=4
N=3
N=2
N=1
0 1 2 3 40
2
4
6
8
10
Módulo
da T
F
R(Å)
N=4
N=3
N=2
N=1
0 1 2 3 40
2
4
6
8
10
Módulo
da T
F
R(Å)
N=4
N=3
N=2
N=1
0 1 2 3 40
2
4
6
8
10
Módulo
da T
F
R(Å)
N=4
N=3
N=2
N=1
Changes on the EXAFS signal with variations on the Coordination number
Understanding the XAFS equation
Changes onthe EXAFS signal with a variation onthe0 5 10 15 20
-3
-2
-1
0
1
2
3
x k
2
k(Å-1)
R0
R0 + R
0 1 2 3 4 50
2
4
6
8
10
Módulo
da T
F
R(Å)
R0
R0 + R
0 5 10 15 20
-3
-2
-1
0
1
2
3
x k
2
k(Å-1)
R0
R0 - R
0 1 2 3 4 50
2
4
6
8
10
Módulo
da T
F
R(Å)
R0
R0 - R
Å1.0R
Understanding the XAFS equation
Changes on theEXAFS with a variation onthe structuraldisorder
0 1 2 3 4 50
2
4
6
8
10
Módulo
da T
F
R(Å)
Sem desordem
Com desordem
0 1 2 3 4 50
2
4
6
8
10
Módulo
da T
F
R(Å)
Sem desordem
Com desordem
0 5 10 15 20
-3
-2
-1
0
1
2
3
x k
2
k(Å-1)
Sem desordem
Com desordem
0 5 10 15 20
-3
-2
-1
0
1
2
3
x k
2
k(Å-1)
Sem desordem
Com desordem
Gaussian Disorder: σ = 0.03 Å
m
mm
0
m0m
12600 12800 13000 13200 13400 13600 13800
0.0
0.5
1.0
1.5
2.0
ab
so
rbâ
ncia
Energia(eV)
xm
bkg
Victoreen
CdSe - Borda K do Se
Data treatment1 – background extraction
12800 13000 13200 13400 13600 13800
-0.10
-0.05
0.00
0.05
0.10
(E
)
Energia (eV)
Understanding the XAFS equation
0 2 4 6 8 10 12 14 16 18
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
k(Å-1)
k)*
k2
-2 0 2 4 6 8 10 12 14 16 18
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
k
k(Å-1)
0 2 4 6 8 10 12 14 16 18
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
k(Å-1)
k)*
k2
Conversion Ek
2
)(2
Le EEmk
K-weigthing
Understanding the XAFS equation
0 2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
|FT
((k
))|
R(Å)
0 2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
|FT
((k
))|
R(Å)
0 2 4 6 8 10 12 14 16 18
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
k(Å-1)
k)*
k2
0 2 4 6 8 10 12 14 16 18
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
k(Å-1)
k)*
k2
Structural parameters: Minimal Square fitting
Phases and amplitudes of the retrodispersion
Understanding the XAFS equation
)](2sin[ kkR ii
i
R
i
i
i
i
ik
eekFSkR
N
2
2
02
222
)()(k
iR
iN
i2
2
0S)(kF
)(k
Estructural parameters
ab initio
Atomic parameters: Absoption and dispersion of thePhotoelectron
Understanding the XAFS equation
Principal hypothesis:•Final states are plane waves•Gaussian disorder•Dipolares transitions•One active electron•Photoelectron dispersion is single
Sayers et al.,PRL 27, 1204 (1971)
)(ê)(2
f
EE
f
EirfEFf
m
But remeber....
Obrigado pela sua atenção!
Questions, please email me:[email protected]
More info about XAFS:https://speakerdeck.com/bruceravel?page=2http://cars.uchicago.edu/ifeffit/Mailing_Listhttp://xafs.org/Tutorialshttp://www.ixasportal.net/ixas/http://cars.uchicago.edu/ifeffit/DocumentationAcknowlegments: To Gustavo Azevedo, Valmor Mastelaro, AnatolyFrenkel por some slides