of 31
8/12/2019 Basics of XAFS to Chi 2009
1/31
Basics of EXAFSProcessing
Shelly Kelly
2009 UOP LLC. All rights reserved.
8/12/2019 Basics of XAFS to Chi 2009
2/31
2 File Number
X-ray-Absorption Fine Structure
Attenuation of x-raysIt= I0e
-(E)x
Absorption coefficient(E) If/I0
8/12/2019 Basics of XAFS to Chi 2009
3/31
3 File Number
X-ray-Absorption Fine Structure
R0
Photoelectron
ScatteredPhotoelectron
8/12/2019 Basics of XAFS to Chi 2009
4/31
4 File Number
Fourier Transform of (k)
Similar to an atomic radial distribution function
- Distance
- Number- Type- Structural disorder
Fourier transform is not a radial distribution function
- See http://www.xafs.org/Common_Mistakes
8/12/2019 Basics of XAFS to Chi 2009
5/31
5 File Number
Outline
Definition of EXAFS- Edge Step- Energy to wave number
Fourier Transform (FT) of (k)
- FT is a frequency filter- Different parts of a FT and backward FT- FT windows and sills- Determining Kmin and Kmax of FT
IFEFFIT method for constructing the background function- FT and background (bkg) function- Wavelength of bkg
EXAFS Equation
8/12/2019 Basics of XAFS to Chi 2009
6/316 File Number
(E)=(E) -
0(E)
(E)
Definition of EXAFS
Measured Absorptioncoefficient
Evaluated at the Edge step (E0)
~(E) -0(E)(E0)
Bkg: Absorption coefficient withoutcontribution from neighboring atoms(Calculated)
Normalizedoscillatory partof absorptioncoefficient
=>
8/12/2019 Basics of XAFS to Chi 2009
7/317 File Number
Pre-edge region 300 to 50 eV before the edge
Edge regionthe rise in the absorption coefficient
Post-edge region 50 to 1000 eV after the edge
Absorption coefficient
8/12/2019 Basics of XAFS to Chi 2009
8/318 File Number
Edge step
Pre-edge line 200 to 50 eV before the edge
Post-edge line 100 to 1000 eV after the edge Edge step the change in the absorption coefficient at the edge-Evaluated by taking the difference of the pre-edge and
post-edge lines at E0
8/12/2019 Basics of XAFS to Chi 2009
9/319 File Number
Athena normalization parameters
8/12/2019 Basics of XAFS to Chi 2009
10/3110 File Number
k2 = 2 me
(E E0)
Energy to wave number
E0Must besomewhereon the edge
Mass of theelectron
Planksconstant
EdgeEnergy
~ E3.81
8/12/2019 Basics of XAFS to Chi 2009
11/3111 File Number
Athena edge energy E0
8/12/2019 Basics of XAFS to Chi 2009
12/3112 File Number
FT of Sin(2Rk) is a peak at R=1
FT of infinite sine wave is a delta function
Signal that is de-localized in k-space is localized in R-space FT is a frequency filter
Fourier Transform is a frequency filter
8/12/2019 Basics of XAFS to Chi 2009
13/3113 File Number
Fourier Transform of a function that is:
De-localized in k-space localized in R-space
Localized in k-space de-localized in R-space
8/12/2019 Basics of XAFS to Chi 2009
14/3114 File Number
The signal of a discrete sine wave is the sum of an infinite sine waveand a step function.
FT of a discrete sine wave is a distorted peak. EXAFS data is a sum of discrete sine waves.
Solution for finite data set is to multiply the data with a window.
Fourier Transform is a frequency filter
Regularly spaced rippleIndicates a problem
8/12/2019 Basics of XAFS to Chi 2009
15/3115 File Number
Fourier Transform
Multiplying the discrete sine wave by a windowthat gradually increases the amplitude of the
data smoothes the FT of the data.
8/12/2019 Basics of XAFS to Chi 2009
16/3116 File Number
Fourier Transform Windows
dk
kmin
kmax
dkWelchParzen
Sine
Kaiser-Bessel
Hanning
8/12/2019 Basics of XAFS to Chi 2009
17/3117 File Number
Athena plotting in R-space
8/12/2019 Basics of XAFS to Chi 2009
18/3118 File Number
Parts of the Fourier transform
The Magnitude of the Fourier transform does not contain as
much information as the Real or Imaginary parts of the FT.
0 2 4 6 8-0.8
-0.4
0.0
0.4
0.8
0 2 4 6 8 10 12
-0.8
-0.4
0.0
0.4
0.8
0 2 4 6 8
-0.8
-0.4
0.0
0.4
0 2 4 6 80.0
0.2
0.4
0.6
0.8
0 2 4 6 8 10 1-0.8-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0 2 4 6 8-0.8
-0.4
0.0
0.4
0.8
R
e(FT((k)k
3))(-4)
R ()k (-1)
(k)k
2(
-2)
R ()
Im
(FT((k)k
2))(-3)
|FT((k)k
2)|(-3)
R () k (-1)
|(q)|an
d
(k)k
2(
-2)
Partso
fFT((k)k
2)(-
3)
R ()
Real part of FT (k)
= Re [(R)]
magnitude of FT (k) = |(R)|
Imaginary part of FT (k)
= Im [(R)](k) data and FT window
back FT of (R) = (q)
8/12/2019 Basics of XAFS to Chi 2009
19/31
19 File Number
Backward Fourier transform
Only the wavelengths that are contained in the back Fouriertransform R range are present in the Re[chi(q)] spectra
As a larger R range is included the back FT looks more like theoriginal spectra (blue symbols)
0 1 2 3 4 5 60.0
0.2
0.4
0.6
0.8
1.0
1.2
|FT((k)k
2)
|(-3)
R ()0 2 4 6 8 10 12 14
-0.75
0.00
0.75
1.50
2.25
3.00
k (-1)Re[(q)]and
(k)k
2(
-2)
4321
43
21
8/12/2019 Basics of XAFS to Chi 2009
20/31
20 File Number
How to Choose Minimum K of FT
Choose Kmin in the region where the backgrounddoesnt change rapidly.- Often around 2 to 4 -1
- Vary E0 and plot the resulting spectra with low k-weight todetermine the best value.
0 2 4 6 8 10 12
-0.4
-0.2
0.0
0.2
0.4
17150 17200 172500.0
0.10.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
k (-1)
(k)k(-1
)
(E)x
Incident x-ray energy (eV)
8/12/2019 Basics of XAFS to Chi 2009
21/31
21 File Number
Choosing Maximum K-range
The FT should be smooth and free of ringing To choose Kmax make vary the kmax value and plot
the data using the largest k-weight that will be usedin modeling Look for ringing in the real or imaginary part of FT In the example above kmax of 10 or 11 -1 best
0 2 4 6
-4
-2
0
2
4
0 2 4 6
-4
-2
0
2
4
0 2 4 6 8 10 12
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15kmax = 8
-1
kmax = 9 -1
kmax = 10 -1
R ()
Re[FT((
k)k
1)](-2)
kmax = 10 -1
kmax = 11 -1
kmax = 12 -1
Re[FT((
k)k
1)](-2)
R ()
(k)k
2(
-2)
k (-1)
8/12/2019 Basics of XAFS to Chi 2009
22/31
22 File Number
Effect of K-weight on FT
These spectra have been k-weighted by 1, 2, and 3and then rescaled so that the first peak in the FT arethe same height
The higher k-weight values give more importance tothe data above 6 -1, this emphasizes the signal dueto the P neighbor relative to the O in the first shell
0 2 4 60
5
10
15
0 2 4 6
-10
-5
0
5
10
15
0 2 4 6 8 10 12 14-20
-10
0
10
20
R ()
|FT((k
)kx)|(-x-1)
Re(FT((k)kx))(-x-1)
R () k (-1)
(k)
.kkw
(-1-kw)
Kw=1Kw=2Kw=3
O P
8/12/2019 Basics of XAFS to Chi 2009
23/31
23 File Number
Fourier transform parameters in Athena
8/12/2019 Basics of XAFS to Chi 2009
24/31
24 File Number
Background function overview
A good background function removes long wavelengthoscillations from (k).
Constrain background so that it cannot contain oscillations
that are part of the data. Long wavelength oscillations in (k) will appear as peaks in
FT at low R-values
FT is a frequency filter use it to separate the data from
the background!
8/12/2019 Basics of XAFS to Chi 2009
25/31
25 File Number
Separating the background function from the datausing Fourier transform
Min. distance betweenknots defines minimumwavelength of background
Rbkg
Background function is made up of knots connected by 3rd ordersplines.
Distance between knots is limited restricting background fromcontaining wavelengths that are part of the data.
The number of knots are calculated from the value for Rbkg and the
data range in k-space.
8/12/2019 Basics of XAFS to Chi 2009
26/31
26 File Number
Rbkg value in Athena
8/12/2019 Basics of XAFS to Chi 2009
27/31
27 File Number
How to choose Rbkg value
An example where background distorts the first shell peak. Rbkg should be about half the R value for the first peak.
Rbkg= 2.2
Rbkg= 1.0
A Hint that Rbkg may be too large.Data should be smooth, not pinched!
8/12/2019 Basics of XAFS to Chi 2009
28/31
28 File Number
FT and Background function
Rbkg= 1.0 Rbkg= 0.1
An example where long wavelength oscillations appearas (false) peak in the FT
8/12/2019 Basics of XAFS to Chi 2009
29/31
29 File Number
Frequency of Background function
Constrain background so that it cannot containwavelengths that are part of the data.
Use information theory, number of knots = 2 Rbkg k /
8 knots in bkg using Rbkg=1.0 and k = 14.0
Background may contain only longer wavelengths.Therefore knots are not constrained.
Data contains this and
shorter wavelengths
Bkg contains this and
longer wavelengths
Photoelectron
8/12/2019 Basics of XAFS to Chi 2009
30/31
30 File Number
The EXAFS Equation
(NiS02)Fi(k) exp(i(2kRi + i(k)) exp(-2i2k2) exp(-2Ri/(k))
kRi2i(k) = Im( )
Ri = R0 + R
k2 = 2 me(E-E0)/
Theoretically calculated valuesFi(k) effective scattering amplitude
i(k) effective scattering phase shift(k) mean free path
Starting valuesR0 initial path length
Parameters often determinedfrom a fit to dataNi degeneracy of path
S02 passive electron reduction factori2 mean squared displacement ofhalf-path length
E0 energy shift
Rchange in half-path length
(k) = i i(k)
with
R0
Photoelectron
ScatteredPhotoelectron
More Information
8/12/2019 Basics of XAFS to Chi 2009
31/31
More Information
www.xafs.org
Kelly, S D, Hesterberg, D and Ravel, B. Analysis of soils andminerals using X-ray absorption spectroscopy. In Methods ofsoil analysis, Part 5 -Mineralogical methods; Ulery, A. L.,Drees, L. R., Eds.; Soil Science Society of America: Madison,WI, USA, 2008; pp 367.