basics of xafs to chi 2009

8/12/2019 Basics of XAFS to Chi 2009

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Basics of EXAFSProcessing

Shelly Kelly

2009 UOP LLC. All rights reserved.


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2 File Number

X-ray-Absorption Fine Structure

Attenuation of x-raysIt= I0e

-(E)x

Absorption coefficient(E) If/I0


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3 File Number

X-ray-Absorption Fine Structure

R0

Photoelectron

ScatteredPhotoelectron


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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


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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


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

=>


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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


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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


9/319 File Number

Athena normalization parameters


10/3110 File Number

k2 = 2 me

(E E0)

Energy to wave number

E0Must besomewhereon the edge

Mass of theelectron

Planksconstant

EdgeEnergy

~ E3.81


11/3111 File Number

Athena edge energy E0


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


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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


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


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.


16/3116 File Number

Fourier Transform Windows

dk

kmin

kmax

dkWelchParzen

Sine

Kaiser-Bessel

Hanning


17/3117 File Number

Athena plotting in R-space


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)


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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


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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)


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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)


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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


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Fourier transform parameters in Athena


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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!


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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.


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Rbkg value in Athena


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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!


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FT and Background function

Rbkg= 1.0 Rbkg= 0.1

An example where long wavelength oscillations appearas (false) peak in the FT


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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


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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


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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.

basics of xafs to chi 2009

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