EXAFS data analysis Giuliana Aquilanti Elettra Sincrotrone Trieste - - PowerPoint PPT Presentation

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EXAFS data analysis Giuliana Aquilanti Elettra Sincrotrone Trieste - - PowerPoint PPT Presentation

Jan 15, 2023 461 likes •923 views

Introduction to the EXAFS data analysis Giuliana Aquilanti Elettra Sincrotrone Trieste Material almost integrally taken from Carlo Meneghini: EXAFS tutorial at Synchrotron Radiation school of Duino 2011 Characteristics of a XAS spectrum

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SLIDE 1

Introduction to the EXAFS data analysis

Giuliana Aquilanti

Elettra – Sincrotrone Trieste

Material almost integrally taken from Carlo Meneghini: EXAFS tutorial at Synchrotron Radiation school of Duino 2011

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SLIDE 2

Characteristics of a XAS spectrum

Pre-edge background Post edge atomic background Edge Energy Jump XANES

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SLIDE 3

Data collection Extraction of XAFS structural signal: c(k) Structural refinement Check the results END Preliminary data treatment

Structural model(s)

revision revision revision

XAFS study: from experiment to results

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SLIDE 4

Data collection Extraction of XAFS structural signal: c(k) Structural refinement Check the results END Preliminary data treatment

Structural model(s)

revision revision revision

XAFS study: from experiment to results

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SLIDE 5

Optimize your beamtime!

  • Check the proposal submission deadlines
  • discuss your experiment with local contacts

Data collection

Considerations: 1) Proposal submission + proposal evaluation + beamtime scheduling = 6 to 12 months 2) Difficult to have new beamtime in case of proposal failure

Choose properly the experimental set-up & sample preparation Check data quality constantly during the experiment Choose properly data collection strategy Measure reference samples

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SLIDE 6
  • For massive concentrated samples: TRANSMISSION

inhomogeneities, holes, not parallel surfaces, etc...

  • For thin concentrated or thin diluted samples: FLUORESCENCE

Self absorption, detector linearity, Bragg reflections

Data collection

Choose properly the experimental set-up & sample preparation

Jump Total absorption

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SLIDE 7

Data collection

Choose properly the data collection strategy

  • Acquisition time per point
  • Single scan or repeated scans
  • ΔE or Δk step

E-Eo (eV) ΔK

1 2 3 4 5 6

  • 100

400 900 1400 1900 E-Eo(eV)

DE(eV)

Eo Δk=0.03

Constant Δk acquisition

  • Optimizes the number of collected points
  • More efficient
  • Faster
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SLIDE 8

Data collection

Measure reference samples

I0 I1 I2

Ref.Sample Sample

μref=ln I1/I2 μ exp=ln Io/I1

6530 6540 6550 6560 6570 6580 0.0 0.5 1.0 1.5

4+ 3+ 2.6+

Normalized Absorption Energy (eV)

2+

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SLIDE 9

Data collection

Check data quality constantly during the experiment

  • Evaluate signal/noise ratio
  • 0.0006
  • 0.0004
  • 0.0002

0.0002 0.0004 13200 13500 13800 (E) E (eV)

0.3 0.6 0.9 1.2 12000 12300 12600 12900 13200 13500 (E) E (eV)

J

High degree polynomial

  • 0.0003
  • 0.0002
  • 0.0001

0.0001 0.0002 0.0003 13200 13500 (E) E (eV)

5 10 15 20 25 30

s = 1.1e-4

S/N ~ J/s

S/N ratio should be less than 10-3

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SLIDE 10

Data collection

Check data quality constantly during the experiment

  • Check for:

0.3 0.6 0.9 1.2 12000 12300 12600 12900 13200 13500 (E) E (eV)

Glitches Discontinuities edge shift

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SLIDE 11

Data collection Extraction of XAFS structural signal: c(k) Structural refinement Check the results END Preliminary data treatment

Structural model(s)

revision revision revision

XAFS analysis: from experiment to results

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SLIDE 12

do not use the blue one!

a

Preliminary data treatment

Choose the best spectra and useful data regions

do not use data beyond 13000 eV !

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SLIDE 13

Preliminary data treatment

De-glitch

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SLIDE 14

Preliminary data treatment

Align

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SLIDE 15

Preliminary data treatment

Average

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SLIDE 16

Preliminary data treatment

Preliminary data treatment is boring, it may be long… While you are waiting for your data collection to finish…

Do it on already collected data!! You will save your time at home!!

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SLIDE 17

Data collection Extraction of XAFS structural signal: c(k) Structural refinement Check the results END Preliminary data treatment

Structural model(s)

revision revision revision

XAFS analysis: from experiment to results

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SLIDE 18

mo calculation Fourier Transform Fourier Filtering pre-edge line + post-edge line structural signal c(k) Structural refinement

revise preliminary treatment

Extraction of the EXAFS signal

Normalized data

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SLIDE 19

Extraction of the EXAFS signal

pre-edge line + post-edge line Normalized data

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SLIDE 20

Extraction of the EXAFS signal

mo calculation structural signal c(k)

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SLIDE 21

Extraction of the EXAFS signal

mo calculation

1) Define E0 Eo E0 will allow to set the starting point of χ(k). It is generally taken at the maximum of the 1st derivative of the absorption 2) Calculate μ0 mo is the bare atom atomic background. It is calculated empirically as a smooth curve across the data. Different XAFS data analysis softwares apply different (equivalent) approaches 3) Subtract μ0 from μ

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SLIDE 22

Extraction of the EXAFS signal

Fourier Transform

FT shows more intuitively the main structural features in the real space: the FT modulus represent a pseudo-radial distribution function (RDF) |FT| peaks represent interatomic correlation Peak position are not the true correlation distances due to the phase shift effect

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SLIDE 23

Fourier Transform – window size effect

Minor effects are given by type of windows (Hanning, Kaiser-Bessel, Sine) and apodization

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SLIDE 24

Extraction of the EXAFS signal

DO NOT REMOVE TRUE STRUCTURAL FEATURES DO NOT DO THE OPPOSITE ERROR

Large |FT| contributions at low (unphysical) distances may signify "wrong mo"

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SLIDE 25

Fourier filtering allows isolating contributions

  • f selected regions of

the FT

Background contribution

Fourier Filtering

Extraction of the EXAFS signal

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SLIDE 26

Data collection Extraction of XAFS structural signal: c(k) Structural refinement Check the results END Preliminary data treatment

Structural model(s)

revision revision revision

XAFS analysis: from experiment to results

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SLIDE 27

Choose a model Refine the structural parameters: N, R, s2 Define the relevant structural contributions add new contributions? Change the model?

Y Y

END Revise your data extraction?

Y

Theoretical c(k) Experimental c(k)

Exp. c(k)

Structural refinement

Require data analysis programs

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SLIDE 28

https://icsd.fizkarlsruhe.de Database for inorganic structures

ICSD database

How to find a model structure How to visualize the structure How to calculate distances and geometries

http://database.iem.ac.ru/mincryst/

http://millenia.cars.aps.anl.gov/cgi-bin/atoms/atoms.cgi

Structural refinement

Choose a model

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SLIDE 29

ex p fit

Data refinement program

Amplitude and phase functions from atomic cluster models

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SLIDE 30

XAFS data analysis softwares

http://www.xafs.org/ www.ixasportal.net

http://cars9.uchicago.edu/ifeffit/

Click DOWNLOADS Click ifeffit-1.2.11.exe

http://bruceravel.github.io/demeter/

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SLIDE 31

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone

Data treatment: strategy

31

Step for reducing measured data to μ(E) and then to c(k):

  • 1. convert measured intensities to μ(E)
  • 2. subtract a smooth pre-edge function, to get rid of any instrumental

background, and absorption from other edges.

  • 3. normalize μ(E) to go from 0 to 1, so that it represents 1 absorption

event

  • 4. remove a smooth post-edge background function to approximate

μ0(E) to isolate the XAFS c.

  • 5. identify the threshold energy E0, and convert from E to k space:
  • 6. weight the XAFS c(k) and Fourier transform from k to R space.
  • 7. isolate the c(k) for an individual “shell” by Fourier filtering.

 

2

2  E E m k  

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SLIDE 32

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone

Converting raw data to μ(E)

32

For transmission XAFS: I = I0 exp[-μ(E) t] μ(E) t = ln [I0/I]

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SLIDE 33

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone

Absorption measurements in real life

33

Transmission The absorption is measured directly by measuring what is transmitted through the sample 𝐽 = 𝐽0𝑓−𝜈 𝐹 𝑢 𝜈 𝐹 𝑢 = α = ln 𝐽0 𝐽1 Fluorescence The re-filling the deep core hole is detected. Typically the fluorescent X- ray is measured 𝛽 ∝ 𝐽𝐺 𝐽0

synchrotron source monochromator sample

I0 IF I1

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SLIDE 34

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone

Pre-edge subtraction and normalization

34

Pre-edge subtraction We subtract away the background that fits the pre edge region. This gets rid of the absorption due to

  • ther edges (say, the Fe LIII edge).

Normalization We estimate the edge step, μ0(E0) by extrapolating a simple fit to the above μ(E) to the edge.

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SLIDE 35

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone

Determination of E0

35

Derivative and E0 We can select E0 roughly as the energy with the maximum

  • derivative. This is somewhat

arbitrary, so we will keep in mind that we may need to refine this value later on.

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SLIDE 36

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone

Post-edge background subtraction

36

Post-edge background

  • We do not have a measurement
  • f μ0(E) (the absorption

coefficient without neighboring atoms).

  • We approximate μ0(E) by an

adjustable, smooth function: a spline.

  • A flexible enough spline should not

match the μ(E) and remove all the

  • EXAFS. We want a spline that will

match the low frequency components of μ0(E).

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SLIDE 37

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone

Χ(k), k-weighting

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χ(k) The raw EXAFS χ(k) usually decays quickly with k, and difficult to assess

  • r interpret by itself.

It is customary to weight the higher k portion of the spectra by multiplying by k2 or k3. k-weighted χ(k): k2χ (k) χ(k) is composed of sine waves, so we’ll Fourier Transform from k to R-space. To avoid “ringing”, we’ll multiply by a window function.

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SLIDE 38

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone

Fourier Transform: χ(R)

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χ(R) The Fourier Transform of k2(k) has 2 main peaks, for the first 2 coordination shells: Fe-O and Fe- Fe. The Fe-O distance in FeO is 2.14Å , but the first peak is at 1.66Å . This shift in the first peak is due to the phase-shift, δ(k): sin[2kR + δ(k)] . A shift of -0.5 Å is typical. χ(R) is complex: The FT makes c(R) complex. Usually only the amplitude is shown, but there are really oscillations in c(R). Both real and imaginary components are used in modeling.

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SLIDE 39

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone

Fourier filtering

39

c(R) often has well separated peaks for different “shells”. This shell can be isolated by a Filtered Back-Fourier Transform, using the window shown for the first shell of FeO. This results in the filtered c(k) for the selected shell. Many analysis programs use such filtering to remove shells at higher R. Beyond the first shell, isolating a shell in this way can be difficult.

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SLIDE 40

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone

The information content of EXAFS

40

  • The number of parameters we can reliably measure from our data is

limited: where Dk and DR are the k- and R-ranges of the usable data.

  • For the typical ranges like k = [3.0, 12.0] Å−1 and R = [1.0, 3.0] Å,

there are ~ 11 parameters that can be determined from EXAFS.

  • The “Goodness of Fit” statistics, and confidence in the measured

parameters need to reflect this limited amount of data.

  • It is often important to constrain parameters R, N, s2 for different

paths or even different data sets (different edge elements, temperatures, etc)

  • Chemical Plausibility can also be incorporated, either to weed out
  • bviously bad results or to use other knowledge of local

coordination, such as the Bond Valence Model (relating valence, distance, and coordination number).

  • Use as much other information about the system as possible!

 R k N D D  2

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SLIDE 41

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone

Modeling the first shell of FeO - 1

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FeO has a rock-salt structure. To model the FeO EXAFS, we calculate the scattering amplitude f(k) and phase-shift d(k), based on a guess of the structure, with Fe-O distance R = 2.14 Å (a regular octahedral coordination). We will use these functions to refine the values R, N, s2, and E0 so our model EXAFS function matches our data. Fit results N = 5.8 ± 1.8 R = 2.10 ± 0.02 Å E0 = -3.1 ± 2.5 eV σ2 = 0.015 ± 0.005 Å 2.

|χ(R)| for FeO (blue), and a 1st shell fit (red).

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SLIDE 42

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone

Modeling the first shell of FeO - 2

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1st shell fit in k space The 1st shell fit to FeO in k space. There is clearly another component in the XAFS 1st shell fit in R space |χ(R)| and Re[χ(R)] for FeO (blue), and a 1st shell fit (red).

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SLIDE 43

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone 43

Modeling the second shell of FeO - 1

To add the second shell Fe to the model, we use calculation for f(k) and d(k) based on a guess of the Fe-Fe distance, and refine the values R,N, s2. Such a fit gives a result like this: |χ(R)| data for FeO (blue), and fit of 1st and 2nd shells (red). The results are fairly consistent with the known values for crystalline FeO: 6 O at 2.13Å, 12 Fe at 3.02Å .

Fit results (uncertainties in parentheses):

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SLIDE 44

Lessons 8-9 Tecniche di caratterizzazione con luce di sincrotrone 44

Modeling the second shell of FeO - 2

Other views of the data and two-shell fit: The Fe-Fe EXAFS extends to higher-k than the Fe-O EXAFS. Even in this simple system, there is some

  • verlap of shells in R-space.

The agreement in Re[χ(R)] look especially good – this is how the fits are done. The modeling can get more complicated than this