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

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

XAFS study: from experiment to results Data collection Structural Preliminary data model(s) treatment Extraction of XAFS revision structural signal: c (k) revision Structural refinement Check the results revision END

XAFS study: from experiment to results Data collection Structural Preliminary data model(s) treatment Extraction of XAFS revision structural signal: c (k) revision Structural refinement Check the results revision END

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 - Check the proposal submission deadlines - discuss your experiment with local contacts Choose properly the experimental set-up & sample preparation Check data Choose Optimize your quality constantly properly data beamtime! during the collection experiment strategy Measure reference samples

Data collection Choose properly the experimental set-up & sample preparation • For massive concentrated samples: TRANSMISSION Jump Total absorption 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 data collection strategy Δ K • Acquisition time per point • Single scan or repeated scans • Δ E or Δ k step 6 Δ k=0.03 DE(eV) 5 E o E-E o (eV) 4 Constant Δ k acquisition 3 • Optimizes the number of collected points 2 • More efficient 1 • Faster 0 -100 400 900 1400 1900 E-Eo(eV)

Data collection Measure reference samples Ref.Sample Sample I 2 I 1 I 0 μ ref =ln I 1 /I 2 μ exp =ln I o /I 1 1.5 2+ Normalized Absorption 1.0 2.6+ 0.5 3+ 4+ 0 0.0 6530 6540 6550 6560 6570 6580 Energy (eV)

Data collection Check data quality constantly during the experiment • Evaluate signal/noise ratio  (E) 1.2 High degree polynomial 0.0004 0.9  (E) J 0.0002 0.6 0 -0.0002 0.3 -0.0004 -0.0006 12000 12300 12600 12900 13200 13500 13200 13500 13800 s = 1.1e -4 E (eV) E (eV) 0.0003  (E) 0.0002 0.0001 0 S/N ratio should be less than 10 -3 -0.0001 -0.0002 S/N ~ J/ s -0.0003 0 5 10 15 20 25 30 13200 13500 E (eV)

Data collection Check data quality constantly during the experiment • Check for: Glitches  (E) 1.2 0.9 0.6 edge shift 0.3 12000 12300 12600 12900 13200 13500 E (eV) Discontinuities

XAFS analysis: from experiment to results Data collection Structural Preliminary data model(s) treatment Extraction of XAFS revision structural signal: c (k) revision Structural refinement Check the results revision END

Preliminary data treatment Choose the best spectra and useful data regions a do not use the blue one! do not use data beyond 13000 eV !

Preliminary data treatment De-glitch

Preliminary data treatment Align

Preliminary data treatment Average

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!!

XAFS analysis: from experiment to results Data collection Structural Preliminary data model(s) treatment Extraction of XAFS revision structural signal: c (k) revision Structural refinement Check the results revision END

Extraction of the EXAFS signal pre-edge line + post-edge line revise Normalized preliminary data treatment m o calculation structural signal c (k) Structural Fourier Transform refinement Fourier Filtering

Extraction of the EXAFS signal pre-edge line + post-edge line Normalized data

Extraction of the EXAFS signal structural signal c (k) m o calculation

Extraction of the EXAFS signal m o calculation 1) Define E 0 2) Calculate μ 0 E o m o is the bare atom atomic background. It is calculated 3) Subtract μ 0 from μ empirically as a smooth curve across the data. Different XAFS data analysis softwares apply different (equivalent) E 0 will allow to set the approaches starting point of χ (k). It is generally taken at the maximum of the 1 st derivative of the absorption

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

Fourier Transform – window size effect Minor effects are given by type of windows (Hanning, Kaiser-Bessel, Sine) and apodization

Extraction of the EXAFS signal DO NOT DO THE DO NOT REMOVE TRUE OPPOSITE ERROR STRUCTURAL FEATURES Large |FT| contributions at low (unphysical) distances may signify "wrong m o "

Extraction of the EXAFS signal Fourier filtering allows isolating contributions Fourier Filtering of selected regions of the FT Background contribution

XAFS analysis: from experiment to results Data collection Structural Preliminary data model(s) treatment Extraction of XAFS revision structural signal: c (k) revision Structural refinement Check the results revision END

Structural refinement Exp. c (k) Choose a model Theoretical c (k) Define the relevant structural contributions Refine the structural Experimental c (k) parameters: N, R, s 2 Y add new contributions? Y Change the model? Revise your data Y extraction? Require data analysis programs END

Structural refinement Choose a model How to calculate How to visualize How to find a distances and the structure model structure geometries https://icsd.fizkarlsruhe.de http://millenia.cars.aps.anl.gov/cgi-bin/atoms/atoms.cgi Database for inorganic structures http://database.iem.ac.ru/mincryst/ ICSD database

Amplitude and phase functions from atomic cluster models Data refinement program ex fit p

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/

Data treatment: strategy 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 μ 0 (E) to isolate the XAFS c .   m E E  5. identify the threshold energy E 0 , and convert from E to k space: 2 k  0 2  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. Tecniche di caratterizzazione con luce di sincrotrone Lessons 8-9 31

Converting raw data to μ (E) For transmission XAFS: I = I 0 exp[- μ (E) t] μ (E) t = ln [I 0 /I] Tecniche di caratterizzazione con luce di sincrotrone Lessons 8-9 32

Absorption measurements in real life I F synchrotron source I 1 I 0 monochromator sample Transmission The absorption is measured directly by measuring what is transmitted through the sample 𝐽 = 𝐽 0 𝑓 −𝜈 𝐹 𝑢 𝜈 𝐹 𝑢 = α = ln 𝐽 0 𝐽 1 Fluorescence The re-filling the deep core hole is detected. Typically the fluorescent X- ray is measured 𝛽 ∝ 𝐽 𝐺 𝐽 0 Tecniche di caratterizzazione con luce di sincrotrone Lessons 8-9 33

Pre-edge subtraction and normalization Pre-edge subtraction We subtract away the background that fits the pre edge region. This gets rid of the absorption due to other edges (say, the Fe L III edge). Normalization We estimate the edge step , μ 0 (E 0 ) by extrapolating a simple fit to the above μ(E) to the edge. Tecniche di caratterizzazione con luce di sincrotrone Lessons 8-9 34

Determination of E 0 Derivative and E 0 We can select E 0 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. Tecniche di caratterizzazione con luce di sincrotrone Lessons 8-9 35

Post-edge background subtraction Post-edge background • We do not have a measurement of μ 0 (E) (the absorption coefficient without neighboring atoms). • We approximate μ 0 (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 μ 0 (E). Tecniche di caratterizzazione con luce di sincrotrone Lessons 8-9 36