Lecture 3. Data Analysis. Common errors in EXAFS analysis Z ± 10 N ± 1 R ± 0.02 Å

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1 Lecture. Data Analysis Tutorials and other Training Material Bruce Ravel's notes on using FEFFIT for data analysis Daresbury Laboratory lectures on data analysis (EXURV9) Grant Buner's XAFS tutorials Frenel et al on comparing PA with other methods hantler (Uni. Melbourne) on the absolute determination of x-ray absorption Programs ESRF Software catalog XFIT EXAFSPAK Athena and Artemis FEFFIT and IFEFFIT DL EXURV WinXAS Z ± ± R ±. Å χ ()= where and EXAFS - Frequency bondlength Phase scatterer Shape scatterer - (Å - ) s A s ()S exp ( σ as )exp ( R as λ ) sin R as + φ as () R as = m e ( E E o ) h χ()= μ( E) μ o( E) μ( E) μ s( E) ( E) ( E) μ o μ b Amplitude coordination number ( ) +E, μ b,λ The job of a least-squares fitting program is to give you the best (smallest deviation) solution, not to give you the right solution. If you see something, it tells you something; if you see nothing, it tells you nothing. Fourier transformation can be used to visualize frequencies contributing to EXAFS χ()= s A s ()S R as exp ( σ as )exp R as λ + χ( ) = A( ) sin( R φ) φ = φ + Rφ + R φ +K ( ) sin( R as + φ as () ) ommon errors in EXAFS analysis Least-squares minimization Fourier Filtering Resolution R + α ( Å)

2 Iterative refinements are especially susceptible to multiple minima P P R Phosphorus scattering c Pd a b Me H Me lot, et al., J. Am. hem. Soc,, arbon scattering Minima give very different structures but nearly identical EXAFS free vs. obs obs ~ (Δ =. Å; max = Å) free ~ ( Δ ΔR ) / π M-P M- sum M-O at. and. Å give two apparently well resolved peas in FT Fourier transform magnitude R + α (Å) Fitting each filtered pea gives the appearance of M-O and M-S EXAFS EXAFS - - "M-O" pea "M-S" pea (Å - ) EXAFS resolution is ~ π/δ =. Å EXAFS - R =.7 Å, R =. Å R =. Å, R =. Å R =. Å, R =. Å R=.7 Å R=.9 Å R=.9 Å, damped (Å - ) Further explorations of the difficulty of multiple minima and σ R and E Anatoly Frenel EXAFS Data ollection and Analysis Worshop, SLS

3 How to model metal (Pt) foil data: # Pt foil, T= K guess S =.9 S guess ss = χ( ) = guess dr = r guess th = guess e = sin r data = ptfoil-av.chi out = ptfoil-av rmin =. rmax =. min = max= w = d=!% st path: eshift e amp S path p.dat id SS Pt-Pt(), r=.779 delr dr sigma abs(ss) third th f ( ) e [ + δ ( ) ] eff σ χ(), Å - χ(), Å -. K , Å - 7 K, Å S =.7.9 ss =.9. dr = th = -..9 e =..9 S =.77.7 ss =.9. dr =.7.77 th =.9.7 e =.9.97 This is not physically reasonable. What caused S to be different at K and 7 K? - correlation with other fit variables: S χ( ) = f r sin Fit Results ( ) e [ r + δ ( ) ] eff σ χ(), Å S χ( ) = f r eff ( ) e χ() of Pt foil: temperature dependence σ K K 7 K 7 K, Å - How to brea the correlation? sin [ r + δ ( ) ] One possible solution: a multiple-data-set (mds) fit. What variables are not expected to change at different temperatures? ΔE, σ = σ + σ s σ s d ΘE h + exp( ΘE σ d = ωμ exp( Θ E, T ) T ) K MDS fit results K ss =..9 theins = s =.7.7 dr = -.. dr = -.9. dr = -.. dr =.. th = -.. th = -.7. th =.. th = K K Physical (chemical, engineering, mat.science, life science etc.) reality checs: ) Debye temperature: K for Pt As obtained (through Θ E ): () K ) Static disorder σ s : ~ ) orrections to model distances: ~ ) Thermal expansion: evident e = ) S: reasonable (between.7 and.) How to model XAFS data in nanoparticles? A priori nowledge or a woring hypothesis must exist (the zero approximation) otherwise: the transferability of amplitude/phase will not wor!) ) Hemispherical ) rystal order ) Size: about Å What information can be obtained from st shell EXAFS analysis? ) Size of the particle (via ) ) Distances, thermal vibration, expansion ) Static disorder (icosahedral? surface tension?) Average First-Shell oordination Average 9 7 anoparticle Diameter (A) (Å) Relative Abundance K. MDS fit (shell) to the nanoparticles EXAFS - oordination number is now guessed (a variable) S - is fixed to be equal to that in Pt foil EXAFS - E is fixed to be equal to that in Pt foil EXAFS... K ss =.7.77 theins = n = K... 7 K. dr = dr = -.7. dr = -.. dr = -..7 th = -.7. th =..9 th =.9.7 th =..79

4 K K Mo K-edge..... K K Fe K-edge {Mo 7 Fe } Modeling pair distribution functions using XRD results g AB ( r) = {Mo } d dr AB Mo-O. 7 Mo-O Mo-O Å shift -. Å shift Mo-Fe Mo-Mo -. Å shift Mo-Mo Å shift Fe-Mo Fe-O Å shift Fe-O Mo K-edge T= K. Fe K-edge T= K Mo K-edge T= K Fe K-edge T= K Summary 7 Mo-O Mo-O Mo-O..... Fe-O Mo-Mo Mo-Fe Mo-Mo Bond K K.7().7() r (Å) Mo-O.7 σ (Å ).().() Mo-O. Mo-O. Fe-O. Mo-Mo.7 Fe-Mo. Mo-Fe.7 Mo-Mo.7 r (Å).().() σ (Å ).(9).(7) r (Å).7().7() σ (Å ).(7).7() r (Å).().() σ (Å ).().(7) r (Å).().() σ (Å ).7().7() r (Å).().() σ (Å ).().() r (Å). f. f σ (Å ). f. f r (Å).9().9() σ (Å ).().9(9) The more variables you control, the more liely you are to obtain a unique solution Multiple data sets (elements, temperature, concentration, time, etc.) almost always help onclusions are only as good as your model Outer shell scattering can provide ligand identification and geometric information Multiple scattering maes EXAFS sensitive to angular arrangement of ligands Fourier Transform Magnitude Zn H Zn H 7 Radius + α (Å)

5 However, ability to reliably determine geometry is limited Information Parameters A case study in data under-determination R M O R O R M R O R O O lar-baldwin, et al. "The limitations of X-ray absorption spectroscopy for determining the structure of zinc sites in proteins. When is a tetrathiolate not a tetrathiolate?" J. Am. hem. Soc. 99,, -9. L L Zn SR SR Zn EXAFS is remarably insensitive to changes in ligation. Z ±??? EXAFS FT Magnitude ZnS ZnS ZnS - - (Å - ) ZnS ZnS ZnS.. 7. R + α (Å) XAES spectra are sensitive to ligation but show greater variation between different compounds than with changes in ligation. ormalized Absorption (cm /g) ormalized Absorption (cm /g) Peptide ZnS ZnS ZnS Inorganic ZnS ZnS ZnS EXAFS Zn-S and Zn- EXAFS signals are approximately out of phase - Zn-S Zn- - - (A - ) EXAFS The observed EXAFS for mixed S/ sites is dominated by Zn-S scattering - - Zn-S Zn- ZnS - (A - )

6 One solution is to measure data over wide range (ZnS inorganic) FT Magnitude 7 Δ=- Å - Δ=- Å - Δ=- Å - Δ=- Å - Δ=- Å - Δ=- Å R + α (Å) ote ΔR ~. π/δ =. Å Δ min ~. EXAFS High resolution EXAFS is required to reliably distinguish Zn-S from Zn- - - Zn-S Zn- ZnS - (A - ) and even with high resolution data, extremely high signal/noise ratios are required to detect Zn- in the presence of Zn-S EXAFS - - Zn-S Zn- ZnS - - (A - ) It is possible to reliably distinguish between ZnS, ZnS, and ZnS if variable parameters are carefully controlled. ote that fit quality always improves for mixed ligation fits. P i (%) P i (%) lar-baldwin, K et al, J. Am. hem. Soc. 99,, ZnS ZnS ZnS Peptide 7 9 % sulfur ZnS ZnS ZnS Inorganic 7 9 % sulfur σ (Å x - ) In addition to P i, σ depends on ligation % sulfur Threshold energy changes apparent ligation S max ZnS ZnS 9 ZnS 7 alibrated E E (ev),s ev is enough to change a sulfur into a nitrogen!

7 EXAFS Distinction between S and rests largely on phase, which depends on E Zn-S Zn- (A - ) XAES spectra contain useful information regarding structure Quantitative comparisons (e.g., titration) requires accurate normalization. orrection for various artifacts (selfabsorption) requires accurate normalization. ommon normalization procedures were developed for extracting EXAFS and do not necessarily wor well for XAES. onventional ormalization Schemes onventional normalization is sensitive to bacground shape MBAK MBAK shows much weaer sensitivity onventional normalization is sensitive to range of data MBAK shows only slight sensitivity for E max ev above edge Absorption (cm /g)

8 onventional normalization misses changes in XAES possible difference specta should all be the same.. onventional.. MBAK reveals subtle changes when thiolate is added With new normalization, difference signal is detectable Dependence of XAES on Oxidation State ormalized Absorption II/II II/III III/III III/IV 7 9 Edge energy is poorly defined d(abs)/de Absorption Simon Bare, SLS worshop

9 X = U SV T l () l T X = usv = is the closest l-ran matrix to X (see Energy Time oulston et al., Science 7 (997) 9-9 Factor Analysis in hemistry, nd Ed. John Wiley & Sons, Y, 99 9