Part 1: What is XAFS? What does it tell us? The EXAFS equation. Part 2: Basic steps in the analysis Quick overview of typical analysis

Transcription

1 Introduction to XAFS Part 1: What is XAFS? What does it tell us? The EXAFS equation Part 2: Basic steps in the analysis Quick overview of typical analysis Tomorrow Measurement methods and examples The Advanced Photon Source is an Office of Science User Facility operated for the U.S. Department of Energy Office of Science by Argonne National Laboratory

2 Absorption Absorption What is XAFS? XAFS stands for X-ray Absorption Fine Structure and appears in the vicinity of absorption edges EXAFS Extended XAFS XANES X-ray Absorption Near Edge Structure L edge What is an absorption edge? Cu example K edge XANES E (ev) EXAFS E (ev)

3 EXAFS sensitive to local atomic structure Kr under pressure Nearest neighbor information: Distance Atomic type Coordination number Vibrational amplitude Typically useful for the first few coordination shells DiCicco etal PRB 54, 9086

4 XANES sensitive to chemical state and valence Chromium XANES

5 Normalized absorption XANES sensitive to chemical state and valence Fe compounds Fe2O3 FeO Fe3O4 Fe metal hematite E (ev)

6 Analyzing EXAFS After removing the smooth background k 2mE e h E = E x-ray - binding energy c(k) often multiplied by a power of k to emphasize high k region

7 Why is x-ray absorption useful? Short range order probe - crystallinity not required Element specific (Fe 7111 ev, Cu 8980, etc.) Near edge sensitive to chemistry Valence Site symmetry Extended structure sensitive to atomic neighbors Number and type of neighbors Distance to neighbors Disorder in neighbors Orientation of bonds (using x-ray polarization) Can be applied to dilute systems

8 Calculation of Absorption From Fermi s golden rule i Initial state: 1s or 2p electron localized in the core of the atom f Final state: outgoing photoelectron wave + interactions with the neighboring atoms r(e f ) Density of final states

9 The XAFS equation c ( k) ( k) N e ( k) kr 0 j k A k p sin 2kR k 0 j 2 j j j j j k 2mE e h The electron wavevector, E=E x-ray -E edge µ 0 - "atomic" absorption R - distance to atoms of shell j N - number of atoms in shell j A - amplitude factor p - polarization factor ψ - phase factor

10 Fourier Transform can separate the shells

11 The amplitude factor 2 A k S F k Q k e j 0 j j 2 / R j S amplitude reduction due to multi-electron excitation Typically (almost constant with k) F j (k) - magnitude of the complex backscattering amplitude f j (k,p) Q j (k) - disorder term - mean free path of photoelectron (includes contribution from core hole lifetime) f j (k,p) calculated with theory such as FEFF

12 EXAFS amplitude (F j (k)) Heavy atoms peak at higher k

13 The Phase factor k 2 ( k) ( k) j c j j c - p-wave (for K-edge) phase shift due to central atom potential j (k) - the phase of the backscattering factor f j (k,π) j (k) - phase factor related to the disorder of the j th shell

14 Backscattering phase ( j (k)) Approx. linear but overall phase can change

15 Central atom phase (2 c ) Also nearly linear the oscillation frequency remains uniform, but shifted to lower R

16 Polarization Factor Synchrotron radiation generally linearly polarized For the K-shell the photoelectron emitted with p-wave symmetry: p j (e) = 3<cos 2 > cos cos i N j i 3-fold or higher symmetry <cos 2 θ> = 1/3, p=1 Uniaxial symmetry (i.e. surface): c Q = [2c 0 cos 2 (Q) + c 90 sin 2 (Q)]/3

17 YBa 2 Cu 3 O 7 structure Sample is oriented powder: c-axis of all grains are aligned, no alignment of a-b axes. Two types of Cu sites: Planes have bonds in a-b plane Ribbons have bonds along c axis Consider the Cu-O near neighbor bonds: Polarization in a-b plane both sites contribute, but dominated by Plane sites Polarization along c axis the signal is dominated by the Ribbon sites

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19 Disorder terms k 2 ( k) φ j (k) ( k) j c j j 2 Q j (k) A k S F k Q k e j 0 j j 2 / Qj( k)exp i j( k) drpj ( r)exp i2 k( r Rj) P j (r) - real space distribution of atoms in shell j Simplest case is Gaussian disorder (i.e. thermal motion) To lowest order: Q j (k) = exp(-2k 2 s j2 ) (Debye-Waller factor) s j 2 - mean squared vibrational amplitude j (k)=0 R j

20 Change in disorder with temperature

21 Choice of Absorption edge Low energies require high vacuum and x-ray penetration small At high energies lifetime broadening washes out the spectra Most convenient to work in range 4-30 kev K edges: L edges: Ca Sn Sn U For lighter elements must work at low energies X-ray Raman allow low energy edges to be studied using higher energies.

22 L edges L 1-2s initial state - Same symmetry as K edge L 2,3-2p initial state - can have transitions to s or d final states Three possible contributions to c(k): c ss, c sd, c dd M dd M01 ss 2 M01M 21 sd M21 M01 / 2 c c c c Each contribution has its own polarization dependence p p p j 22 j 00 j cos cos 2 j j

23 L edges (cont.) Two important simplifications: M 01 typically about 0.2M 21 can generally ignore M 2 01 term unoriented or symmetric samples: p 02 = 0 For unoriented or symmetric samples L edges can be treated the same as the K edge For oriented asymmetric samples (i.e. surface site) the crossterm must be included (40% of dd term)

24 Multiple Scattering Strong Weak Collinear (focusing) Triangular Not important for first shell Must be considered in analyzing all shells above first Dominates at large distances Typically limits analysis to first few shells

25 Multiple scattering in Cu Calculated EXAFS for 1 st four shells R N Rel. Amp Type Single Single Triangle Triangle Single Triangle Triangle Single Collinear Collinear Collinear

26 Measuring XAFS Need to measure absorption Direct method: I 0 I 0 Ie t t ln( I / I ) ln( I / I) 0 0 Indirect methods (proportional to absorption) Fluorescence Electron Yield Reflectivity Optical emission

27 Normalized absorption Absorption k 2 c(k) Transform Magnitude Part 2: Analyzing the EXAFS E (ev) Normalization Background removal k (Å -1 ) Fourier Transform R (Å) Fitting to extract structural parameters E (ev)

28 Fourier filtering

29 Independent Data Points From information theory: N I = 2DkDR/p + 1 Dk - range of data used in k-space DR - range of data used in R-space Example: k range is 2-18 Å -1 R space filtering or fitting window is Å Then maximum number of independent fitting parameters is 11 If data range short (kmax ~ 10) then number of possible fitting parameters will be constrained.

30 Example of noisy data

31 Typical fitting parameters ΔE 0 match the experimental and theoretical edge positions Overall amplitude factor (S 02 ) Each shell needs disorder factor (σ 2 ) May also need ΔR ΔE 0 and S 0 2 can generally be common to all shells Therefore, typically need 4 parameters for simple first shell fit and 2 more for each additional shells.

32 Programs for Analyzing the EXAFS 4 main programs: Athena graphical interface to IFEFFIT analysis program for extracting XAFS and simple analysis Atoms calculate the atomic coordinates using crystallographic data FEFF theoretical calculation of amplitude and phase factors Artemis Graphical interface to Atoms, FEFF and IFEFFIT fitting to extract structural parameters All of these can be downloaded from (google: athena xafs)

33 Athena Set up parameters for: Background Removal Fourier transforming Plotting Analysis and data menus Align scans Remove glitches Note: Red buttons plot highlighted file. Purple buttons plot checked files (use for overplotting)

34 Athena reading in raw data Choose data channels Choose reference channels List of channels (Can also open.prj files for data previously read in)

35 Athena XANES fitting select Analysis linear combination fitting

36 Artemis - Atoms Open Atoms input file Cu.dat for online database of structure files see Hit Run Atoms This will generate a FEFF input file

37 Artemis FEFF input file

38 Artemis After running FEFF (only imported the first path in this example)

39 Artemis Read in data and set up for fitting first shell (Open athena project file and select data file) (Click on Path 1 to see path parameters these can be renamed or even math expressions)

40 Artemis Setting up the fit (Guess, Def, Set screen) ( check that fitting parameters agree with path parameters)

41 Artemis set up fitting ranges for the data (click on data file name - need to adjust r and k space ranges to match data)

42 Artemis after fitting

43 Start with Example projects CuData.prj Athena project containing example data CuFirstShell.apj Artemis project for fitting the first shell of Cu Cu.inp - Atoms input file for Cu metal Athena open a prj file and import all of the data. Try varying some of the transform parameters and see how it changes the data. Artemis Start by opening the Cu.inp file. This is an atoms structure file for Cu. Run atoms then Feff to generate Cu theory. Then load data from the Athena.prj file. Extra credit look at Cu4shell.apj to see an example of fitting first four shells, need to include multiple scattering paths to fit the longer bonds. Look at write in project journal under edit for some notes and hints Warning - don t close the plot window.