Your Second EXAFS Lecture

36b429d92ffc266d1abf718a18865c0e?s=47 Bruce Ravel
December 31, 2012

Your Second EXAFS Lecture

In which we explore the ins and outs of absorption spectroscopy, learn of some the ways to interpret our data, and prepare for the rest of an XAFS course

36b429d92ffc266d1abf718a18865c0e?s=128

Bruce Ravel

December 31, 2012
Tweet

Transcript

  1. 1.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Your Second EXAFS Lecture In which we explore the ins and outs of absorption spectroscopy, learn of some the ways to interpret our data, and prepare for the rest of this XAFS course Bruce Ravel Synchrotron Methods Group, Ceramics Division Materials Measurement Laboratory National Institute of Standards and Technology & Local Contact, Beamline X23A2 National Synchrotron Light Source EXAFS Data Analysis workshop 2011 Diamond Light Source November 14–17, 2011 1 / 34 Your Second EXAFS Lecture
  2. 2.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Copyright This document is copyright c 2010-2011 Bruce Ravel. This work is licensed under the Creative Commons Attribution-ShareAlike License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. You are free: to Share  to copy, distribute, and transmit the work to Remix  to adapt the work to make commercial use of the work Under the following conditions: Attribution – You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). Share Alike – If you alter, transform, or build upon this work, you may distribute the resulting work only under the same, similar or a compatible license. With the understanidng that: Waiver – Any of the above conditions can be waived if you get permission from the copyright holder. Public Domain – Where the work or any of its elements is in the public domain under applicable law, that status is in no way affected by the license. Other Rights – In no way are any of the following rights affected by the license: Your fair dealing or fair use rights, or other applicable copyright exceptions and limitations; The author’s moral rights; Rights other persons may have either in the work itself or in how the work is used, such as publicity or privacy rights. Notice – For any reuse or distribution, you must make clear to others the license terms of this work. This is a human-readable summary of the Legal Code (the full license). 2 / 34 Your Second EXAFS Lecture
  3. 3.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Abstract This lecture is the introductory lecture to a short course on the technique of X-ray Absorption Spectroscopy and the anaylsis of XAS data. This is not a ground-level introduction for the complete beginner. We will not derive the EXAFS equation nor explore the fundamental physics of the interaction between the photon and the absorbing atom. I assume that you have already been to the synchrotron and measured some XAS data. The lecture will set the stage for what is to come in this short course. We will motivate the importance of studying XAS in depth, even for those who will never make the practice of XAS their primary occupation. We will see an overview of many of the ways to interpret and analyze your XAS data. Finally, we look ahead to the end of the course to consider how good experimental practice and attention to statistics benefit every XAS practitioner. 3 / 34 Your Second EXAFS Lecture
  4. 4.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Acknowledgements Matt Newville, the author of , without which and would not exist. Shelly Kelly and Scott Calvin, old friends, relentless finders of software bugs, and long-time co-conspirators in this XAS education gig. My teachers, Ed Stern and John Rehr, who have done so much for the XAS community and who instilled in me a love of the discipline of XAS. My most wonderful boss, Dan Fischer, for letting me duck out of work to do things like this. The folks who make the great software I use to write my codes: Perl, wxPerl, Emacs, The Emacs Code Browser, Git, GitHub. The folks who make the great software used to write this talk: L A TEX, Beamer, The Gimp, Gnuplot. Paul Quinn and Diamond for the gracious invitation. And especially, all of you. It is astonishing and deeply flattering that so many people line up to hear what I have to say. 4 / 34 Your Second EXAFS Lecture
  5. 5.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS The measurement goals of an XAS experiment Somehow the wiggles in the XAS data tell us something about the atomic and electronic structure of the material measured. Valence the charge state of the absorber Species what kinds of atoms surround the absorber Number how many of those atoms there are Distance how far away they are Disorder how they are distributed due to thermal motion and structural disorder 5 / 34 Your Second EXAFS Lecture
  6. 6.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS What can XAS be measured on Well ... just about anything and with most elements of the periodic table No assumption of symmetry or periodicity Crystals Liquids or amorphous/highly disordered solids Mixed phases Thin films and engineered materials Surface sorbed species Organic and organometallic species Quasicrystals and on and on Beamline choice and sample preparation matter The beamline covers the absorber edge energy Sample is homogeneous Sample is not too thick, not too thin Sample is properly contained 6 / 34 Your Second EXAFS Lecture
  7. 7.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Who uses XAS Look to your left and right. If you study catalysis, you may be sitting next to a biologist. If you are a materials scientist, you might be sitting next to a geologist. This fall,∗ just at my beamline NSLS X23A2, the users include 2 groups from the microelectronics industry 2 groups of electrochemists a group working on fuel cell catalysts a group working on photocathode materials a group working on nuclear waste containment a group working on materials for nuclear reactor vessels to say nothing of the biologists, enironmental scientists, geologists, and chemical scientists visiting the other beamlines at NSLS at the same time. 7 / 34 Your Second EXAFS Lecture ∗ September-December 2011
  8. 8.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Sometimes XAS is easy... Here we have a single scan of the Ge K edge of a 50 nm film of Ge/Sb alloy on silica measured at glancing angle on a beamline (NSLS X23A2) without focusing optics and using a Si(311) crystal. 8 / 34 Your Second EXAFS Lecture These data are courtesy of Joseph Washington and Eric Joseph (IBM Research)
  9. 9.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Sometimes XAS is hard... Here are 42 scans taken over the course of 22 hours at APS 20BM (one of the top XAS beamlines in North America) on a sample with 3 mM Hg bound to an engineered DNA complex. Each scan is quite noisy, but the central limit theorem always works. We were able to use the resulting ˜ χ(R) data to good effect. 9 / 34 Your Second EXAFS Lecture B. Ravel, et al., EXAFS studies of catalytic DNA sensors for mercury contamination of water, Radiation Physics and Chemistry 78:10 (2009) pp S75-S79. DOI:10.1016/j.radphyschem.2009.05.024
  10. 10.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS In any case... Regardless of how easy or difficult an experiment is, we have to know how to Evaluate the statistical quality of our data 10 / 34 Your Second EXAFS Lecture
  11. 11.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS In any case... Regardless of how easy or difficult an experiment is, we have to know how to Evaluate the statistical quality of our data Recognize both statistical and systematic errors in our data and understand how to address each kind of error 10 / 34 Your Second EXAFS Lecture
  12. 12.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS In any case... Regardless of how easy or difficult an experiment is, we have to know how to Evaluate the statistical quality of our data Recognize both statistical and systematic errors in our data and understand how to address each kind of error Know when to stop measuring a sample – I mean this both in the sense of knowing how far above the edge to measure and knowing how many repetitions to measure 10 / 34 Your Second EXAFS Lecture
  13. 13.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS In any case... Regardless of how easy or difficult an experiment is, we have to know how to Evaluate the statistical quality of our data Recognize both statistical and systematic errors in our data and understand how to address each kind of error Know when to stop measuring a sample – I mean this both in the sense of knowing how far above the edge to measure and knowing how many repetitions to measure Know how to process our data for further analysis 10 / 34 Your Second EXAFS Lecture
  14. 14.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Sometimes we elaborate experiments New technologies and modern, 3rd generation synchrotrons offer in- triguing new experimental possibilties. In each case, one of the results of these elaborate experiments is an XAS spectrum. 11 / 34 Your Second EXAFS Lecture
  15. 15.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Imaging and µXAS Here is an extraordinary XRF map of a metal hyperaccumulating plant that also forms star-shaped, inorganic nodules on its leaves. 12 / 34 Your Second EXAFS Lecture R. Tappero, et al., Hyperaccumulator Alyssum murale relies on a different metal storage mechanism for cobalt than for nickel, New Phytologist 175:4 (2007) pp 641-654 DOI:10.1016/10.1111/j.1469-8137.2007.02134.x
  16. 16.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Imaging and µXAS Here is an extraordinary XRF map of a metal hyperaccumulating plant that also forms star-shaped, inorganic nodules on its leaves. While the image is itself a great result, we end up measuring XAS spectra with the microbeam. 12 / 34 Your Second EXAFS Lecture R. Tappero, et al., Hyperaccumulator Alyssum murale relies on a different metal storage mechanism for cobalt than for nickel, New Phytologist 175:4 (2007) pp 641-654 DOI:10.1016/10.1111/j.1469-8137.2007.02134.x
  17. 17.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Time-resolved XAS and mountains of data Energy dispersive XAS and quick-XAS are two ways of doing time-resolved XAS with 10 ms to 10 s time resolution. Both approaches require specially- equipped beamlines and both focus on the dynamics of the system. 13 / 34 Your Second EXAFS Lecture Data from W.A. Caliebe et al., HASYLAB Annual Report (2006) pp. 283-284; EDE schematic from SPring-8 press release, 30 April, 2009; QXAS schematic from SLS SuperXAS beamline webpage.
  18. 18.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Time-resolved XAS and mountains of data Energy dispersive XAS and quick-XAS are two ways of doing time-resolved XAS with 10 ms to 10 s time resolution. Both approaches require specially- equipped beamlines and both focus on the dynamics of the system. At then end of the day, these are XAS spectra. 13 / 34 Your Second EXAFS Lecture Data from W.A. Caliebe et al., HASYLAB Annual Report (2006) pp. 283-284; EDE schematic from SPring-8 press release, 30 April, 2009; QXAS schematic from SLS SuperXAS beamline webpage.
  19. 19.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Diffraction Anomalous Fine Structure With coordinated motion between monochromator and goniometer, DAFS measures the height of a diffraction peak with respect to energy through the resonant energy of an atom in the crystal. 14 / 34 Your Second EXAFS Lecture B. Ravel et al., X-ray-absorption edge separation using diffraction anomalous fine structure, Phys. Rev. B 60 (1999) pp 778-785. DOI:10.1103/PhysRevB.60.778
  20. 20.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Diffraction Anomalous Fine Structure With coordinated motion between monochromator and goniometer, DAFS measures the height of a diffraction peak with respect to energy through the resonant energy of an atom in the crystal. In the end, we extract a site-specific χ(k) function which is analyzed like normal EXAFS. 14 / 34 Your Second EXAFS Lecture B. Ravel et al., X-ray-absorption edge separation using diffraction anomalous fine structure, Phys. Rev. B 60 (1999) pp 778-785. DOI:10.1103/PhysRevB.60.778
  21. 21.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Non-resonant Inelastic X-ray Scattering Here is NIXS data from a non-resonant inelastic scattering data on CaZrTi2O7 from 20ID at APS. 15 / 34 Your Second EXAFS Lecture Lerix-I instrument: G. Seidler et al.; Data: D. Reid, N.C. Hyatt, B. Ravel, to be published in PRB
  22. 22.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Non-resonant Inelastic X-ray Scattering Here is NIXS data from a non-resonant inelastic scattering data on CaZrTi2O7 from 20ID at APS. Again, a XANES spectrum comes from this elaborate experiment. 15 / 34 Your Second EXAFS Lecture Lerix-I instrument: G. Seidler et al.; Data: D. Reid, N.C. Hyatt, B. Ravel, to be published in PRB
  23. 23.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Some vocabulary Words commonly used to describe specific parts of the XANES spectrum. pre-edge Small (possibly large, certainly meaningful!) features between the Fermi energy and the threshold edge The main rising part of XAS spectrum near-edge Characteristic features above the edge white line Large, prominent peak just above the edge, particularly in L or M edge spectra The EXAFS, then, is the data beyond the near-edge. 16 / 34 Your Second EXAFS Lecture
  24. 24.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Fingerprinting The simplest way of using XAS is to simply identify chemical species in a sample of unknown composition. 1 Ferrihydrite? 2 Iron pyrite? 3 Iron metal? 4 Hematite? 17 / 34 Your Second EXAFS Lecture
  25. 25.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Fingerprinting The simplest way of using XAS is to simply identify chemical species in a sample of unknown composition. 1 Ferrihydrite 2 Iron pyrite 3 Iron metal 4 Hematite Compare the signal from your ( dirt / catalyst / paint chip / animal tissue / whatever ) with the standards to identify the dominant species. 17 / 34 Your Second EXAFS Lecture
  26. 26.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS XANES Interpretation Fingerprinting, though useful, is purely qualitative. There are a variety of quantitive tools available for interpreting XANES data. 1 Positioning 2 Peak fitting 3 Linear combination fitting 4 Principle components analysis 5 Application of theory 18 / 34 Your Second EXAFS Lecture
  27. 27.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS XANES: Positioning U6+ is partially reduced by G. sulfurreducens under a variety of conditions. By measuring the edge positions and comparing to U6+ and U4+ standards, the amount of reduction is quatified between 24% and 88%. Farges et al. showed that Ti clusters by valence when the position of the largest pre-edge is plotted against peak position in energy. 19 / 34 Your Second EXAFS Lecture B.H. Jeon et el., Microbial Reduction of U(VI) at the Solid-Water Interface, Environ. Sci. Technol. 38(21) pp. 5649-5655. (2004), DOI:10.1021/es0496120 F. Farges, G.E. Brown, Jr., and J.J. Rehr, PRB 56:4, (1997) p. 1809. DOI:10.1103/PhysRevB.56.1809
  28. 28.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS XANES: Positioning U6+ is partially reduced by G. sulfurreducens under a variety of conditions. By measuring the edge positions and comparing to U6+ and U4+ standards, the amount of reduction is quatified between 24% and 88%. Farges et al. showed that Ti clusters by valence when the position of the largest pre-edge is plotted against peak position in energy. Either analysis requires careful attention to data processing. 19 / 34 Your Second EXAFS Lecture B.H. Jeon et el., Microbial Reduction of U(VI) at the Solid-Water Interface, Environ. Sci. Technol. 38(21) pp. 5649-5655. (2004), DOI:10.1021/es0496120 F. Farges, G.E. Brown, Jr., and J.J. Rehr, PRB 56:4, (1997) p. 1809. DOI:10.1103/PhysRevB.56.1809
  29. 29.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS XANES: Peak fiting Peak fitting presumes that the XANES data can be explained as a sum of simple line shapes – usually a combination of arctangent (for the edge step) Gaussian Lorentzian Voight or pseudo-Voight The shortcoming of peak fitting It is difficult in general to ascribe physical meaning to the lineshapes. Peak fitting is, therefore, best used to quantify changes in a related ensemble of data. 20 / 34 Your Second EXAFS Lecture
  30. 30.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS XANES: Linear Combination Fitting In this example, XAS is measured as a function of time as a gold chloride is reduced to metallic gold in the presence of sulfurous biomass. At an intermediate time step, the spectrum is understood as a linear combination of the initial state (Au3+ Cl), the final state (Au metal), and an intermediate state (some Au1+ sulfide species). (There will be an entire lecture on this topic tomorrow.) 21 / 34 Your Second EXAFS Lecture M. Lengke et el., Mechanisms of Gold Bioaccumulation by Filamentous Cyanobacteria from Gold(III)-Chloride Complex, Environ. Sci. Technol. 40(20) p. 6304-6309. (2006), DOI:10.1021/es061040r
  31. 31.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS XANES: Principle Components Analysis PCA is a bit of linear algebra which breaks down an ensemble of related data into abstract components. The components can then be used to try to construct a standard as a test to see whether that standard is present in the ensemble. The number of species represented in the ensemble is related to the number of statistically significant components. 22 / 34 Your Second EXAFS Lecture The data in the upper left are from M. Lengke et el., Environ. Sci. Technol. 40(20) p. 6304-6309. (2006), DOI:10.1021/es061040r. That paper did not include any PCA analysis.
  32. 32.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS XANES: Theory Forward simulation with 9 Fitting of XANES spectra is not built into , but other options exist by Benfatto and Della Longa allows variation of structural parameters to refine a full multiple scattering calculation against measured data F I by Smolentsev and Soldatov fits measured data by pre-computing spectra on a multidimensional grid of caluclated spectra and interpolating to best fit the data. It can use either or Joly’s 23 / 34 Your Second EXAFS Lecture Feff homepage, http://leonardo.phys.washington.edu/feff/ MXAN homepage, http://www.esrf.eu/computing/scientific/MXAN/index.html FitIt homepage, http://www.nano.sfedu.ru/index.html
  33. 33.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS EXAFS analysis can be simple... Here is a quick first shell fit to the Fe K edge of lepidocrocite, γ-FeO(OH). Using and a simple first shell fitting model, it takes under a minute to fill in all the boxes and to get a fit of this quality, providing a first stab at near-neighbor coordination and distance. Fit: N = 4.6 ± 0.3, R = 2.01 ± 0.01, σ2 = 0.00586 ± 0.00088 Crystal structure: N = 5, ¯ R = 2.05, C2 = 0.00679 24 / 34 Your Second EXAFS Lecture
  34. 34.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS EXAFS analysis can be sophisticated... Well ... this is the point of this course! You will learn how to: 1 Use one or more to fit your data 2 Build interesting contraints between and restraints on your fitting parameters 3 Do multiple data set fitting 4 Do multiple k-weight fitting 5 Evaluate the statistical quality of your fits 6 Present your fitting results defensibly in journal articles 25 / 34 Your Second EXAFS Lecture
  35. 35.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS EXAFS analysis can be quite elaborate... Oxygen Octahedral site Tetrahedral site Manganese zinc ferrite nanoparticles Each element can occupy each either metal site Oxygen vacancies can exist Data collected at 3 edges and on various sample preparations Scott created a fitting model using all the data simultaneously and considering occupancies of each metal on each site, oxygen vacancy, and nanoparticle undercoordination 26 / 34 Your Second EXAFS Lecture S. Calvin et el., Multiedge refinement of extended x-ray-absorption fine structure of manganese zinc ferrite nanoparticles, Phys. Rev. B 66(22) p. 224405. (2002), DOI:10.1103/PhysRevB.66.224405 Ferrite image from http://wikis.lib.ncsu.edu/index.php/Image:Size21.png
  36. 36.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS A simple picture of X-ray absorption An incident x-ray of energy E is absorbed, destroying a core electron of binding energy E0 and emitting a photo-electron with kinetic energy (E − E0 ). The core state is eventually filled, ejecting a fluorescent x-ray or an Auger electron. An empty final state is required. No available state, no absorption! When the incident x-ray energy is larger than the binding energy, there is a sharp increase in absorption. For an isolated atom, µ(E) has a sharp step at the core-level binding energy and is a smooth function of energy above the edge. 27 / 34 Your Second EXAFS Lecture
  37. 37.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS X-ray absorption in condensed matter The ejected photo-electron can scatter from neighboring atoms. R has some relationship to λ and there is a phase shift associated with the scattering event. Thus the outgoing and scattered waves interfere. The scattering of the photo-electron wave function interferes with itself. µ(E) depends on the density of states with energy (E − E0 ) at the absorbing atom. This interference at the absorbing atom will vary with energy, causing the oscillations in µ(E). 27 / 34 Your Second EXAFS Lecture
  38. 38.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Computing X-ray Absorption from First Principles In XAS we measure the dipole mediated[1] transition of an electron in a deep core[2] state |i into an unoccupied[3] state |f : Fermi’s Golden Rule µ(E) ∝ Ef >EF f f |ˆ· r|i 2 δ(Ef ) Broadly speaking, there are two ways to solve this equation: 1 Accurately represent |i [4] and |f [5] , then evaluate the integral directly. This is the approach taken, for example, by molecular orbital theory. 2 Use multiple scattering theory, AKA a Green’s function[6] or propagator formalism: µ(E) ∝ − 1 π Im i|ˆ∗ · r G(r, r ; E)ˆ· r |i Θ(E − EF ). 1. A photon interacts with an electron 2. Typically a 1s, 2s, or 2p electron 3. A bound or continuum state not already containing an electron 4. Easy  basic quantum mechanics 5. Hard work, lots of computation 6. G is called a Green’s function. 28 / 34 Your Second EXAFS Lecture
  39. 39.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Real Space Multiple Scattering In multiple scattering theory, all the hard work is in computing the Green’s function. G the function that describes all possible ways for a photoelectron to interact with the surrounding atoms G0 the function that describes how an electron propagates between two points in space t the function that describes how a photo-electron scatters from a neighboring atom Expanding the Green’s function G = 1 − G0t −1 G0 (XANES) =G0 + G0 t G0 + G0 t G0 t G0 + G0 t G0 t G0 t G0 + ... (EXAFS) 29 / 34 Your Second EXAFS Lecture
  40. 40.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Scattering Paths Full multiple scattering (XANES): Solving G = 1 − G0t −1 G0 considers ALL paths within some cluster of atoms: single scattering path x x (2 legs) double scattering path x x x (3 legs) triple scattering path x x x (4 legs) EXAFS path expansion The clever thing about is that each term is further expanded as a sum of all paths of that order. G0 t G0 is expanded as a sum of single scattering paths G0 t G0 t G0 is a sum of all double scattering paths and so on. 30 / 34 Your Second EXAFS Lecture
  41. 41.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Real space multiple scattering in pictures Here are some examples (in two dimensions) of single, double, and triple scattering paths. For SS, expands G0 t G0 , computing the three SS paths shown and all others (up to some maximum length). SS and collinear MS paths tend to be the dominant contributions to the EXAFS. 31 / 34 Your Second EXAFS Lecture
  42. 42.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Real space multiple scattering in pictures Here are some examples (in two dimensions) of single, double, and triple scattering paths. For SS, expands G0 t G0 , computing the three SS paths shown and all others (up to some maximum length). SS and collinear MS paths tend to be the dominant contributions to the EXAFS. The trick to EXAFS analysis Artemis helps you evaluate each path and choose which ones to include in a fit. 31 / 34 Your Second EXAFS Lecture
  43. 43.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS The EXAFS equation For each kind of path, we evaluate the EXAFS equation: χ(k, Γ) = (NΓ S2 0 )FΓ (k) 2 kR2 Γ sin (2kRΓ + ΦΓ (k))e−2σ2 Γ k2 e−2RΓ/λ(k) (1) χtheory (k) = Γ χ(k, Γ) (2) RΓ = R0,Γ + ∆RΓ (3) k =N (E0 − ∆E0 ) (4) (and therefore and ) treats SS and MS paths equivalently. FΓ and φΓ are the effective scattering amplitude and phase shift for the path. Here is something you will hear me say frequently In the terms in red are not themselves the fitting parameters. They are written in terms of the actual fitting parameters. 32 / 34 Your Second EXAFS Lecture
  44. 44.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS XAS out of the vacuum You will never do an XAS experiment without some experimental con- text. You always have some priot knowledge about your system. You XAS results must be interpreted in the context of the Electron microscopy or EDX X-ray diffraction UV/Vis, IR or Raman spectroscopy TGA, Mass spec, ICP, etc. ... and so on that you have also done on your sample. 33 / 34 Your Second EXAFS Lecture
  45. 45.

    Why we measure XAS How we measure XAS How we

    use XAS How we understand XAS Ready, set, go! Shall we begin? 34 / 34 Your Second EXAFS Lecture