The Ramsauer-Townsend effect in X-ray Absorption Spectroscopy

This is a short overview of how to recognize and understand the effect of a Ramsauer-Townsend resonance in EXAFS analysis.

Transcript

1. The Ramsauer-Townsend effect in EXAFS Bruce Ravel Synchrotron Methods Group, Ceramics Division Materials Measurement Laboratory National Institute of Standards and Technology & Local Contact, Beamline X23A2 National Synchrotron Light Source July 3, 2012 1 / 11 The Ramsauer-Townsend effect in EXAFS
2. 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 / 11 The Ramsauer-Townsend effect in EXAFS
3. Here’s a beginner’s question Here are data on a gold foil. Gold is an FCC metal with 12 neighbors in the first coordination shell at ∼ 2.9 ˚ A and 6 in the second shell at ∼ 4.1 ˚ A. The Fourier transform of these data – done with k-weight = 1 in order to emphasize the point – clearly show a split peak in the |˜ χ(R)| spectrum with peaks at about 2.5 ˚ A and 3.0 ˚ A. How can this be? 3 / 11 The Ramsauer-Townsend effect in EXAFS
4. Sum of sine waves Here is an overly simplified representation of the EXAFS signal using pure, undamped sine waves. The blue wave has a frequency of 5, representing a distance of 2.5 ˚ A. The red wave has a frequency of 6, representing a distance of 3 ˚ A. The green wave is the sum of those two. This summation results in a beating pattern. 4 / 11 The Ramsauer-Townsend effect in EXAFS
5. The Fourier transform of the sum Here I show an EXAFS-like, finite-range Fourier transform over 2k. The k-range was 3 ˚ A – 16 ˚ A, the window sill was 1 ˚ A, and a Kaiser-Bessel window was used. The blue and red waves have peaks at 2.5 ˚ A and 3 ˚ A, as expected. The Fourier transform of the sum, the green wave, has peaks at both 2.5 ˚ A and at 3 ˚ A. 5 / 11 The Ramsauer-Townsend effect in EXAFS
6. Interpreting the Au foil data Does this mean that we actually have 2 near-neighbor distances in our gold foil? 6 / 11 The Ramsauer-Townsend effect in EXAFS
7. Interpreting the Au foil data Does this mean that we actually have 2 near-neighbor distances in our gold foil? Certainly not! 6 / 11 The Ramsauer-Townsend effect in EXAFS
8. 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) RΓ = R0,Γ + ∆RΓ (2) k =N (E0 − ∆E0 ) (3) It is certainly true that we sum up terms with sin(2kRΓ ) (like in our simple, sine-wave example), however we also have the terms FΓ (k) and ΦΓ (k) in the EXAFS equation. What does FΓ (k) look like for something as heavy as Au? 7 / 11 The Ramsauer-Townsend effect in EXAFS
9. The scattering amplitude Here is FΓ (k). as calculated by for the first shell Au atom in FCC gold. The minimum just above 5 ˚ A will introduce structure to the EXAFS equation that resembles the beat due to the sum of sine waves. 8 / 11 The Ramsauer-Townsend effect in EXAFS Here I am plotting columns 1 v. 3 from the file ‘feff0001.dat’.
10. Simple model from quantum scattering theory The basic physics of this phenomenon is related to the well-known problem of scattering from a square potential. All first-year physics graduate students have to solve the 1D problem of scattering from a square potential. In the quantum problem, there is a large tunneling probability at certain enegies (wavelengths). At the minimum in FΓ (k), we are seeing tranmission of the photoelectron through the scatterer. 9 / 11 The Ramsauer-Townsend effect in EXAFS These images from Wikimedia Commons. See the Wikipedia “Rectangular potential barrier” page
11. Feff’s calculation of the first shell in Au accounts for the Ramsauer-Townsend effect correctly in its calculation, enabling analysis in the same manner as for lighter elements. One moral of this story is that it is always wise to compare a calculation with your data before jumping to conclusions about the interpetation of the peaks in ˜ χ(R). ˜ χ(R) is NOT a radial distribution function! The Ramsauer-Townsend effect on FΓ (k) is among the many reasons ˜ χ(R) is NOT an RDF. 10 / 11 The Ramsauer-Townsend effect in EXAFS
12. Bibliography Searching for “Ramsauer Townsend EXAFS” on Google Scholar turns up dozens of examples of papers discussing this phenomenon in EXAFS. Here is a small bibliography of papers explaining this topic in much more depth than this presentation. 1 P.A. Lee et al., Extended x-ray absorption fine structure–its strengths and limitations as a structural tool, Rev. Mod. Phys. 53, 769-806 (1981) doi:10.1103/RevModPhys.53.769 2 A.G. McKale et al., Generalized Ramsauer-Townsend effect in extended x-ray-absorption fine structure, Phys. Rev. B 38, 10919-10921 (1988) doi:10.1103/PhysRevB.38.10919 3 J.J. Rehr, et al., X-ray-absorption fine structure in embedded atoms, Phys. Rev. B 49, 12347-12350 (1994) doi:10.1103/PhysRevB.49.12347 Here are some discussions from the Ifeffit Mailing List on this topic: http://millenia.cars.aps.anl.gov/pipermail/ifeffit/2006-November/007243.html http://millenia.cars.aps.anl.gov/pipermail/ifeffit/2011-October/010241.html 11 / 11 The Ramsauer-Townsend effect in EXAFS