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

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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

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

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

(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

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’.

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

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

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