Transmission EXAFS

In addition to transmission, EXAFS data can be recorded through the detection of... 

The last three detection schemes apply only under very special circumstances. Transmission EXAFS is strictly a probe of bulk structure, i.e., more than about a thousand monolayers. The electron- and ion-yield detection methods, which are used in reflection rather than transmission schemes, provide surface sensitivity, 1-1,000 A, and are inherendy insensitive to bulk structure. X-ray fluorescence EXAFS has the widest range of sensitivity—from monolayer to bulk levels. The combination of electron or ion yield and transmission EXAFS measurements can provide structural information about the X-ray absorbing element at the surface and in the bulk, respectively, of a sample. 

Measuring EXAFS spectra In general, transmission EXAFS can be used, provided that the concentration of the element to be investigated is sufficiently high. The sample is placed between two ionization chambers, the signals of which are proportional to the incident intensity Iq and the transmitted intensity through the sample 7f The transmission of the sample is dependent on the thickness of the sample X and on the absorption coefficient, //, in a Beer-Lambert relationship ... 

Figure 11. Schematic diagram of a transmission EXAFS experiment. I0 and Ix refer to the incident and transmitted intensities, respectively.

Figure 17. In situ transmission EXAFS cell for the study of Ni oxide electrodes. (From Ref. 83, with permission.)...

Figure 4.1-10 Schematic of transmission EXAFS cell. Reproduced from reference 36 with permission.

The reflectivity spectra R(E) and the reflectivity-EXAFS Xr(E) = R(E) — Rq(E)]/R()(E) are similar, but not identical, to the absorption spectra and x(E) obtained in transmission mode. R(E) is related to the complex refraction index n(E) = 1 — 8(E) — ifl(E) and P(E) to the absorption coefficient /i(E) by ji fil/An. P and 8 are related to each other by a Kramers-Kronig transformation, p and 8 may be also separated in an oscillatory (A/ , AS) and non-oscillatory part (P0,80) and may be used to calculate Xr- This is, briefly, how the reflectivity EXAFS may be calculated from n(E). which itself can be obtained by experimental transmission EXAFS of standards, or by calculation with the help of commercial programs such as FEFF [109] with the parameters Rj, Nj and a, which characterize the near range order. The fit of the simulated to measured reflectivity yields then a set of appropriate structure parameters. This method of data evaluation has been developed and has been applied to a few oxide covered metal electrodes [110, 111], Fig. 48 depicts a condensed scheme of the necessary procedures for data evaluation. 

Fig. 48. Scheme for the calculation of the X-ray reflectivity from experimental transmission EXAFS of standards or calculation with a first set of structure parameters (Rj, Nj, [Pg.347]

Hie evaluation of the data yields Rjy Nj, and Sjy i.e., the near-range order parameters of the material seen from the absorber atom. XAS permits the evaluation of the near-range order in the vicinity of the atoms of various elements of one specimen if the energies of their absorption edges are different enough and thus are well separated within the spectrum. It should be mentioned that XAS in reflection looks similar to XAS in transmission mode, however it is different and the evaluation of measurements requires the comparison with reflectivity data calculated form transmission EXAFS spectra. These evaluation procedures involving Kramers-Kronig transform are described in the literature [i-v]. 

Fig. I3.X -ray absorption spectra (in arbotrary units) in a region including the terbium L3 edge. The spectra were taken at SSRL beam line 1-5 using a standard transmission EXAFS set up and Si 220 monochromator crystals.

Hannemann, S., Casapu, M., Grunwaldt, J.-D., Haider, P., Triissel, P., Baiker, A. and Welter, E. (2007) A versatile in situ spectroscopic cell for fluorescence/ transmission EXAFS and X-ray diffraction of heterogeneous catalysts in gas and liquid phase. J. Synchrotron Rad., 14, 345—354. 

The above formalism is quite general, and can be used to study the effects of doing transmission EXAFS on non-uniform samples and particles of all sorts. However, the mathematics quickly become forbidding if one looks at a realistic situation such as a particle illuminated by a Gaussian beam. Such situations require numerical methods. For a simple, analytically accessible example, imagine a uniform foil with a hole in it such that a fraction/of the beam goes through the hole. Then, we have... 

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