Energy threshold, EXAFS

In the present study we have extracted the EXAFS from the experimentally recorded X-ray absorption spectra following the method described in detail in Ref. (l , 20). In this procedure, a value for the energy threshold of the absorption edge is chosen to convert the energy scale into k-space. Then a smooth background described by a set of cubic splines is subtracted from the EXAFS in order to separate the non-osciHatory part in ln(l /i) and, finally, the EXAFS is multiplied by a factor k and divided by a function characteristic of the atomic absorption cross section (20). 

The last two result in damping terms, while the interatom separation can be determined very accurately, essentially by a Fourier transform of the oscillatory part of the pattern. Although there may be very little atomic structure in the continuum, it cannot be completely neglected. There is one situation in which care is needed in the interpretation doubly-excited configurations may extend far into the continuum above an inner-shell threshold and may coincide in energy with EXAFS for some atoms. They are then not easily separated from each other, which may become a source of error in the interpretation. 

Fig. 1. (a) Reproduction of a historic spectrogram of the Sm Ljn absorption line in Sm2(S04)2 + aq. The dark FeK j, fluorescence lines serve as calibration marks for the energy scale. The energy increases from the left to the right (adapted from Nishina 1925). (b) Photometric curve of the spectrogram in fig. la. The narrow spike at the Lm absorption threshold corresponds to the white line in (a). Noise masks the absorption fine structure at the high-energy side (EXAFS) of the spectrum. Note that the photometric curve exhibits the transmitted intensity, not the absorption ld (adapted from Nishina 1925). 

Local surface structure and coordination numbers of neighbouring atoms can be extracted from the analysis of extended X-ray absorption fine structures (EXAFS). The essential feature of the method22 is the excitation of a core-hole by monoenergetic photons modulation of the absorption cross-section with energy above the excitation threshold provides information on the distances between neighbouring atoms. A more surface-sensitive version (SEXAFS) monitors the photoemitted or Auger electrons, where the electron escape depth is small ( 1 nm) and discriminates in favour of surface atoms over those within the bulk solid. Model compounds, where bond distances and atomic environments are known, are required as standards. 

The spectral features of XANES have been interpreted as the result of multiple-scattering resonances of the low kinetic energy photoelectrons. Examples of the strong and sharp XANES peaks above the continuum threshold and below the beginning of the weak EXAFS oscillations in the absorption spectra of condensed molecular complexes, are shown in Fig. 4.6. 

Monoenergetic photons excite a core hole. The modulation of the absorption cross section with energy at 100 - 500 eV above the excitation threshold yields information on the radial distances to the neighbouring atoms. The cross section can be measured by fluorescence as the core holes decay or by attenuation of the transmitted photon beam. EXAFS is one of the many fine -structure techniques. 

An EXAFS spectrum is a plot of the X-ray intensity transmitted by the sample, as a function of the energy E = fiv of the monochromatic X-rays. Each time E reaches the threshold for photoemission of a core electron with binding energy... 

Fig. 5. Schematic of X-ray absorption cross section as a function of the photon energy showing the threshold region (including pre-edge and edge regions), the EXAFS region, and relevant electron processes excitation of a core electron to a higher unoccupied atomic level, to the Fermi level (at absorption edge), and to the continuum (atom ionization).

Fig. 13. Pictorial view of the final-state radial wave functions relevant for core transitions in a molecule. The core transitions take place in an effective molecular potential seen by the excited photoelectron. The final states in the continuum XANES region are quasi-bound multiplescattering resonances (MSR), also called shape resonances. Below the continuum threshold E0 transitions to unoccupied valence states appear. 0 is the energy of the core ionization potential (from ESCA). Ec is the energy where the wavelength of initially excited photoelectrons conforms to the interatomic distance. For E < E0, discrete transitions to unoccupied valence states. E0 < E < Ec, continuum XANES. For < Ec, the EXAFS theory breaks down. The dotted curves show the wave functions of the initially excited photoelectron. From Bianconi (30).

If the independent variable, E, is replaced by the photoelectron wave-vector, k = 2ir/A = V2me(E — E0)/h2, where me is the mass of the electron, and E0 is the threshold energy for the excitation of a core electron, the EXAFS is given by ... 

TTie solution phase ionization potentials of Br in 16 solvents have been determined by photoeiectron emission spectroscopic technique. The values obtained as the threshold energy E for Br" in various solvents are found to be correlated well with the Mayer-Gutmann acceptor number of solvent. The reorganization energy AC, of solvent after the photoionization of Br" has been obtained from the E value. The AG, values are well reproduced by using a simple model which incorporates the dipole-dipole repulsion and the hydrogen-bond formation in the first solvation layer. The solvation structures of Br" determined by EXAFS are used for the AG, calculation. 

The characteristics of reforming catalysts make them one of the most frequent cases where EXAFS is used. The very small metallic particles cannot be detected in transmission electron microscopy the long range order required for XRD analysis is absent, and the low metal contents make XPS analysis difficult. The observation of XANES structures at Pi and Re thresholds can be used to determine the electronic state. Some examples of reference compounds are shown in Figure 11.10. In particular a sharp peak (called a white line for historical reasons) is visible at the edge with an intensity related to the oxidisation state of the element. This peak in the absorption coefficient is a consequence of the existence of the empty electron states close to zero binding energy. 

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