EXAFS constructive interference

Fig.1. TiiC edge X-ray absorption spectrum of the (dense) titanosilicate mineral aenigmatite showing the partition into XANES and EXAFS regions. The physical processes leading to the different features in the spectrum are depicted schematically a pre-edge absorption featmes (magnified in the inset), b multiple scattering features, c single scattering featnres which lead to minima and maxima in the spectrum in the cases of d constructive interference and e destructive interference...

Fig. 2. The mechanism leading to EXAFS for the first ligand shell of an iron porphyrin. (Left) Constructive interference of the outgoing and backscattered waves leads to an increase in absorption. (Right) Destructive interference leads to a decrease in absorption. Reproduced with permission fi om Ref. [13]...

Fig. 16.9 An electron photoionized in an EXAFS experiment may be thought of as giving rise to a transient standing wave. In the upper diagram the wave from the emitted electron (ejected from the larger black, metal, atom) constructively interferes along the metal-ligand axis with the reflected wave from the ligand.

Fig. 8. In EXAFS, the absorption of X-ray radiation is determined as a function of photon energy. The photoelectrons generated in the photoabsorption process at an adsorbate-atom are backscattered from substrate atoms and lead to modulation of the absorption cross section through interference phenomena. In the center figure the lines of equal phase of the backscattered radiation go through the excited atom (see top) resulting in constructive interference, whereas in the bottom figure the photoelectron kinetic energy is slightly different, resulting in destructive interference at the position of the excited atom.

Figure 2 Molybdenum K-edge X-ray absorption spectrum, ln(i /i ) versus X-ray energy (eV), for molybdenum metal foil (25- jjn thick), obtained by transmission at 77 K with synchrotron radiation. The energy-dependent constructive and destructive interference of outgoing and backscattered photoelectrons at molybdenum produces the EXAFS peaks and valleys, respectively. The preedge and edge structures marked here are known together as X-ray absorption near edge structure, XANES and EXAFS are provided in a new compilation of literature entitled X-rsy Absorption Fine Structure (S.S. Hasain, ed.) Ellis Norwood, New York, 1991.

Extended X-ray absorption fine structure (EXAFS) A technique for observing the local structure around a metal centre, using X-rays from a synchrotron source. The atom of interest absorbs photons at a characteristic wavelength and the emitted electrons, undergoing constructive or destructive interference as they are scattered by the surrounding atoms, modulate the absorption spectrum. The modulation frequency corresponds directly to the distance of the surrounding atoms while the amplitude is related to the type and number of atoms. In particular, bond lengths and coordination numbers may be derived. 

FIGURE 2.23 The EXAFS process (a) the photoelectron is ejected by X-ray absorption, (b) the outgoing photoelectron wave (solid line) is backscattered constructively by the surrounding atoms (dashed line), and (c) destructive interference between the outgoing and the backscattered wave. 

Figure 2.13 A schematic representation of the EXAFS process. An atom (filled circle) absorbs X-rays, emitting a photoelectron wave which is back-scattered by neighbouring atoms (hatched circles). The solid circles denote outgoing electron waves and the broken circles back-scattered electron waves. Constructive or destructive interference can occur when the waves overlap.

Fig. 10.16. Absorption of X-rays as a function of photon energy h by a free atom and by an atom in a lattice. The spherical electron wave from the central atom is scattered back by the neighbouring atoms, which leads to interference, which is constructive or destructive depending on the wavelength of the electron wave (or the kinetic energy of the electron) and the distance between the atoms. As a result, the X-ray absorption probability is modulated and the spectrum shows fine structure which represents the EXAFS spectrum [37],...

Extended X-ray Absorption Fine Structure (EXAFS) is the oscillating portion of an X-ray absorption spectrum that is a result of constructive and destructive interference of the outgoing wave of a photoelectron and the backscatter from the surrounding atoms [26]. EXAFS is a unique tool for structural determination, as it does not depend on long-range order. The measurement of a particular X-ray absorption edge means that it is element specific. In addition, modern X-ray sources from synchrotrons are intense enough to make measurements on dilute samples, for example on the impurities doped into host crystals. 

---