EXAFS destructive interference

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.

Figure 3 Schematic illustration of the EXAFS phenomenon (A) outgoing photoelectron (solid curve) from X-ray absorbing atom (B) destructive interference at the absorbing atom between outgoing (solid curve) and backscattered (dashed curve) photoelectron from neighboring atom (C) constructhra interference at the absorbing atom between outgoing (solid curve) and backscat-tared (dashed curve) photoelectron from neighboring atom. Adapted from T. M. Hayes and J. B. Boyce. Solid State Phys. 37.173,1982.

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.

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. 

Clear evidence for the close approach of metal atoms in Cdy-metal-lothionein is well established by Cd NMR spectroscopy. Indications of the intermetallic distances involved for cadmium and other metals have been sought from EXAFS. Although some indications of back-scattering of metals bound within metallothioneins have been obtained (31, 47), the principal conclusion is that these metal-metal separations are not coherent. Therefore, the backscattered waves, especially with their high frequency at distances >3 A, engage in destructive interference, which effectively renders them silent in the EXAFS. 

By comparing the total cross section obtained from a full multiple scattering calculation shown in the upper part of Fig. 10 with the EXAFS term we observe that the two spectra are very similar above 3 Rydberg. This effect is determined by the destructive interference between the n 3 contributions. The negative interference between n = 3 and n = 4 contributions is clearly shown in Fig. 10. This destructive interference between higher order contributions is characteristic of octahedral coordination and disappears for distortion of the octahedra. 

In microcrystalline or amorphous materials, EXAFS has proved its usefulness since a long time. Limits and weaknesses of the technique have also been put forward variation of the EXAFS signal with temperature, occurrence of multiple scattering or destructive interference effects which complicate the extraction of the information. Sect. 2.2 presents how it is possible to overcome these apparent drawbacks and to obtain from them more information about the coordination site, its possible distortion and even about 3D organization of the material. 

Fig. 3. Schematic of the outgoing and backscattered photoelectron wave, which illustrates the concept of interference in EXAFS. The central atom is the absorbing atom, and the photoelectron is backscattered from the surrounding atoms, (a) The backscattered wave is in phase with the outgoing wave at energy E. This leads to an increase in the absorption coefficient at ,. (b) At energy Ei the backscattered wave destructively interferes with the outgoing wave, which leads to a decrease in the cross section at Ei. (c) Attenuation in the cross section in the absorption coefficient. [Adapted from D. B. Goodin, Ph.D. Dissertation, University of California, Berkeley. Lawrence Berkeley Laboratory Report, LBL 16901 (1983) and R. A. Scott, in Structural and Resonance Techniques in Biological Research (D. L. Rousseau, ed.), p. 295. Academic Press, Orlando, Florida, 1984.]...

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]...

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