Photoelectron wave

Figure 7. Depiction of origin of EXAFS. An X-ray photon is absorbed by A, resulting in the photoionization of a core-level electron represented as an outgoing ( + ) photoelectron wave which is backscattered (<- ) by a near neighbor, B.

The EXAFS, which occurs at higher energies above the edge, is due to the interference between the outgoing and the backscattered photoelectron waves (10-14). EXAFS provides information about the local structure of the x-ray absorbing atom. Typically, nearest neighbor bond lengths and coordination numbers can be determined to 0.02 A (1%) and one atom in four (25%) (4 ). The accuracy of these determinations is somewhat worse for outer-shell atoms, for disordered systems, or for systems with asymmetric distributions of atoms within a shell (15,16). 

The ejected photoelectron may be approximated by a spherical wave, which is backscattered by the neighboring atoms. The interference between the outgoing forward scattered, or ejected, photoelectron wave and the backscattered wave gives rise to an oscillation in the absorbance as a function of the energy of the incident photon. These oscillations, which may extend up to 1000 eV above the absorption edge, are called the EXAFS, extended X-ray absorption fine structure. Analysis of the EXAFS provides information regarding the identity of, distance to, and number of near neighboring atoms. 

Figure 2. Typical X-ray absorption spectrum. Inset is schematic illustration of out-going and backscattered photoelectron wave for energies E (left) and E (nght).

Multiple scattering, where the photoelectron wave samples severd scatteiers before returning to the absorbCT, is only important in KAFS for cases where two scatterers and the absc rber are nearly coUinear. In such cases, the EXAFS amplitude of the outer scatterer will be significantly enhanced. See Teo, B.K., /. Am. Chem. Soc., 1981,103,3990-4001. 

The Fe EXAFS data from inactive aconitase and its Fourier transform are shown in Figure 6. EXAFS of metal complexes arises from the interference of outgoing photoelectron waves (generated from the absorption of X-rays by the Is electrons of the metal) with waves back-scattered from neighboring atoms. 

The damping factors take into account 1) the mean free path k(k) of the photoelectron the exponential factor selects the contributions due to those photoelectron waves which make the round trip from the central atom to the scatterer and back without energy losses 2) the mean square value of the relative displacements of the central atom and of the scatterer. This is called Debye-Waller like term since it is not referred to the laboratory frame, but it is a relative value, and it is temperature dependent, of course It is important to remember the peculiar way of probing the matter that EXAFS does the source of the probe is the excited atom which sends off a photoelectron spherical wave, the detector of the distribution of the scattering centres in the environment is again the same central atom that receives the back-diffused photoelectron amplitude. This is a unique feature since all other crystallographic probes are totally (source and detector) or partially (source or detector) external probes , i.e. the measured quantities are referred to the laboratory reference system. 

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.

The photoelectron wave-vector k is evaluated using = 2m(E — E ) where E is the energy of the X-ray photon, , a reference energy and m, the mass of the electron. x(k) is multiplied by k"(n = 2 or 3 usually) to magnify the faint EXAFS at large k (Lytle et al, 1975) /c"x(k) is Fourier transformed to yield the RSF, < (R). In the model compound, the first peak at a distance Rj represents the distance to the nearest-neighbour shell and may be compared to R[, the known distance. We can then define a as (R — Rj), which represents the experimentally determined phase correction. In principle, 2a should be equal to the theoretically estimated k-dependent part of /k), viz. if the identity of the scatterer environment has been correctly assumed. It must be emphasized that wherever scatterer identities are obscure (e.g. in several covalently bonded and disordered systems) use of a (and not j) is advisable. Further, the k-dependence of < /k) introduces an intrinsic limitation to its quantitative accuracy. 

Figure 10 Direct (Hartree) part of the effective potential Veff (r), Equation (4), seen by a ep photoelectronic wave arising from Nels photoionization of Ne C 0 for z = —5, —2, —1,0, and +5, as in [28],...

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