$$ (3)One can envision the EXAFS phenomena by the help of a schematic of the outgoing and backscattered waves as shown in Fig. 2b. As the energy of the photoelectron changes, so does the wavelength of the photoelectron. At a particular energy E 1, the outgoing and the backscattered waves are in phase and constructively interfere, thus increasing the probability of X-ray absorption or, in other words, increase the absorption coefficient. At a different energy E 2, the outgoing and selleck screening library backscattered waves are out-of-phase
and destructively interfere, decreasing the absorption coefficient. This modulation of the absorption coefficient by the backscattered wave from neighboring atoms is essentially the basic phenomenon of EXAFS. And, Fourier transform (FT) of the modulation provides distance information describing the vector(s) between Selleckchem Torin 1 the absorbing atom and atoms to which it is bound—typically within a range limit of 4–5 Å. A quantitative EXAFS modulation χ(k) can be expressed as follows: $$ \chi (k) = \sum\limits_\textj \fracN_\textj \leftkR_\textaj^2 \sin [2kR_\textaj + a_\textaj (k)] , $$ (4)where N
j is the number of equivalent backscattering atoms j at a distance R aj from the absorbing atom, f j(π, k) is the backscattering
amplitude which is a function of the atomic number of the backscattering element j, and α aj(k) includes the phase shift from the central atom absorber as well as the backscattering element j. The phase shift occurs due to the presence of atomic potentials that the photoelectron else experiences as it traverses the potential of the absorber atom, the potential of the backscattering atom, and then back through the potential of the absorber atom. In real systems, there is an inherent static disorder due to a distribution of distances R aj, and dynamic disorder due to thermal vibrations of the absorbing and scattering atoms. Equation 4 is modified to include this disorder term or the Debye–Waller factor \( \texte^ – 2\sigma_\textaj^2 k^2 , \) where \( \sigma_\textaj \) is the root-mean-square deviation to give the following equation: $$ \chi (k) = \sum\limits_j \fracN_\textj \leftkR_\textaj^2 \,\texte^ – 2\sigma_\textaj^2 k^2 \sin [2kR_\textaj + a_\textaj (k)] .