EXAFS
spectra are displayed as plots of the absorption coefficient of a given material versus
energy, typically in a 500 – 1000
eV range beginning before an
absorption edge of an element in the sample. The x-ray absorption coefficient is usually normalized to unit step height. This is done by regressing a line to the region before and after the absorption edge, subtracting the pre-edge line from the entire data set and dividing by the absorption step height, which is determined by the difference between the pre-edge and post-edge lines at the value of E0 (on the absorption edge). The normalized absorption spectra are often called
XANES spectra. These spectra can be used to determine the average oxidation state of the element in the sample. The XANES spectra are also sensitive to the coordination environment of the absorbing atom in the sample. Finger printing methods have been used to match the XANES spectra of an unknown sample to those of known "standards". Linear combination fitting of several different standard spectra can give an estimate to the amount of each of the known standard spectra within an unknown sample. The dominant physical process in x-ray absorption is one where the absorbed photon ejects a core
photoelectron from the absorbing atom, leaving behind a core hole. The ejected photoelectron's energy will be equal to that of the absorbed photon minus the
binding energy of the initial core state. The atom with the core hole is now excited and the ejected photoelectron interacts with electrons in the surrounding non-excited atoms. If the ejected photoelectron is taken to have a
wave-like nature and the surrounding atoms are described as point scatterers, it is possible to imagine the
backscattered electron waves interfering with the forward-propagating waves. The resulting interference pattern shows up as a
modulation of the measured absorption coefficient, thereby causing the oscillation in the EXAFS spectra. A simplified plane-wave single-scattering theory has been used for interpretation of EXAFS spectra for many years, although modern methods (like FEFF, GNXAS) have shown that curved-wave corrections and multiple-scattering effects can not be neglected. The photoelectron scattering amplitude in the low energy range (5-200 eV) of the photoelectron kinetic energy become much larger so that multiple scattering events become dominant in the
XANES (or NEXAFS) spectra. The
wavelength of the photoelectron is dependent on the energy and phase of the backscattered wave which exists at the central atom. The wavelength changes as a function of the energy of the incoming photon. The
phase and
amplitude of the backscattered wave are dependent on the type of atom doing the backscattering and the distance of the backscattering atom from the central atom. The dependence of the scattering on atomic species makes it possible to obtain information pertaining to the chemical coordination environment of the original absorbing (centrally excited) atom by analyzing these EXAFS data.
EXAFS Equation The effect of the backscattered photoelectron on the absorption spectra is described by the EXAFS equation, first demonstrated by Sayers, Stern, and Lytle. The oscillatory part of the dipole matrix element is given by \chi(k), where the sum is over the j sets of neighbors of the absorbing atom, N_j is the number of atoms at distance R_j, k is the
wavenumber and is proportional to energy, \sigma is the thermal vibration factor with \sigma_{j}^2 being the mean square amplitude of the atom's relative displacements, \lambda(k) is the mean free path of the photoelectron with momentum k (this is related to coherence of the quantum state), and f_{j}(k) is an element dependent scattering factor. \chi(k) = \sum_j\frac{N_j e^{-2k^2 \sigma^2_j} e^{-2R_j / \lambda_k} f_{j}(k)}{k R^2_j}\sin[2 k R_j + \delta_{j}(k)] The origin of the oscillations in the absorption cross section are due to the \sin term which imposes the
interference condition, leading to peaks in absorption when the wavelength of the photoelectron is equal to an integer fraction of 2R_{j} (the round trip distance from the absorbing atom to the scattering atom). This is analogous to eigenstates of the
particle in a box toy model. The \delta_{j} factor inside the \sin is an element dependent phase shift. ==Experimental considerations==