Extended X-ray absorption fine structure

Extended X-ray absorption fine structure (EXAFS), along with X-ray absorption near edge structure (XANES), is a subset of X-ray absorption spectroscopy (XAS). Like other absorption spectroscopies, XAS techniques follow Beer's law. The X-ray absorption coefficient of a material as a function of energy is obtained by directing X-rays of a narrow energy range at a sample, while recording the incident and transmitted x-ray intensity, as the incident x-ray energy is incremented.

When the incident x-ray energy matches the binding energy of an electron of an atom within the sample, the number of x-rays absorbed by the sample increases dramatically, causing a drop in the transmitted x-ray intensity. This results in an absorption edge. Every element has a set of unique absorption edges corresponding to different binding energies of its electrons, giving XAS element selectivity. XAS spectra are most often collected at synchrotrons because the high intensity of synchrotron X-ray sources allows the concentration of the absorbing element to reach as low as a few parts per million. Absorption would be undetectable if the source were too weak. Because X-rays are highly penetrating, XAS samples can be gases, solids or liquids.

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.

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 ${\displaystyle \chi (k)}$, where the sum is over the ${\displaystyle j}$ sets of neighbors of the absorbing atom, ${\displaystyle N_{j}}$ is the number of atoms at distance ${\displaystyle R_{j}}$, ${\displaystyle k}$ is the wavenumber and is proportional to energy, ${\displaystyle \sigma }$ is the thermal vibration factor with ${\displaystyle \sigma _{j}^{2}}$ being the mean square amplitude of the atom's relative displacements, ${\displaystyle \lambda (k)}$ is the mean free path of the photoelectron with momentum ${\displaystyle k}$ (this is related to coherence of the quantum state), and ${\displaystyle f_{j}(k)}$ is an element dependent scattering factor.