EXAFS

Extended X-ray Absorption Fine Structure (EXAFS) is the portion of an X-ray absorption spectrum that lies above an element’s absorption edge, where oscillations are observed. These oscillations arise from the interference of the outgoing photoelectron wave with waves scattered by neighboring atoms, making EXAFS sensitive to the local atomic structure around the absorber.

In EXAFS, information is encoded in the photoelectron wavenumber k = sqrt(2m (E − E0)/ħ^2). The measured signal χ(k) can be modeled as a sum over neighboring shells: χ(k) ≈ Σ_j (N_j f_j(k) / (k R_j^2)) exp(−2k^2 σ_j^2) exp(−2R_j/λ) sin(2kR_j + δ_j(k)). Here N_j is the coordination number, R_j the absorber-backscatter distance, f_j(k) the scattering amplitude, σ_j^2 the Debye-Waller factor (disorder), λ the mean free path, and δ_j(k) the phase shifts.

Experimentally, EXAFS data are collected in transmission or fluorescence yield modes. Data processing involves background subtraction, normalization, and conversion to χ(k). A Fourier transform of χ(k) yields a radial-distribution function whose peaks relate to distances to neighboring atoms, though not directly equal to R_j. Quantitative structural parameters are refined by fitting with theoretical standards generated by ab initio methods (for example FEFF) or by multiple-scattering analyses.

Applications of EXAFS span materials science, catalysis, chemistry, biology, and environmental science. It provides element-specific local structure in crystalline, amorphous, or liquid systems, and can be performed under various conditions, including in situ or ex situ environments.