The general theoretical framework underlying the GNXAS multiple-scattering (MS) data-analysis method for x-ray absorption spectroscopy (XAS) is presented. The main approximations leading to the reduction of the many-body process in that of a photoelectron scattering in an effective potential are summarized. The methods available to expand the extended x-ray-absorption fine-structure χ(k) into physically meaningful terms are described. In particular, emphasis is given to the definition of the irreducible n-body signals ${\gamma }^{\left(\mathit{n}\right)}$ that can be calculated directly by means of linear combinations of continued fractions, or by using their respective multiple-scattering series. It is found that even for an infinite system the expansion of the χ(k) signal in terms of ${\gamma }^{\left(\mathit{n}\right)}$ has a better convergence rate than the MS series. Simple expressions for performing the configurational averages of the structural signals in the presence of thermal and structural disorder are derived. These can be used for the structural analysis of molecular, crystalline, or moderately disordered systems. It is shown that in the case of highly disordered systems the expansion in terms of the ${\gamma }^{\left(\mathit{n}\right)}$ signals is the natural framework for the interpretation of the XAS signal. General equations for the ensemble-averaged χ(k) signal as a function of a series of integrals over the n-body n≳2 distribution functions ${\mathit{g}}_{\mathit{n}}$ are provided and the possible use of advanced strategies for the inversion of the structural information is suggested.

The practical and theoretical aspects of the GNXAS method for multiple-scattering extended x-ray-absorption fine-structure (EXAFS) data analysis are treated in a comprehensive account. The model function used to fit the raw absorption coefficient is described and details on the least-squares fitting procedure and parameter definition are reported. Large emphasis is given, in EXAFS analysis, to the description of criteria for a complete statistical evaluation of the results, including error estimate and model evaluation. An extensive set of applications to prototypical molecular (${\mathrm{Br}}_2$, ${\mathrm{CS}}_2$), and crystalline [c-Ge and Pd (fcc)] systems is reported. Structural parameters always coincide with the known values within statistical accuracy indicating that systematic errors due to approximations in the theory are negligible. The present results also demonstrate that x-ray absorption spectroscopy can provide information on three-body atomic arrangements like average geometrical and vibrational parameters with statistical significance. In all examples, despite the inclusion of several three-body contributions, the total number of fitting parameters does not exceed the information content of the spectra; details on error evaluation and correlation plots in the parameter space are reported.

The high-pressure local structure of zinc oxide has been studied at room temperature using combined energy-dispersive x-ray-diffraction and x-ray-absorption spectroscopy experiments. The structural parameter u and the lattice-parameter ratio $c/a$ of the wurtzite phase is given as a function of pressure and compared with results from ab initio calculations based on a plane-wave pseudopotential method within the density-functional theory. It is shown that an accurate study of ZnO requires the explicit treatment of the d electrons of Zn as valence electrons. In good agreement with present calculations, our experimental data do not show any variation of $u\left(P\right)\mathrm{}$ in the low-pressure wurtzite phase between 0 and 9 GPa, pressure at which the phase transition to the rocksalt phase occurs. Moreover, no dramatic modification of the r-phase K-edge position up to $\sim 20\mathrm{GPa}$ is observed, indicating the absence of metallization. In view of all these results, theoretical models identifying the wurtzite-to-rocksalt transition as an homogeneous path are discussed.

Polarized Cu $L_3$-edge x-ray absorption spectra of a single crystal of Y${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6.8}$ have been measured to determine the symmetry of the orbital of the electronic holes induced by doping. The states induced by doping in $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ ($0<\mathrm{}\delta <\sim 0.5$) have been found to be ligand holes ${\mathit{L}}^{*}$, giving the ${3d}^9{\mathit{L}}^{*}$ configuration, and their weight is correlated with $T_c$. The polarization dependence shows that the hole ${\mathit{L}}^{*}$, induced by doping, is found to be mainly in the Cu-O orbital oriented along the $\mathbf{c}$ axis involving the $\mathrm{O} {2p}_z$ orbital of the O(4) atom in the Ba plane and the $\mathrm{Cu} {3d}_{z^2}$ orbitals. This result indicates the important role of BaO layers and shows that theories of high-$T_c$ superconductivity have to take account of a second band with different symmetry, beyond the single band (the two-dimensional band derived from the $\mathrm{Cu} {3d}_{x^2-y^2}$ and O ${2p}_x$, ${2p}_y$ orbitals in the $\mathbf{a}-\mathbf{b}$ plane of the Cu${\mathrm{O}}_2$ layers) usually considered in models of the electronic structure of high-$T_c$ superconductors.

We describe state-of-the-art experimental techniques using the beamline BM29 of the European Synchrotron Radiation Facility (ESRF). This station exploits the unique characteristics of an ESRF bending magnet source to provide a tunable, collimated, x-ray beam to perform high quality x-ray absorption spectroscopy within the energy range of $\text{E=5–75}$ keV using Si(111), Si(311), and Si(511) crystal pairs. Energy scans can be performed over this wide energy range with excellent reproducibility, stability and resolution, usually better than ${\text{ΔE/E≃5×10}}^{\text{−5}}.$ The experimental setup has been exploited to study condensed matter under extreme conditions. We describe here two sample environment devices; the L’ Aquila–Camerino oven for high-temperature studies up to 3000 K in high vacuum and the Paris–Edinburgh press suitable for high-pressure high-temperature studies in the range 0.1–7 GPa and temperatures up to 1500 K. These devices can be integrated in an experimental setup which combines various control and detection systems suitable to perform x-ray absorption spectroscopy, x-ray absorption temperature scans, and energy scanning x-ray diffraction (ESXD). The ESXD setup is based on a scintillator detector behind a fixed angle collimator aligned to the sample. The combination of these three measurements, which can be performed in rapid sequence on the sample during the experiment, provides an essential tool for structural investigations and in situ sample characterization.

The local structure of simple liquids is significantly different from that of corresponding crystalline systems. Signatures of fivefold local ordering have been previously found, but current knowledge is limited to pair distribution, leaving considerable uncertainty in the determination of the geometrical structure. New x-ray absorption experimental results on liquid and undercooled liquid copper, interpreted using an advanced data-analysis method based on multiple-scattering simulations, are shown to contain direct information on triplet correlations making feasible a reliable determination of the bond-angle distribution and fraction of nearly icosahedral configurations in liquids.