For all these techniques samples are usually powders (mgs) or glass chips (mm). For some experiments such as transmission mode XAS experiments, however, care must be taken to ensure that the sample thickness is appropriate for the experimental conditions. If the sample is too thick, then self‐absorption effects negate any useful data.
3.2 EXAFS and XANES
The closely related techniques EXAFS and XANES together constitute XAS. An XAS spectrum is divided into three regions: that of XANES, typically 0–50 eV above the X‐ray absorption edge; of EXAFS or XAFS, typically ~50–1500 eV above the X‐ray edge; and of the pre‐edge ~20–30 eV below the edge (Figure 3). Both EXAFS and XANES are element‐specific and potentially can be obtained from any element in the periodic table down to concentrations that can be as low as ~100 ppm.
EXAFS data are used for determining quantitatively bond distances, CN, the nature of the atoms surrounding the central atom of interest, and Debye–Waller factors. As illustrated for GeO2 glass, the EXAFS portion of an XAS spectrum may be background corrected, normalized to 1 (Figure 4a), and then converted to k‐space (reciprocal space) to get what is termed the χ(k) spectrum (Figure 4b). Part of this χ(k) spectrum is then Fourier transformed back into real space (R‐space). The magnitude of the Fourier transform is essentially an RDF made up of the different atom pairs contributing to the χ(k) spectrum (Figure 4c), which is similar to the X‐ray RDF. The first peak represents the Ge─O distances whereas peaks at higher R are due to multiple scattering and/or Ge─Ge, second Ge─O distances, etc. Modeling of the data (in R‐ or k‐space) with reference to a crystalline standard (e.g. trigonal GeO2 in this example) is necessary to extract the real interatomic distance. Without such modeling the interatomic distances are not accurate, being generally shorter than the real ones by ~0.5 Å.
Figure 3 Typical information drawn from XAS spectra: processes causing the features observed in each energy range of interest. Spectrum of SiO2 glass taken as an example.
Figure 4 EXAFS portion of the XAS spectrum of GeO2 glass. (a) Background corrected and normalized to 1. (b) Converted to k‐space (reciprocal space) for derivation of the χ(k) spectrum. (c) Magnitude of the Fourier transformed χ(k) spectrum, essentially a radial distribution function made up of the different atom pairs contributing to the source χ(k) spectrum.
The information drawn from XANES (Figure 5) on the electronic structure, oxidation state, CN, and nature of the bonding within the glass is more qualitative. This limitation is illustrated by the XANES spectra of Figure 5a where fewer and broader features are observed for SiO2 glass than for quartz. Each peak represents an electronic transition of the Si 1s electrons to 2p states mixed with unoccupied oxygen states (orbitals). Comparison of the experimental XANES with first‐principles calculations greatly facilitates detailed analysis of the electronic states.
One can also use XANES to determine the relative fractions of the different phases that are present in a mixture of crystalline materials. For this purpose, it suffices to perform a linear combination analysis whereby spectra of crystalline standards are summed together in different ratios and compared with the experimental spectrum.
Of particular interest in glass science is the oxidation state and coordination of transition metal (TM) elements. For these elements, one predominantly uses the pre‐edge features of the K‐edge XAS, which represent excitation of a 1s electron to a 2p state (Figure 5b). These pre‐edge features arise from formerly spin‐forbidden electronic transitions that become “allowed” through site distortion. For some Ti‐bearing crystals, the pre‐edge shown in Figure 5b may contain from 1 to 3 peaks whose intensity is highest for the second or middle peak (fourfold coordinated Ti) and decreases with increasing Ti coordination (cf. [8, 9]). For iron (Fe) there can be two to three pre‐edge features whose actual number and relative intensities depend upon whether or not there is Fe2+ and/or Fe3+, as well as upon the coordination geometries fourfold (tetrahedral or square planar), fivefold (trigonal bipyramid, square pyramid), sixfold (octahedral), or higher coordination (eightfold, etc.) of the different oxidation states.
Figure 5 Information drawn from XANES data. (a) Fourfold coordination of Si in SiO2 glass and quartz, and ordering contrast between the two phases. (b) From bottom to top, four‐, five‐, and sixfold coordination of Ti in crystals as derived from the pre‐edge regions of Ti K spectra.
Source: Reproduced with permission from [7].
Fits to the pre‐edge features can be made to extract the positions and intensities of the different contributions. Interpretation of the data requires a comparison of both the peak positions and intensities for accurate results (see [7]). Once determined, these parameters can be used in comparison with crystalline standards to determine likely coordination and oxidation states in the glass.
In XANES experiments the L‐edge of transition metals can also be used for qualitative determination of oxidation state and coordination. But this edge is inherently more difficult to interpret because it originates in excitations (of a 2p electron principally to 3d or higher states) that are affected by spin–orbit coupling of the electrons. Analysis and interpretation of both K‐ and L‐edge XANES spectra are greatly facilitated if one has access to first‐principles calculations (simulations) of the edge of interest. Provided the partial densities of states (p‐DOS) are yielded by the simulations, individual peaks can be assigned to interactions between specific unoccupied states (orbitals).
In addition, the position of the edge also depends upon coordination and oxidation state, moving to higher energies with increasing oxidation, whereas the overall shape of the XANES spectrum depends on the nature of the next‐nearest neighbor interactions. Consequently, one can use a “fingerprint” technique to compare the glass XANES spectrum with those of common crystalline analogues where the element of interest is