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 in different coordination and/or oxidation states. This approach has been widely used to estimate qualitatively CN and oxidation states.
4 Nuclear Magnetic Resonance Spectroscopy
Electrons, protons, and neutrons all have spin quantum numbers of ½ and can therefore interact with magnetic fields externally imposed or arising from nearby particles. Nuclear magnetic resonance (NMR) occurs when NMR‐active nuclei in a magnetic field absorb and re‐emit electromagnetic radiation at a specific resonance frequency. This frequency depends on the strength of the magnetic field and the magnetic properties of the nuclei of interest. The sample (~1–500 mg) is perturbed while in the magnetic field by a short radiofrequency (RF) pulse (usually 90° to the applied magnetic field), which releases the energy of the resonance transition measured as a free induction decay (FID) curve in the time domain. This curve is then Fourier transformed to the frequency domain to obtain the NMR spectrum. Because the FID is very weak, usually multiple curves are collected and time‐averaged. Also of importance is the time taken for the excited spin states to return to their equilibrium distributions; the spin lattice (T1) or longitudinal magnetic relaxation, as well as the time for the FID to reach 1/e of its initial amplitude, the spin–spin (T2) or transverse relaxation. The line width of an NMR signal is determined by T2 (a long T2 means sharper lines) and the maximum repetition rate during acquisition of an NMR signal is governed by T1 (short T1 means a spectrum can be acquired in less time). Additional information about the perturbed system can be obtained when one uses multiple and often complex RF pulse sequences and investigates the time and frequency dependence of the relaxation times. The reader should see [10] and references therein for a much more detailed description of solid‐state NMR.
What makes this technique important is that the measured spin energies are affected by interactions with other electrons and nuclei in the sample and, consequently, by the local chemical environment around the element of interest. Furthermore, one can also probe the dynamics of these interactions on timescales of seconds to nanoseconds that makes its application to high‐temperature studies particularly useful.
Although NMR spectroscopy is used to investigate site‐specific information on elements with nonzero spin quantum numbers, it is most commonly carried out for elements whose numbers are ½ or multiples of ½ such as 3/2, 5/2, 7/2, and 9/2. Little information can usually be drawn from the very broad NMR spectra of solids that result from the strong anisotropy of the NMR frequencies caused by variations
