**2. X-ray absorption spectroscopy (XAS)**

XAS, also known as X-ray absorption fine structure (abbreviated as XAFS) spectroscopy, is a powerful tool that provides information on a very local scale (4–5 Å) around a selected atomic species and is well suited for the characterization of not only crystals but also materials that possess little or no long-range translational order. It is based on the absorption: when a sample is exposed to X-rays, it will absorb part of the incoming photon beams, which is mainly generated by the photoelectric effect for energy in the hard X-rays regimes (3–50 KeV). XAS is even selective for the atomic species and also allows us to tune the X-rays beam selectively to a specific atomic core (the absorption energy of next elements are sufficiently spaced), and therefore it probes the local structure around only the selected element that are contained within a material. The element-specific characteristic of XAS, providing both chemical and structural information at the same time, differentiates it from other techniques, such as the X-ray scattering. In this respect, it serves as a unique tool for the investigation of battery materials during charge-discharge cycles.

XAS experiment measures the absorption coefficient μ as a function of energy *E*: as *E* increases, μ generally decreases (*μ* ~ *E*−3), that is matter becomes more transparent and X-rays more penetrating, save for some discontinuities, where μ rapidly rises up. These exceptions correspond to particular energies, the so-called absorption edges *E*<sup>0</sup> , which are the characteristic of the material, where the amount of energy exactly matches the core electron binding energy. The edge energies vary with atomic number approximately as a function of *Z*<sup>2</sup> and both *K* and L levels can be used in the hard X-ray regime (in addition, M edges can be used for heavy elements in the soft X-ray regime), which allows most elements to be probed by XAS with X-ray energies between 4 and 35 keV. Because the element of interest is chosen in the experiment, XAFS is element-specific.

XAS (or XAFS) is generally used to refer to the entire spectrum, which is constituted by the edge region called X-ray absorption near edge spectroscopy (XANES), which is limited at the first 80–100 eV above the edge, and a post-edge region extended X-ray absorption fine structure (EXAFS), which is extended up to 1000 eV above the absorption edge. The distinction between XANES and EXAFS remains arbitrary, but some important approximations in the theory allow us to interpret the extended spectra in a more quantitative way than is currently possible for the near-edge spectra. The XANES region, comprising the pre-edge and the absorption edge itself, is strongly sensitive to oxidation state and coordination chemistry of the absorbing atom of interest. The EXAFS region has been largely exploited to gain quantitative structural information such as first shell distance of the metal site and the coordination number. EXAFS comprises periodic undulations in the absorption spectrum that decay in intensity as the incident energy increases well over (~1000 eV) the absorption edge. These undulations arise from the scattering of the emitted photoelectron with the surrounding atoms. A striking feature of XAFS is that this technique can be applied to all states of matter, and for both crystalline and amorphous materials, it has been used with great success in many research fields, such as liquids [22], catalysis [23–25], biology [26], inorganic metal complexes [27] and electrochemical interfaces [28]. Several excellent books are also available [29–32]. The website of the International XAFS society is reachable at http://www.ixasportal. net/ixas/.

When discussing XAS, we are primarily concerned with the absorption coefficient *μ*, which gives the probability that X-rays will be absorbed according to Beer's Law:

$$
\mu \cdot \infty = \ln \text{(} I\_0 \text{|} \text{I)} \tag{1}
$$

X-Ray Absorption Spectroscopy Study of Battery Materials http://dx.doi.org/10.5772/66868 55

$$\left(\frac{\mu}{\rho}\right) \cdot \rho \cdot \mathbf{x} = \ln\left(I\_0 I\right) \tag{2}$$

being *I* 0 is the intensity of X-ray incident on a sample, *x* is the sample thickness and *I* is the intensity transmitted through the sample, as shown in **Figure 2**. The measured quantity, *μ* (cm−1), is the linear X-ray absorption coefficient which is closely related to its inverse 1/*μ* called the absorption length (cm). The absorption length is defined as the linear distance of the material over which the X-ray intensity results attenuated by a factor 1/*e* ~ 37%. This quantity is important in planning the experiment, as it sets the scale for choosing an appropriate sample thickness.

**Figure 2.** Sketch for the X-Ray absorption measurement in transmission mode.

is exposed to X-rays, it will absorb part of the incoming photon beams, which is mainly generated by the photoelectric effect for energy in the hard X-rays regimes (3–50 KeV). XAS is even selective for the atomic species and also allows us to tune the X-rays beam selectively to a specific atomic core (the absorption energy of next elements are sufficiently spaced), and therefore it probes the local structure around only the selected element that are contained within a material. The element-specific characteristic of XAS, providing both chemical and structural information at the same time, differentiates it from other techniques, such as the X-ray scattering. In this respect, it serves as a unique tool for the investigation of battery materials during

XAS experiment measures the absorption coefficient μ as a function of energy *E*: as *E* increases, μ generally decreases (*μ* ~ *E*−3), that is matter becomes more transparent and X-rays more penetrating, save for some discontinuities, where μ rapidly rises up. These exceptions correspond

material, where the amount of energy exactly matches the core electron binding energy. The

levels can be used in the hard X-ray regime (in addition, M edges can be used for heavy elements in the soft X-ray regime), which allows most elements to be probed by XAS with X-ray energies between 4 and 35 keV. Because the element of interest is chosen in the experiment,

XAS (or XAFS) is generally used to refer to the entire spectrum, which is constituted by the edge region called X-ray absorption near edge spectroscopy (XANES), which is limited at the first 80–100 eV above the edge, and a post-edge region extended X-ray absorption fine structure (EXAFS), which is extended up to 1000 eV above the absorption edge. The distinction between XANES and EXAFS remains arbitrary, but some important approximations in the theory allow us to interpret the extended spectra in a more quantitative way than is currently possible for the near-edge spectra. The XANES region, comprising the pre-edge and the absorption edge itself, is strongly sensitive to oxidation state and coordination chemistry of the absorbing atom of interest. The EXAFS region has been largely exploited to gain quantitative structural information such as first shell distance of the metal site and the coordination number. EXAFS comprises periodic undulations in the absorption spectrum that decay in intensity as the incident energy increases well over (~1000 eV) the absorption edge. These undulations arise from the scattering of the emitted photoelectron with the surrounding atoms. A striking feature of XAFS is that this technique can be applied to all states of matter, and for both crystalline and amorphous materials, it has been used with great success in many research fields, such as liquids [22], catalysis [23–25], biology [26], inorganic metal complexes [27] and electrochemical interfaces [28]. Several excellent books are also available [29–32]. The website of the International XAFS society is reachable at http://www.ixasportal.

When discussing XAS, we are primarily concerned with the absorption coefficient *μ*, which

*μ* ⋅ *x* = ln(*I*

gives the probability that X-rays will be absorbed according to Beer's Law:

, which are the characteristic of the

<sup>0</sup>/*I*) (1)

and both *K* and L

charge-discharge cycles.

XAFS is element-specific.

net/ixas/.

to particular energies, the so-called absorption edges *E*<sup>0</sup>

54 X-ray Characterization of Nanostructured Energy Materials by Synchrotron Radiation

edge energies vary with atomic number approximately as a function of *Z*<sup>2</sup>

Normalization to the density of the material results quite convenient, as different states of matter may be analyzed: the mass absorption coefficient *μm* (cm2 /g) is the linear absorption coefficient divided by the density of the absorber.

X-rays ionize and the absorbing atom turns to an excited ion after the electron liberation. Relaxation may occur in two different ways: (i) the core-hole may be filled by a higher-energy electron and the energy difference is released as a second photon, whose energy is smaller compared to that of the primary absorption, for an inner transition occurs (the detection of which is at the basis of another x-ray analytical technique, X-ray Fluorescence Spectroscopy—XFS) or (ii) an Auger secondary electron may be freed, after having absorbed the second photon. The measurement of these electrons is made possible by Auger spectrometers. In the soft X-ray region (<2 keV), the Auger process is more likely to occur, unlike for higher energies where X-ray fluorescence dominates.

#### **2.1. Extended X-ray absorption fine structure (EXAFS)**

When X-ray is absorbed by a core-level electron, a photoelectron with wavevector *k* is created and propagates away from the atom as a spherical wave as seen from the blue lines of **Figure 3**. The wavevector *k* is related to the excess of the energy *ħω*-*E*<sup>0</sup> of the incoming X-ray beam by:

$$k = \sqrt{\frac{2m}{\hbar^2} (\hbar \omega - E\_0)}\tag{3}$$

**Figure 3.** Emission of a photo-electron for an isolated (left) and a coordinated (right) atomic species. In the latter the absorption coefficient measured at a central atom threshold shows a fine structure due to the presence of neighboring atoms. Reproduced from Ref. [18].

where *E*<sup>0</sup> is the binding energy of the core-electron that is excited and *E* = *ħω* is the energy of the absorbed x-ray photon. Thus, the excess of energy rules out the optical property of the photo-electron created by the photoabsorption process. In case of isolated atoms, the propagation is simply described by one wave going away from the atom and the absorption coefficient *μ* is described by a smooth function of energy, indicated in the lower panel of **Figure 3**. Its value depends on the sample density *ρ*, atomic number *Z*, atomic mass *A* and the X-ray energy *E*, roughly expressed as:

$$
\mu\_0 \approx \frac{\rho Z^4}{AE^3} \tag{4}
$$

The appendix 0 indicates the value for an isolated atom. It is remarkable here that due to its *Z*<sup>4</sup> dependence, the absorption coefficients of different elements exhibit big discrepancies, (spanning several orders of magnitude) so a good contrast between different materials can be achieved for any sample thickness and concentrations by selecting the X-ray energy. This fact is at the origin of the X-rays imaging techniques based on contrast.

If other atoms are located in the vicinity of the absorber (the central atom), the photoelectron is scattered by the neighbors (yellow atoms) and so does every atom in the material. The incoming and the scattered wave interferes either constructively or destructively as a function of the energy of the X-ray beam. Therefore, the observed absorption coefficient is expected to vary periodically as a function of the energy as depicted at the bottom right of **Figure 3**. In the latter case, the total absorption coefficient *μ* can be expressed as the isolated atomic absorption *μ*<sup>0</sup> , modulated by a correction factor *χ*(*E*), the oscillation, which is also defined as the EXAFS signal:

$$
\mu(E) = \mu\_0(E) \left[ 1 + \chi(E) \right] \tag{5}
$$

This allows one to extract the oscillations from a raw experimental spectrum:

$$\chi\_{\chi} = \left[ \left( \mu(E) - \mu\_o(E) \right] / \mu\_o(E) \right] \tag{6}$$

For practical purpose, the denominator is often replaced by *μ*<sup>0</sup> (*E*0 ), which is the atomic absorption evaluated at the edge energy. *χ*(*k*) can be considered as the fractional change in absorption coefficient induced by the presence of neighboring atoms.

Within this simple description, the EXAFS can be represented by an oscillation, which of course can be described by terms of amplitude and phase. In a first approximation, the amplitude term depends on the nature and the number of near neighbors around the central atoms and the phase on the mutual distance photoabsorber scatterer. This leads to a simple expression for EXAFS in terms of different parameters affecting the fine structure:

$$\hat{\chi}\_{\text{Matterers affecting the fine structure:}}^{\text{MARM}}$$

$$\chi\_{\text{M}}(\mathbf{k}) \sim \sum\_{\mathbf{k}\_{\rangle}} \frac{N\_{\rangle} F\_{\rangle}^{\text{(k)}}(\mathbf{k})}{k\_{\rangle} r\_{\rangle}^2} \sin \left[2k\_{\rangle} \mathbf{R}\_{\rangle} + \delta(\mathbf{k})\right] \tag{7}$$

where *Nj* represents the coordination number of identical atoms at approximately the same distance *rj* from the central atom. This group of atoms is called as a coordination shell and contributes to one components of the EXAFS signal. The peculiar *Fj* (*k*) term is called the backscattering amplitude and depends on the nature of the scatterer atom. Different atom types have different backscattering amplitude. A crucial issue is given by the inverse quadratic dependence of the oscillation to the distance. This is due to the decay of the photoelectron as a function of time and distance and thus making the EXAFS a short-range structural probe. The first term of the phase 2*kRj* is due to the geometrical phase shift suffered by the photoelectron with wavevector *k* on its trajectory twice the distance *rj* between the photo absorber and the scatterer. In addition, as the electron is not moving in a constant potential, a phase shift *δ*(*k*) has to be added to this expression to account for the interaction of the electron with the varying potential of the absorbing and backscattering atom.

where *E*<sup>0</sup>

atoms. Reproduced from Ref. [18].

its *Z*<sup>4</sup>

is the binding energy of the core-electron that is excited and *E* = *ħω* is the energy of the

absorbed x-ray photon. Thus, the excess of energy rules out the optical property of the photo-electron created by the photoabsorption process. In case of isolated atoms, the propagation is simply described by one wave going away from the atom and the absorption coefficient *μ* is described by a smooth function of energy, indicated in the lower panel of **Figure 3**. Its value depends on the sample density *ρ*, atomic number *Z*, atomic mass *A* and the X-ray energy *E*, roughly expressed as:

**Figure 3.** Emission of a photo-electron for an isolated (left) and a coordinated (right) atomic species. In the latter the absorption coefficient measured at a central atom threshold shows a fine structure due to the presence of neighboring

> *<sup>μ</sup>*<sup>0</sup> <sup>≈</sup> *<sup>ρ</sup> <sup>Z</sup>*<sup>4</sup> \_\_\_\_

The appendix 0 indicates the value for an isolated atom. It is remarkable here that due to

If other atoms are located in the vicinity of the absorber (the central atom), the photoelectron is scattered by the neighbors (yellow atoms) and so does every atom in the material. The incoming and the scattered wave interferes either constructively or destructively as a function of the energy of the X-ray beam. Therefore, the observed absorption coefficient is expected to vary periodically as a function of the energy as depicted at the bottom right of **Figure 3**. In the latter

is at the origin of the X-rays imaging techniques based on contrast.

56 X-ray Characterization of Nanostructured Energy Materials by Synchrotron Radiation

 dependence, the absorption coefficients of different elements exhibit big discrepancies, (spanning several orders of magnitude) so a good contrast between different materials can be achieved for any sample thickness and concentrations by selecting the X-ray energy. This fact

*<sup>A</sup> <sup>E</sup>*<sup>3</sup> (4)

Several effects have to be taken into account to complete the description of real systems, and they all can be considered damping terms. They are (i) the structural and thermal disorder; (ii) the limited mean free path of the photoelectron; and (iii) the relaxation of all the other electrons in the absorbing atom in response to the hole in the core level. The first term is due to the fact that atoms in matter vibrate around their equilibrium position depending on temperature. This atomic motion reduces the EXAFS amplitude, and a term called the EXAFS Debye-Waller factor *σ*<sup>2</sup> is introduced. In EXAFS, this term corresponds to the mean square average of the difference of the displacement of the backscatterer relative to the displacement of the absorber. The second term is due to inelastic scattering processes of the photoelectron with other electron and thus an additional damping factor is introduced, where *Λ*(*k*) is the photoelectron mean free path (how far the electron travels before scattering inelastically). Finally, the amplitude reduction term *S*<sup>0</sup> 2 accounts for the shake-up/shake-off processes of the central atom. Those processes (multi-excitations) refer to the excitations of the remaining *Z* − 1 "passive" electrons of the excited atom. This is a scale factor, and it is usually in the 0.7–1 range. By taking in consideration with these effects, the EXAFS equation becomes:

$$
\text{Jaccard with these effects, the EXAFS equation becomes:}
$$

$$
\chi(k) = \sum\_{\varnothing \neq \varnothing} \frac{N\_{\rangle} \overline{r}\_{\rangle}^{\langle k \rangle}}{k \ r\_{\rangle}^2} e^{-2k \overline{\nu} \cdot \overline{r}} e^{-2k \overline{\mu} \langle \hbar | 0 \rangle} S\_0^2 \sin \left[ 2k \, R\_{\rangle} + \delta(k) \right] \tag{8}
$$

This is valid for the plane wave approximation, *K* threshold, single scattering, single electron approximation and "sudden" approximation. A similar equation valid for the other edges (LIII, etc.) must be considered. The structural and non-structural parameters appearing in the equation sum up to compose the EXAFS spectrum. To access these parameters in an experimental EXAFS spectrum, a data analysis has to be performed. This procedure is time consuming and it should be considered the slow step of the overall XAFS methodology.

EXAFS data analysis is normally done by using code programs, which permit to calculate the theoretical EXAFS spectrum based on *ab initio* calculations, followed by a further step which compares the experimental signals to the theoretical ones (fitting procedures). A rather complete list of the available software can be found at: http://www.esrf.eu/Instrumentation/ software/data-analysis/Links/xafs. Typical widely used computer programs are GNXAS [33], FEFF [34, 35] and EXCURV [36]. EXCURV is a program, which simulates EXAFS spectra using rapid curved-wave theory. GNXAS package is based on multiple-scattering (MS) calculations and a fitting procedure of the raw experimental data, also allowing multiple edge fittings and a non-Gaussian distribution models for the atoms pair distribution. FEFF allows MS calculations of both EXAFS and XANES spectra for atomic clusters. The code yields scattering amplitudes and phases used in many modern XAFS analysis codes. It is also linked to the IFEFFIT package [37, 38], a suite of interactive code for XAFS analysis, combining high-quality and well-tested XAFS analysis algorithms, tools for general data manipulation and graphical display of data.

Two more considerations should be made on EXAFS data analysis. The first is that XAS (and therefore the results obtained by an EXAFS analysis) is a bulk technique and thus all the atoms irradiated by the beam contribute to the overall XAS spectrum. The same is true in the case of a multicomponent system (for instance two phases in equilibrium of a polymorphic species). Each component or phase gives its contributions. An example to disclose the simple component of a species, such as in the case of gold nanoparticles and its precursors, appeared [39]. Alternatively, an efficient use of chemometry has been proposed for the analysis of XAS data in such cases [40]. This approach has interesting implication for the interpretation of spectra recorded during an *operando* acquisition and an example will be presented in the next section.

The second consideration concerns the EXAFS data analysis of nanoparticles and nanostructures [41, 42]. This issue has been addressed for metal nanoparticles first [43], evidencing that by decreasing the size of the material there is a significant effect on the observed coordination number, due to the increased surface/bulk ratio. A specific example of this effect on a battery material will be presented in the case study section.
