This group of atoms is called as a coordination shell and contributes to one components of the EXAFS signal. The peculiar F j 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 kR j is due to the geometrical phase shift suffered by the photoelectron with wavevector k on its trajectory twice the distance r j between the photo absorber and the scatterer.
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. 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. This is a scale factor, and it is usually in the 0. 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 L III , etc. The structural and non-structural parameters appearing in the equation sum up to compose the EXAFS spectrum.
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.
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. The code yields scattering amplitudes and phases used in many modern XAFS analysis codes. 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 ]. A specific example of this effect on a battery material will be presented in the case study section.
The XANES region is sensitive to the geometrical structure of the metal center but also probes its effective charge.
It turns out that the position of the edge which can be evaluated by the edge inflection point is shifted to higher energies when the formal valence of the photo-absorber increases. Below the absorption edge, the presence of pre-edge structures can be observed [ 44 ]. The occurrence of this peak in a metal first raw transition metal K-edge is due to 1s-3d electronic transition [ 45 ] that is electric-dipole forbidden but quadrupole allowed. Its intensity can be used as a probe for geometry, as the geometrical distortion of the metal core from centrosymmetric coordination favors the transition, while the energy position is relative to the metal core formal oxidation state.
This fact is frequently used for investigating the charge associated to positive- and negative-electrode materials during reduction and oxidation reactions in batteries. If we now consider the form of the absorption edge, it can be seen that it reflects the empty density of states and it strongly depends on the coordination, while the forms of the absorption traces up to 60—80 eV are due to the multiple scattering resonances of the ejected photoelectron.
The simplest way to study the structural end electronic modification of a cathode or anode material is by ex situ XAS. In this case, the battery is stopped at the chosen state of charge or discharge and disassembled; the recovered material, protected from air in adapted sample holders, is transported to a synchrotron to perform the experiment in a suitable XAS beamline [ 32 ].
Basically, two geometries are used for this purpose, namely transmission and fluorescence. The fluorescence detection is carried out by tilting the sample at 45 degrees and collecting the fluorescence X-rays by using a solid-state detector at the right angle with respect to I 0. Such ex situ XAS studies of electrode materials are now extensively completed by operando measurements, i.
Such an approach allows one to avoid several drawbacks due to the sample transfer needed for the ex situ measurements. Alteration of air- or moisture-sensitive species is avoided, as well as the occurrence of relaxation reactions which might show up when the electrical circuit is open, inducing a transformation of the unstable cycled material [ 49 ].
The Effect of a Surrounding Box on the Spectrum of Scattered X-Rays. A. H. Compton and J. A. Bearden. PNAS February 1, 11 (2) ;. Semantic Scholar extracted view of "The Effect of a Surrounding Box on the Spectrum of Scattered X-Rays." by Arthur Holly Compton et al.
The effects of sampling deviations are also eluded since the sample remains in the same position during the whole measurement series. Finally, the whole study can be performed on a single test cell suppressing the effects of uncontrolled differences in a set of cells which are needed for a stepwise ex situ study of the electrochemical mechanism. To perform such an experiment, a special in situ electrochemical cell, obeying to the specific requirements of XAS, has to be used.
This cell consists of an electrode containing the active material, a lithium foil, a separator, which is typically a polymeric membrane such as Celgard, and an electrolyte, usually based on organic carbonate solvents such as propylene carbonate PC , dimethyl carbonate DMC and ethylene carbonate EC. The first one left is a typical pouch cell which is characterized by a large dimension of the cathode. In this case, a film containing the active material is previously deposited on a square Al or Cu current collector of 4 cm 2 and assembled in a glove box together with a Li Na counter-electrode, a separator and the electrolyte.
The figure on the right displays a typical stainless steel cell [ 50 ], which uses self-supported films or pellets of electrode material of smaller dimension 1 cm diameter. Typical in situ electrochemical cells used for operando XAS studies of batteries: A pouch cell left and a stainless steel cell right mounted on different XAS beamlines.
Given the large amount of physico-chemical information that it usually carries, already mentioned in the previous sections, XAS has been largely applied to the study of battery materials [ 18 , 19 ]. A few particular case studies, specifying specific features of this technique in particular cases involving nanostructured species, are presented in the following paragraphs. Itwill be stressed, in particular, the importance of performing in situ studies compared to more simple, but also often less reliable, ex situ measurements.
The relative abundance of manganese coupled with their variety of oxides structures, which provides generally a three-dimensional array of edge-shared MnO 6 octahedra for the lithium insertion and release, has aroused the interest of developing positive-electrode materials based on manganese oxide.
However, the occurrence of an initial activation process during the first delithiation step first charge is always accompanied by a large irreversibility in terms of specific capacity.
To gain a deeper understanding of the initial activation step and to study the following delithiation-lithiation process, an electronic and local structural characterization of the host material is required and the XAS is the technique of choice. A series of electrodes with different lithium concentration state of charge, SOC were studied in a series of lithium-rich, cobalt-poor Li[Li 0.
Due to the strong sensitivity of the XAS to the metal site, spectra at the three different metal edges can be measured, allowing the study of the evolution of the physico-chemical properties and of the local structure of each metal site. The numbered points in the curve indicates predetermined states of charge SOC at which cells were prepared for the XAS measurements.
The pre-edge analysis the Mn K-edge is displayed in the figure, showing two components allowed the authors to check the variation of the Mn local site, in terms of symmetry and charge. This information is complementary with respect to XRD which probes the long-range order in crystalline materials.
Representative points of 1—10 in the process of XAS measurements are indicated. Reference and counter electrode: Li. On the upper X axis the capacity detected in each step is reported. XAS data analysis for the cathode material. The picture displays analysis of the pre-edge data obtained at the Mn K-edge left panel including the fitting of the observed peaks at the bottom.
These data provide both charge and symmetry information around the investigated metal.
The electrochemical performance of the material, considering the full and partial redox inactivity of Mn and Co, also reveals the participation of oxygen in the overall electrochemical redox process. A particularly interesting case for the application of operando XAS is that of electrode materials undergoing a so-called conversion reaction, which was reviewed a few years ago by Cabana et al.
Conversion reactions were first verified for transition metal oxides [ 56 ], but are rather common also for other chalcogenides, pnictogenides and carbon group semimetals. Conversion materials, i.
They have thus been considered as possible alternatives for the development of new high-energy storage devices. Recent studies have shown that, for conversion reactions, due to the formation of nanosized species, the composites obtained at the end of discharge are particularly unstable [ 49 ] and therefore the use of operando techniques for the study of reaction mechanisms is essential. Several methods were used to improve the cycling life of antimonides such as nanostructuration of the electrodes [ 58 ], carbon coating and optimization of the formulation [ 59 ].
M a Sb b compounds are expected to react with lithium by forming a matrix of Li 3 Sb in which nanoparticles of the transition metal M are embedded.
Actual reaction mechanisms, however, can be more complex and often dependent on the specific compound. For instance, several conversion pnictogenides, such as FeSb 2 [ 60 ] and MnSb [ 61 ], form intermediate lithiated insertion phases before starting the veritable conversion reaction, while additional phases could also form throughout the whole electrochemical cycle.
In this material, the possible formation of an intermediate ternary insertion solid solution was suggested by a slight shift of the XRD reflections during the first part of the discharge [ 62 ]. The complete amorphisation of the system during the conversion, however, made it impossible to follow the reaction by XRD. In particular, the formation of Ni nanoparticles at the end of discharge, which are expected for typical conversion reactions, could not be verified.
The fourier transform FT signal of pristine NiSb 2 exhibits a main contribution with a dominant peak at about 2. During lithiation, the first contribution is gradually replaced by a peak pointing at about 2. The spectrum of the fully lithiated material was fitted using 12 Ni neighbors at 2. Since S 0 2 is directly correlated to the coordination number, such a low value indicates that the effective number of Ni neighbors is much smaller than 12, in line with the formation of Ni nanoparticles with a significant fraction of surface atoms.
Such reduced coordination numbers are often observed for supported metal nanoparticles in heterogeneous catalysts with sizes below about 2 nm [ 64 ]. The nanosized nature of the Ni particles is also confirmed by the absence of the following coordination shells in the FT signal. The presence of Ni nanoparticles at the end of lithiation and their following partial reaction during delithiation to reform a nanosized form of NiSb 2 , allowed the author to confirm that NiSb 2 is a veritable conversion material.
Li metal. Evolution with lithiation is shown on going from darker to brighter spectra only selected spectra are shown for the sake of clearness.
At the end of this paper, the authors compared the operando spectra with those of ex situ samples cycled vs. Li about 5 days prior to the XAS measurement campaign, which turned out to be rather different in spite of the precautions taken in order to avoid the decomposition of the latter materials.