Introduction

Extended X-Ray Absorption Fine Structure (EXAFS) is a part of XAS (X-Ray Absorption Spectroscopy). More precisely, it is the area between 30 eV and up to 1000 eV after the absorption edge (Figure 1).^[1] The analysis of this fine structure gives the possibility to use XAS not only as a spectroscopy method, but also as structural technique.^[2]

 With the fine structure structural properties like interatomic distances, near neighbour coordination numbers and lattice dynamics can be determined.^[2] This technique can be used in crystalline, nanostructured or amorphous materials, liquids and molecular gases.^[3]

Figure 1. X-ray absorption spectrum around an absorption edge with the two parts XANES (X-ray absorption near edge structure) and EXAFS. Figure from Wikipedia. (License: CC BY-SA 3.0)

Principle

The aim of EXAFS is to analyse the local surrounding of an atom type of interest. With this method, the surrounding of circa five angstrom can be investigated.^[4] Therefore, an X-ray absorption spectrum with a monochromatic X-ray radiation and successively change of the energy is measured. The amount of the absorption in this spectrum depends mainly on the photo-electric effect. This effect occurs, when X-ray radiation of equal energy as the binding energy of a core level electron is used. The x-ray photon will then be absorbed by the core level electron and the electron is ejected from the atom as a photo-electron (see fig. 2). When the photo-electric effect occurs, a photon can be absorbed, which leads to a strong increase in the absorption, called absorption edge. If the X-ray energy is higher than the binding energy, the photo-electric effect also occurs. Therefore, the absorption is also high behind the absorption edge. The difference is that there is some rest energy, which is transferred to kinetic energy of the photo-electron.^[1] Each atom type has several absorption edges depending on the binding energies of the electrons (see fig. 2). Since the binding energies are specific for the elements, also the absorption edges are element specific and therefore EXAFS as well. To get EXAFS, the spectrum is measured in an energy range from an absorption edge to circa 1000 eV behind it. Therefore, it is necessary to know the energy of the absorption edge of interest. The values for it can be found in literature data.

Figure 2. Schematic ilustration of the photo-electric effect (left figure by Elisabeth Robens) and the different absorption edges in one atom and the nomenclature (right figure by Nea Möttönen, inspired by reference^[4]).

Moreover, the height of the absorption is described via the absorption coefficient µ. This coefficient is related to the starting intensity of the x-ray beam I₀, the transmitted beam intensity I and the thickness of the sample x. ^[1]

The interesting part of the measured spectrum for the EXAFS analysis is the fine structure after the absorption edge. This structure is caused by the interaction of the photo-electron with neighbouring atoms. Therefore, there is no fine structure for single atoms (see fig. 3).

^[5]

Figure 3. X-ray absorbition spectrum of a single atom (Figure: Elisabeth Robens).

To understand the building of the fine structure, it is important to know that the absorption probability of an x-ray photon depends on the initial and the final state of the electron.^[1] The initial state is the core level electron and the photon. The final state differs depending on the existence of neighbouring atoms. When there are no neighbouring atoms, the final state of the electron is just the outcoming photo-electron wave. But when there are neighbouring atoms, the photo-electron is backscattered at them and an incoming electron wave is produced (see fig. 4).^[1]

Figure 5. Schematic illustration of the effect of neighboring atoms (Figure: Elisabeth Robens).

The final state is then the combination of the outcoming and incoming wave, thus the final wave. The outcoming wave depends on the x-ray photon energy, because the energy influences the wavelength of the electron wave. For example, if the energy is high, the photo-electron has also a high kinetic energy and therefore a smaller wavelength than a photo-electron which absorbed a photon with a smaller amount of energy. The incoming wave depends on the outcoming wave, the distance from the absorbing atom and the scattering atom, and the atom type of the scattering atom. The interaction of the outcoming and incoming wave can be described as an interference behaviour.^[2] When there is a constructive interference, the electron wave is intensified and therefore the final state more probable. This leads to a higher absorption probability and a maximum in the oscillating fine structure. When there is destructive interference, the electron wave is reduced and the final state is less probable than without neighbouring atoms. Therefore, the absorption probability decreases and the fine structure has a minimum.

In the surrounding of the atom type of interest, neighbours of different atom types and different distances to the absorbing atom can exist. Hence, several final waves caused by the different neighbours occure. EXAFS is the sum of these final waves.^[1] Therefore, a Fourier transformation of the measured data is necessary to receive a radial distribution function.^[5] From this, for example, the distances to the neighbouring atoms can be received.

Distances, near neighbour coordination numbers, and lattice dynamics can be received from this method, because the fine structure depends on these parameters. Therefore, with a change of, for example, the coordination number, the evolution of the fine structure changes as well. 

Experimental methods

For this experiment a monochromatic x-ray source, a detector of the initial x-ray beam intensity, the sample and a detector for the resulting intensity is needed (see fig. 5). The choice of the x-ray source and the different detection possibilities are discussed hereafter.

Figure 5. Experimental set-up for the EXAFS method. For the experiment, it can be chosen between the Auger-, Fluorescence- and transmitted-detector (Figure: Elisabeth Robens).

To receive good results, it is important to have an x-ray source that can produce a constant x-ray beam with respect to the energy. Moreover, it is necessary that the energy can be changed precisely. Because of these requirements, the best x-ray source for this method is a synchrotron.^[2]

To measure the absorption coefficient, the detection is important. There are three different possibilities of detection: transmission, fluorescence and Auger electrons. At the transmission detection, the rest intensity of the x-ray beam after transmitting the sample is measured. In contrast, the fluorescence and Auger electron methods are based on the detection of secondary radiation. After the ejection of a core level electron, an electron of a higher shell refills this hole. By this process the energy difference is emitted as fluorescence radiation (see fig. 6), which can be detected. Another possibility is that the emitted energy is used to eject another electron in the atom, which is called an Auger electron (see fig. 6).  These electrons are then detected and can be related to the photon absortion.^[5]

Figure 6. Formation of fluorescence radiation (left) and Auger-electron radiation (right) (Figure: Elisabeth Robens).

Simple example

For a better understanding of this method, there are simple examples following. In figure 7 there are four different molecules. The difference between molecule one and two is that the distance between the red and green atoms is smaller in molecule two. This difference results in a smaller frequency of the oscillating fine structure. The other two molecules differ in the coordination number. Molecule three has six neighbours and molecule four only two. Because of the higher coordination number of molecule three, there is a higher amplitude in the fine structure than for molecule four.

Figure 7. Influence of the distance and number of neighboring atoms on the fine structure (Figure: Nea Möttönen, inspired by reference^[6]).

Application example

Blik et al. used the EXAFS method to analyse the structure of a rhodium catalyst before and after carbon monoxide adsorption.^[7]Via a Fourier Transformation they calculated the distances R between rhodium, oxygen and carbon monoxide. Moreover, they were able to determine the average value of the near neighbor coordinating number N. 

With the help of this values and X-ray photoelectron spectroscopy (XPS), electron spin resonance (ESR), temperature programmed reduction (TPR), CO infrared spectroscopy, and H₂ and CO chemisorption they found out that after the reduction all rhodium was reduced and they formed three-dimensional metallic crystallites. After CO adsorption the metalic bounds were destroyed and Rh⁺ with two carbon monoxide molecules and three oxygen aniones were formed.

Advantages and Disadvantages

One advantage of EXAFS is that it is sensitive for the bulk and for the surface. Moreover, it can be used in several system like crystalline, nanostructured or amorphous materials, liquids and molecular gases.^[3] This is especially in contrast to X-ray diffraction (XRD) a huge advantage, because there a long-range order is needed. Another advantage is that the fine structure is selective for an atom type. The big disadvantage of this method is that a synchrotron is needed and therefore this method can not be used in normal laboratories and is quite expensive.^[5]

References