X-rays with Matter

When an X-ray beam passes through matter, some photons wiU be absorbed inside the material or scattered away from the original path, as illustrated in Fig. 11.1. The intensity Iq of an X-ray beam passing through a layer of thickness d and density p is reduced to an intensity I according to the well-known Lambert—Beer law  

The number of photons (the intensity) is reduced but their energy is generally unchanged. The term p is called the mass attenuation coefficient and has the dimension cm g . The product pi = pp is called the linear absorption coefficient and is expressed in cm . p(E) is sometimes also called the total cross section for X-ray absorption at energy E. 

The mass absorption coefficient//(M) of a complex matrix M consisting of a mixture of several chemical elements (e. g., an alloy such as brass), can be calculated from the mass attenuation coefficients of the n constituting elements  

The mass absorption coefBdent// plays a very important role in quantitative XRF analysis. Both the exciting primary radiation and the fluorescence radiation are attenuated in the sample. To relate the observed fluorescence intensity to the concentration, this attenuation must be taken into account As illustrated in Fig. 11.1, the absorption of radiation in matter is the cumulative effect of several types of photon—matter interaction processes that take place in parallel. Accordingly, in the X-ray range the mass attenuation coefficient of element i can be expressed as  

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All analytical methods that use some part of the electromagnetic spectrum have evolved into many highly specialized ways of extracting information. The interaction of X-rays with matter represents an excellent example of this diversity. In addition to straightforward X-ray absorption, diffraction, and fluorescence, there is a whole host of other techniques that are either directly X-ray-related or come about as a secondary result of X-ray interaction with matter, such as X-ray photoemission spectroscopy (XPS), surface-extended X-ray absorption fine structure (SEXAFS) spectroscopy, Auger electron spectroscopy (AES), and time-resolved X-ray diffraction techniques, to name only a few [1,2]. 

Since their discovery in 1895, X-rays have been one of the primary probes with which chemists and physicists have investigated the stractuie of matter. Although most well known for their use in crystallography, the earliest studies with X-rays emphasized spectroscopic measurements, hi the early years of this century X-ray spectroscopy, in particular tiie work of Moseley, played a key role in the discovery and characterization of new elements. Following Aese early successes however, the potential chemical applications of X-ray spectroscopy were largely unappreciated until the mid-seventies. "Die reasons for this can be traced both to the weak interactions of X-rays with matter and to the low intensities available horn conventional X-ray sources. These factors combine to limit conventional X-ray spectroscopy to relatively concentrated samples. 

The interaction of X-rays with matter is weak compared to that of electrons. This leads to a large penetration depth of some /xm... 

X-ray spectroscopy — X-ray spectroscopy of matter can be performed as emission or absorption spectroscopy. In electrochemical investigations only the latter is of interest. Interaction of X-rays with matter results in removal of an electron from an inner, core-near shell. There, electronic states next to the state from which the electron is removed are filled so that the electron has to be transferred to empty outer states, actually it is removed from the atom. Upon passage of X-rays through a sample of thickness x the intensity after passage I as compared to the initial intensity Iq is given by... 

Since the interaction of hard X-rays with matter is small, the kinematical approximation of single scattering is valid in most cases, except for perfect crystals near Bragg scattering. The intensity scattered by a block-shaped crystal with N, q and N, unit cells along the three crystal axes defined by the vectors Uj, a and a, takes the form ... 

Since the discovery of x-rays by Roentgen in 1896, this region of the electromagnetic spectrum has been a source of significant contributions to our fundamental knowledge of atomic structure and to our techniques for chemical analysis. By 1927, six Nobel prizes in physics had been awarded for studies on the physics of x-rays and the interaction of x-rays with matter. 

This review aims to provide chemists working on porous materials with a basic understanding of XAS and related methods and to show them where the techniques might be of help in their research. After a short section on the basic physics of the interaction of X-rays with matter (Sect. 2), the basic physical processes and a theoretical description of XAFS are discussed (Sect. 3) in such a way that the method can be understood. Section 4 presents some experimental details and an example of a typical data analysis procedure. The next section is devoted an explanation of the type of information contained in X-ray absorption spectra by using examples from zeoHte chemistry (Sect. 5). Newer developments, especially with regard to time-resolved and in situ studies, as well as related techniques such as electron energy loss spectroscopy (EELS) and anomalous diffraction, are described in Sect. 6. 

Analytically useful x-rays interact almost exclusively with the electrons in matter. For this reason, any discussion of the interaction of x-rays with matter should begin with a description of the interaction of an x-ray photon with a single free electron and proceed to multielectron atoms and thence to multiatom solids. It will be shown that two basic interaction processes dominate (1) the photoelectric effect and (2) x-ray scattering. 

The primary effect of the interaction of X-rays with matter includes the production of high-energy electrons, which are the main agents through which all the effects of X-rays arise. 

Thanks to the full understanding of the interaction processes of X-rays with matter, computer techniques, particularly those based on Monte Carlo simulation, are able to predict the spectral response without limitations in approximations or idealizations of the sample geometry. Hence, they allow methods for calibration and correction for radiation absorption, thus opening up the way to perform reliable quantitative analysis. 

Since the interaction of hard X-rays with matter is weak, provided that the exact Bragg conditions for a perfect crystal are not met, the kinematical scattering approximation, in which scattering is treated as a single event, can be used. For a crystal volume defined by A i, N2, and A 3 unit cells along the crystal axes defined by the vectors ai, 82, and 33, the scattered intensity can be written as the product of two scattering amplitudes, one from the unit cell and one from the lattice of unit... 

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