X-Ray Absorption Process

As is the case with other forms of radiation, some of the intensity of the incident beam may be absorbed by the sample while the remainder is transmitted. We can write a Beer s law expression for the absorption of X-rays by a thin sample  

I(k) is the transmitted intensity at wavelength k Iq(K) is the incident intensity at the same wavelength is the mass absorption coefficient (craVg) p is the density of the sample (g/cm ) 

The mass absorption coefficient is a constant for a given element at a given wavelength and is independent of both the chemical and physical state of the element. An updated compilation of mass absorption coefficients can be found online at the NIST website http //www.nist.gov/pml/ data/xraycoef/index.cfm (J.H. Hubbell and S.M. Seltzer) or in the text by Bertin or handbooks listed in the bibliography or references in the literature. 

Of course, most samples do not consist of a single pure elonent The total mass absorption coefficient for a sample can be calculated by adding the product of the individual mass absorption coefficients for each element times the weight fraction of the element present in the sample. That is, for a metal alloy like steel. 

For accurate quantitative woik, the mass attenuation coefficient is used in place of the mass absorption coefficient. The mass attenuation coefficient takes into account both absorption and scattering of X-rays by the sample. 

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Virtually all prior reviews and textbooks on XAFS spectroscopy begin with a derivation of the XAFS equation, coupled with a theoretical background. Given the depth and excellence of some of these reviews, we do not repeat this work here. The reader is referred to these articles (Iwasawa, 1996 Koningsberger and Prins, 1988 Teo, 1986 Teo and Joy, 1981) and to online tutorials (http //xafs.org/) only a brief synopsis of the X-ray absorption process is given here, together with the pertinent parameters that are measured in an XAFS experiment. 

The X-ray absorption process acts on a very fast timescale, essentially instantaneously with respect to molecular vibrations or thermal averaging between conformers. This is in contrast with diffraction techniques where data is collected over a period of hours and is an average of the whole crystal. Thus EXAFS is capable of probing the instantaneous local geometry of the absorbing species. 

For the x-ray absorption process, the transition probability can also be estimated by the approximation of the dipole transition. In the x-ray process, the oscillator strength is evaluated from the dipole matrix element between a core state c and a unoccupied molecular state I and is given by... 

Figure 8.4 (A) Squematic representation of the X-ray absorption process for K edge excitation. The energy of photons are hus> hu2> hu. (B) X-ray absorption spectrum of polyfaniline) doped with Fe(lll) at Fe K-edge. (Data acquired at EXAFS beam line of the Brazilian Nationai Synchrotron Lab, Brazil.) Generally, it is considered that the EXAFS region starts after SOeV of...

Since X-ray absorption is an atom-specific process, any atoms known to be, or deliberately placed, on a solid consisting of different atoms can be studied with high sensitivity. 

In the preceding discussion of Beer s Law, it was argued that x-ray absorption is a simpler process than the absorption of ultraviolet, visible, and infrared wavelengths. This greater simplicity becomes particularly obvious when x-ray absorption coefficients are examined. 

The second feature, the use of a secondary radiator, entails a loss of intensity because it introduces a second x-ray excitation process, but this loss is, offset to a large extent by the increased absorption of the characteristic lines from the radiator. The third feature also merits further comment. As Figure 11-7 shows, the proportional counter... 

X-ray absorption is a well understood process. It provides precise quantification of e.g., contrast agent concentration in the tissue or body cavities and excellent spatial and temporal resolution. Diagnostic applications do not require advancing the X-ray source... 

Surface extended X-ray absorption fine structure (SEXAFS). In order to understand the SEXAFS approach it may first be useful to give a brief recap of X-ray absorption. In addition to the scattering process described above, an X-ray photon may instead be absorbed. X-ray absorption results in the excitation of a core electron into one of the continuum of empty levels in the lowest unoccupied band of the sample this is shown for copper in Figure 2.72. To a first approximation, the attenuation of the beam is given by a form of the Beer-Lambert expression ... 

Temperature-programmed reduction combined with x-ray absorption fine-structure (XAFS) spectroscopy provided clear evidence that the doping of Fischer-Tropsch synthesis catalysts with Cu and alkali (e.g., K) promotes the carburization rate relative to the undoped catalyst. Since XAFS provides information about the local atomic environment, it can be a powerful tool to aid in catalyst characterization. While XAFS should probably not be used exclusively to characterize the types of iron carbide present in catalysts, it may be, as this example shows, a useful complement to verify results from Mossbauer spectroscopy and other temperature-programmed methods. The EXAFS results suggest that either the Hagg or s-carbides were formed during the reduction process over the cementite form. There appears to be a correlation between the a-value of the product distribution and the carburization rate. 

El Fallah, J., Boujani, S., Dexpert, H., Kiennemann, A., Majerus, J., Touret, O., Villain, F., and Le Normand, F. 1994. Redox processes on pure ceria and on Rh/ Ce02 catalyst monitored by x-ray absorption (fast acquisition mode)../. Phys. Chem. 98 5522-33. 

Ffirai and Toshima have published several reports on the synthesis of transition-metal nanoparticles by alcoholic reduction of metal salts in the presence of a polymer such as polyvinylalcohol (PVA) or polyvinylpyrrolidone (PVP). This simple and reproducible process can be applied for the preparation of monometallic [32, 33] or bimetallic [34—39] nanoparticles. In this series of articles, the nanoparticles are characterized by different techniques such as transmission electronic microscopy (TEM), UV-visible spectroscopy, electron diffraction (EDX), powder X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) or extended X-ray absorption fine structure (EXAFS, bimetallic systems). The great majority of the particles have a uniform size between 1 and 3 nm. These nanomaterials are efficient catalysts for olefin or diene hydrogenation under mild conditions (30°C, Ph2 = 1 bar)- In the case of bimetallic catalysts, the catalytic activity was seen to depend on their metal composition, and this may also have an influence on the selectivity of the partial hydrogenation of dienes. 

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