X-ray absorption coefficient

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. 

Extended X-ray absorption fine structuret (EXAFS) refers to the modulation in the X-ray absorption coefficient beyond an absorption edge. Such modulations can extend up to about 1000 eV beyond the edge and have a magnitude of typically less than 20% of the edge jump. 

Bulk processes can also be probed by an appropriate photon spectroscopy. For example, EXAFS provides an excellent spatial resolution with respect to the atomic surroundings. The information from Extended X-ray Absorption Fine Structure spectroscopy is contained in the oscillations of the X-ray absorption coefficient near an absorption edge e.g., the K- or L-edge). 

Second, the use of meshed particles versus a pressed wafer will typically lead to nonuniformity of X-ray absorption thickness. This can be directly observed by placing an X-ray sensitive camera behind the sample a sample of a powder pressed into a wafer is spectroscopically more uniform than a catalyst bed of meshed particles. Naturally the contrast becomes more extreme as the meshed particles become larger. Moreover, if the sample is spatially nonuniform then severe constraints are placed on the positional stability of the X-ray beam. Any motion of the position of the X-ray beam will then probe different thicknesses of the sample, with direct consequences on the measured S/N. From the perspective of XAFS spectroscopy, any nonuniformity of the sample thickness could directly affect the accuracy of the measurement of the amplitude of the X-ray absorption coefficient. It is the amplitude that contains information about the coordination number and site disorder. As has been discussed elsewhere (Koningsberger and Prins, 1988), these amplitude distorting effects are given the general heading of "thickness effects." In brief, a thickness effect occurs when part of the incident X-ray beam is not attenuated by the sample. In the case of meshed particles this would be in the form of pinholes in the sample. 

The contribution to the X-ray absorption coefficient due to the excitation of a deep core level may be expressed as /rc = nco-c, where nc is the density of atoms with the core level of concern and absorption cross section for this level on a single atom. Assuming the X-ray field to be a small perturbation, the latter can be evaluated from the golden rule transition rate per unit photon flux. The general X-ray absorption cross section is given by... 

EXAFS Spectroscopy. The EXAFS, x(E), is defined as the fractional modulation of the X-ray absorption coefficient ... 

X-ray absorption coefficients are listed in the International Tables of Crystallography IIP 2) From the numerous empirical formulae used for the Computation of X-ray absorption coefficents we just mention... 

For a modern XRF equipped with a powerful computer system, the fundamental parameter method (FP method) is most widely used for quantitative analysis. The method determines the concentration of an element when its theoretical intensity matches its measured intensity. The fluorescence X-ray intensity of a given composition can be calculated using theoretical formulas with given specimen physical and instrumental parameters. The physical parameters include specimen density, thickness, X-ray absorption coefficients and fluorescence yield. The instrumental parameters include excitation voltage of the X-ray tube, optical geometry and detector characteristics. 

EXAFS Results. In order to estimate the cohesiveness of the ionic aggregates, we applied EXAFS spectroscopy to examine the coordination structure about the cation. The EXAFS signal is a modulation of the x-ray absorption coefficient on the high-energy side of an elemental absorption edge. The photoelectrons that are ejected by the absorbed x-rays can be backscattered by atoms coordinated to the... 

The superposition of the outgoing and incoming waves alters the wave function of the photoelectron at the site of the given emitter. The final state wave function, /), becomes q> + (psc) where (pe and (pscSXQ the emitted and scattered wave functions. The photoelectron absorption process involves the final state wave function and the quantum mechanical expression for the X-ray absorption coefficient is given by. 

The second process, namely the absorption of X-rays. can also be used to obtain information about the local order around a certain element, since the line structure of the X-ray absorption coefficient on... 

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