Absorption edge coefficient

AT the path length, and P (A) the mass absorption coefficient at wavelength A. Between absorption edges, P (A) is proportional to Z A and is nearly independent of physical or chemical state. An absorption measurement on each side of an absorption edge is required for each element analyzed. X-ray absorption is especially useful in determining heavy elements in mixed materials of lower Z, such as lead in gasoline and uranium in aqueous solution. 

For good spectra to be obtained, the difference between the ln(I /lQ) before and after the absorption edge, the edge jump, should be between 0.1 and 1. This may be calculated from the mass absorption coefficient of a sample ... 

Fig. 1-10. Log-log plot showing mass absorption coefficient as a function of wavelength for three common metals. Note that the discontinuities locate the absorption edges, (K) and (L). (Liebhafsky, Ann. N.Y. Acad. Sci., 53, 997.)...

Between absorption edges, the photoelectric (true) mass absorption coefficient r can be expressed as the following approximate empirical function of Z and X ... 

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. 

Log-log plot of mass absorption coefficient against wavelength for lead showing K and L absorption edges. 

The effect of increased x-ray absorption on sensitivity was explored by conducting monochromatic exposures of a bromine-containing resist, poly(N-allyl maleimide-vinyl benzyl bromide), at photon energies which bracket the bromine absorption edges between 1.6 and 1.8 keV contrast curves obtained for these monochromatic exposures are shown in Figure 7. The results are also plotted as l/D "5 vs absorption coefficient in Figure 8 the data accurately follow the predicted inverse relationship defined by Equation 1. 

The absorption edge spectrum function expresses p, the TiC-absorption coefficient, in terms of Ex. n is defined here by normalization conditions and the equation ... 

In practical cases the absorption edge is not sharp and absorption coefficients of semiconductors decrease as the wavelength approaches the bandgap wavelength. The absorbed photon flux can then be written as [109]... 

The optical properties of amorphous solids are interesting. These solids are optically isotropic. Furthermore, the sharp features present in crystal spectra are absent in the spectra of amorphous solids even at low temperatures. The overall features in the electronic spectra of amorphous solids (broad band maxima) are, however, not unlike those of crystals, reflecting the importance of short-range order in determining these characteristics. The optical absorption edges of amorphous materials are not sharp and there is an exponential tail in the absorption coefficient (Fig. 7.13) associated with the intrinsic disorder. 

The absorption edge of (Ga,Mn)As is not sharp, as shown in fig. 20 (Kuroiwa et al. 1998 Szczytko et al. 1999b). This is probably due to impurity band formation caused by the high concentration of ionized Mn and compensating donors (Kuroiwa et al. 1998). Even below the fundamental absorption edge, the absorption coefficient is rather large due to free-carrier (Casey et al. 1975) and intra-Mn absorption. There is no report on the observation of exciton states or photoluminescence, which is probably due to non-radiative recombination, carrier screening, and the formation of an impurity band (Ando et al. 1999). 

The importance of X-ray diffraction (discussed in Chapter 3) to biochemistry is obvious, but techniques related to absorption of X-rays and y-rays have also come into widespread use.117 Abbreviations such as XANES and EXAFS are common in the metallopro-tein literature. The names arise from the sharp increase in the absorption coefficient for X-rays as their energy is increased to what is called the K absorption edge. At slightly lower energies absorption of an X-ray by an atom leads to expulsion of an electron or the raising of an electron to an excited state. Absorption of X-rays will expel all except the inner Is electrons. 

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). 

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