Critical absorption edge

The effective wavelength provides a useful way of characterizing polychromatic beams that are not appreciably affected by the presence of an absorption edge. One suspects intuitively that the presence of an absorption edge critically located could cause complications in absorptiometry with polychromatic beams. That this does happen has been demonstrated,13 and it limits the usefulness of the effective wavelength. 

Figure 1-12 summarizes some of the relations developed above. This curve gives the short-wavelength limit of the continuous spectrum as a function of applied voltage. Because of the similarity between Eqs. (1-4) and (1-16), the same curve also enables us to determine the critical excitation voltage from the wavelength of an absorption edge. 

Fig. 1-12 Relation between the voltage applied to an x-ray tube and the short-wavelength limit of the continuous spectrum, and between the critical excitation voltage of any metal and the wavelength of its absorption edge.

X-ray and electron diffraction methods are applied in order to measure atomic distances in the crystal lattice and their changes. Hence, the diffraction methods are also basically suitable for measuring the strain/stress behaviour in thin films. However, since the film thickness and the crystallite size in thin films are small, some line broadening already arises from this. In order to determine what contribution the mechanical stresses have on the diffuse lines, careful analysis of the line profiles must be undertaken [148, 151]. This method is less suitable for routine determination of stresses in thin films. In some cases, it is possible though rarely applied to determine the stresses in the films through their influence on other, known film properties, at least approximately. Such properties are, for example, the position of an absorption edge [152], the Hall effect [153], electron spin resonance spectra [155] and in the case of superconducting films, variations in the critical transition temperature [156]. However, these effects can, unfortunately, also arise for other reasons, and thus these techniques can usually only be used as supplemental experiments. 

Figure 2. Effect of energy on critical-angle beam penetration near the Mn absorption edge.

The sharp discontinuities in the absorption curve are related to the critical excitation energies (and their corresponding wavelengths) of the element for the K-shell/ Lj, Ln, and Lni subshells of the L-shell/ Mj, Mu, Mm, Mjv, and Mv subshells of the M-shell, etc. The K- and L-shell absorption edges for a few elements given in wavelength (A) by Bearden (1967), converted in keV,... 

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