Kronig fine structure

Quantitative data on local structure can be obtained via an analysis of the decaying slope next to the absorption edge. The absorption of an X-ray photon boosts a core electron up into an unoccupied band of the material which, in a metal, is the conduction band above the Fermi level. Electrons in such a band behave as if nearly free and no fine structure would be expected on the absorption tail . However, fine structure is observed up to 500 to 1000eV above the edge (see Figure 2.73(b)). The ripples are known as the Kronig fine structure or extended X-ray absorption fine structure (EX AFS). 

Absorption of X-ray radiation of energy well above the threshold for an X-ray transition will result in the ejection of a photoelectron since the initial unoccupied band stale to which the transition takes place will be above the vacuum level. The Kronig fine structure is due to oscillations induced in the absorption cross-section of the absorbing atom as a result of interference... 

Figure 2.74 Schematic representation of the electron wave interference effects giving rise to the Kronig fine structure on X-ray absorption edges (sec text).

The Kronig theory has been used to explain the extended fine structure, occurring in the energy range 100 to 500 ev. above the principal edge. Closer to the edge, difficulties arise, perhaps related to the interactions of the slow photoelectron with the lattice. 

A new approach to the explanation of fine structure has been offered by Hayasi (S). Like Kossel, he assumes bound states, but of short lifetime and of positive energy. These states, which he refers to as quasi-stationary, are stabihzed by Bragg reflections from important planes in the crystal. In the theory of Kronig the Bragg reflections of the photoelectron lead to minima in the absorption coefficient, in that of Hayasi to maxima. 

The spectrum of titanium metal foil is in Fig. 23. The foil, originally of 12/t thickness, was reduced by etching in HF to about 4/. A corresponding spectrum of titanium metal powder (not shown here) contained the same peaks but with only about half the amplitude, and with greater scatter of data points. This is an illustration of the advantages of having uniformity of thickness, which is especially difficult to achieve with metal powders. The titanium metal spectrum appears to be Kronig type fine structure. 

This fine structure has been known for a long time—H. Fricke [2] and G. Hertz 31 discovered it in 1920—but the effect could not be explained satisfactorily by theory at the lime. R. de L. Kronig 4,5] already had the correct fundamental ideas in the 1930s, but the interpretation remained confusing until the 1970s w hen D.E. Sayers. F.A. Stern and F.W. Lytle [6,7] formulated a theory that has remained generally accepted until today. This theory will be briefly outlined below... 

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