International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C. ch. 4.2, pp. 213-214

Section 4.2.3.1.3. Normal attenuation, XAFS, and XANES

D. C. Creaghb

4.2.3.1.3. Normal attenuation, XAFS, and XANES

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The curves shown in Fig. 4.2.3.1[link] are the result of theoretical calculations of the interactions of an isolated atom with a single photon. Experiments are not usually performed on isolated atoms, however. When experiments are performed on ensembles of atoms, a number of points of difference emerge between the experimental data and the theoretical calculations. These effects arise because the presence of atoms in proximity with one another can influence the scattering process. In short: the total attenuation coefficient of the system is not the sum of all the individual attenuation coefficients of the atoms that comprise the system.

Perhaps the most obvious manifestation of this occurs when the photon energy is close to an absorption edge of an atom. In Fig. 4.2.3.2[link] , the mass attenuation of several germanium compounds is plotted as a function of photon energy. The energy scale measures the distance from the K-shell edge energy of germanium (11.104 keV). These curves are taken from Hubbell, McMaster, Del Grande & Mallett (1974[link]). Not only does the experimental curve depart significantly from the theoretically predicted curve, but there is a marked difference in the complexity of the curves between the various germanium compounds.

[Figure 4.2.3.2]

Figure 4.2.3.2| top | pdf |

The dependence of the X-ray attenuation coefficient on energy for a range of germanium compounds, taken in the neighbourhood of the germanium absorption edge (from IT IV, 1974[link]).

Far from the absorption edge, the theoretical calculations and the experimental data are in reasonable agreement with what one might expect using the sum rule for the various scattering cross sections and one could say that this region is one in which normal attenuation coefficients may be found.

Closer to the edge, the almost periodic variation of the mass attenuation coefficient is called the extended X-ray absorption fine structure (XAFS). Very close to the edge, more complicated fluctuations occur. These are referred to as X-ray absorption near edge fine structure (XANES). The boundary of the XAFS and XANES regions is somewhat arbitrary, and the physical basis for making the distinction between the two will be outlined in Subsection 4.2.3.4[link].

Even in the region where normal attenuation may be thought to occur, cooperative effects can exist, which can affect both the Rayleigh and the Compton scattering contributions to the total attenuation cross section. The effect of cooperative Rayleigh scattering has been discussed by Gerward, Thuesen, Stibius-Jensen & Alstrup (1979[link]), Gerward (1981[link], 1982[link], 1983[link]), Creagh & Hubbell (1987[link]), and Creagh (1987a[link]). That the Compton scattering contribution depends on the physical state of the scattering medium has been discussed by Cooper (1985[link]).

Care must therefore be taken to consider the physical state of the system under investigation when estimates of the theoretical interaction cross sections are made.

References

First citation Cooper, M. J. (1985). Compton scattering and electron momentum determination. Rep. Prog. Phys. 48, 415–481.Google Scholar
First citation Creagh, D. C. (1987a). The resolution of discrepancies in tables of photon attenuation coefficients. Nucl. Instrum. Methods, A255, 1–16.Google Scholar
First citation Creagh, D. C. & Hubbell, J. H. (1987). Problems associated with the measurement of X-ray attenuation coefficients. I. Silicon. Acta Cryst. A43, 102–112.Google Scholar
First citation Gerward, L. (1981). X-ray attenuation coefficients and atomic photoelectric absorption cross sections of silicon. J. Phys. B, 14, 3389–3395.Google Scholar
First citation Gerward, L. (1982). X-ray attenuation coefficients of copper in the energy range 5 to 50 keV. Z. Naturforsch. Teil A, 37, 451–459.Google Scholar
First citation Gerward, L. (1983). X-ray attenuation coefficients of carbon in the energy range 5 to 20 keV. Acta Cryst. A39, 322–325.Google Scholar
First citation Gerward, L., Thuesen, G., Stibius-Jensen, M. & Alstrup, I. (1979). X-ray anomalous scattering factors for silicon and germanium. Acta Cryst. A35, 852–857.Google Scholar
First citation Hubbell, J. H., McMaster, W. H., Del Grande, N. K. & Mallett, J. H. (1974). X-ray cross sections and attenuation coefficients. International tables for X-ray crystallography, Vol. IV, edited by J. A. Ibers & W. C. Hamilton, pp. 47–70. Birmingham: Kynoch Press.Google Scholar
First citation International Tables for X-ray Crystallography (1974). Vol. IV. Birmingham: Kynoch Press.Google Scholar








































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