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. 214-215

Section 4.2.3.2.1. Experimental configurations

D. C. Creaghb

4.2.3.2.1. Experimental configurations

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Experimental configurations that set out to determine the X-ray linear attenuation coefficient [\mu_l] or the corresponding mass absorption coefficients (μ/ρ) must have characteristics that reflect the underlying assumptions from which equation (4.2.3.1)[link] was derived, namely:

  • (i) the incident and transmitted beams are parallel and there is no divergence in the transmitted beam;

  • (ii) the photons in the incident and transmitted beams have the same energy;

  • (iii) the specimen is of sufficient thickness.

Because of the considerable discrepancies that often exist in X-ray attenuation measurements (see, for example, IT IV, 1974[link]), the IUCr Commission on Crystallographic Apparatus set up a project to determine which, if any, of the many techniques for the measurement of X-ray attenuation coefficients is most likely to yield correct results. In the project, a number of different experimental configurations were used. These are shown in Fig. 4.2.3.3[link] . The configurations used ranged in complexity from that of Fig. 4.2.3.3(a)[link], which uses a slit-collimated beam from a sealed tube and a β-filter to select its characteristic radiation, and a proportional counter and associated electronics to detect the transmitted-beam intensity, to that of Fig. 4.2.3.3[link](f), which uses a modification to a commercial X-ray-fluorescence analyser. Sources of X-rays included conventional sealed X-ray tubes, X-ray-fluorescence sources, radioisotope sources, and synchrotron-radiation sources. Detectors ranged from simple ionization chambers, which have no capacity for photon energy detection, to solid-state detectors, which provide a relatively high degree of energy discrimination. In a number of cases (Figs. 4.2.3.3c, d, e, and f[link]), monochromatization of the beam was effected using single Bragg reflection from silicon single crystals. In Fig. 4.2.3.3(i)[link], the incident-beam monochromator is using reflections from two Bragg reflectors tuned so as to eliminate harmonic radiation from the source.

[Figure 4.2.3.3]

Figure 4.2.3.3| top | pdf |

Schematic representations of experimental apparatus used in the IUCr X-ray Attenuation Project (Creagh & Hubbell, 1987[link]; Creagh, 1985[link]). X: characteristic line from sealed X-ray tube; b: Bremsstrahlung from a sealed X-ray tube; r: radioactive source; s: synchrotron-radiation source; β: β-filter for characteristic X-rays; S: collimating slits; M: monochromator.

The performance of these systems was evaluated for a range of materials that included:

  • (i) highly perfect silicon single crystals (Creagh & Hubbell, 1987[link]);

  • (ii) polycrystalline copper foils that exhibited a high degree of preferred orientation; and

  • (iii) pyrolytic graphite that contained a high density of regular voids.

The results of this study are outlined in Section 4.2.3.2.3[link].

References

First citation Creagh, D. C. (1985). Theoretical and experimental techniques for the determination of X-ray anomalous dispersion corrections. Aust. J. Phys. 38, 371–404.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 International Tables for X-ray Crystallography (1974). Vol. IV. Birmingham: Kynoch Press.Google Scholar








































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