Techniques for the measurement of X-ray attenuation coefficients

Creagh, D. C.

doi:10.1107/97809553602060000592

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

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International Tables for Crystallography (2006). Vol. C. ch. 4.2, pp. 214-215

Section 4.2.3.2. Techniques for the measurement of X-ray attenuation coefficients

D. C. Creagh^b

4.2.3.2. Techniques for the measurement of X-ray attenuation coefficients

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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) 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), 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 . The configurations used ranged in complexity from that of Fig. 4.2.3.3(a), 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(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), monochromatization of the beam was effected using single Bragg reflection from silicon single crystals. In Fig. 4.2.3.3(i), 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| top | pdf |

Schematic representations of experimental apparatus used in the IUCr X-ray Attenuation Project (Creagh & Hubbell, 1987; Creagh, 1985). 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);
(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.

4.2.3.2.2. Specimen selection

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Although the most important component in the experiment is the specimen itself, examination of the data files held at the US National Institute of Standards and Technology (Gerstenberg & Hubbell, 1982; Saloman & Hubbell, 1986; Hubbell, Gerstenberg & Saloman, 1986) has shown that, in general, insufficient care has been taken in the past to select an experimental device with characteristics that are appropriate to the specimen chosen. Nor has sufficient care been taken in the determination of the dimensions, homogeneity, and defect structure of the specimens. To achieve the best results, the following procedures should be followed.

(i) The dimensions of the specimen should be determined using at least two different techniques, and sample thicknesses should be chosen such that the Nordfors (1960) criterion, later confirmed by Sears (1983), that the condition $[2\le\ln(I_0/I)\le4\eqno (4.2.3.7)]$ be satisfied. This enables the best compromise between achieving good counting statistics and avoiding multiple photon scattering within the sample.

Wherever possible, different sample thicknesses should be chosen to enable a test of equation (4.2.3.1) to be made. If deviations from equation (4.2.3.1) exist, either the sample material or the experimental configuration, or both, are not appropriate for the measurement of $[\mu_l]$ . If the attenuation of the material under test falls outside the limits set by the Nordfors criterion and the material is in the form of a powder, the mixing of this powder with one with low attenuation and no absorption edge in the region of interest can be used to bring the total attenuation of the sample within the Nordfors range.
(ii) The sample should be examined by as many means as possible to ascertain its regularity, homogeneity, defect structure, and, especially for very thin specimens, freedom from pinholes and cracks. Where a diluent has been used to reduce the attenuation so that the Nordfors criterion is satisfied, care must be taken to ensure intimate mixing of the two materials and the absence of voids.

Since the theory upon which equation (4.2.3.1) is based envisages that each atom scatters as an individual, it is necessary to be aware of whether such cooperative effects as Laue–Bragg scattering (which may become significant in single-crystal specimens) and small-angle X-ray scattering (SAXS) (which may occur if a distribution of small voids or inclusions exists) occur in polycrystalline and amorphous specimens. Knowledge that cooperative scattering may occur influences the choice of collimation of the beam.
(iii) The sample should be mounted normal to the beam.

4.2.3.2.3. Requirements for the absolute measurement of μ_l or (μ/ρ)

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The following prescription should be followed if accurate, absolute measurements of $[\mu_l]$ and $[(\mu/\rho)]$ are to be obtained.

(i) X-ray source and X-ray monochromatization. The energy of the incident photons should be measured directly using reflections from a single-crystal silicon monochromator, and the energy spread of the beam should be measured. Measurements should be made of the state of polarization, since X-ray-polarization effects are known to be significant in some measurements (Templeton & Templeton, 1982, 1985a, 1986). The results of a survey on X-ray polarization were given by Jennings (1984). If a single-crystal monochromator is employed, it should be placed between the sample and the detector.
(ii) Collimation. It is of some advantage if both the incident-beam- and the transmitted-beam-defining slits can be varied in width.

Should it be necessary to combat the effects of Laue–Bragg scattering in a single-crystal specimen, an incident beam with a high degree of collimation is required (Gerward, 1981).

To counter the effects of small-angle X-ray scattering, it may be necessary to widen the detector aperture (Chipman, 1969). That these effects can be marked has been shown by Parratt, Porteus, Schnopper & Watanabe (1959), who investigated the influence collimator and monochromator configurations have on X-ray-attenuation measurements.
(iii) Detection. Detectors that give some degree of energy discrimination should be used. Compromise may be necessary between sensitivity and energy resolution, however, and these factors should be taken into account when a choice is being made between proportional and solid-state detectors.

Whichever detection system is chosen, it is essential that the system dead-time be determined experimentally. For descriptions of techniques for the determination of system dead-time, see, for example, Bertin (1975).

References

Bertin, E. P. (1975). Principles and practice of X-ray spectrometric analysis. New York: Plenum.Google Scholar

Chipman, D. R. (1969). Conversion of relative intensities to an absolute scale. Acta Cryst. A25, 209–214.Google Scholar

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

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

Gerstenberg, H. & Hubbell, J. H. (1982). Comparison of experimental with theoretical photon attenuation cross sections between 10 eV and 100 GeV. Nuclear data for science and technology, edited by K. H. Bockhoff, pp. 1007–1009. Amsterdam: North-Holland.Google Scholar

Gerward, L. (1981). X-ray attenuation coefficients and atomic photoelectric absorption cross sections of silicon. J. Phys. B, 14, 3389–3395.Google Scholar

Hubbell, J. H., Gerstenberg, H. M. & Saloman, E. B. (1986). Bibliography of photon total cross section (attenuation coefficient) measurements 10 eV to 13.5 GeV. Report NBSIR 86-3461. National Institute of Standards and Technology, Gaithersburg, MD, USA.Google Scholar

International Tables for X-ray Crystallography (1974). Vol. IV. Birmingham: Kynoch Press.Google Scholar

Jennings, L. D. (1984). The polarization ratio of crystal monochromators. Acta Cryst. A40, 12–16.Google Scholar

Nordfors, B. (1960). The statistical error in X-ray absorption measurements. Ark. Fys. 18, 37–47.Google Scholar

Parratt, L. G., Porteus, I. O., Schnopper, H. W. & Watanabe, T. (1959). X-ray absorption coefficients and geometrical collimation of the beam. Rev. Sci. Instrum. 30, 344–347.Google Scholar

Saloman, E. B. & Hubbell, J. H. (1986). X-ray attenuation coefficients (total cross sections): comparison of the experimental data base with the recommended values of Henke and the theoretical values of Scofield for energies between 0.1–100 keV. Report NBSIR 86-3431. National Institute of Standards and Technology, Gaithersburg, MD, USA.Google Scholar

Sears, V. F. (1983). Optimum sample thickness for total cross section measurements. Nucl. Instrum. Methods, 213, 561–562.Google Scholar

Templeton, D. H. & Templeton, L. K. (1982). X-ray dichroism and polarized anomalous scattering of the uranyl ion. Acta Cryst. A38, 62–67.Google Scholar

Templeton, D. H. & Templeton, L. K. (1985a). X-ray dichroism and anomalous scattering of potassium tetrachloroplatinate(II). Acta Cryst. A41, 356–371.Google Scholar

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International Tables for Crystallography (2006). Vol. C. ch. 4.2, pp. 214-215

Section 4.2.3.2. Techniques for the measurement of X-ray attenuation coefficients

4.2.3.2. Techniques for the measurement of X-ray attenuation coefficients

4.2.3.2.1. Experimental configurations

4.2.3.2.2. Specimen selection

4.2.3.2.3. Requirements for the absolute measurement of μl or (μ/ρ)

References

4.2.3.2.3. Requirements for the absolute measurement of μ_l or (μ/ρ)