Photon Attenuation Coefficients

You would like to analyze the atomic structure of Pd by grazing incidence X-ray diffraction. After penetrating a distance x, the intensity of the beam is decreased by I = J0 e x. Your diffractometer uses photons of 10 keV energy. Is the wavelength sufficiently small to analyze atomic structures At this energy a handbook tells you that the photon attenuation coefficient, nip, is 691 cm2/g. The density is 12.0 g/cm3. Assume you want 20% of the incident X-rays to be scattered within the topmost layer of 1 nm thickness. Which angle do you have to choose ... 

Figure 12.31 Photon attenuation coefficients for germanium. The dashed line is the approximate total linear attenuation coefficient.

Although gamma rays are much less subject to attenuation than alpha and beta particles, a density correction is needed if the density of the sample deviates significantly from the density of the calibration standards. The effect of density on self-absorption for both the standard and the sample is estimated by Eq. (7.2) [x for this purpose is the photon attenuation coefficient in cm /g and x is the sample area density in g/cm. Values for ix in some common materials are listed in Table 2.2 and in its cited reference. If a large set of samples with consistent density is analyzed, it may be possible to prepare radioactivity standards at the same density to avoid the need for correction. Interpolating efficiency values as a function of density is feasible at energies above 0.1 MeV because the effect of minor density difference on counting efficiency is small. 

PHOTON ATTENUATION COEFFICIENTS Martin J. Berger and John H. Hnbbell... 

Calculations according to O Eq. (30.43) require the knowledge of the photon attenuation coefficients /r of the sample matrix (see Sect. 11.5.1 in the Appendix of Vol. 1). Experimental calibrations are readily conducted by placing an unirradiated sample between the activated sample and the detector, thus determining the attenuation coefficients for an unknown or unlisted matrix. By using an irradiated standard identical to the sample, as is possible in the comparator method, the need for geometry, self-shielding, and self-absorption corrections is eliminated, and thus the potential errors are reduced. 

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