Absorption and fluorescence corrections for X-ray analysis with large-solid-angle detectors: Thin films and spheres

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The absorption and fluorescence corrections used in X-ray microanalysis in transmission electron microscopy are normally derived under the assumption that the X-ray detector is at infinite distance from the analyzed sample. These corrections may become inadequate when there is a range of photon directions which will be subtended by the detector as in the case of large-solid-angle detectors. In this article, a model that takes into account the variation in detector acceptance angles in the absorption and fluorescence corrections of thin specimens is developed. This is accomplished by integrating over the solid angle subtended by the X-ray detector, and hence treating the X-ray emergence angle as a variable. The results show that for spheres, both corrections are insensitive to specimen and detector geometry. The thin-film corrections, however, are found to be sensitive to detector geometry especially when both the detector solid angle and the corrections are large. Moreover, when the detector solid angle is large, tilting of the film to minimize the magnitude of the corrections becomes a must and the optimum tilt angle occurs at a minimum in the product of the two corrections. Finally, a general expression for the fluorescence corrections of thin films which accounts for secondary absorption is derived.