Absorption correction for cylindrical and annular specimens and their containers or supports

The absorption correction for cylindrical specimens, typically capillary or annular, is affected by absorption in both the specimen and the supporting material. These corrections are calculated here using numerical integration of the lengths through the different regions of the specimen that the beam traverses. Suitable formulae have been derived and built in to a computer program for calculating the absorption correction for a range of cylindrical geometries. The influence of absorption in the support is most significant for annular specimens on a highly absorbing core, and for capillary specimens of highly absorbing compounds. The error arising from neglecting absorption in the specimen and additionally in the capillary is demonstrated in Rietveld refinements of LaB₆. Interpolation of correction factors between values calculated at discrete θ intervals, and θ offsets arising from absorption, are also discussed.