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

Abstract

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.

On squaring triangles – Structural motifs in Cu–In–Sb compounds

“…Powder neutron diffraction (PND) experiments were per-85 formed on beamline D2B[17] at the Institute Laue-Langevin in Grenoble, France, at 293 K using a wavelength of 1.594Å. To limit the effects of absorption, cylindrical containers (∅ = 6 mm) were used, and an expedient absorption correction was been applied [18].…”

Structure, Morphology, and Faceting of TiO2 Photocatalysts by the Debye Scattering Equation Method. The P25 and P90 Cases of Study

“…Separate air and empty capillary scattering measurements were performed, and the linear absorption coefficients of the samples were estimated through "radiographic" measurements (attenuated direct beam with and without the sample), while the one for the empty capillary was calculated from the glass certified composition and the tables provided by NIST website. The transmission of each specimen was numerically estimated using an X-ray tracing approach [42,43]. Raw data were then corrected for systematic errors (zero position and offsets) and absorption effects; the extra-sample contributions to the diffraction pattern, namely, the empty capillary and the sample environment scattering, were properly subtracted.…”

Neutron Powder Diffraction

“…Correction for this type of geometry has been tabulated [31]. Bowden and Ryan have calculated absorption correction for cylindrical and annular specimens [32]. Contrary to the common belief, they found that the shape of the sample holder has a stronger influence for specimen having higher absorption.…”