Resolution corrections in diffuse scattering experiments

Abstract

The variation of diffuse scattered intensities with scattering angle due to resolution effects is described by different Lorentz factors depending on the dimensionality of the disorder (e.g. diffuse streaks or planes) and the type of scan. Intensities are calculated by folding the cross section of the diffuse scattering with the resolution function of the instrument. For the most general results existing calculations of the resolution function are extended to include (i) a characteristic line spectrum used together with a monochromator, (ii) a possible mis-set of the monochromator (e.g. between Kα1 and Kα2) and (iii) a perpendicular arrangement of the scattering planes at the monochromator and at the sample. Both a Gaussian and a slightly simplified rectangular approximation have been applied. Explicit formulae are derived for sharp diffuse streaks and planes for a point measurement as well as integrated intensities. Since the evaluation of point measurements requires exact knowledge of the instrumental divergences and, moreover, there are differences between the two approximations, it is strongly recommended that integrated intensities be used, preferably from scans perpendicular to the streak or plane.