A correction procedure for the errors in single-crystal intensities due to the inhomogeneity of the primary X-ray beam

Graphite monochromators are known to give rise to non-homogeneous primary X-ray beams. When intensities of single crystals are measured the effective cross section of a non-spherical crystal in the X-ray beam depends on its orientation in the beam. Therefore, systematic errors in the measured integrated intensities are introduced by the inhomogeneity of the incoming beam. A correction for these errors can be made, knowing the intensity profile of the primary beam and the dimensions and orientation of the crystal in the beam. The correction can conveniently be applied with the absorption correction. Examples of the corrections are given for crystals with rational boundary planes. It is shown that the intensity of an X-ray reflection as a function of the rotation about the scattering vector (ψ rotation) can be calculated with fair accuracy. In some cases (large elongated crystals in an inhomogeneous beam) correction for absorption only may give results which are worse than those with no correction at all.