Correction of X-ray Intensities for Multiple Diffraction: Effects on Atomic Parameters and Charge Density

Abstract

The standard theory for secondary extinction based on intensity transfer equations has been extended to three-beam diffraction for a finite crystal in the Laue case. The expression for the primary diffracted intensity was used to first order to calculate correction factors for the two-beam integrated power assuming a type I mosaic crystal. The corrections were employed to study the effects of multiple diffraction on structure parameters and deformation density for three different crystals with unit-cell volumes in the range 385-1410 A3. In these data sets, 5-8% of all reflections with (sinO/A) :S 0 -7 A-I had relative shifts in integrated power tl'P/'P> 10%. The weak intensities are affected the most, and thus, among the weakest third of the data, 15-21% had relative corrections >10%. The crystallographic Rand goodness-of-fit factors were significantly improved after correction of the data for multiple diffraction. Atomic positional and displacement parameters, obtained from the refinements on corrected and uncorrected data respectively, have been compared, as have also pairs of deformation density maps. Rather unexpectedly, all shifts were very small, within 20" for atomic parameters and within 2·50" for the deformation densities. This implies that the effects of multiple diffraction are nearly random relative to the structure model and even relative to the deformation density.