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.

Crystal structure of an orthorhombic form of 1,2-bis(phenylsulfonyl)ethane at 86 K

“…5.5% of all intensities had corrections AI/I> 10%. A study of the influence of multiple diffraction on atomic Parameters and Charge density will be reported elsewhere (Hauback, Mo and Thorkildsen, 1990). After the final round of corrections, 31 reflections in set 1 were deleted because of irregulär backgrounds.…”

catena-Poly[[bis(acetonitrile-κN)manganese(II)]-bis(μ-trifluoromethanesulfonato-κ2O:O′)]

“…intensity(reflB)  intensity(reflB À reflA)/[F(000) 2 calc  sinth], where sinth = sin()/. We did not try to correct the affected intensities for multiple diffraction (Hauback et al, 1990), but omitted all reflections with a Renninger score larger than 500 from the final data set. This omission corresponds to 3.8% of all reflections.…”

Intensity ofN-beam X-ray diffraction: kinematical theory for a small crystal

“…where @=@x i denotes partial differentiation along the direction of the ith beam (Hauback et al, 1990).…”

“…The knowledge of this phenomenon in terms of either the kinematical or the dynamical theory of X-ray diffraction has been reviewed by Chang (1984), and recently revived by Authier (2003). Although much progress has been achieved in dynamical theory (Thorkildsen & Larsen, 2002;Okitsu, 2003), the kinematical theory still has an advantage in its simplicity for experimental studies that treat large numbers of beams (Tanaka & Saito, 1975;Hauback et al, 1990;Tanaka et al, 1994). In this article, we revive this kinematical theory to treat the phase-independent part of the phenomena, so-called Umweganregung and Aufhellung.…”