Die Streuung von Rontgen-Strahlen an Kristallen mit statistisch verteilten Defekten / On the Scattering of X-rays from Crystals Containing a Random Distribution of Defects

Abstract

The static correlation function governing elastic scattering of X-rays or neutrons by a defective crystal is discussed for three degrees of imperfections, that is for slight, severe, and medium distortions of the scattering crystal. In the exponent of this correlation function the main term, which is linear in the defect concentration, is shown to be fairly independent of the particular type of statistics describing the random distribution of the defects. One condition for a successful analysis of defect structures using diffuse scattering data is that the scattering function can be split into the individual contributions of all single defects. For two regions, that is for the immediate vicinity of Bragg reflections (Huang scattering) and for the asymptotic regions of distortion scattering, this "single-defect approximation" is shown to be useful even for higher concentrations. In this case the correlations due to a single defect have to be corrected by a factor which takes into account the average correlation reduction by all other defects (static Debye-Waller factor in the Huang regions and a similar but variable factor in the asymptotic regions). The formulas given in this paper are applied to the sacttering by isotropic crystals containing point defects of spherical symmetry.