On formalism of extinction correction within the validity limits of the mosaic model

Abstract

The results of an investigation of the polarization coefficient of X-ray radiation diffracted in real crystals are given. The form of the angular dependence of the polarization coefficient in the range of the Bragg reflection is found to be qualitatively different in the cases of primary and secondary extinction. It allows the unambiguous identification of the type of extinction in the crystal. On the basis of the experimental data analysis of the polarization coefficients for silicon and germanium crystals with different dislocation densities, it is shown that the mosaic model of a crystal is suitable for describing X-ray scattering in real crystals if the dislocation density is higher than 104 mm-2 and in practice only primary extinction is present in mosaic crystals. An expression is given for the primary extinction factor for the mosaic crystal, obtained on the basis of the solution of the Takagi-Taupin equations for finite crystals. This expression was used for the analysis of the LiF and NaF structure factors measured by different authors. The effective size which was obtained for the domains appeared to be physically reasonable and to be directly connected with the value of the dislocation density in the crystal.