Anisotropic extinction corrections in the Zachariasen approximation

Refinement of crystal structures incorporating an extinction parameter in an approximation developed by Zachariasen has led to the experimental observation that some crystals show anisotropic extinction effects. A formalism is presented for refinement of anisotropic extinction coefficients for both extreme crystal types: Type I (extinction dominated by mosaic spread) and Type II (extinction dominated by particle size). For Type I crystals, an anisotropic rather than isotropic Gaussian mosaic spread distribution function is assumed. For Type II crystals, the average particle shape is described as an ellipsoid rather than as a sphere. In each case, the six independent components of a symmetrical second-order tensor are added to the list of parameters refined in a conventional crystallographic least-squares program. Results on several data sets from both neutron and X-ray diffraction experiments indicate that anisotropy of extinction is often significant. The inclusion of such parameters is recommended in all least-squares refinements of extinction affected data. Furthermore the detailed study of the effects may be of some promise in the study of crystal texture inasmuch as the refined parameters are of a magnitude which suggests physical significance.