Extinction within the limit of validity of the Darwin transfer equations. III. Non-spherical crystals and anisotropy of extinction

Previously derived formalisms for extinction are extended to include crystals of non-spherical shape and anisotropy of mosaic spread and particle size. Expressions derived for extinction in an ellipsoidal crystal are compared with numerical calculations on a polyhedral specimen. A pseudo-spherical approximation for polyhedral crystals is described which is accurate to within 2% of the extinction factor y for crystals whose ratio of maximum and minimum dimensions is less than two. Anisotropy of mosaic spread is introduced in both the Coppens-Hamilton (C.H.) and Thornley-Nelmes (T.N.) descriptions, with both a Lorentzian or a Gaussian distribution function. The formalisms are applied to neutron data sets on LiTbF₄ (100°K and 300°K), tetracyanoethylene and LiOH. H₂O, and an X-ray data set on α-deutero oxalic acid dihydrate. The distinction between type I and type II crystals is quite clear on the basis of a comparison of R values. Only for LiF, which was studied earlier, was extinction dominated by particle size. In all other cases the best fit corresponds to mosaic-spread-dominated extinction, with a Lorentzian shape of the distribution function. This is especially clear when partial R values summed over the severely extinction-affected reflections are compared. The new formalisms are further supported by the consistency of the final parameters among various refinements in which the most severely extinction-affected reflections are eliminated. Simultaneous refinement on both the particle size and the mosaic spread was only successful in the earlier studied case of SrF₂. The T.N. description of anisotropy leads to lower partial R values, in agreement with physical arguments supporting the validity of this distribution.