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

1975; International Union of Crystallography; Volume: 31; Issue: 4 Linguagem: Inglês

10.1107/s0567739475000976

1600-8596

Pierre Becker, P. Coppens,

Radioactive element chemistry and processing

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.