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A Universal Treatment of X-ray and Neutron Diffraction in Crystals. II. Extinction

A Universal Treatment of X-ray and Neutron Diffraction in Crystals. II. Extinction Based on the formalism for calculating the integrated reflection power ratio of a plane mosaic crystal by using three dimensionless parameters as described in paper I Hu (1997). Acta Cryst. A53, 0-0, exact and universal expressions for the secondary-extinction factors in X-ray and neutron crystallography are developed that can be applied to reflections of all possible values of extinction factor, reflection symmetry and the absorption-to-scattering cross-section ratio of the crystal. The representation by three parameters gives a clear and definite physical meaning to the concept of extinction. The theory has been extended to treat the extinction of a spherical crystal, and the striking difference in the evaluated secondary-extinction factor between the equivalent single-plate and the exact method in the spherical-crystal treatment under B = 0Degrees is explained. As a demonstration of the feasibility of using these expressions, the diffraction data for LiF and MgO crystal plates measured by Lawrence Acta Cryst. (1972), A28, 400-404; (1973), A29, 208-210 are reanalyzed by this method. All the reflections including the strongest ones (Yo down to 0.026) are reanalyzed simultaneously with single-valued particle size and mosaic spread as fitting parameters and allowing for primary extinction if necessary. The results (R-factor = 0.014 and 0.053 for LiF and MgO, respectively) are unprecedentedly good. Furthermore, in disagreement with Lawrence, the extinction of LiF is found to be of secondary type and in the case of MgO both primary and secondary extinction should be considered. The analysis also shows that the formula Y ~ YpYp is valid only for very weak extinctions and that the Hamilton-Darwin equations are valid in a range much broader than previously anticipated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Foundations of Crystallography International Union of Crystallography

A Universal Treatment of X-ray and Neutron Diffraction in Crystals. II. Extinction

A Universal Treatment of X-ray and Neutron Diffraction in Crystals. II. Extinction


Abstract

Based on the formalism for calculating the integrated reflection power ratio of a plane mosaic crystal by using three dimensionless parameters as described in paper I Hu (1997). Acta Cryst. A53, 0-0, exact and universal expressions for the secondary-extinction factors in X-ray and neutron crystallography are developed that can be applied to reflections of all possible values of extinction factor, reflection symmetry and the absorption-to-scattering cross-section ratio of the crystal. The representation by three parameters gives a clear and definite physical meaning to the concept of extinction. The theory has been extended to treat the extinction of a spherical crystal, and the striking difference in the evaluated secondary-extinction factor between the equivalent single-plate and the exact method in the spherical-crystal treatment under B = 0Degrees is explained. As a demonstration of the feasibility of using these expressions, the diffraction data for LiF and MgO crystal plates measured by Lawrence Acta Cryst. (1972), A28, 400-404; (1973), A29, 208-210 are reanalyzed by this method. All the reflections including the strongest ones (Yo down to 0.026) are reanalyzed simultaneously with single-valued particle size and mosaic spread as fitting parameters and allowing for primary extinction if necessary. The results (R-factor = 0.014 and 0.053 for LiF and MgO, respectively) are unprecedentedly good. Furthermore, in disagreement with Lawrence, the extinction of LiF is found to be of secondary type and in the case of MgO both primary and secondary extinction should be considered. The analysis also shows that the formula Y ~ YpYp is valid only for very weak extinctions and that the Hamilton-Darwin equations are valid in a range much broader than previously anticipated.

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References (4)

Publisher
International Union of Crystallography
Copyright
Copyright (c) 1997 International Union of Crystallography
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S0108767397004066
Publisher site
See Article on Publisher Site

Abstract

Based on the formalism for calculating the integrated reflection power ratio of a plane mosaic crystal by using three dimensionless parameters as described in paper I Hu (1997). Acta Cryst. A53, 0-0, exact and universal expressions for the secondary-extinction factors in X-ray and neutron crystallography are developed that can be applied to reflections of all possible values of extinction factor, reflection symmetry and the absorption-to-scattering cross-section ratio of the crystal. The representation by three parameters gives a clear and definite physical meaning to the concept of extinction. The theory has been extended to treat the extinction of a spherical crystal, and the striking difference in the evaluated secondary-extinction factor between the equivalent single-plate and the exact method in the spherical-crystal treatment under B = 0Degrees is explained. As a demonstration of the feasibility of using these expressions, the diffraction data for LiF and MgO crystal plates measured by Lawrence Acta Cryst. (1972), A28, 400-404; (1973), A29, 208-210 are reanalyzed by this method. All the reflections including the strongest ones (Yo down to 0.026) are reanalyzed simultaneously with single-valued particle size and mosaic spread as fitting parameters and allowing for primary extinction if necessary. The results (R-factor = 0.014 and 0.053 for LiF and MgO, respectively) are unprecedentedly good. Furthermore, in disagreement with Lawrence, the extinction of LiF is found to be of secondary type and in the case of MgO both primary and secondary extinction should be considered. The analysis also shows that the formula Y ~ YpYp is valid only for very weak extinctions and that the Hamilton-Darwin equations are valid in a range much broader than previously anticipated.

Journal

Acta Crystallographica Section A: Foundations of CrystallographyInternational Union of Crystallography

Published: Jul 1, 1997

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