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The pair‐functional method. III. The pairing forces

The pair‐functional method. III. The pairing forces The theory of the pair‐functional ensemble is developed to provide estimates of the pairing forces from experimental X‐ray intensities. The statistical mechanics of the grand ensemble leads to a diagram expansion for the forces, in terms of the direct correlation function of the fluid ensemble combined with a series of small higher‐order corrections. A simpler treatment, based on a biased Gaussian probability distribution, gives approximate formulae, valid for reflections of any type in all space groups. The role of symmetry is analysed. The entropy of an asymmetrical ensemble can always be increased by averaging it over equivalent positions of the atoms in the true space group, with the result that the atoms naturally tend to adopt the highest symmetry compatible with the data. In a cell with different types of atom, the atoms experience a single force function but they interact with a strength proportional to the products of their scattering factors. Numerical estimates are given for typical cases. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A Foundations of Crystallography Wiley

The pair‐functional method. III. The pairing forces

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References (18)

Publisher
Wiley
Copyright
Copyright © 2001 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S0108767300013714
Publisher site
See Article on Publisher Site

Abstract

The theory of the pair‐functional ensemble is developed to provide estimates of the pairing forces from experimental X‐ray intensities. The statistical mechanics of the grand ensemble leads to a diagram expansion for the forces, in terms of the direct correlation function of the fluid ensemble combined with a series of small higher‐order corrections. A simpler treatment, based on a biased Gaussian probability distribution, gives approximate formulae, valid for reflections of any type in all space groups. The role of symmetry is analysed. The entropy of an asymmetrical ensemble can always be increased by averaging it over equivalent positions of the atoms in the true space group, with the result that the atoms naturally tend to adopt the highest symmetry compatible with the data. In a cell with different types of atom, the atoms experience a single force function but they interact with a strength proportional to the products of their scattering factors. Numerical estimates are given for typical cases.

Journal

Acta Crystallographica Section A Foundations of CrystallographyWiley

Published: Mar 1, 2001

Keywords: ;

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