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The Cochran Distribution

  • Michael M. Woolfson
Chapter
Part of the NATO ASI Series book series (NSSB, volume 274)

Abstract

All the earlier published work using direct methods, right up to the end of the 1950’s, involved the application of inequality relationships, usually of the Harker-Kasper type (Harker & Kasper, 1948) and/or the triple sign relationship for solving either centrosymmetric structures or centrosymmetric projections of non-centrosymmetric structures. In fact some of the very earliest theoretical work pointed towards the possibility of applying direct methods to non-centrosymmetric structures as well. The determinant inequalities, developed by Karle & Hauptman (1950), which will later be described in greater detail, could restrict general phases in the non-centrosymmetric case and Sayre’s equation (Sayre, 1952) could be applied to any equal-atom structure regardless of space group and therefore could put some constraints on the phases of the involved structure factors.

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References

  1. Cochran, W., 1955, Relations between the phases of structure factors. Acta Cryst., 8, 473–478.CrossRefGoogle Scholar
  2. Harker, D. and Kasper, J. S.,1948, Phases of Fourier coefficients directly from crystal diffraction data. Acta Cryst., 1, 70–75.CrossRefGoogle Scholar
  3. Karle, J. and Hauptman, H., 1950, The phases and magnitudes of the structure factors. Acta Cryst., 3, 181–187.CrossRefGoogle Scholar
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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Michael M. Woolfson
    • 1
  1. 1.Physics DepartmentUniversity of YorkYorkUK

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