The Sayre Equation

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


A landmark in direct methods was the simultaneous publication of three papers by Sayre (1952), Cochran (1952) and Zachariasen (1952) . They all dealt with the same ultimate topic, the sign relationship
$$ {\text{s}}\left( {\text{h}} \right){\text{ s}}\left( {\text{k}} \right){\text{ s}}\left( {{\text{h}} + {\text{k}}} \right) \approx + 1 $$
, from different points of view but in the paper by Sayre there was derived a powerful and elegant equation which gave exact relationships between structure factors. While exact equations, in particular cases, also resulted from the determinantal inequalities of Karle and Hauptman (1950) the Sayre equation had the advantage that it linked the structure factors in a very simple way.


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  1. Cochran, W., 1952, A relation between the signs of structure factors. Acta Cryst. , 5, 65–67.CrossRefGoogle Scholar
  2. Glover, I., Haneef, I., Pitts, J., Wood, S., Moss, D. , Tickle, I. and Blundell, T., 1983, Conformational flexibility in a small globular hormone: X-ray analysis of Avian Pancreatic Polypeptide at 0.98Å resolution. Biopolymers, 22, 293–304.CrossRefGoogle Scholar
  3. Karle, J. and Hauptman, H., 1950, The phases and magnitudes of the structure factors. Acta Cryst., 3, 181–187.CrossRefGoogle Scholar
  4. Sayre, D., 1952, The squaring method: a new method for phase determination. Acta Cryst., 5, 60–65.CrossRefGoogle Scholar
  5. Shiono, M., 1989, An investigation of the Sayre equation. D.Phil. Thesis, University of York.Google Scholar
  6. Woolfson, M.M., 1958, An equation between structure factors for structures containing unequal or overlapped atoms. I. The equation and its properties. Acta Cryst. , 11, 277–283.CrossRefGoogle Scholar
  7. Zachariasen, W.H., 1952, A new analytical method for solving crystal structures. Acta Cryst., 5, 68–73c.CrossRefGoogle Scholar

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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