Sayre equation
From Online Dictionary of Crystallography
Équation de Sayre (Fr); Equazione di Sayre (It).
In direct methods, the Sayre equation is used to calculate probable values for the phases of some reflections. Its formulation is the following:
| Fhkl = | ∑ | Fh'k'l'Fh − h',k − k',l − l' |
| h'k'l' |
and states that the structure factor of a reflection hkl can be calculated as a function of structure factors whose Laue indices sum to the desired values of hkl. In particular, in a centrosymmetric structure, the phases of three reflections satisfying the above relation of Laue indices can only be 0 or π and the Sayre equation reduces to a relation between signs of structure factors:
where the signs S are positive if the phase is 0 and negative if it is π and the 
symbol indicates a certain degree of probability that the relationship is true, which becomes higher the stronger the reflections are.
