 #jsDisabledContent { display:none; } My Account |  Register |  Help Flag as Inappropriate This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate?          Excessive Violence          Sexual Content          Political / Social Email this Article Email Address:

# Sayre equation

Article Id: WHEBN0035454394
Reproduction Date:

 Title: Sayre equation Author: World Heritage Encyclopedia Language: English Subject: Collection: Crystallography Publisher: World Heritage Encyclopedia Publication Date:

### Sayre equation

In crystallography, the Sayre equation, named after David Sayre who introduced it in 1952, is a mathematical relationship that allows to calculate probable values for the phases of some diffracted beams. It is used when employing direct methods to solve a structure and its formulation is the following:

F_{hkl} = \sum_{h'k'l'} F_{h'k'l'}F_{h-h',k-k',l-l'}

which states how the structure factor for a beam can be calculated as the sum of the products of pairs of structure factors whose indices sum to the desired values of h,k,l. Since weak diffracted beams will contribute a little to the sum, this method can be a powerful way of finding the phase of related beams, if some of the initial phases are already known by other methods.

In particular, for three such related beams in a centrosymmetric structure, the phases can only be 0 or \pi and the Sayre equation reduces to the triplet relationship:

S_{h} \approx S_{h'} S_{h-h'}

where the S indicates the sign of the structure factor (positive if the phase is 0 and negative if it is \pi) and the \approx sign indicates that there is a certain degree of probability that the relationship is true, which becomes higher the stronger the beams are.