In crystallography, the Sayre equation, named after David Sayre who introduced it in 1952, is a mathematical relationship that allows one to calculate probable values for the phases of some diffracted beams. It is used when employing direct methods to solve a structure. Its formulation is the following:
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
In particular, for three such related beams in a centrosymmetric structure, the phases can only be 0 or
\pi
where the
S
\pi
≈