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. Its formulation is the following:

${\displaystyle F_{hkl}=\sum _{h'k'l'}F_{h'k'l'}F_{h-h',k-k',l-l'}}$

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 ${\displaystyle h,k,l}$. 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.

...
Wikipedia