On the application of phase relationships to complex structures. XXIV. The Sayre tangent formula

The application of the condition that a true set of phases for a substantial subset of normalized structure factors should satisfy Sayre's equation leads to a phase-refining equation called the Sayre tangent formula. Phases refined by this formula tend to satisfy Sayre's equation for a subset of E's containing some of large magnitude and some of small (ideally zero) magnitude. Trials indicate that the new formula, incorporated into a computer program SAYTAN, is more effective than MULTAN80, especially for symmorphic structures.