REDUC: an automated procedure for the determination of structure-factor phases from the estimated values of structure (sem)invariant phase combinations

An algorithm is described to determine structure-factor phases from the estimated phases of (sem)invariants of any order, in a mixed mode if desired. The method essentially consists of a reduction of a redundant set of linear equations by successive elimination of unknowns. The main result of the procedure is a set of mutually independent equations in which structure-factor phases are expressed as linear combinations of a limited number of unknowns (among which a suitable set of origin-defining phases must exist), and (sem)invariant phases of which (reliable) estimates are available. Application to an unknown P2₁ structure using triple products only, followed by a tangent refinement, is given. From further tests it appeared that the method is preeminently expedient as a troubleshooter in intricate structure determinations.