Structure invariants and seminvariants for noncentrosymmetric space groups

Abstract

The nature of the dependence of phase on the choice of origin is clarified for the non-centrosymmetric space groups by means of special linear combinations of the phases, the structure invariants and seminvariants. The theory yields simple answers to the following questions: Which phases have values determined uniquely by tile crystal structure and independent of the choice of origin? If the values of certain phases are specified, what phases have values which are then uniquely determined by the structure? The values of which phases are to be specified in order to fix the origin uniquely? Simple procedures for fixing the origin by suitably specifying the values of certain phases are described in detail.