Abstract
The refinement criteria (consistency criteria) of the Σ2 and tangent formulae are discussed. From these criteria the properties of Σ2 solutions in various space groups are evaluated. Structure determinations can then be divided into five categories according to the properties of the most consistent Σ2 solution. In three of these, trivial phases are obtained. For solving non-centrosymmetric structures in which the Σ2 formula produces centrosymmetric phases (such as structures in P21), a new method (Σ2P method) is proposed which makes use of both Σ2 and Patterson techniques. In structures for which the most consistent Σ2 solution corresponds to the trivial set of phases ψhkl = 0, Harker–Kasper inequalities or other methods have to be used in order to select the most reliable solution from the different sets of phases built up by means of the Σ2 relation. In an appendix, new weighting schemes for the tangent refinement are proposed.
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