A theory of phase determination for the four types of non-centrosymmetric space groups 1<i>P</i>222, 2<i>P</i>22, 3<i>P</i>₁2, 3<i>P</i>₂2

Abstract

Joint probability distributions and relevant expected values and variances are obtained for selected (but typical) non-centrosymmetric space groups belonging to the four types 1P222, 2P22, 3P12, 3P22. These lead to formulas for phase determination the analysis and interpretation of which constitute the major goal of this paper. The analysis is strongly dependent on the theory of invariants and seminvariants, and the agreement between this theory and certain consequences of the probability theory is noteworthy.