The Cochran Distribution
All the earlier published work using direct methods, right up to the end of the 1950â€™s, involved the application of inequality relationships, usually of the Harker-Kasper type (Harker & Kasper, 1948) and/or the triple sign relationship for solving either centrosymmetric structures or centrosymmetric projections of non-centrosymmetric structures. In fact some of the very earliest theoretical work pointed towards the possibility of applying direct methods to non-centrosymmetric structures as well. The determinant inequalities, developed by Karle & Hauptman (1950), which will later be described in greater detail, could restrict general phases in the non-centrosymmetric case and Sayre’s equation (Sayre, 1952) could be applied to any equal-atom structure regardless of space group and therefore could put some constraints on the phases of the involved structure factors.
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