Determination of one-dimensional crystal structures using the double Patterson function
The properties and previous use of the double Patterson function in x-ray crystallography are briefly reviewed followed by an account of a new iterative technique, based on the double Patterson, which is being developed by the author. The technique starts with an approximation to the double Patterson which does not require phases, then improves the approximation by making it conform to the known projections and known magnitudes of the Fourier coefficients. The latter are 3-phase structure invariants and estimating their phases is an important step in the direct determination of structure factor phases. Tests carried out on one-dimensional centro-symmetric structures show that the technique is successful. At best, it determines correct phases for all 3-phase invariants. At worst, it fails to improve on the estimate of all phases being zero. It consistently does very much better than the B3, 0 formula which is also based on the double Patterson. Further development is necessary to apply the technique to non-centrosymmetric structures and to real structures in three dimensions.
Volume 134, 2022
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