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Direct phasing from Patterson syntheses by δ recycling

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The direct methods origin‐free modulus sum function [Rius (1993). Acta Cryst. A49, 406–409] includes in its definition the structure factor G(Φ) of the squared crystal structure expressed in terms of Φ, the set of Φ phases of the normalized structure factors E's of the crystal structure of unit‐cell volume V. Here the simpler sum function variant = ∑ H E H V δP,Δ(Φ)exp(iHr)dV extended over all H reflections is introduced which involves no G's and in which the δP,Δ function corresponds to δP = FT−1{()exp[iΦ H (Φ)]} (where FT = Fourier transform) with all values smaller than Δ = 2.5σP equated to zero ( is the variance of δP calculable from the experimental intensities). The new phase estimates are obtained by Fourier transforming δP,Δ. This iterative phasing method (δ recycling) only requires calculation of Fourier transforms at two stages. Since δM≃δP/2, similar arguments are valid for δM = FT−1[(E H −〈E〉)exp(iΦ H )] from which the corresponding phasing function follows.

Document Type: Research Article


Affiliations: Institut de Ciència de Materials de Barcelona (CSIC), Campus de la UAB, 08193-Bellaterra, Catalunya, Spain

Publication date: January 1, 2012


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