This paper reports the results of X-ray powder diffraction experiments on C60Brzn(Br2)2. This material is a C60 derivative and shows rhombohedral symmetry at room temperature. At low temperature, a rhombohedral-totriclinic phase transition can be observed that involves a large distortion of the cell while the volume of the unit cell remains almost constant. This is a sufficiently complicated system that high-resolution synchrotron data and a combination of different tactics were required to reach a structure solution.
In this paper, a new integer minimal principle model for centrosymmetric structures is presented; one which fully accounts for reciprocal-space phase shifts present in non-symmorphic space groups. Additionally, characterization of false minima of the model is done in terms of even and odd triplets. Based on this characterization, a triplet sieve method is proposed. First, Gaussian elimination using only a subset of reliable triplets is employed for phasing. Triplet subsets are generated using a progressively smaller set of the strongest reflections. Several phase solution sets are generated by enumerating the degrees of freedom present. To facilitate computational evaluation of the quality of these phase solutions, these phase sets are passed into the crystallographic software SnB, which expands the reflection set in two cycles. The final solution is identified via statistics of two crystallographic figures of merit. Computational results are presented for a variety of structures.
A new version of the direct-methods program SnB has been developed. This version incorporates the triplet sieve method for phasing centrosymmetric structures in a way that is transparent to users. The triplet sieve procedure may decrease significantly the time required to achieve a solution for such structures.
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