A new type of constraint in the maximum-entropy method using ambiguous phase information from anomalous-scattering powder data.

Anomalous scattering of X-rays at a synchrotron source can be used for the ab initio structure determination of unknown crystal structures using only powder diffraction data. For noncentrosymmetric crystals, the phases of structure factors can only be determined with a remaining ambiguity, when one chemical element is used as resonant scatterer. A corresponding additional constraint function has been built into an enhanced version of the program MEED, so that now all types of information gained from an anomalous-scattering powder diffraction experiment can be used in a maximum-entropy calculation of the electron-density distribution: phased reflections, unphased reflections, intensities of groups of overlapping reflections, and now also reflections with a remaining ambiguity in the phase. This is important for practical use, since a lot of information is already lost in the powder diagram compared with single-crystal datasets and it is essential to use all remaining information. The new constraint is demonstrated with the structure of Cu(5)Zn(8).

The generalized Debye-Waller factor for atoms in a twisted environment. I. Sites at the core of a double helix.

Lattice sites which have a proper or improper subgroup of 222 as the site group may exhibit an anharmonic twisted local potential. The generalized Debye-Waller factor for atoms occupying such sites is derived. If the twist axis is fixed by symmetry considerations the approximation used needs, in addition to three harmonic parameters, one anharmonicity parameter, essentially the local pitch. In the most general case with no symmetry restrictions three Eulerian angles are needed in addition to the pitch.