X-Cell:: a novel indexing algorithm for routine tasks and difficult cases

X-Cell is a novel indexing algorithm that makes explicit use of systematic absences to search for possible indexing solutions from cells with low numbers of calculated reflections to cells with high numbers of reflections. Space groups with the same pattern of systematic absences are grouped together in powder extinction classes, and for a given peak number range an independent search is carried out in each powder extinction class. The method has the advantage that the correct cell is likely to be found before the rapid increase of possible solutions slows down the search significantly. A successive dichotomy approach is used to establish a complete list of all possible indexing solutions. The dichotomy procedure is combined with a search for the zero-point shift of the diffraction pattern, and impurity peaks can be dealt with by allowing for a user-defined portion of unindexed reflections. To rank indexing solutions with varying numbers of unindexed reflections, a new figure of merit is introduced that takes into account the highest level of agreement typically obtained for completely incorrect unit cells. The indexing of long and flat unit cells is facilitated by the possibility to search for rows or zones in reciprocal space first and then to use the lattice parameters of the dominant row or zone in the unit-cell search. The main advantages of X-Cell are robustness and completeness, as demonstrated by a validation study on a variety of compounds. The dominant phase of phase mixtures can be indexed in the presence of up to 50% of impurity peaks if high-quality synchrotron data are available.