Improved treatment of severely or exactly overlapping Bragg reflections for the application of direct methods to powder data

Abstract

A new method has been developed for the improved intensity assignment of severely or exactly overlapping Bragg reflections in a powder diffraction pattern. This fast iterative Patterson squaring (FIPS) method addresses, in particular, the systematic lack of small and large normalized intensities (IEI values) in severely overlapping powder data, which causes (a) the intensity statistics to be strongly acentric (even when the structure itself is centrosymmetric) and (b) the underestimation of strong structure-invariant relationships. Direct methods for structure determination are more likely to succeed with FIPS-improved data than with conventionally used equipartitioned data (ratio of lEI values for overlapping reflections set to 1.0). In the case of the molecular sieve AFR (in which 65 % of the reflections severely overlap), the ab initio structure solution was only possible after a redistribution of the intensities by the FIPS method.

Charge flipping combined with histogram matching to solve complex crystal structures from powder diffraction data

“…As might be expected, structure solution was less successful as the degree of overlap (and thereby the percentage of incorrect jF h j) increased. The Fast Iterative Patterson Squaring (FIPS) algorithm (Estermann and Gramlich, 1993) for repartitioning overlapping reflections was then applied to the datasets, and a distinct improvement in the success rate could be observed.…”

Solving Crystal Structures from Powder Data. IV. The Use of the Patterson Information for Estimating the |F|'s

“…This second technique was used with satisfactory results by Estermann et al (1992) and by Estermann & Gramlich (1993) The first contribution on the right-hand side of (1) arises from the origin peak inversion; the second comes from the interatomic peaks. (instead of the squaring criterion) is used.…”

Electron crystallography as a complement to X-ray powder diffraction techniques

“…The problem can be reduced by collecting high-resolution data at a synchrotron facility, but it cannot be eliminated entirely. Several approaches that use the intensities of the non-overlapping reflections to estimate those of the overlapping ones have been developed [6,7,8], but for a diffraction pattern with a high degree of overlap these methods are not very reliable. In such cases, more elaborate data collection strategies, in which several diffraction patterns are measured on the same sample under different conditions, can be employed (e.g.…”