Ab initio phasing of X-ray powder diffraction patterns by charge flipping.

Determining crystal structures from powder X-ray diffraction data remains a challenging problem in materials science. By embedding a Le-Bail-like procedure within the recently discovered charge-flipping phasing algorithm, an extremely simple, fast and effective ab initio method has been developed to determine phases directly from indexed powder diffraction patterns. The algorithm solves the degeneracy problem by applying spherical averaging for overlapping Bragg reflections, while solving the phase problem by using the Oszlányi-Süto charge-flipping algorithm. The processes of peak decomposition and phasing are integrated within the same iteration, and a dynamic support is used. The Fienup hybrid input-output algorithm is also incorporated to minimize stagnation. The ability of the algorithm to find structure-factor phases rapidly is found to assist with the fundamental problem of degeneracy (overlapping reflections) which is intrinsic to powder diffraction data. Space-group and chemical-composition information are not needed as inputs, and can be determined from the result. The method is illustrated using several experimental powder patterns of indifferent quality.