Ab initio structure determination from severely overlapping powder diffraction data

A new method for unravelling the intensities of severely or exactly overlapping reflections in a powder diffraction pattern has been developed. The fast iterative Patterson squaring (FIPS) method involves an iterative procedure in which (1) a Patterson function is calculated using equipartitioned data (intensity ratio for overlapping reflections set to 1.0), (2) each point in the map is squared, (3) the new map is back-transformed to obtain new Fourier coefficients, and (4) these coefficients are then extrapolated to give a new set of |F|^{2 overlap}_hkl values and a new intensity distribution for the overlapping reflections (non-overlapping ones remain unaffected). The cycle is repeated until the intensity statistics of the overlapping reflections approximate those of the non-overlapping ones. Only after a redistribution of the intensities by the FIPS method was the ab initio structure solution possible for the molecular sieve SAPO-40 (structure-type code AFR), in which 65% of the reflections severely overlap.