Ab initio structure determination from severely overlapping powder diffraction data

Abstract

A new method for unravelling the intensities of severely or exactly overlapping reflections in a powder diffraction pattern has been developed. The fast iterafive 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 extrapo-~W 2 ow.,rl~tp lated to give a new set of ~ hkl values and a new intensity distribution for the overlapping reflections (nonoverlapping 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.

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

“…Furthermore, a true test on a polycrystalline material with an unknown structure (AFR, 65% overlap), which could not be solved from equipartitioned data, was successful (Estermann, McCusker & Baerlocher, 1992). Another successful structure determination was that of the aluminophosphate MCS-1 (Simmen, 1992), where the FIPS treatment of the overlapping intensities (although only 10%) was necessary for the structure solution.…”

“…However, the intensity statistics can still be used for discrimination between centrosymmetric and noncentrosymmetric structures when based on the nonoverlapping reflections only. In the structure solution of AFR (Estermann, McCusker & Baerlocher, 1992), this was used to discriminate the correct centrosymmetric space group from two other possible noncentrosymmetric candidates. The only exception is the data set for LTA, whose nonoverlapping reflections also give the wrong indication of acentric statistics.…”

“…The peak-shape function, the peak asymmetry and the particular extraction program may also influence the choice of the value of~. 0021-8898/93/030396-09506.00 © 1993 International Union of Crystallography Estermann, McCusker & Baerlocher (1992), powder in rotating capillary measured on a Stoe (laboratory) diffractometer; (4) Baerlocher (1990b), powder in rotating capillary measured on HASYLAB Beamline B2 (synchrotron), Hamburg; (5) Gramlich & Meier (1971), pulverized single-crystal data; (6) McCusker (1990), powder in rotating capillary measured on SRS Station 9.1 (synchrotron), Daresbury.…”

Direct Methods and Powder Data: State of the Art and Perspectives

“…The structure-factor amplitudes derived were transformed by SIRPOW.92 (Altomare, Cascarano, The final suggestion coming from the above observations is that the Wilson statistics may not be so informative about the presence of the inversion centre in the space group as occurs for single-crystal data. Indeed, most of the features of the experimental distribution function are pattern-decomposition-method dependent rather than crystal-structure dependent (see also Cascarano, Favia & Giacovazzo, 1992;Estermann, McCusker & Baerlocher, 1992).…”

“…Since they extract the phase values from 2 the moduli, wrong phases will probably be derived from biased moduli. In order to reduce the ambiguity caused by the overlap, some procedures based on the Patterson squaring method (David, 1987;Cascarano, Giacovazzo, Guagliardi & Steadman, 1991;Estermann, McCusker & Baerlocher, 1992;Estermann & Gramlich, 1993) can be used in combination with profile-fitting procedures.…”