International
Tables for Crystallography Volume H Powder diffraction Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk © International Union of Crystallography 2018 |
International Tables for Crystallography (2018). Vol. H, ch. 3.5, p. 284
Section 3.5.3.1. Consequences of (exact or accidental) overlap^{a}Université du Maine, Institut des Molécules et Matériaux du Mans, UMR CNRS 6283, Avenue Olivier Messiaen, 72085 Le Mans Cedex 9, France |
The uncertainties of the |F_{hkl}| values of overlapped reflections cannot be overcome in a single powder-diffraction experiment. This problem has led to various approaches, all being more or less inefficient: equipartition, non-equipartition by random distribution etc. If direct methods are applied, the trend is to multiply the number of solution attempts, trying to identify the most convincing one by using structural arguments (such as atoms in chemically reasonable positions). When applying real-space methods (which require chemical knowledge, such as the three-dimensional molecular structure or the presence of definite polyhedra) one generally chooses to work either directly on the raw powder pattern or on a pseudo pattern built from the extracted |F_{hkl}| values, so that wrong individual values are less of a problem, since only the sums of the contributions in overlapping regions are checked during the search for the molecule, polyhedra or atom positions. Indeed, working on the raw powder pattern does not need reduction to |F_{hkl}| values in theory, but in practice either the Pawley or Le Bail methods are applied first in order to fix the zero point, background, cell and profile parameters which will then be applied during the structure model checking, and to speed the calculations. The extracted |F_{hkl}| values can be used in mathematical expressions defining correlations induced by the overlap. These equations were developed by David et al. (1998) for the Pawley method in the real-space structure solution program DASH and by Pagola et al. (2000) for the Le Bail method in PSSP. Regenerating a powder pattern from the extracted |F_{hkl}| values was carried out in the ESPOIR real-space computer program (Le Bail, 2001) using a simple Gaussian peak shape whose width follows the Caglioti relation established from the raw pattern. With such a pseudo powder pattern (without profile asymmetry, background etc.), the calculations are much faster than if the raw pattern is used. When using direct methods instead of real-space methods, the approaches are different, because direct methods require a more complete data set (up to d = 1 Å) of accurate |F_{hkl}| values. However, removing up to half of them (those with too much overlap, i.e. where the overlap is greater than half the FWHM, for instance) can lead to success with direct methods. One can even remove up to 70–80% of the data if the Patterson method is applied and if only a small number of heavy atoms are to be located.
References
David, W. I. F., Shankland, K. & Shankland, N. (1998). Routine determination of molecular crystal structures from powder diffraction data. Chem. Commun. pp. 931–932.Google ScholarLe Bail, A. (2001). ESPOIR: A program for solving structures by Monte Carlo analysis of powder diffraction data. Mater. Sci. Forum, 378, 65–70.Google Scholar
Pagola, S., Stephens, P. W., Bohle, D. S., Kosar, A. D. & Madsen, S. K. (2000). The structure of malaria pigment beta-haematin. Nature, 404, 307–310.Google Scholar