Tables for
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 3.5, pp. 284-285

Section 3.5.3. Pitfalls in the extraction of accurate |Fhkl| values using the Pawley and Le Bail methods

A. Le Baila*

aUniversité du Maine, Institut des Molécules et Matériaux du Mans, UMR CNRS 6283, Avenue Olivier Messiaen, 72085 Le Mans Cedex 9, France
Correspondence e-mail:

3.5.3. Pitfalls in the extraction of accurate |Fhkl| values using the Pawley and Le Bail methods

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In the Rietveld refinement guidelines published by the IUCr Commission on Powder Diffraction (McCusker et al., 1999[link]), it is said that the Rietveld Rwp value should approach the value obtained in a structure-free refinement (i.e. using WPPD methods). Such a refinement is recommended for the estimation of initial values of the Rietveld profile parameters. Consequently, |Fhkl| values extracted by WPPD can be used to make a good reproduction of the experimental powder pattern if the cell is correct (which is ultimately only proven if the structure is solved and refined). Pitfalls can occur during post-treatment and application of the |Fhkl| data if one neglects the possible errors that are inherently present due to exact or accidental overlap, preferred orientation effects or wrong background estimations, citing only three of the main possible causes of errors in these |Fhkl| values. Consequences of (exact or accidental) overlap

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The uncertainties of the |Fhkl| 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 |Fhkl| 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 |Fhkl| 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 |Fhkl| values can be used in mathematical expressions defining correlations induced by the overlap. These equations were developed by David et al. (1998[link]) for the Pawley method in the real-space structure solution program DASH and by Pagola et al. (2000[link]) for the Le Bail method in PSSP. Regenerating a powder pattern from the extracted |Fhkl| values was carried out in the ESPOIR real-space computer program (Le Bail, 2001[link]) 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 |Fhkl| 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. Preferred-orientation effects

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One has to ensure that preferred orientation is minimized during the recording of the powder pattern if the extracted |Fhkl| values are to be used for structure solution. In transmission geometry with a capillary specimen (provided that it is not composed of long needle-shaped particles that are all aligned), there is generally no problem. But in reflection geometry with samples pressed on the holder, preferred orientation is not rare, even if it is not obvious in the data. Collecting a second pattern from a sample dusted onto the holder through a fine sieve can be informative. However, some WPPD applications may not be sensitive to such a problem. If only the cell parameters have to be accurately estimated for thermal-expansion studies (Evans et al., 1996[link]), it can be much faster to use WPPD rather than the Rietveld method. However, it is not recommended to do this systematically, especially if the structure is complex and the resolution is low [see the warnings in Peterson (2005[link])]. Background-estimation effects

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Logically, a background value will never be higher than the observed intensity at the diffraction angle where it is visually estimated. In the first refinement cycles by the Pawley or Le Bail methods, it is preferable to keep the background fixed as well as the cell parameters, which assumes that the starting values have been carefully estimated or even (in the cell-parameter case) have already been refined from the peak positions that were used for indexing. This is because all refinement processes need to start from parameters close to the final values. Selecting background values leading to negative intensities after background removal could result in negative |Fhkl| values if the software does not account for this.


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 Scholar
Evans, J. S. O., Mary, T. A., Vogt, T., Subramanian, M. A. & Sleight, A. W. (1996). Negative thermal expansion in ZrW2O8 and HfW2O8. Chem. Mater. 8, 2809–2823.Google Scholar
Le 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
McCusker, L. B., Von Dreele, R. B., Cox, D. E., Louër, D. & Scardi, P. (1999). Rietveld refinement guidelines. J. Appl. Cryst. 32, 36–50.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
Peterson, V. K. (2005). Lattice parameter measurement using Le Bail versus structural (Rietveld) refinement: a caution for complex, low symmetry systems. Powder Diffr. 20, 14–17.Google Scholar

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