International
Tables for
Crystallography
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. 285-286

Section 3.5.4. Applications and by-products

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: lebail@univ-lemans.fr

3.5.4. Applications and by-products

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The first modern WPPD method with cell restraints was developed for neutron data by Pawley (1981[link]), 12 years after the publication of the paper that described the Rietveld (1969[link]) method. In Le Bail et al. (1988[link]) a new WPPD approach was used to extract intensities, making use of iterations of the Rietveld decomposition formula. It is clear that both these WPPD methods are children of the Rietveld method. Today most users of the Rietveld method do not cite the original Rietveld papers, but only refer to the computer program that they used. This is also now increasingly the case for the WPPD methods.

From the Thomson Reuters ISI citation index consulted in May 2015, the papers for the Pawley and Le Bail methods scored 892 and 1425 direct citations, respectively. There are several highly cited papers that then cite these two papers. The most highly cited paper (>5100 times) that cites both WPPD methods concerns use of the Le Bail intensity-extraction method by FULLPROF for solving magnetic structures (Rodriguez-Carvajal, 1993[link]). This paper is also given as a reference for FULLPROF used in more standard Rietveld refinements. This suggests that the impact of WPPD methods is higher than commonly believed. The list of possible WPPD applications includes phase identification, quantitative phase analysis, measurement of crystallite sizes and strains, creation of Fourier maps for partially solved structures, structure refinement by the two-step method, studies of electron-density distribution, and characterization of pole figures, using either the Pawley or Le Bail methods. All routes to SDPD use at least one of them. WPPD has even entered into the indexing step, with Kariuki et al. (1999[link]) using the Le Bail fit for testing cell hypotheses (for which it is faster than the Pawley method) in a new computer program that uses a genetic algorithm. But the main applications of the WPPD methods are to provide support for cell-parameter refinement and the determination of the space group, as a prelude to the full use of the extracted |Fhkl| values for ab initio structure solution.

3.5.4.1. Supporting indexing and space-group determination

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As they yield the smallest possible profile Rp and Rwp factors (smaller than from the Rietveld method, which is limited by the crystal-structure refinement), the Pawley and Le Bail methods provide strong support for both the proposed indexing and the determination of the space group. Some computer programs provide an automated suggestion for the latter. This support is needed to show that it is worth attempting to solve the structure. Once the structure is solved, the structure constraint will remove the ambiguity between intensities of close Bragg peaks and necessarily improve the quality of the cell parameters. If the structure is already known, the best approach is the Rietveld method. There is a progression in the precision of the refined cell parameters from the lowest level (least squares from individually extracted peak positions) to a medium level (WPPD with cell restraint) to the highest possible level (Rietveld, adding the structure constraint). With both Pawley and Le Bail methods, the fit quality is checked using agreement factors which are the same as with the Rietveld method: Rp and Rwp (moreover, a careful visual check is recommended). The reliabilities relative to the structure (RB and RF), which can still be calculated, are meaningless (WPPD programs tending to obtain a value close to zero for both of them).

3.5.4.2. Structure solution

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SDPD can be undertaken by various approaches, depending on the chemical knowledge of the sample (formula, molecular formula, presence of defined polyhedra…), either directly using the |Fhkl| values for structure solution by direct or Patterson methods, or by rebuilding a pseudo powder pattern from them, or by applying fixed profile parameters from the Pawley or Le Bail fits during whole-powder-pattern fitting wherein the structure solution is attempted by real-space methods. In order to illustrate the power of WPPD methods and to show the progress realized over the last 30 years, the decafluorocyclohexene structure that was unsolved in the Pawley method paper of 1981[link] is reconsidered. As stated by Pawley, from plausible extinctions the space group of the C6F10 crystal structure at 4.2 K could well be P21/n. The |Fhkl| values were extracted from the rebuilt neutron powder pattern by applying the Le Bail method and used for attempting the structure solution by real-space methods. The neutron powder pattern was rebuilt from the 109 intensities extracted up to 54° 2θ, in space group P2/m, given in Table 2 of the original paper. The fit (using FULLPROF) in P21/n of the data rebuilt in P2/m is satisfactory (Fig. 3.5.1[link]). The three-dimensional C6F10 molecule was rotated and translated (six degrees of freedom) in the cell using the ESPOIR (Le Bail, 2001[link]) Monte Carlo program, leading to a plausible starting model (Rp = 13.6%) ready for Rietveld refinement. This program builds a pseudo powder pattern from the extracted |Fhkl| values, which is then compared to the data calculated from the model (Fig. 3.5.2[link]). Unrefined atomic coordinates are available from the Crystallography Open Database (COD, CIF No. 3500009) (Grazulis et al., 2009[link]); a projection of the corresponding structure is shown in Fig. 3.5.3[link]. The true crystal structure is apparently more complex (Solovyov et al., 2014[link]). Final resolution of the structure will require collection of a better experimental powder pattern. However, the coordinates have been refined by energy minimization in the solid state (Smrčok et al., 2013[link]).

[Figure 3.5.1]

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Data reduction to |Fhkl| values for the C6F10 Pawley (1981[link]) test case by the Le Bail method using FULLPROF. The neutron powder pattern (4.2 K) was rebuilt (λ = 1.909 Å) from the intensities given in the original paper (P2/m). The extraction of |Fhkl| values was carried out in the space group P21/n.

[Figure 3.5.2]

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The C6F10 Monte Carlo molecule positioning by the real-space ESPOIR program produces that best fit (Rp = 13.6%) of the pseudo powder pattern built from the previously extracted |Fhkl| values (Fig. 3.5.1[link]), overcoming the equipartition problem at the reduction stage. Compared to Fig. 3.5.1[link], which shows intensities, the multiplicity and geometrical factors are removed, leading to structure-factor amplitudes.

[Figure 3.5.3]

Figure 3.5.3 | top | pdf |

Projection along the b axis of the C6F10 structure model in P21/n before Rietveld refinement.

References

Grazulis, S., Chateigner, D., Downs, R. T., Yokochi, A. F. T., Quirós, M., Lutterotti, L., Manakova, E., Butkus, J., Moeck, P. & Le Bail, A. (2009). Crystallography Open Database - an open-access collection of crystal structures. J. Appl. Cryst. 42, 726–729.Google Scholar
Kariuki, B. M., Belmonte, S. A., McMahon, M. I., Johnston, R. L., Harris, K. D. M. & Nelmes, R. J. (1999). A new approach for indexing powder diffraction data based on whole-profile fitting and global optimization using a genetic algorithm. J. Synchrotron Rad. 6, 87–92.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
Le Bail, A., Duroy, H. & Fourquet, J. L. (1988). Ab-initio structure determination of LiSbWO6 by X-ray powder diffraction. Mater. Res. Bull. 23, 447–452.Google Scholar
Pawley, G. S. (1981). Unit-cell refinement from powder diffraction scans. J. Appl. Cryst. 14, 357–361.Google Scholar
Rietveld, H. M. (1969). A profile refinement method for nuclear and magnetic structures. J. Appl. Cryst. 2, 65–71.Google Scholar
Rodriguez-Carvajal, J. (1993). Recent advances in magnetic structure detemination by neutron powder diffraction. Physica B, 192, 55–69.Google Scholar
Smrčok, Ľ., Mach, P. & Le Bail, A. (2013). Decafluorocyclohex-1-ene at 4.2 K – crystal structure and theoretical analysis of weak interactions. Acta Cryst. B69, 395–404.Google Scholar
Solovyov, L. A., Fedorov, A. S. & Kuzubov, A. A. (2014). Complete crystal structure of decafluorocyclohex-1-ene at 4.2 K from original neutron diffraction data. Acta Cryst. B70, 395–397.Google Scholar








































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