THE PRACTICE OF STRUCTURE DETERMINATION FROM
POWDER DATA : HOW TO SUCCEED

A. Le Bail, Laboratoire des Fluorures, URA CNRS 449,
Université du Maine, 72017 Le Mans Cedex, France.

Structure determination from powder data can be done as a routine business. This is attested by the following list of selected non-trivial structures, although moderately complex, determined during three years, in one laboratory, following the same general procedure : 

Formula              Space   V(A3)  x,y,z   N of   RB(%)  RWP(%) Ref
                     group         refined  hkl
LiSbWO6              Pbcn     406    12     306    2.1    6.5   (1)
KVO2HPO4             Pbca    1050    27     760    4.4    8.5   (2)
Li2TbF6              P21/c    395    27     812    4.0    8.5   (3)
alpha-VO(HPO4).2H2O  P21/c    534    42     785    4.1    9.4   (4)
beta-VO(HPO4).2H2O   P-1      529    54     967    3.9    9.2   (5)
alpha-(NH4)2FeF5     Pbcn    1067    21     792    4.7   12.1   (6)
NaPbFe2F9            C2/c     700    14     445    5.1    9.2   (7)
Cu3V2O7(OH)2.2H2O    C2/m     447    16     340    3.5    6.3   (8)
beta-BaAlF5          P21/n    760    42    1130    5.2    9.9   (9)
gamma-BaAlF5         P21      377    41     615    5.4   11.3   (9)
NiV2O6               P-1      294    42    1175    5.6   11.3  (10)
As nothing replaces experience, the discussion will be mainly based on these examples. None of these materials could be obtained as a single crystal (until now), for known reasons in some cases (phase transition leading to fragmentation and/or systematic twinning, syntheses from soft chemistry processes, dehydration...).

The success concerns 80% of the attempts ; it does not come from something new but from the systematic application of an efficient mode of operation and of efficient algorithms.

First of all, data are from a conventional Bragg-Brentano X-ray diffractometer, not adjusted to its maximal resolution (Cu-Kalpha radiation, reflected-beam monochromator) ; the minimal FWHM being between 0.12 and 0.20° (2-theta) ; this is probably one of the reasons why the Rwp (calculated after background subtraction) seem abnormally low for such X-ray studies (i.e. the increase of the resolution also increases systematic errors and problems in the whole pattern fitting). Such a resolution is sufficient to ensure |mean-delta-2-theta| ~ 0.015° at the automatic indexing stage, providing that a 0.02°(2-theta) counting step is used with an internal standard, and that the positions are obtained from a profile fitting procedure.

Once a proposition for a space group is made, the extraction of |Fobs| is realized by using a local unpublished cell constrained profile fitting program able to produce 5 < Rwp < 8%. The main originality of this program is that the individual |Fobs| are not refined in a least squares sense, but they are determined by an iterative procedure based on the so-called "|Fobs|" in all Rietveld-type refinement programs.

Structure solution is obtained mainly by using the direct methods from either the whole or a reduced data set. The fortunate ability of direct methods to locate either the whole or part of the independent atoms from |Fobs| values, more or less dubious, will be emphasized.

These points and also the refinement stage will be discussed in details. Particular problems encountered in this series of structure determinations will be reviewed briefly.

(1) A. Le Bail, H. Duroy and J.L. Fourquet, Mat. res. Bull. 23 (1988) 447-452.
(2) P. Amoros, D. Beltran-Porter, A. Le Bail, G. Ferey and G. Villeneuve, Eur. J. Solid State Inorg. Chem. 25 (1988) 599-607.
(3) Y. Laligant, A. Le Bail, G. Ferey, D. Avignant and J.C. Cousseins, Eur. J. Solid State Inorg. Chem. 25 (1988) 551-563.
(4) A. Le Bail, G. Ferey, P. Amoros and D. Beltran-Porter, Eur. J. Solid State Inorg. Chem. 26 (1989) 419-426.
(5) A. Le Bail, G. Ferey, P. Amoros, D. Beltran-Porter and G. Villeneuve, J. Solid State Chem. 79 (1989) 169-176.
(6) J.L. Fourquet, A. Le Bail, H. Duroy and M.C. Moron, Eur. J. Solid State Inorg. Chem. 26 (1989) 435-443.
(7) A. Le Bail, J. Solid State Chem. 83 (1989) 267-271.
(8) M.A. Lafontaine, A. Le Bail and G. Ferey, J. Solid State Chem. 85 (1990) 220-227.
(9) A. Le Bail, G. Ferey, A.M. Mercier, A. de Kozak and M. Samouel, J. Solid State Chem. 89 (1990) 282-291.
(10) A. Le Bail and M.-A. Lafontaine, Eur. J. Solid State Inorg. Chem. 27 (1990) 671-680.

Powder Diffraction
Satellite Meeting of the XVth Congress of the International Union of Crystallography
Toulouse, France, July 16-19, 1990
Abstracts, pages 99-100.

See also