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

Abstract :

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

Full text of the conference and slides

Ab-initio structure determination from powder data has been practiced now for more than 13 years. The first and well known published works are those of Werner and co-workers in 1977.
Slide 1
It is difficult to define what exactly a "non-trivial structure" is, if we put arbitrarily a limit at 10 refined atomic coordinates, then the total number of such "non-trivial structures" determined up to now from powder data is between 30 and 40: very small. However, the interest for this subject is such that numerous reviews and general papers have been already published. My speech will have inevitably some common aspects with these reviews.
As you can see from this histogram, it seems that a second start began in 1984 or 1986. Two reasons are generally given to explain this second start:
The first reason is : Improvements in the applicability of the Rietveld method to X-ray diffraction due to the use of more adapted profile shapes than the pure Gaussian or Lorentzian shapes. This consideration implies that structure determination was expected to be easier from X-ray data than from Neutron data by the use of the so-called "heavy atom method".
The second reason is the advent of a new generation of high-resolution powder diffractometers at the Rutherford-Appleton Laboratory, ILL Grenoble and the Brookhaven National Light Source.
In fact, the examination of 30 published cases shows that 80% of the structure determination from powder data were made by using standard in-laboratory X-ray diffractometer and that an increasing number is obtained from the direct methods. This is to some extent in contradiction with the two previous considerations.
Probably, the main reason which could explain the increasing number of applications is that more and more potential users are convinced that structures can be determined from powder data and refined to a reasonable accuracy.
Slide 2
Generally, the problem starts when a solid state Chemist or Physicist, with some notions of Crystallography, performs a new synthesis or is interested by a structurally uncharacterized phase cited in the literature.
Theoretically, all possible efforts should be aimed at obtaining single crystals. However, there are domains of material science where difficulties in obtaining single crystal are frequent: for example phase transition or phase transformation by dehydration or gas-loss. The development of real-time thermodiffractometry, applied mainly on these domains, demands that structure determination from powder data becomes a routine business.
Slide 3
So how to succeed ? Structure determination from single crystal data is well established. The strategy which must be adopted for powder data is different only on some points as you can see on this view: the order of the different steps may be reversed; what is easy for single crystal becomes generally difficult for powder data.
So I will emphasize now the points which are really different when you determine a structure from powder data instead of single crystal data, and which can be the reason of either the success or the failure.
Slide 4
First point, the choice of the instrument: the common idea is to turn towards the so called high-Resolution Powder Diffractometer: synchrotron, neutrons. In fact, if you have not made a serious preliminary study, your proposal for neutron or synchrotron will probably not be accepted, but there could be a few exceptions.
So, it is clear that your material must be firstly examined by your own in-Laboratory X-ray diffractometer or Guinier-Hägg camera. There is the first step: collect the highest resolution pattern you can for indexation purpose. You can note that the resolution of good conventional X-ray diffractometer is as good as the resolution of any neutron theta-two theta diffractometer.
Slide 5
Indexation can be done from powder data only or with the aid of electronic microdiffraction or even from " bad quality crystals". Actually, more than ten indexation programs are on the market and easily accessible. The user's guide of some of these programs may contain more than ten or twenty pages of recommendations for success. I limit myself to give you the most important recommendations: be sure of your data, and try with several programs. With Guinier-Hagg or diffractometer data the Figures of Merit published show that the average absolute magnitude of the discrepancy between observed and calculated two theta can reach these values. Such a precision is obtained either by the well known derivative method for extracting the peak positions or by profile fitting. The pattern must be calibrated (that is to say, the zeropoint must be determined) by using an internal standard or several series of recognized harmonics.
The space group determination is much more difficult to achieve from powder data than from single crystal data. The reason is, of course, overlapping: systematic absences have to be established from a few low angle reflections, leading to some uncertainty. The finding of an unambiguous space group, with no extinction anomalies, is a strong argument proving that your indexation is not false: particularly when the lattice is centered, face-centered or all face centered!
Slide 6
At this stage you may estimate your chances of success from the  cell volume and the symmetry class. This is why I can claim eighty per cent success: I simply do not try to determine structures from powder data beyond certain limits. That is to say a maximum of 50 or 70 atomic coordinates to be refined in the case of conventional X-ray when the spacegroup is centric. This corresponds to various maximal volume limits according to the different symmetry classes.
For acentric space groups, these values are to be reduced by a factor of two. Also if you expect a medium accuracy on bond length, you must reduce by a factor of two. With ultrahigh-resolution powder diffractometer, these values can be multiplied by a factor of two or three. For quadratic-hexagonal-trigonal-cubic systems, difficulties will be encountered in the low Laue symmetry classes, because of inherent strict superposition of a lot of reflections. All that is evident and the cubic case may be the more difficult for such reasons.
However, as a preliminary conclusion, the powder method can be used currently to determine not only moderately complex structures as it has been done until now, but also relatively complex structures using the best diffractometers. It is actually clear that the most impressive structure determinations from powder data will come from high resolution synchrotron data; but up to now, the most difficult cases were solved from conventional X-ray sources.
Slide 7
Difficult cases cannot be solved by using the strictly non overlapping reflections of a powder pattern for the structure solution stage. One must try to estimate the structure factor of all reflections before applying the classical structure solution methodology. The only way to obtain an estimation of the intensities of all reflections is by profile fitting techniques. We come now to the most important point in my opinion. A classification of the actual profile fitting techniques may be done: programs may be classified according to wether the reflection positions are cell-constrained or not and the intensities are refined or not. I have reported here the main methods which were used until now for structure determination from powder data. You can see that to obtain in one time one thousand structure factors is impossible for most of these methods, the number of parameters to be refined being enormous. Because I had problems of such size, I have imagined a way to obtain a cell-constrained whole pattern profile fitting program, which could proceed without refining the intensities so that, in any case, the maximum number of parameters to be refined is 15. It is interesting to note that any Rietveld program can be transformed in a cell-constrained profile fitting program according to this way, when the structure part has been removed:
Slide 8
For those who have looked inside the Rietveld program, the following will be evident: the subroutine of interest here is generally named "SUMMAT" called by the subroutine "ITER" in which the "observed" structure factors are in fact not observed, as you know, but estimated by a partition of the point by point observed intensities according to the calculated contributing structure factors. The way to proceed for a profile refinement only is as follow: the starting structure factors have arbitrarily all the same value; then at the end of each cycle they are replaced by the "observed" ones according to this equation. This is a very efficient iterative procedure. The behaviour of strictly overlapping reflections is to keep the same value without the necessity of the slack contraints as in the Pawley's program.
I cannot say if the chances of success are greater when a cell constrained whole pattern fitting program is used or when it is a non-cell constrained program. In my opinion, the knowledge of the cell and of the spacegroup must not be neglected at this stage. A definitive conclusion could be drawn by a survey of the whole pattern profile fitting methods with an intercomparison of the ability of solving structures of various complexity from the estimated structure factors.
Structure solution is a very well established domain for single crystal data. If you have admitted the necessity that powder data must not be limited to the non-overlapping reflections, simply because they are not sufficient for the structure solution methods for the most complex cases, then the success of structure determination from powder data will depend on the efficiency of the Patterson and direct methods when using poor quality data.
The majority of the structure determinations by the Patterson method are from data set limited to non-overlapping reflexions, but some of them used the complete dataset obtained from the Pawley's program with success. A recent paper of C.C. Wilson suggests that the Patterson method has a definite advantage over the direct methods when the data are of poor quality. I disagree with that. The two methods are known to be at their advantage in rather different cases, and this is true as well as for single crystals as for powder data. The interesting point is that both methods seem to be rather insensitive to the presence of many dubious data. I think that I have contributed to demonstrate this, for the direct methods, from more than ten experimental cases, I will show you the last of these cases.
Slide 9
The compound is a nickel-vanadium oxyde frequently cited in the last twenty years by several workers. The structure was of course unknown and only a non-indexed pattern could be found in a paper which is more than 30 years old! I must add that this compound is not included in the JCPDS cards up to now, no more comment about that! Indexation was not very difficult and led to a triclinic cell with a volume of approximately 300 angstroem-cube. More than one thousand structure factors were extracted at one time from this powder pattern by the cell constrained profile fitting technique.
Slide 10
Then a lot of attempts were made to obtain a starting part of solution either by using the Patterson method or direct methods, using the centric or acentric triclinic space group, from either the whole data set or a reduced one. The limited data sets were selected by the application of a "non-overlapping" criterion defined as "angular reflection position differing by more than n counting step".
The human intervention in complex problems of structure solution is limited to the choice of a program, then to run the program and try to identify the solution between the multiple propositions. This is true even for single crystal but the solution is much less evident for powder data.
I was not able to obtain the correct proposition by using an automated Patterson method based program. It must be noted that the heaviest atoms in this case are both the nickel and the vanadium atoms and that five independent nickel and vanadium atoms are located in the asymmetric unit. So, probably the direct methods were more efficient here and a part of the solution including all the heaviest atoms was obtained from any of these datasets, furthermore, the more complete proposition was from the complete dataset. This seems to demonstrate the paradoxical fact that the inclusion of doubtful data is advantageous. I won't really try to explain that. This could be an effect of the implicit Fourier transformation which reveals periodic events even when they are mixed with random events.
Slide 11
A few words to describe the structure: it is an intergrowth of equal fractions of rutile and ramsdellite blocks.
Slide 12
The nickel and vanadium atoms are strictly ordered; there is a tripling of the rutile-chains c-axis, due to the jump of one third of the vanadium atoms on tetrahedral sites. The relation with gamma-MnO2, a material widely used in the battery industry is obvious.

For the refinement stage I will limit myself to recommend the Rietveld method. The ROUND ROBIN SURVEY OF RIETVELD REFINEMENT will produce probably some interesting conclusions.From a convenient starting part of solution, there is generally no problem for the structure completion by alternated Rietveld refinements followed by Fourier difference synthesis. About the particular problems encountered in the series of structure determination collected in the abstract, I do not have the time to develop them but I can make a list:
- Anisotropic line broadening due to non-spherical small crystallites in the case of the copper-vanadium oxyde hydrate.
- Diffusive bumps on the X-ray pattern induced by partial disorder for the nickel-vanadium oxyde.
- Weak superstructure reflections for the potassium-vanadium hydrogenphosphate, associated with stacking faults, inducing the broadening of reflections with odd l indices.
Also, some more general problems:
- Low accuracy on bond lengths due to the presence of heavy atoms: improvements were obtained from neutron data for the terbium and the baryum compounds.
- Presence in all cases of impurities and of preferred orientation effects.
finally I must add that I have not the response to the question: where is the background at large angle where there is strong overlapping!
All these works are published or in press.
Thank you for your attention and good luck !

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