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
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is realized by using a local unpublished cell constrained profile fitting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
(2) P. Amoros, D. Beltran-Porter, A. Le Bail, G. Ferey and G. Villeneuve,
J. Solid State Inorg. Chem. 25 (1988) 599-607.
(3) Y. Laligant, A. Le Bail, G. Ferey, D. Avignant and J.C. Cousseins,
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,
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
(9) A. Le Bail, G. Ferey, A.M. Mercier, A. de Kozak and M. Samouel,
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.
Satellite Meeting of the XVth Congress of the International Union of
Toulouse, France, July 16-19, 1990
Abstracts, pages 99-100.
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.
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
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
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
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
MY PURPOSE IS TO SHOW HOW SUCCESS CAN BE OBTAINED
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.
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.
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.
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!
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
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:
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 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
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.
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.
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.
A few words to describe the structure: it is an intergrowth of equal
fractions of rutile and ramsdellite blocks.
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
- Presence in all cases of impurities and of preferred orientation
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 !
Satellite Meeting of the XVth Congress of the International Union of
Toulouse, France, July 16-19, 1990
Abstracts, pages 99-100.