
August 4, 1999, SECC, Glasgow, Scotland, U.K. 
IUCr Workshop 
The
Practice of "Fobs" Extraction
from
Powder Diffraction Data
Armel
Le Bail

Université
du Maine  France
So, the conference will give : a short recall and an introduction to cell constraint Whole Powder Pattern Fitting ; the meaning of the extracted structure factors ; which software to use ; what alternative ; how fast it is ; can we overcome overlapping ; why everybody need it, even those saying not, and finally the listing of applications and byproducts.
The concept of cell constraint whole powder pattern fitting for structure factors extraction is a kind of response to complexity.
If your powder pattern is simple like this, then you don’t really need it.
But if your powder pattern is a forest of peaks, you need it, absolutely !
Very curiously, fitting a whole powder pattern without the structure constraint is much more recent than the Rietveld method. Fits without cell constraint were not applied before the seventies. Fits with cell constraint appeared in the eighties. Without cell constraint, the reflection profiles are fitted where you believe they are, and you may be easily in error. With cell constraint, the intensities are extracted where the reflections should be. Thus, errors are only due to biasing as a consequence of overlapping.
Nowadays, two main cell constraint methods are really dominating the market : the Pawley and Le Bail methods, with some variants.
About the powder extracted structure factors meaning and accuracy and their estimated standard deviations. What is exactly the Rietveld decomposition formula used for obtaining Fobs, allowing the reliability R_{Bragg} calculation ? Here it is. As you can see, a partition is made according to the calculated structure factors. Consequently, the structure factors may only be "observed", under quotes, because they are more or less biased, due to overlapping. For instance : if the Fcalc of two exactly overlapping reflections are equal, then the Fobs will be equal too. If the two Fcalc are different, the ratio of the two Fobs will equal the ratio of the two Fcalc. Find another way to proceed if you can ! Anyway, iterating this formula starting from arbitrarily identical Fcalc provides a way to estimate Fobs without any starting structure model.
We certainly know how to obtain estimated standard deviations for structure factors recorded from a single crystal. In this case, no overlapping occurs, in principle (if we don’t speak of twinning for instance). But how to obtain estimated standard deviations for structure factors extracted by powder diffractometry ? Only those corresponding to nonoverlapping reflections can really be estimated, so that in fact we obtain also estimated standard deviations UNDER QUOTES.
But who needs really ESDs at the solving structure stage ? In SHELXS, the estimated standard deviations allow to omit dubious structure factors, but it is recommended to discard data with extreme care ! ESDs are not used for something else.
There was a comparison of Pawley and Le Bail methods by Giacovazzo, giving advantage to the latter, on wich I don’t want to come back, or just for saying that one continues to see the publication of structures determined from structure factors extracted by both methods. So that both of them appear to work well. The relation with the Rietveld method explains the easy introduction of the LB method in numerous Rietveld codes.
Here is the list of available programs based on the Pawley and Le Bail methods together with the number of successful applications in the field of structure determination. In fact, few of them are really available directly by a free download on Internet. There is no Pawley software with direct Internet access, to my knowledge... Or, if yes, please give me the Uniform Resource Locator ? In fact, I have used an old version obtained at ILLGrenoble. But is it really to me to make it available ?
Alternative is to use softwares extracting structure factors without cell constraint. The most popular is MLE (meaning Maximum Likelihood Estimation) from Rudolf and Clearfield. On this figure, PD is meaning Pattern Decomposition, and corresponds to 15 publications, which were not providing the name of the programs, but explicitly indicated the method for obtaining integrated intensities.
How fast it is. Concerning my method, it is very fast. Sufficiently fast for trying to extract one thousand reflections, just now, in a few seconds. I could do it with my own program but it is a kind of dinosaurian, not user friendly. So, I will do it with FULLPROF or WinMProf.
Both programs have a more or less friendly graphical user interface under Microsoft Windows. Anyway, you need some knowledge in crystallography and several weeks or months before being familiar with them.
Twenty cycles with FULPROF for almost one thousand of reflections for cimetidine. (live demo)
About the estimated standard deviations which are sometimes said to lack to the Le Bail method, if we look at the extracted structure factors SHELXlike output for the cimetidine, the standard deviations are there : (demo)
If you say that ESDs by the Le Bail method are false, you should also say that they are false by the Rietveld method because the same Rietveld decomposition formula is used in both methods. And this is true, they ARE FALSE, or if you prefer, they are UNDER QUOTES "ESDs".
Now with WinMprof on another experimental case with more than 1000 reflections : (live demo)
Concerning the Pawley method, time for obtaining similar results is longer because each intensity is a parameter to be refined. I can't perform any demonstration for it.
Overcoming overlapping, is that possible ? The default output of the Pawley and Le Bail methods is the equipartition of overlapping reflections. Alternatively, the data may be further modified. Many artifices were used, including for instance giving a random repartition of intensity instead of equipartition, or using the expected positivity of the Patterson map, or using the triplet and quartet relations from direct methods. The simplest approach is the preparation of a series of data sets from which are excluded reflections having a neighbouring one at less than some small angular value depending of the Full Width at Half Maximum. All these methods may enhance the success rate for structure solution.
There are two people categories. Those who need extracted structure factors because they are absolutely necessary for methods like the Patterson and direct methods. And those who are doing molecular replacement and prefer to do it by checking rotation and translation of their models directly on the raw data.
But at least those fitting directly the raw data use the Pawley or Le Bail methods for getting the best starting profile and cell parameters which are reused each time a pattern is calculated. So, finally, they need it !
Using the raw data is quite time computer consuming : 20000 Monte Carlo moves meaning 20000 powder pattern calculations and checking with the observed data.
A new process partly overcomes this problem, by using the full set of extracted structure factors. A pseudo pattern is regenerated from those extracted structure factors, with same Caglioti law, but without background, Lorentzpolarisation, asymmetry, and with an optimal number of points (3 to 5 steps above the FWHM line).
Calculations on this pseudo pattern are much faster (by a factor three at least) than by using the raw data.
Up to now, this facility was implemented in ESPOIR, a new program able to solve moderately complex structures by Monte Carlo, starting either from completely random models or from a molecule fragment.
For instance, the cimetidine structure can be solved either from "scratch" or from molecule location by the ESPOIR program, using extracted structure factors. If you choose the option to regenerate a pseudo powder pattern from these extracted structure factor, then the program will check the model after each Monte Carlo step on this unreal pattern, showing here hundred first reflections :
Using such a pseudo pattern really saves time. A demo will be given at the Computer Fayre, August 9th.
Structure determination is the main application of the whole powder pattern fitting with cell constraint process. However, there are some quite interesting byproducts which are the possibility to take account of impurities of unknown structure, but known cell, during Rietveld refinement (not easily possible by Pawley method).
Some use them for fitting texture data without structure. Many of us are checking the correctness of cells proposed at indexing stage and also are checking a space group proposition by the Pawley or Le Bail methods which have become two of the most useful tools for a modern powder diffractionist.
And do not forget to visit the SDPD Database and to subscribe to the SDPD Mailing List !
Thanks for your attention.
A. Le Bail
IUCr XVIII, Glasgow,
August 4, 1999.
See some amazing pictures from this congress.