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August 15-20, 1998 Microsymposia C - Structural Aspects in Chemistry, Chemical Crystallography. Topic C4 - Structure Determination by Powder Diffractometry Trends in Structure Determination by Powder Diffractometry A. Le Bail Full conference text and slides : T1 - During the past 10 years, the number of SDPD (structure determinations by powder diffractometry) increased from 28 to more than 300. The production in the first 40 years was ranging episodically from 0 to 4 papers maximum per year. Then the annual production was more or less stable with about 10 structures per year till 1992 showing a new expansion with 31 structures up to 55 structures last year. So that, after 50 years of SDPD, we only just exceed 300 structure determinations by powder diffractometry. T2 - Will be discussed in this conference the following points: more statistics from the SDPD-Database; the trends in the SDPD steps like indexation; structure factors extraction; data massaging and dealing with overlapping reflections; the Patterson and direct methods; the model building and location methods; the structure completion stage; the final Rietveld refinement step; some words about complexity and accuracy. Trends are expected to come from the clearly dominant methods and softwares. Finally, the preliminary SDPD Round Robin results will be given. T3 - The 295 papers are distributed in 51 periodicals. Inorganic phases are dominant, and most of them are oxides. Indeed, only 31 organic, 63 organometallic and 8 polymers were studied. As many as 570 peoples are authors or co-authors of these papers. These contributions attest for an increasing professionalism. Popularity of SDPD can be also measured by the quantity of review papers : 33 are already published. T4 - All crystal systems were the subject of SDPD, the monoclinic and orthorhombic systems being the more studied with respectively 42 and 30%. The crystal system repartition for these modern powder studies does not seem to differ significantly from single crystal studies. T5 - Instruments selected for these SDPD are either neutron reactors (in 65 cases) or synchrotron sources (in 64 cases), or are in-laboratory less-expensive conventional X-ray diffractometers (in 237 cases). This figure does not reflect the possible joint use of 2 or 3 of these instruments. Aniway, neutrons were used scarcely alone. T6 - Automatic indexing is the first step when a sample has been prepared as very small crystallites and is definitely unknown. Three main programs traditionally occupy the market : TREOR with 111 applications, ITO with 90 and DICVOL with 42 applications. Recommendation is to use all of them. In principle one cannot go further if this essential step is not successful, so that we have here undoubtedly a well established trend, with those three programs. At heroic times, structure factor extraction by hand was not rare by cutting peaks on the recording paper and weighting them. Nowadays, mainly the Pawley and Le Bail methods realize this stage. A trend is that these methods are used also in order to check the correctness of the cell and space group. Possibly due to a better stability and faster execution, the Le Bail method dominated over the last 6 years. The abrupt increase of the SDPD application number in 1992 coincides with the availability of this method in a series of Rietveld softwares. T7 - Here is the list of available programs based on the Pawley and Le Bail methods together with the number of successful applications. Both methods allow whole powder pattern fitting with cell constraint. The difference comes from the consideration of intensities as independent refinable parameters, in the Pawley method, or not, in the Le Bail method. The current rate of use of both methods does not indicate any tendency to abandon them. T8 - 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. T9 - 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. The SDPD Round Robin results will tell you in a few minutes if those methods have clearly improved the success rate. T10 - The main softwares used for Patterson and direct methods are shown in this list. SHELX and SIRPOW are the clear leaders. It should be realized that in 1/3 of the SDPD cases, only 1 or 2 heavy atoms had to be located for obtaining a partial model allowing to start refinements. For solving these rather trivial structures, 30 or 40 intensities may suffice. The use of Patterson and direct methods rules for an alternative to the equipartitionning of the overlapping reflections was already mentioned, the program SIRPOW dominates this field. But no trend is obvious, that using directly softwares developed for single crystal data is decreasing. T11 - In the 40 first SDPD years, the Patterson method dominated the direct methods with a ratio 3/1. Since 1988, the tendency is reversed with a ratio of 1/2. The SDPD-Database contains also 18 structures guessed from some convergent informations. Model building methods concern the 51 remaining structures in this figure. T12 - When those previous standard methods fail, the alternative is to build a model and to locate it in the cell. This could be either a simple or a formidable task, depending on the existence or not of prior informations. For instance, the PATSEE program is an old SHELX companion. It was also applied to powder diffraction data in two cases. The program requires extracted structure factors and attempts to combine the merits of both Patterson and direct methods in order to position a fragment of known geometry in the unit cell. Early works in this model-location category consisted in the brute force : searching for a molecular position and orientation following a systematic grid search. The dominant trend is given on this list by the Monte Carlo and Patterson-search methods. Variants have incorporated restrained relaxation of the molecular geometry or a high degree of molecular flexibility. Even more sophisticated, maybe, are methods applying simulated annealing, possibly through a genetic algorithm, because a set of internal coordinates defines the geometry of the molecule, allowing torsional angles to vary (in addition to the usual external degree of freedom defining position and orientation). Anyway, the impact of these methods on the routine analysis is small, up to now. We will see in a few minutes if these methods succeeded in the SDPD Round Robin. T13 - Structure completion is usually performed by Fourier syntheses applied to the structure factors provided by the Rietveld decomposition formula. Only 50 percent of users are really explicit on softwares selected to realize this step. Not many Rietveld softwares are able to give a Fourier synthesis as output. GSAS and XRS are part of them; this explains their presence in this list. The great majority of the other softwares are directly issued from single crystal packages. Again, SHELX dominates and gives the trend. T14 - The final Rietveld refinement stage is dominated by two programs essentially. GSAS, with 84 applications and FULLPROF with 57 applications as shown in this list. Five other softwares totalize more than 6 applications, and 20 softwares, whose names are not reported here, were applied 1 to 5 times. T15 - There is a perpetual race for the publication of the most complex structure ever determined from powder diffraction data. The SDPD-Database actually sorts compounds according to 4 complexity criteria. The first of them is the number of independent atoms. Looking at this figure, showing the variation of the maximum and mean values during the last 10 years, one is tempted to conclude that the complexity of structures, which can be determined from SDPD, is slightly increasing. T16 - The second complexity criterion is the number of refined atomic coordinates. The mean value in 1997, near of 50, is almost twice the value observed in the initial 40 years of SDPD. Such an evolution is really expected because of increasing instrumental resolution at synchrotron sources and also in laboratories. T17 - More interesting is the third complexity criterion which is the number of atoms initially located at the first Patterson or direct methods application. The mean is noted M1 here. A partial mean, denoted M2, is also reported, excluding the 100 structures for which 1 or 2 atoms were found to represent a sufficient starting model. In fact, only the maximum shows some tendency to increase but remains rather small, with still less than 20 atoms. T18 - Finally, the fourth criterion was considered to be applicable to model building and location methods, corresponding to the number of independent molecules or fragments simultaneously located. Only 26 unknown structures were determined since 5 years, corresponding to this criterion, so that statistics are hardly possible. Other possible complexity criteria for model building could be the number of internal degrees of freedom (actually the maximum is 24), or the number of external degrees of freedom (the maximum is actually 15) and the specific number of torsion angles, the maximum being 10, up to now, and to my knowledge. T19 - IUCr is reluctant to publish single crystal data when the ratio of the reflection number on the number of refined parameters is less than 10. A kind of limit has been attained recently for some organic compounds of which the structures were determined by molecule location methods, with ratios lower than 2or 3. The trend is to use geometrical restraints in the final refinement. Anyway, one could doubt about some details of the structure when this ratio is not much larger than 1. T20 - A cleavage is now apparent between the unknown structures for which it will be possible to guess a molecule or a sufficiently large fragment (or several ones) and those for which no sufficient prior information will be available. In the latter case, the ab initio methods will continue to be applied (that is to say, the Patterson and direct methods). Some times ago, it was stated that we were unable to determine structures as large as those we could refine by the Rietveld method. The new paradox is that we can locate now molecules in much bigger cells than we could refine without constraints. A few softwares, free for academic research, dominate each step of the SDPD whole process. Not all softwares are in the public domain and some methods are the exclusivity of their developers. SDPD will not expand faster before a larger distribution of these new programs. And what about SDPD "on demand" ? The answer is in the preliminary conclusions of the SDPD Round Robin.
The preprint of the paper submitted for publication in the ECM-18 book is available as :
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