Claim for a 'R' (Rietveld) Mark in the Powder Diffraction File





Abstract


It is shown that the full powder data characterizing a moderately 


complex structure determined ab initio and refined by the Rietveld (R)


method are hardly inserted into the Powder Diffraction File (PDF) mould. 


The Rietveld method allows to estimate 'observed' intensities at d 


positions unobservable in the usual PDF sense (although cell parameters 


are refined), hence the claim for a 'R' quality mark taking account of 


this paradox.





Introduction


Quality marks are assigned to powder pattern data by the Powder 


Diffraction File (PDF) editors. In the guidelines for a 'C' mark 


(calculated from structural parameters), it is explicitly specified that 


"if the structure was derived by X-ray Rietveld methods, the calculated 


pattern is accepted only in unusual circumstances ; the original powder 


pattern is preferred" (Wong-ng, Hubbard, Stalick & Evans, 1988). Such a 


preference is paradoxical because the Rietveld (1967, 1969) (R) method 


is recognized to propose the more complete way to characterize a powder 


pattern when the structure has been determined. More and more crystal 


structures are determined ab initio from powder diffraction data 


(Cheetham & Wilkinson, 1991, 1992) and the majority is from conventional


X-ray data, monochromatized or not. Once determined, these structures 


are refined by the R method whose efficiency and credibility are 


uncomparable to those of methods used to produce dobs and Iobs which are 


then called the "original powder pattern". Arguments are thus given here


in order to support the creation of a 'R' quality mark to distinguish 


the powder data that have been the more fully characterized.





Experimental and data analysis


The Table 1 referenced below is from one experimental case which is used 


as a support for the arguments developped here : [Pd(NH3)4]Cr2O7 


(Laligant & Le Bail, 1995).





Claim for a 'R' mark in the PDF


The PDF lists essentially data observed from an experimental powder 


pattern (dobs and Iobs). Since no dobs are available from the R method, 


the decision of the PDF editors to prefer the "original powder pattern" 


instead of a calculated one may be understood. However, things are not 


so simple. The R method delivers 'Iobs' so called because they are 


estimated in a quite specific way by the Rietveld decomposition formula.


Also, the R method proposes refined cell parameters that fit the whole 


experimental powder pattern with the structure constraint, so that the 


associated dcalc should be better considered than those originating from 


a single crystal study (a fortiori when no single phase powder was 


prepared) or the dobs of a few unambiguously indexed reflections. Not 


any PDF card was given in the form presented in Table 1 (Laligant & Le 


Bail, 1995). Either from the structure factor extracting stage 


(structure unknown but cell and eventually space group tentatively 


proposed) or the final Rietveld refinement stage (structure determined), 


we can list 'Iobs' values for which we have no corresponding dobs in the 


usual sense (that we could reasonably estimate/refine from the raw data 


by various methods not requiring the cell knowledge), we have only 


dcalc. When the structure is unknown, Iobs are extractable by whole 


pattern fitting techniques with cell constraint like in the Pawley 


(1981) or Le Bail (1992) methods (with the Rietveld 'Iobs' sense in the 


latter). Of course, several exactly overlapping reflections are 


generally given the same structure factor by such extracting methods, 


there is no miracle. Such 'observed' intensities are also biased in the 


R method because they are obtained by a partition of the raw data 


according to the calculated intensities (i.e. two superposed reflections 


are given 'Iobs' values in the same ratio that the Icalc ones, whereas 


the sums of these observed or calculated intensities may be different). 


In spite of these disadvantages, 'Iobs' are of great value. The RB 


factor is calculated from them compared to the Icalc and they allow to 


perform more or less efficient Fourier difference syntheses. It is 


suggested here for the first time that best 'Iobs' for Fourier 


difference map would even be obtained after a few iterations of the R 


decomposition formula instead of one application at the last refinement 


cycle. The paper from Laligant & Le Bail (1995) gives at least the 50th 


demonstration that 'Iobs' extracted by iterating the Rietveld 


decomposition formula are sufficiently well estimated for attempting 


with success a structure determination by the direct or Patterson 


methods.On another hand, the statement "the original powder pattern is 


preferred" merits some examination because dobs and Iobs are in fact 


extracted by pattern decomposition methods (those without cell 


constraint) that may fail to estimate them accurately. Many of the 


reflections listed in Table 1 (Laligant & Le Bail, 1995) have clearly 


not excellent observed d positions. The EVA Socabim software gives 


understandably poor estimation of the weak reflections positions (for 


instance 020 and 002, with I/Io < 1%), in part because stripping the 


alpha-2 component introduces additional noise (data were not smoothed). 


In case of strongly overlapping reflections, shoulders are detected by 


eyes that are not located automatically in spite of efforts in varying 


the search parameters (of the 022 and 102 reflections, only the 022 


was detected although both are very intense and their separation exceed 


half the FWHM - but note their different estimated 'Iobs' in Table 1). 


Some observed positions are clearly the mean for a series of 


neighbouring reflections. Sometimes numerous weak overlapping 


reflections of almost equal intensities produce a large bump for which 


the automatic search proposes not any position (see ranges 24.1 - 24.6 


or 27.6 - 28.0 2-theta degrees). Even if a position is suggested, the 


practice to give in the PDF one dobs value for numerous more or less 


overlapping reflections is quite not satisfying. In such cases peak 


fitting techniques are not more efficient. Indeed, we were not able to 


produce better peak position (if compared to dcalc) and intensity 


estimations than those obtained by the derivative method by the use of 


the profile fitting FIT Socabim program with various tests on peak 


shapes. Knowing or not the number of peaks and their calculated position 


in a set of neighbouring reflections can make a large difference at the 


extracting stage of the 'observed' reflection positions. Finally, one of 


the criteria for a star(*) quality mark is that "intensity must be 


measured objectively", something difficult to realize with decomposition


methods without cell constraint. This is a brief summary of the main 


difficulties encountered by somebody asked for a moderately complex 


powder pattern by the JCPDS-ICDD. We believe that the best estimation of 


the peak positions are those calculated from the cell parameters refined 


directly from whole pattern fitting (without dobs production). We think 


the JCPDS-ICDD should revise its policy and allow inclusion of 'Iobs' 


and dcalc with a 'R' mark in the PDF or at least, should not prefer 


traditional Iobs and dobs to Is and ds calculated from Rietveld 


refinement results.





Conclusion


Ways to observe powder data have considerably changed over the 30 past 


years. Difficulties to insert the present data in the usual PDF form 


have been emphasized. We have suggested that calculated ds and 'Iobs' 


from Rietveld refinement should be preferred to the "original powder 


pattern" to be included in the PDF. Maybe one point prevents the 'R' 


quality being systematically recognized as the higher evaluation, even 


better than the star(*) category : for that, the Rietveld refinement 


should be performed on a sample mixed with a standard.





References


Cheetham, A.K. & Wilkinson, A.P. (1991). J. Phys. Chem. Solids 52, 


    1199-1208.


Cheetham, A.K. & Wilkinson, A.P. (1992). Angew. Chem., Int. Ed. Engl. 


    31, 1557-1570.


Laligant, Y. & Le Bail, A. (1995). Powder Diffraction, 10, 159-164.


Le Bail, A. (1992). NIST Special Publication 846, 213.


Pawley, G.S. (1981). J. Appl. Crystallogr. 14, 357-361.


Rietveld, H.M. (1967). Acta Crystallogr. 22, 151-152.


Rietveld, H.M. (1969). J. Appl. Crystallogr. 2, 65-71.


Wong-ng, W., Hubbard, C.R, Stalick, J.K. & Evans, E.H. (1988). Methods 


    & Practices in X-ray Powder Diffraction, JCPDS-ICDD, 9.3, 1-7.





A. Le Bail


Laboratoire des Fluorures, CNRS URA 449, Universite du Maine, 


Avenue O. Messiaen, 72017 Le Mans Cedex, France


E-mail : armel@one.univ-lemans.fr