Armel Le Bail July 22, 1993

Laboratoire des Fluorures

Université du Maine

72017 Le Mans Cedex

FRANCE

To: Dr. H. Toraya

Ceramics Research Laboratory

Nagoya Institute of Technology

Asahigaoka, Tajimi 507, Japan

Dear Dr. Toraya,

It is a pleasure to answer your questions:

1) The name of my computer program for "whole pattern decomposition" is ARITB.

2) It is correct to cite the paper Mat. Res. Bull. Vol 23, 447-452 (1988) as containing the first application of ARITB to extract "|Fobs|" for an ab initio structure determination from powder diffraction data. Note however that no clear information was given in this paper about how run ARITB, even the name was not given.

3) The profile function used was that given in the above paper: analytical Fourier series. However, the program proposes in option the possibility to deal with anisotropic size/microstrain line broadening and in this case the profile function used is the convolution of f and g, both represented by analytical Fourier series (the f profile being Cauchy-like for the size effect and continuously varying between Gaussian and Cauchyan for the microstrain effect as for the Rietveld program ARIT4).

The technique consists in iterating the Rietveld decomposition formula allowing to extract the so-called "|Fobs|" (those used to calculate R_B). So any Rietveld program can easily be modified in order to accomodate an option for "|Fobs|" extraction, one has just to switch off all concerning the calculation of the structure factors from the atomic coordinates. To implement this algorithm, you have to:

a) Locate where are inserted the |Fcalc| in order to calculate the Yi intensities at each counting step in your own Rietveld program.

b) There, instead of using such |Fcalc| at the first cycle, you have to insert arbitrary values (for instance, all starting |F| equal to 100.).

c) Then you have to locate where are calculated the so-called "|Fobs|" and to store them for the next cycle in which they will be used as the new "|Fcalc|". Do 20 to 40 of such iterations, conserving the possibility to refine the profile and cell parameters (maximum a dozen parameters...).. Of course, the scale factor must be kept fixed at an arbitrary value.

That's all. In case of K_1,2 the ratio of the doublet has to be imposed at each cycle by averaging the two "|Fobs|". The rest is a question of strategy as explained in NIST Special Publication 846, p.213 (1992), included (the more complete 'paper' about this algorithm!). I remember you asked me how it runs in front of my poster at Gaithersburg and I was surprised because you were one of the few having made some special use of the Rietveld decomposition formula in a very exotic work on fibrous crystals: you should have the same idea as me in this specific case long time ago but instead of doing 20 to 40 iterations starting from all equal |F| you performed only one such iteration starting from |F| calculated from a partial structural model deduced from a Patterson applied on intensities estimated from unambiguously indexed reflections...

I never published a full paper on this because it was so simple that, at the moment to submit the first application, I was not sure that the procedure had not been yet described previously. Then a number of problems we had in my laboratory were easily solved and the results were presented at the Toulouse Powder Diffraction Satellite Meeting of the XVTH IUCR Congress (1990) (a copy is enclosed). The principle of the method was detailed there, moreover the ARITB program was early installed at the ILL-Grenoble (1989 may be) and J. Rodriguez-Carvajal soon implemented the algorithm in its own Rietveld program (FULLPROF) presented at the same meeting (pages 127-128 of the proceedings) and he gave a name to that ("pattern matching" or now "profile matching", but I do not like it...). Now, 19 ab initio structure determination from powder diffraction data have been published from Le Mans using the ARITB program (see the table and references 1-19), others are in preparation. At Toulouse, D.E. Cox was very interested and the algorithm was quickly introduced in the Brookhaven Rietveld programs resulting in some structure determinations from synchrotron data, for instance (VO)₃(PO₄)₂^.9H₂O (ref. 20) and CuPt₃O₆ (ref. 21). Meantime, I initiated A. Jouanneaux to the ARITB/ARIT4 program in Le Mans, then he goes one year at the Keele University in England and realized a lot of powder patterns at the Daresbury Synchrotron facility. So, to my knowledge, the algorithm is also implemented now in the Rietveld program MPROF (A.D. Murray & A.N. Fitch) and it has been used to extract the structure factors causing the successful structure determinations of Tl₄V₂O₇ (ref. 22), CBrF₃ (ref. 23), -Tl₃VO₄ (ref. 24) and Nb₃(NbO)₂(PO₄)₇ (ref. 25) (in some cases from Daresbury synchrotron data). Two recent application by using the FULLPROF program were published recently for the structure determinations of LiB₂O₃(OH).H₂O (ref. 26) and C₉H₅NO₄SCu.2H₂O (ref. 27). It seems that the algorithm has been introduced in the well known and widely distributed Rietveld program GSAS (may be through A.K. Cheetham who published numerous review articles about ab initio), and a lot of applications have been yet published for the structure determinations (sometimes from synchrotron data) of Ga₂(HPO₃)₃.4H₂O (ref. 28), [(C₅H₅)Fe(C₅H₄CH₂NMe₃)]I (ref. 29), p-CH₃C₆H₄SO₂NH₂ (ref. 30), LiCF₃SO₃ (ref. 31), C₂H₄N₂O₂ (ref. 32), LiMnPO₄(OH) (ref. 33), Zn₄O(BO₃)₂ (ref. 34) and Li₆Zr₂O₇ (ref. 35). Probably some other works have escaped to my attention.

To my knowledge, R.J. Hill is now trying to introduce the algorithm in its own Rietveld program. Sometimes the technique is called "the Le Bail method" by Cheetham or Attfield. It is now so widely used that it seems to me too late to submit a paper in which there will be an already known formula (the Rietveld decomposition formula) and the indication that iterating this formula is efficient to estimate structure factors with advantages against the more direct concurrent (the Pawley method) being stability and speed without problem of matrix size whatever the number of structure factors to extract... You know a large part of the story now.

Sincerely yours,

Armel Le Bail

The main ab initio structure determinations having used the ARITB program from Le Mans applied on conventional X-rays powder data (sometimes neutron powder data were used to improve the refinement or locate H or Li atoms).

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Formula S.G. V(ų) xyz N° R_B(%) R_P(%) R.X. Ref.

refined hkl neutrons

^{___________________________________________________________________________}

LiSbWO₆ Pbcn 406 12 306 2.1 5.2 X 1

KVO₂HPO₄ Pbca 1050 27 706 4.4 7.7 X 2

Li₂TbF₆ P2₁/c 395 27 812 4.0 8.3 X+N 3

-VO(HPO₄).2H₂O P2₁/c 534 42 785 4.1 7.8 X+N 4

-VO(HPO₄).2H₂O P 529 54 967 3.9 7.6 X 5

-(NH₄)₂FeF₅ Pbcn 1067 21 792 4.7 10.1 X 6

NaPbFe₂F₉ C2/c 700 14 445 5.1 8.2 X 7

Cu₃V₂O₇(OH)₂2H₂O C2/m 447 16 340 3.5 6.5 X+N 8

-BaAlF₅ P2₁/n 760 42 1383 3.8 7.2 X+N 9

-BaAlF₅ P2₁ 377 41 728 4.8 8.3 X+N 9

NiV₂O₆ P 294 42 1175 5.6 11.3 X 10

Pd(NO₃)₂(H₂O)₂ Pbca 622 15 377 3.1 6.4 X 11

Co₃(HPO₄)₂(OH)₂ P2₁/n 370 27 625 4.3 7.7 X+N 12

Na₂PdP₂O₇ C2/c 622 16 458 4.5 8.4 X 13

Li₂PdP₂O₇ Imma 548 8 237 5.1 9.9 X 14

-CsAlF₄ Pnma 1254 30 1160 3.9 6.6 X 15

K₂(H₅O₂)Al₂F₉ Pbam 481 14 301 3.5 8.5 X 16

t-AlF₃ P4/_nmm744 15 426 2.4 7.0 X 17

NaBaZrF₇ Pnma 569 17 475 4.2 9.5 X 18

-Ba₃AlF₉ Pnc2 1632 74 1077 2.9 6.8 X 19

^{__________________________________________________________________________}

References

1- A. LE BAIL, H. DUROY, J.L. FOURQUET, Mat. Res. Bull. 23, 447-452 (1988).

2- P. AMOROS, D. BELTRAN-PORTER, A. LE BAIL, G. FEREY and G. VILLENEUVE., Eur. J. Solid State Inorg. Chem. 25, 599-607 (1988).

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