1. Getting Cell Parameters from Powder Diffraction Data
Armel Le Bail
Université du Maine, Laboratoire des Oxydes et Fluorures, CNRS UMR 6010, Avenue O. Messiaen, Le Mans, France

2. Outline The Indexing Problem(s) Indexing Software Indexing Benchmarks
Demonstrations (screen shots)
Live Demonstrations

3. The Indexing Problem(s)
1 to 6 unknowns maximum : a, b, c, , , 
Data : 20 first peak positions
Problem overdetermined, looks simple…

4. Difficulties come from :
- inaccuracy in peak positions (due to zeropoint error, sample misplacement, low resolution, bad crystallinity),
- the presence of impurities providing spurious additional peaks,
- the possibility to miss some large high-symmetry cells which can also be described in smaller sub-cells of lower symmetry,
- the fact that one of the a, b, c parameters can be very short if compared to the two others (dominant zone) so that the first diffraction peak involving it through the hkl Miller indices may not be included among the first 20 which will be exclusively h0l lines for instance (if b is small),
- etc.

5. The best description is in this 2003 Robin Shirley paper :
INDEXING SOFTWARE
The best description is in this 2003 Robin Shirley paper :

6. From Robin Shirley

7. Underlined are inside the CRYSFIRE package
From Robin Shirley
Underlined are inside the CRYSFIRE package

8. The Indexing Benchmarks

11. Bergmann, J. , Le Bail, A. , Shirley, R. & Zlokazov, V
Bergmann, J., Le Bail, A., Shirley, R. & Zlokazov, V. Zeitschrift für Kristallographie 219 (2004)

12. Demonstrations - Screenshots
WinPLOTR, PowderX (peak position hunting, and more)
McMaille, TREOR, DICVOL (indexing)
CHEKCELL (visualization, and more)
FULLPROF (cell-constrained whole pattern fitting, and more)

13. ACADEMIC SOFTWARE WITH TRADITIONAL OPEN ACCESS

14. WinPLOTR saving the Y2O3 peak positions for an indexing program

15. Typical data for indexing in automated mode with McMaille
Y2O3 ! Wavelength, zeropoint and NGRID (NGRID=3: black box mode) ! List of 2theta positions, intensity (min.=20)

16. McMaille displaying its best results for Y2O3

17. McM20 = [100./(RP*N20)] * Br * Sy,
 N20 is the number of possibly existing lines up to the 20th observed line (for a primitive P lattice). Br is a factor arbitrarily set to 6 for F and R Bravais lattices, 4 for I, 2 for A, B, C and 1 for P. Sy is a factor equal to 6 for a cubic or a rhombohedral cell, 4 for a trigonal/hexagonal/tetragonal cell, 2 for an orthorhombic cell, and 1 for a monoclinic or triclinic cell.

18. WinPLOTR displaying the McMaille best cell for Y2O3

19. Background estimation with PowderX for -AlF3

20. K2 stripping with PowderX for -AlF3

21. Peak positions hunting with PowderX for -AlF3

22. McMaille displaying its best results for -AlF3

23. F.o.M. for -AlF3

24. Examining with Chekcell the list of most probable -AlF3 cells from McMaille

25. Pawley or Le Bail methods are used for a penultimate proof of the cell quality (the ultimate being the structure solution and refinement)

26. The Le Bail fit of the -AlF3 conventional laboratory powder pattern by using FULLPROF and the P4/mmm space group, showing the possible (hk0, h+k = 2n) extinction rule

27. WinPLOTR saving the C28H24O8 data for TREOR

28. TREOR running inside of WinPLOTR for C28H24O8

29. The Le Bail fit of the C28H24O8 synchrotron powder pattern by using FULLPROF selecting the P21/c space group
Another plague of SDPD : anisotropic line broadening

30. WinPLOTR saving the tetracycline hydrochloride data for DICVOL

31. Selection of the indexing conditions for DICVOL04

32. DICVOL04 cell Proposition for the tetracycline hydrochloride

33. Live Demonstrations
Once a (good) powder pattern is recorded, and if the compound(s) remain unidentified, the time needed for a successful indexing is somewhere between 15 minutes and never…