Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter (O) June 3, 2020

A new parallel version of a dichotomy based algorithm for indexing powder diffraction data

Ivan Šimeček EMAIL logo , Aleksandr Zaloga and Jan Trdlička


One of the key parts of the crystal structure solution process from powder diffraction data is the determination of the lattice parameters from experimental data shortly called indexing. The successive dichotomy method is one of the most common ones for this process because it allows an exhaustive search. In this paper, we discuss several improvements for this indexing method that significantly reduces the search space and decrease the solution time. We also propose a combination of this method with other indexing methods: grid search and TREOR. The effectiveness and time-consumption of such algorithm were tested on several datasets, including orthorhombic, monoclinic, and triclinic examples. Finally, we discuss the impacts of the proposed improvements.

Corresponding author: Ivan Šimeček, Department of Computer Systems, Faculty of Information Technology, Czech Technical University in Prague, Prague, Czech Republic, E-mail:

Funding source: Czech Technical University in Prague

Award Identifier / Grant number: SGS20/212/OHK3/3T/18


This work was supported by the Grant Agency of the Czech Technical University in Prague, grant No. SGS20/212/OHK3/3T/18.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This research was funded by Czech Technical University in Prague, grant No. SGS20/212/OHK3/3T/18

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.


1. Le Bail, A. Monte carlo indexing with mcmaille. Powder Diffr. 2004, 19, 249–254; in Google Scholar

2. Visser, J. W. A fully automatic program for finding the unit cell from powder data. J. Appl. Crystallogr. 1969, 2, 89–95; in Google Scholar

3. Coelho, A. A. Indexing of powder diffraction patterns by iterative use of singular value decomposition. J. Appl. Crystallogr. 2003, 36 [Online], 86–95; in Google Scholar

4. Kariuki, B. M., Belmonte, S. A., McMahon, M. I., Johnston, R. L., Harris, K. D. M., Nelmes, R. J. A new approach for indexing powder diffraction data based on whole-profile fitting and global optimization using a genetic algorithm. J. Synchrotron Radiat. 1999, 6, 87–92; in Google Scholar

5. Oishi-Tomiyasu, R. Robust powder auto-indexing using many peaks. J. Appl. Crystallogr. 2014, 47, 593–598; in Google Scholar

6. Oishi-Tomiyasu, R. Distribution rules of systematic absences on the Conway topograph and their application to powder auto-indexing. Acta Crystallogr. 2013, A69, 603–610; in Google Scholar

7. Werner, P.-E., Eriksson, L., Westdahl, M. TREOR, a semi-exhaustive trial-and-error powder indexing program for all symmetries. J. Appl. Crystallogr. 1985, 18, 367–370; in Google Scholar

8. Šimeček, I., Rohlíček, J., Zahradnický, T., Langr, D. A new parallel and gpu version of a treor-based algorithm for indexing powder diffraction data. J. Appl. Crystallogr. 2015, 48, 166–170; in Google Scholar

9. Hušák, M., Šimeček, I., Rohlíček, J. Powder data indexation by parallel gpu accelerated grid search method. Acta Crystallogr. 2013, A69, s272.10.1107/S0108767313097663Search in Google Scholar

10. Louer, D., Vargas, R. Automatic indexation of powder diagrams based on successive dichotomies. J. Appl. Crystallogr. 1982, 15, 542–545; in Google Scholar

11. X-Cell. X-cell - a novel and robust indexing program for medium- to high-quality powder diffraction data. J. Appl. Crystallogr. 2003, 36, 356–365.Search in Google Scholar

12. Boultif, A., Louer, D. Indexing of powder diffraction patterns for low-symmetry lattices by the successive dichotomy method. J. Appl. Crystallogr. 1991, 24, 987–993; in Google Scholar

13. Louer, D., Boultif, A. Indexing with the successive dichotomy method, DICVOL04. Z. Kristallogr. 2006, 1, 225–230, 9th European Powder Diffraction Conference, Prague, Czech Republic, SEP 02-05, 2004.10.1524/9783486992526-039Search in Google Scholar

14. Louer, D., Boultif, A. Powder pattern indexing and the dichotomy algorithm. Z. Kristallogr. 2007, 26, 191–196, 10th European Powder Diffraction Conference, Univ Geneva, Geneva, SWITZERLAND, SEP 01-04, 2006.10.1524/9783486992540-030Search in Google Scholar

15. Louer, D., Boultif, A. Some further considerations in powder diffraction pattern indexing with the dichotomy method. Powder Diffr. 2014, 29, S7–S12; in Google Scholar

16. Beebe, N. H. F. Openmp: overview and resource guide. [Online] 2014.∼beebe/openmp/.Search in Google Scholar

17. OpenMP Architecture Review Board. Openmp application program interface. [Online] 2013. in Google Scholar

18. Bergmann, J., Le Bail, A., Shirley, R., Zlokazov, V. Renewed interest in powder diffraction data indexing. Z. Kristallogr. 2004, 219, 783–790; in Google Scholar

19. Dawood, H. Theories of Interval Arithmetic: Mathematical Foundations and Applications; LAP Lambert Academic Publishing: Germany, 2011.Search in Google Scholar

20. Gomes, A., Voiculescu, I., Jorge, J., Wyvill, B., Galbraith, C. Interval Arithmetic; Springer: London, 2009.10.1007/978-1-84882-406-5_4Search in Google Scholar

21. Fortman, G. C., Slawin, A. M. Z., Nolan, S. P. Highly active iridium(III)–NHC system for the catalytic B–N bond activation and subsequent solvolysis of ammonia–borane. Organometallics 2011, 30, 5487–5492; in Google Scholar

22. Plévert, J., Louër, M., Louër, D. The ab initio structure determination of Cd3(OH)5(NO3) from X-ray powder diffraction data. J. Appl. Crystallogr. 1989, 22, 470–475; in Google Scholar

23. Hadicke, E., Frickel, F., Franke, A. Chem. Ber. 1978, 111, 3222.10.1002/cber.19781110926Search in Google Scholar

24. Hušák, M., Kratochvíl, B., Jegorov, A., Mat’ha, V., Stuchlik, M., Andrysek, T. The structure of a new cyclosporin a solvated form. Z. Kristallogr. 1996, 211, 313–318; in Google Scholar

25. Qi, G., Parker, W. Tetrahedron 1996, 52, 2291.10.1016/0040-4020(95)01062-9Search in Google Scholar

26. Smith, G. S. Estimating unit cell volumes from powder diffraction data: the triclinic case. J. Appl. Crystallogr. 1976, 9, 424–428; in Google Scholar

27. Smith, G. S. Estimating the unit-cell volume from one line in a powder diffraction pattern: the triclinic case. J. Appl. Crystallogr. Aug 1977, 10, 252–255; in Google Scholar

28. Paszkowicz, W. On the estimation of the unit-cell volume from powder diffraction data. J. Appl. Crystallogr. 1987, 20, 161–165; in Google Scholar

29. Šimeček, I., Zaloga, A., Rohlíček, J. Paracell home page. [Online] 2019. in Google Scholar

30. Powder diffraction indexing benchmarks. [Online] 2004. Available: in Google Scholar

Received: 2020-03-17
Accepted: 2020-05-18
Published Online: 2020-06-03
Published in Print: 2020-07-28

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 27.1.2023 from
Scroll Up Arrow