Tables for
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 3.4, p. 278

Section McMaille: indexing via a Monte Carlo search method

A. Altomare,a* C. Cuocci,a A. Moliternia and R. Rizzia

aInstitute of Crystallography – CNR, Via Amendola 122/o, Bari, I-70126, Italy
Correspondence e-mail: McMaille: indexing via a Monte Carlo search method

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The information in the whole powder diffraction profile is exploited by the program McMaille (Le Bail, 2004[link]), which is based on the random generation of cell parameters and uses the Monte Carlo optimization technique. Once the trial cell parameters have been generated and the Miller indices and the peak positions have been calculated, the quality of the cell is assessed by using, as figure of merit, the conventional Rietveld profile reliability factor Rp (Young, 1993[link]) or McM20 (see Section[link]). The program uses some tricks that can increase the success of the Monte Carlo algorithm:

  • (1) Only the trial cells corresponding to a value of Rp that is smaller than a user-defined value (∼50%) are retained for successive refinement.

  • (2) If all the observed peaks, except for a user-defined number of tolerated impurity peaks, are `explained' whatever the Rp value, the cell is retained for successive examination.

  • (3) If either of the conditions (1) or (2) is fulfilled, the cell parameters are randomly changed in 200 to 5000 attempts (for cubic to triclinic cases, respectively) in which small random parameter variations via the Monte Carlo algorithm are carried out. The new parameters are preserved if an improvement of Rp is verified in 85% of the attempts.

This procedure is not sensitive to impurity lines, provided that the sum of their intensities is less than 10–15% of the total intensity. A zero-point error up to 0.05° is tolerated. To reduce the long computing time required to successfully complete the procedure, a significant increase in speed has been obtained by using idealized profiles generated by applying simplified line profiles to extracted line positions. A parallelized version of McMaille has also been developed. The indexing problem can usually be solved in few minutes if: (a) no triclinic symmetry is handled (because this requires more computing time); (b) the cell volume is less than 2000 Å3; (c) no cell length is longer than 20 Å.


Le Bail, A. (2004). Monte Carlo indexing with McMaille. Powder Diffr. 19, 249–254.Google Scholar
Young, R. A. (1993). Introduction to the Rietveld method. In The Rietveld Method, edited by R. A. Young, pp. 1–38. Oxford: IUCr/Oxford University Press.Google Scholar

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