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. 276

Section TREOR90 (Werner et al., 1985[link])

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: TREOR90 (Werner et al., 1985[link])

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Classified by Shirley (1980[link], 2003[link]) as semi-exhaustive, TREOR90 is based on the index-heuristics strategy (see Section[link]) and uses a trial-and-error approach. It performs the following steps:

  • (1) Some basis lines are selected among the experimental d values, generally from the low-2θ region of the powder diffraction pattern. Five sets of basis lines are generally sufficient for orthorhombic tests, whereas more than seven sets may be necessary for the monoclinic system. At least 20–25 experimental d values are potentially required.

  • (2) The trial unit cells in the index space are searched by varying the Miller indices that are tentatively assigned to the basis lines.

  • (3) The analysis starts with cubic symmetry and, in a stepwise manner, tests for lower-symmetry crystal systems are performed. In the case of monoclinic symmetry, a special short-axis test is carried out.

  • (4) The solution of the linear system in equation (3.4.8)[link] gives the possible cell parameters. Different combinations of the basis lines are tested.

  • (5) Each possible solution is checked by using the full list of experimental lines.

  • (6) The quality of the trial cell parameters is mainly assessed by using the M20 figure of merit [see equation (3.4.4)[link]]. An effective rule for identifying a reliable solution is M20 > 10 and no more than one unindexed line.

The success of the program is related to the use of some suitable standard sets of parameter values (maximum unit-cell volume, maximum cell axis, tolerance of values etc.) arising from the accumulated experience of the authors; they can be easily changed by the user via suitable keywords in the input file.


Shirley, R. (1980). Data accuracy for powder indexing. In Accuracy in Powder Diffraction, edited by S. Block & C. R. Hubbard, NBS Spec. Publ. 567, 361–382.Google Scholar
Shirley, R. (2003). Overview of powder-indexing program algorithms (history and strengths and weaknesses). IUCr Comput. Comm. Newsl. 2, 48–54. .Google Scholar
Werner, P.-E., Eriksson, L. & Westdahl, M. (1985). TREOR, a semi-exhaustive trial-and-error powder indexing program for all symmetries. J. Appl. Cryst. 18, 367–370.Google Scholar

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