International
Tables for
Crystallography
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, pp. 276-277

Section 3.4.4.2. Evolved indexing programs

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:  angela.altomare@ic.cnr.it

3.4.4.2. Evolved indexing programs

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3.4.4.2.1. N-TREOR09 (Altomare et al., 2009[link])

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Implemented in the EXPO program (Altomare et al., 2013[link]) to perform the powder pattern indexing step, N-TREOR09 is an update of N-TREOR (Altomare et al., 2000[link]), which in turn is an evolution of TREOR90, and preserves the main strategies with some changes introduced to make the program more exhaustive and powerful. In particular:

  • (a) If the default indexing process fails, the unit-cell search is automatically repeated by changing some default choices, e.g., increasing the tolerance value on the observed d values. If still no solution is obtained, the maximum (hkl) Miller indices assigned to the orthorhombic or monoclinic base lines are increased and the tolerance limits of the default values are halved in order to avoid the generation of wrong large unit cells.

  • (b) At the end of the first run, whatever the obtained results, a possible 2θ zero-position shift is taken into account: the indexing process starts again by applying positive and negative 2θ zero-position shifts to the original peak search result.

  • (c) An exhaustive triclinic search is performed. The dominant-zone tests that are usually carried out for the monoclinic system have been extended to include the triclinic case.

  • (d) A new figure of merit, WRIP20, more powerful than the classical M20, is used. It is calculated when more than one possible cell is found and takes into account the M20 value, the full experimental pattern, the degree of reflection overlap, the systematically absent reflections and the number of unindexed lines (see Section 3.4.2.1[link]).

This program is also able to index powder patterns from small proteins: see Example 4[link] in Section 3.4.4.6.2[link].

3.4.4.2.2. DICVOL06 (Louër & Boultif, 2006[link], 2007[link]) and DICVOL14 (Louër & Boultif, 2014[link])

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The most recent of a series of versions, DICVOL14 is the successor of DICVOL04 (Boultif & Louër, 2004[link]) and DICVOL06. DICVOL06 includes DICVOL04 with its optimized search procedure and an extended search in shells of volumes. DICVOL04 represented an improvement of DICVOL91. Among the features of DICVOL06 are:

  • (a) A tolerance for unindexed lines that can result from the presence of unwanted additional phases or inaccurately measured peaks. The program can tolerate a user-defined number of unindexed lines. Care must be taken when using this option to avoid the possibility of generating erroneous cells. It is worth noting that the inclusion of the possibility of at least one unindexed peak has markedly increased the success rate of DICVOL06.

  • (b) A correction of the zero-point error in the measured data. Via an a priori zero-origin evaluation, two different approaches can be followed: (i) if there is a non-negligible zero shift (i.e., ~0.1°), the reflection-pair method is adopted (Dong et al., 1999[link]); (ii) if the shift is small (<0.03°), a refinement of the experimental data zero point together with the cell parameters is carried out as soon as a solution is found. In the monoclinic and triclinic systems, a reduced-cell analysis is performed to choose among equivalent solutions.

  • (c) When a solution is found in a 400 Å3 shell of volume, the exhaustive search is extended to the whole domain.

No formal limits on the number of input Bragg peaks have been established but, for reliable indexing, it is recommended that 20 or more peaks (in the low-2θ region) are used.

Compared to DICVOL04/DICVOL06, DICVOL14 includes: an optimization of filters in the final stages of the convergence of the successive dichotomy process; an optimization and extension of scanning limits for the triclinic case; a new approach for zero-point offset evaluation; a detailed review of the input data from the resulting unit cells; and cell centring tests. DICVOL14 has been improved particularly for triclinic cases, which are generally the most difficult to solve with the dichotomy algorithm.

References

Altomare, A., Campi, G., Cuocci, C., Eriksson, L., Giacovazzo, C., Moliterni, A., Rizzi, R. & Werner, P.-E. (2009). Advances in powder diffraction pattern indexing: N-TREOR09. J. Appl. Cryst. 42, 768–775.Google Scholar
Altomare, A., Cuocci, C., Giacovazzo, C., Moliterni, A., Rizzi, R., Corriero, N. & Falcicchio, A. (2013). EXPO2013: a kit of tools for phasing crystal structures from powder data. J. Appl. Cryst. 46, 1231–1235.Google Scholar
Altomare, A., Giacovazzo, C., Guagliardi, A., Moliterni, A. G. G., Rizzi, R. & Werner, P.-E. (2000). New techniques for indexing: N-TREOR in EXPO. J. Appl. Cryst. 33, 1180–1186.Google Scholar
Boultif, A. & Louër, D. (2004). Powder pattern indexing with the dichotomy method. J. Appl. Cryst. 37, 724–731.Google Scholar
Dong, C., Wu, F. & Chen, H. (1999). Correction of zero shift in powder diffraction patterns using the reflection-pair method. J. Appl. Cryst. 32, 850–853.Google Scholar
Louër, D. & Boultif, A. (2006). Indexing with the successive dichotomy method, DICVOL04. Z. Kristallogr. Suppl. 23, 225–230.Google Scholar
Louër, D. & Boultif, A. (2007). Powder pattern indexing and the dichotomy algorithm. Z. Kristallogr. Suppl. 26, 191–196.Google Scholar
Louër, D. & Boultif, A. (2014). Some further considerations in powder diffraction pattern indexing with the dichotomy method. Powder Diffr. 29, S2, S7–S12.Google Scholar








































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