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History of the dichotomy method for powder pattern indexing

Published online by Cambridge University Press:  01 March 2012

Ali Boultif
Ali Boultif
Affiliation:
Laboratoire de Cristallographie, Faculté des Sciences, Département de Physique, Université Mentouri-Constantine, Route Aïn-El-Bey, 25 000 Constantine, Algeria
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Abstract

A short history of the developments of the successive dichotomy method for powder pattern indexing is presented. In the first computer powder indexing programs (P1 and P2), only high lattice symmetries, down to orthorhombic, were considered [Louër and Louër, J. Appl. Crystallogr. 5, 271–275 (1972)]. Later on, an extension to the monoclinic symmetry was reported in DICVOL, including a partition of the volume space to first search solutions with smaller unit cell volumes [Louër and Vargas, J. Appl. Crystallogr. 15, 542–545 (1982)]. However, CPU times were slow in some monoclinic examples. A thorough mathematical analysis resulted in a significant optimization of the CPU times [Boultif and Louër, J. Appl. Crystallogr. 24, 987–993 (1991)]. Simultaneously, the method is extended to triclinic lattices. The stages of development of the various versions of the DICVOL program are described, with a particular emphasis on DICVOL91 (Boultif and Louër, 1991) and DICVOL04 [Boultif and Louër, J. Appl. Crystallogr. 37, 724–731 (2004)]. This article is written to testify to and emphasize the major role played by Daniel Louër, who introduced the successive dichotomy method and continued to its evolution and optimization over almost 40 years.

Keywords

pattern indexingdichotomy methodzero-point shiftreduced cellunindexed diffraction lines

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Type
Invited Articles
Information
Powder Diffraction , Volume 20 , Issue 4 , December 2005 , pp. 284 - 287
Copyright
Copyright © Cambridge University Press 2005

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References

Azároff, L. V. and Burger, M. J. (1958). The Powder Method. McGraw-Hill, New York.Google Scholar
Boultif, A. and Louër, D. (1991). “Indexing of powder diffraction patterns for low-symmetry lattices by the successive dichotomy method,” J. Appl. Crystallogr.JACGAR10.1107/S0021889891006441 24, 987–993.CrossRefGoogle Scholar
Boultif, A. and Louër, D. (2004). “Powder pattern indexing with the dichotomy method,” J. Appl. Crystallogr.JACGAR10.1107/S0021889804014876 37, 724–731.CrossRefGoogle Scholar
Boultif, A. and Louër, D. (2005). “Indexation des diagrammes de poudre par la méthode dichotomique: Stratégies et filtres logiques,” in Abstracts of the 2nd Algerian Crystallography Congress, Constantine, Algeria, p. 15.Google Scholar
Caussin, P., Nusinovici, J., and Beard, D. W. (1988). “Using digitized X-ray powder diffraction scans as input for a new PC-AT search∕match program,” Adv. X-Ray Anal.AXRAAA 31, 423–430.Google Scholar
Coelho, A. A. (2003). “Indexing of powder diffraction patterns by iterative use of singular value decomposition,” J. Appl. Crystallogr.JACGAR10.1107/S0021889802019878 36, 86–95.CrossRefGoogle Scholar
de Wolff, P. M. (1968). “A simplified criterion for the reliability of a powder pattern indexing,” J. Appl. Crystallogr.JACGAR10.1107/S002188986800508X 1, 108–113.CrossRefGoogle Scholar
Dong, C., Wu, F., and Chen, H. (1999). “Correction of zero shift in powder diffraction patterns using the reflection-pair method,” J. Appl. Crystallogr.JACGAR 32, 850–853.CrossRefGoogle Scholar
Eriksson, L., Louër, D., and Werner, P. E. (1989). “Crystal structure determination and rietveld refinement of Zn(OH)(NO3)∙H2O,” J. Solid State Chem.JSSCBI 81, 9–20.CrossRefGoogle Scholar
ICDD (2005). “Powder Diffraction File,” International Centre for Diffraction Data, edited by McClune, Frank, 12 Campus Boulevard, Newton Square, Pennsylvania, 19073-3272.Google Scholar
Jamard, C., Taupin, D., and Guinier, A. (1966). “Méthode d’indexation automatique des diagrammes de poudres,” Bull. Soc. Fr. Mineral. Cristallogr.BUFCAE 89, 312–317.Google Scholar
Ladd, M. F. C. and Palmer, R. A. (1993). Structure Determination by X-ray Crystallography (Plenum Press, New York).CrossRefGoogle Scholar
Louër, D. (1992). “Automatic indexing: Procedures and applications,” Accuracy in Powder Diffraction II, edited by Prince, E. and Stalick, J. K., NIST Spec. Pub. No. 846 (U.S. Dept of Commerce, Gaithersburg, MD), 92–104.Google Scholar
Louër, D. and Boultif, A. (2005). “Indexing with the successive dichotomy method, DICVOL04,” Z. Kristallogr.ZEKRDZ (in press).Google Scholar
Louër, D. and Louër, M. (1972). “Méthode d’essais et erreurs pour l’indexation automatique des diagrammes de poudre,” J. Appl. Crystallogr.JACGAR10.1107/S0021889872009483 5, 271–275.CrossRefGoogle Scholar
Louër, D. and Vargas, R. (1982). “Indexation automatique des diagrammes de poudre par dichotomies successives,” J. Appl. Crystallogr.JACGAR10.1107/S0021889882012552 15, 542–545.CrossRefGoogle Scholar
Louër, D., Boultif, A., Gotor, F. J., and Criado, J. M. (1990). “X-ray powder diffraction analysis of barium titanyl oxalate tetrahydrate,” Powder Diffr.PODIE2 5, 162–164.CrossRefGoogle Scholar
Mighell, A. D. (2000). “Lattice metric singularities and their impact on the indexing of powder patterns,” Powder Diffr.PODIE2 15, 82–85.CrossRefGoogle Scholar
Mighell, A. D. (2001). “Lattice symmetry and identification—The fundamental role of reduced cells in materials characterization,” J. Res. Natl. Inst. Stand. Technol.JRITEF 106, 983–995.CrossRefGoogle ScholarPubMed
Mighell, A. D. and Santoro, A. (1975). “Geometrical ambiguities in the indexing of powder patterns,” J. Appl. Crystallogr.JACGAR10.1107/S0021889875010710 8, 372–374.CrossRefGoogle Scholar
Natl. Bur. Stand. (U.S.) (1963–1985). Monogr. No. 25, Sections 2 to 21.Google Scholar
Natl. Bur. Stand. (U.S.) (1984). Monogr. No. 25, Section 20.Google Scholar
Neumann, M. A. (2003). “X-cell: A novel indexing algorithm for routine tasks and difficult cases,” J. Appl. Crystallogr.JACGAR10.1107/S0021889802023348 36, 356–365.CrossRefGoogle Scholar
Santoro, A. and Mighell, A. D. (1970). “Determination of reduced cells,” Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr.ACACBN10.1107/S0567739470000177 26, 124–127.CrossRefGoogle Scholar
Shirley, R. (1980). “Inaccuracy in Powder Diffraction,” edited by Block, S. and Hubbard, C. R. Nat. Bur. Stand. (U.S.)Spec. Publ. No. 567, 361–382.Google Scholar
Smith, S. G. and Snyder, R. L. (1979). “F N: A criterion for rating powder diffraction patterns and evaluating the reliability of powder-pattern indexing,” J. Appl. Crystallogr.JACGAR10.1107/S002188987901178X 12, 60–65.CrossRefGoogle Scholar
Werner, P.-E. (1964). “Trial-and-error computer methods for the indexing of unknown powder patterns,” Z. Kristallogr.ZEKRDZ 120, 375–387.CrossRefGoogle Scholar