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Lattice metric singularities and their impact on the indexing of powder patterns

Published online by Cambridge University Press:  10 January 2013

Alan D. Mighell
Alan D. Mighell
Affiliation:
Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
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Abstract

A lattice metric singularity occurs when unit cells defining two (or more) lattices yield the identical set of unique calculated d-spacings. The existence of such singularities, therefore, has a practical impact on the indexing of powder patterns. For example, when experimental data from ζ-LiBO2 were indexed, two solutions (a rhombohedral and a monoclinic lattice) with approximately the same figure of merit were found. These two lattices yield the same set of unique d-spacings even though they are characterized by different reduced cells with cell volumes in the ratio 2 to 1. From the indexing point of view, both answers are correct. A singularity of this type is common and not a mathematical rarity. In fact, any rhombohedral cell of this kind has a derivative monoclinic subcell, each of which gives the same set of unique calculated d-spacings. In actual cases like this, one can run into a trap. Due to experimental error and input parameters, an indexing program may determine only one of the cells with a high figure of merit. When this happens, it is critical to recognize that another solution exists, especially if one has determined the lower symmetry lattice.

Type
Technical Articles
Information
Powder Diffraction , Volume 15 , Issue 2 , June 2000 , pp. 82 - 85
Copyright
Copyright © Cambridge University Press 2000

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References

Boultif, A., and Louër, D. (1991). “Indexing of powder diffraction patterns for low-symmetry lattices by the successive dichotomy method,” J. Appl. Crystallogr. 24, 987–993.Google Scholar
de Wolff, P. M. (1968). “A simplified criterion for the reliability of powder pattern indexing.”J. Appl. Crystallogr. 1, 108–113.CrossRefGoogle Scholar
Karen, V. L., and Mighell, A. D. (1991). “NIST*LATTICE-A Program to Analyze Lattice Relationships,” National Institute of Standards and Technology (USA), Tech. Note 1290.Google Scholar
Liang, J., Chen, X., Min, J., Chai, Z., Zhao, S., Cheng, X., Zhang, Y., and Rao, G. (1995). “Crystallization mechanism of dehydrated amorphous LiBO 2,”Phys. Rev. B 51, 756–762.Google Scholar
Louër, D., and Louër, M. (1972). “Méthode d’essais et erreurs pour l’indexation automatique des diagrammes de poudre,” J. Appl. Crystallogr. 5, 271–275.Google Scholar
McMurdie, H. F. (1999). Private communication, Ceramics Division, National Institute of Standards and Technology.Google Scholar
Mighell, A. D., Hubbard, C. R., and Stalick, J. K. (1981). “NBS *AIDS80: A FORTRAN Program for Crystallographic Data Evaluation,” National Bureau of Standards (USA), Tech. Note 1141. (NBS *AIDS83 is a development of NBS *AIDS80).Google Scholar
Mighell, A. D., and Santoro, A. (1975). “Geometrical ambiguities in the indexing of powder patterns,” J. Appl. Crystallogr. 8, 372–374.CrossRefGoogle Scholar
Morris, M. C., McMurdie, H. F., Evans, E. H., Paretzkin, B., Parker, H. S.,and Pyrros, N. P. (1982). “Standard X-ray Diffraction Powder Patterns,” National Bureau of Standards (USA), Monograph 25—Section 19, p 3.Google Scholar
Smith, G. S., 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. 12, 60–65.CrossRefGoogle Scholar
Werner, P. E. (1976). “On the determination of unit-cell dimensions from inaccurate powder diffraction data,” J. Appl. Crystallogr. 9, 216–219.CrossRefGoogle Scholar
Werner, P. E., Eriksson, L., and Westdahl, M. (1985). “TREOR: A semi-exhaustive trial-and-error powder indexing program for all symmetries,” J. Appl. Crystallogr. 18, 367–370.Google Scholar