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Ambiguities in powder pattern indexing: A ternary lattice metric singularity

  • Alan D. Mighell (a1)

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. Lattice metric singularities often involve lattices that are in a derivative relationship one to another. A variety of types of singularities are possible depending on the number of different lattices involved (i.e., binary, ternary, quaternary), on the nature of the derivative lattice relationship (i.e., subcell/supercell, composite), on the Bravais type of each of the lattices, and on the the volume ratio(s) of primitive cells defining the lattices. In the laboratory, an encounter with a singularity can lead one into a trap; viz., the investigator using an indexing program, or by other means, may determine only one of the lattices with a high figure of merit. When this happens, it is critical to recognize that there exists more than one indexing solution. In a previous work, a binary singularity was described involving a monoclinic and a rhombohedral lattice. In the present work, we describe a second type of singularity—a ternary singularity—in which the two of the three lattices are in a derivative composite relationship.

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Andrieu, R., Diament, R., Durif, A., Pouchot, M-T., and Qui, D. T. (1966). “Physique des solides.—Pre´paration et e´tude cristallographique des trime´taphosphates du type (PO3)3MIIK,C. R. Acad. Sc., Ser. B CHDBAN 262, 718720. crb, CHDBAN
Banks, E. (1992). “(Rubidium chromium fluoride, Rb0.225CrF3−PDF#43-0392),” ICDD Grant-in-Aid, Powder Diffraction File, International Centre for Diffraction Data, Newtown Square, PA, 19073-3273.
de Wolff, P. M. (1968). “A simplified criterion for the reliability of powder pattern indexing,” J. Appl. Crystallogr. JACGAR 1, 108113. acr, JACGAR
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.
Mighell, A. D. (2000). “Lattice metric singularities and their impact on the indexing of powder patterns,” Powder Diffr. PODIE2 15 (2), 8285. pdj, PODIE2
Mighell, A. D., and Rodgers, J. R. (1980). “Lattice Symmetry Determination,” Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. ACACBN A36, 321326. aca, ACACBN
Mighell, A. D., and Santoro, A. (1975). “Geometrical ambiguities in theindexing of powder patterns,” J. Appl. Crystallogr. JACGAR 8, 372374. acr, JACGAR
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).
Powder Diffraction File, International Centre for Diffraction Data, Newtown Square, PA, 19073-3273.
Santoro, A., and Mighell, A. D. (1972). “Properties of crystal lattices: The derivative lattices and their determination,” Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. ACACBN A28, 284287. aca, ACACBN
Santoro, A., and Mighell, A. D. (1973). “Coincidence-Site Lattices,” Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. ACACBN A29, 169175. aca, ACACBN
Smith, G. S., and Snyder, R. L. (1979). “FN: A criterion for rating powder diffraction patterns and evaluating the reliability of powder-pattern indexing,” J. Appl. Crystallogr. JACGAR 12, 6065. acr, JACGAR

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Ambiguities in powder pattern indexing: A ternary lattice metric singularity

  • Alan D. Mighell (a1)

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