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Ambiguities in Powder Pattern Indexing: A Ternary Lattice Matric Singularity



Alan D. Mighell


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. Lattices 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 the lattices, and the volume ratio (s) of primitive cells defining the lattices. Earlier a binary singularity was described involving a monoclinic and a rhombohedral lattice. In this 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. In the laboratory, one can run into a trap. 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 other solution(s) exists.
Journal of Research (NIST JRES) -


composite lattices, d-spacings, derivative lattices, figure of merit, geometrical ambiguites, indexing programs, lattice metric singularity, non-uniqueness, powder indexing


Mighell, A. (2004), Ambiguities in Powder Pattern Indexing: A Ternary Lattice Matric Singularity, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed April 16, 2024)
Created November 3, 2004, Updated February 19, 2017