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Publication Citation: Ambiguities in Powder Indexing: Conjunction of a Ternary and Binary Lattice Metric Singularity in the Cubic System

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Author(s): Alan D. Mighell;
Title: Ambiguities in Powder Indexing: Conjunction of a Ternary and Binary Lattice Metric Singularity in the Cubic System
Published: December 01, 2004
Abstract: A lattice metric singualrity 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 and theoretical impact on the indexing of powder patterns. For example, in experimental practice an indexing program may find only the lower symmetry member of a singularity. Obviously, it is important to recognize such cases and know how to proceed. Recently, we described: (1) binary singularity involving a monoclinic and a rhombohedral lattice in a subcell-supercell relationship and (2) a second type of singularity -- a tenary singularity -- in which two of the three lattices are in a derivative composite relationship. In this work, we describe a ternary lattice metric singularity involving a cubic P, a tetragonal P and an orthorhombic C lattice. Furthermore, there is a binary singularity, involving a hexagonal P and orthorhombic P lattice, which is characterized by a set of unique d-spacings very close to that of the ternary singularity. The existence of such singularities is more common than once thought and requires a paradigm shift in experimental practice. In addition singularities provide opportunities as they point to highly specialized lattices that may be associated with unusual physical properties.
Citation: Journal of Research (NIST JRES) -
Volume: 109 No. 6
Keywords: ambiguities in powder indexing;d-spacings;derivative lattices;figure of merit;indexing programs;lattice metric singularity;powder indexing;specialized lattices
Research Areas: Math, Standards