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Author(s): | Alan D. Mighell; |
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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 |