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Lattice Metric Singularities and Their Impact on the Indexing of Powder Patterns

Published

Author(s)

Alan D. Mighell

Abstract

A Lattice Metric Singularity occurs when unit cells defining two (or more) lattices yield the identical set of 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 with 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 other solution exists, especially if one has determined the lower symmetry lattice.
Citation
Powder Diffraction
Volume
15
Issue
2

Keywords

d-spacings, figure of merit, geometrical ambiguities, indexing programs, lattice metric Singularity, lattices, non-uniqueness

Citation

Mighell, A. (2000), Lattice Metric Singularities and Their Impact on the Indexing of Powder Patterns, Powder Diffraction (Accessed February 27, 2024)
Created June 8, 2000, Updated February 19, 2017