Lattice metric singularities and their impact on the indexing of powder patterns

lattice metric singularity occurs when unit cells defining two (or more) la ttices yield the identical set of unique calculated d-spacings. The existen ce of such singularities, therefore, has a practical impact on the indexing of powder patterns. For example, when experimental data from zeta-LiBO2 we re indexed, two solutions (a rhombohedral and a monoclinic lattice) with ap proximately the same figure of merit were found. These two lattices yield t he same set of unique d-spacings even though they are characterized by diff erent reduced cells with cell volumes in the ratio 2 to 1. From the indexin g point of view, both answers are correct. A singularity of this type is co mmon 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 cl-spacings. In actual cases like this, one can run in to a trap. Due to experimental error and input parameters, an indexing prog ram may determine only one of the cells with a high figure of merit. When t his happens, it is critical to recognize that another solution exists, espe cially if one has determined the lower symmetry lattice. (C) 2000 Internati onal Centre for Diffraction Data. [S0885-7156(00)00201-3].