| 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. |
