Lattice Matching (LM)—Prevention of Inadvertent Duplicate Publications of Crystal Structures
Lattice-matching techniques have proved to be extremely effective for the identification of unknown crystalline materials. A commonly employed lattice-matching strategy is based on matching the reduced cell of an unknown against a database of known materials represented by their respective standard reduced cells. The success of the method relies on the fact that the lattice or the lattice plus chemical information (e.g., element types) is highly characteristic of a material—like a fingerprint. Because of its intrinsic power, the procedure has many and diverse applications—in materials characterization, in nano-technology, in epitaxial growth, in materials design, etc. An especially fruitful role for the method is in the journal publication process as the quality of the scientific literature can be enhanced. The focus herein is on the major role that lattice matching can play in the prevention of inadvertent duplicate publications of the same structure and in the determination of key cross-references.
The Geometry of Niggli Reduction III: SAUC -- Search of Alternate Unit Cells
A crystallographic cell is a representation of a lattice, but each lattice can be represented just as well by any of an infinite number of such unit cells. Searching for matches to an experimentally determined crystallographic unit cell in a large collection of previously determined unit cells is a useful verification step in synchrotron data collection and can be a screen for "similar" structures, but it is more useful to search for a match to the lattice represented by the experimentally determined cell. For identification of substances with small cells, a unit cell match may be sufficient for unique identification. Due to experimental error and multiple choices of cells and differing choices of lattice centering representing the same lattice, simple searches based on raw cell edges and angles can miss similarities among lattices. A database of lattices using the G6 representation of the Niggli-reduced cell as the search key provides a more robust and complete search. Searching is implemented by finding the distance from the probe cell to related cells using a topological embedding of the Niggli reduction in G6, so that all cells representing similar lattices will be found. Comparison of results with those from older cell-based search algorithms suggests significant value in the new approach.
A perturbation stable cell comparison technique
A modified method of describing lattices (or, equivalently, unit cells) is described. In the proposed parameterization, there is no discontinuous measure of agreement such as is found in studies of reduced cells. Although the Niggli reduced cell is uniquely defined for every lattice, the angles of the reduced cell may vary wildly with minor lattice distortions. It is proposed that lattices be described by the sets of seven parameters consisting of reduced-cell edge lengths, the lengths of edges of the reduced cell of the reciprocal lattice, and the reduced-cell volume.