The geometry of Niggli reduction:SAUC– search of alternative unit cells

Abstract

A database of lattices using theG6representation of the Niggli-reduced cell as the search key provides a more robust and complete search than older techniques. Searching is implemented by finding the distance from the probe cell to other cells using a topological embedding of the Niggli reduction inG6, so that all cells representing similar lattices will be found. The embedding provides the first fully linear measure of distances between unit cells. Comparison of results with those from older cell-based search algorithms suggests significant value in the new approach.