The Geometry of Niggli Reduction III: SAUC -- Search of Alternate Unit Cells

TL;DR

This paper introduces SAUC, a novel search method for crystallographic lattices using the G6 representation of Niggli-reduced cells, improving robustness and accuracy over traditional cell-based searches.

Contribution

It presents a new lattice search algorithm based on G6 representation and Niggli reduction, enhancing detection of similar lattices in crystallography databases.

Findings

Significantly improves lattice matching accuracy.

Detects similar lattices missed by older methods.

Provides a more robust search for crystallographic data.

Abstract

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.