The Geometry of Niggli Reduction II: BGAOL -- Embedding Niggli Reduction

TL;DR

This paper introduces BGAOL, a new method that embeds Niggli reduction in a higher-dimensional space to accurately compute distances between lattice cells, improving Bravais lattice determination.

Contribution

It presents a novel embedding approach for Niggli reduction and develops BGAOL, a program that enhances lattice classification accuracy over existing algorithms.

Findings

BGAOL provides more accurate Bravais lattice determination.

The embedding improves distance calculations between lattice cells.

Results outperform previous metric-based methods.

Abstract

Niggli reduction can be viewed as a series of operations in a six-dimensional space derived from the metric tensor. An implicit embedding of the space of Niggli-reduced cells in a higher dimensional space to facilitate calculation of distances between cells is described. This distance metric is used to create a program, BGAOL, for Bravais lattice determination. Results from BGAOL are compared to the results from other metric-based Bravais lattice determination algorithms.