Rapid Bravais-lattice determination algorithm for lattice parameters containing large observation errors

Abstract

A new Bravais-lattice determination algorithm is introduced herein. For error-stable Bravais-lattice determination, Andrews & Bernstein [Acta Cryst. (1988), A44, 1009-1018] proposed the use of operations to search for nearly Buerger-reduced cells. Although these operations play an essential role in their method, they increase the computation time, in particular when lattice parameters obtained in (powder) auto-indexing are supposed to contain large errors. The new algorithm requires only several permutation matrices in addition to the operations that are necessary when the lattice parameters have exact values. As a result, the computational efficiency of error-stable Bravais-lattice determination is improved considerably. Furthermore, the new method is proved to be error stable under a very general assumption. The detailed algorithms and the set of matrices sufficient for error-stable determination are presented.