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

Research output: Contribution to journalArticle

11 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)525-535
Number of pages11
JournalActa Crystallographica Section A: Foundations of Crystallography
Volume68
Issue number5
DOIs
Publication statusPublished - Sep 1 2012
Externally publishedYes

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Crystal lattices
Lattice constants
lattice parameters
Observation
Powders
permutations
matrices
Computational efficiency
cells

All Science Journal Classification (ASJC) codes

  • Structural Biology

Cite this

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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.",
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