Ideas of lattice-basis reduction theory for error-stable Bravais lattice determination and abinitio indexing.

In ab initio indexing, for a given diffraction/scattering pattern, the unit-cell parameters and the Miller indices assigned to reflections in the pattern are determined simultaneously. `Ab initio' means a process performed without any good prior information on the crystal lattice. Newly developed ab initio indexing software is frequently reported in crystallography.

A new mathematical approach to finding global solutions of the magnetic structure determination problem.

Determination of magnetic structure is an important analytical procedure utilized in various fields ranging from fundamental condensed-matter physics and chemistry to advanced manufacturing. It is typically performed using a neutron diffraction technique; however, finding global solutions of the magnetic structure optimization problem represents a significant challenge. Generally, it is not possible to mathematically prove that the obtained magnetic structure is a truly global solution and that no solution exists when no acceptable structure is found.

A table of geometrical ambiguities in powder indexing obtained by exhaustive search.

Geometrical ambiguity means the cases in which more than one powder indexing solution exists. Using a new function implemented in the powder indexing software CONOGRAPH, unit cells that involve geometrical ambiguity are exhaustively searched. As a result, many unknown cases are obtained, although the number of such unit cells is still rather limited.

Distribution rules of systematic absences on the Conway topograph and their application to powder auto-indexing.

This paper presents several general properties of systematic absences that are available before unit-cell parameters and the space group have been determined. The properties are given in the form of distribution rules of Miller indices corresponding to systematic absences on a topograph. A topograph is a graph whose edges are associated with a set of four lattice vectors satisfying Ito's equation 2(|l1(*)|(2) + |l2(*)|(2)) = |l1(*) + l2(*)|(2) + |l1(*) - l2(*)|(2).

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

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.