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(|l 1 ^*|² + |l 2 ^*|²) = |l 1 ^* + l 2 ^*|² + |l 1 ^*-l 2 ^*|². It is possible to integrate global information about extinct reflections by using topographs. As an example of the application of these rules, a new powder auto-indexing algorithm is introduced, focusing on its theoretical aspects.