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). 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.