Indexing magnetic structures and crystallographic distortions from powder diffraction: Brillouin zone indexing

A considerable challenge is faced by researchers wishing to identify the propagation vector(s) associated with a magnetic structure or a lattice distortion from powder diffraction data, due to the severe destruction of information by powder averaging and search algorithms based on extracted peak positions. In this article a new method is introduced that is based on the points, lines and planes of the Brillouin zone of the crystal structure before the transition. These correspond to different classifications of the translational symmetry of the resultant order and of the Bloch wave that is used to describe the magnetic structure or phonon mode. An automated search algorithm for the study of magnetic structures is described based on reverse-Monte Carlo refinement of moment orientations for a given k vector that markedly reduces the number of false-positives and allows the straight forward analysis of systems that contain contributions from several unrelated k vectors.