  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.
