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. Part of this difficulty arises from a decoupling of this procedure from the physical nature of the processes that drive the phase transition: indexing is often carried out by first extracting the peak positions and then calculating predicted peak positions for simple cells that are larger and commensurate with that of the crystal cell before the transition. Other methods use the formalism of a propagation vector, k vector, to enable the exploration of both commensurate and incommensurate trial structures, perhaps following a grid search through the possible k values. Non-linear search procedures have also been introduced that allow the k vector to be refined when in a region of reciprocal space that appears to allow the predicted peak positions to matched.

The possible values of the k vector associated with the ordering or distortion can be better understood if its physical drive is understood. In many cases of second order phase transitions, and weakly first order transitions, the observed propagation vectors correspond to the different symmetry points, lines and planes in the Brillouin zone of the crystal structure before the distortion. These correspond to different classifications of the translational symmetry of the resultant order. By using these, trial vectors can be constructed and explored that correspond in turn to the different points (no variables), lines (1 variable), planes (2 variables), and then the general position (3 variables). Sequential exploration of these can be done automatically by methods such as grid searches or trial-and-error. Reverse Monte-Carlo refinement of the moment orientations, in the case of magnetic structures, or atomic positions can then be further used to determine whether appropriate intensities can be generated at the observed positions in the powder diffraction spectrum. Together these techniques enable the characterisation of complex systems, such as those with several propagation vectors which are not symmetry related, that may otherwise have appeared to be associated with a general point in the Brillouin zone.

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