Superstructure reflexions in tilted perovskites Part 1

The superstructure spots that appear in diffraction patterns of tilted perovskites are well documented and easily calculated using crystallographic software. Here, by considering a distortion mode as a perturbation of the prototype perovskite structure, we show how the structure factor equation yields Boolean conditions for the presence of first order superstructure reflexions. A subsequent article describes conditions for second order reflexions, which appear only in structures with mixed in-phase and anti-phase oxygen octahedral tilting. This approach may have some advantages for the analysis of electron diffraction patterns of perovskites.