Fig. 12.

Top. Symmetry tree describing group/subgroup relations between the three Ca₄Nb₂O₉ polymorphs with distinct (1:1, 1:2, and 1:3) arrangements of the B-cations; the numbers in brackets indicate the number of crystallographic variants generated by the corresponding minimal symmetry reductions. Since all three phases feature similar b⁻b⁻c⁺ octahedral tilting, their space groups are subgroups of Pbnm, which describes a disordered perovskite structure with the same tilting. Bottom: a-Dark-field image of the single grain containing the metastable 1:3 ordered Ca₄Nb₂O₉ polymorph. b-Magnified view of the area outlined by rectangular in (a). Twin-type domains I and II in the area labelled a are related to the Pm3m→Pbnm octahedral tilting transition. The domains exhibit a substructure consisting of both rotational (1 and 2 in the area labelled b) and translational (A, B, C, and D) domains. The domains 1 and 2 can be described by the Pbnm→P1 symmetry reduction, while the domains A, B, C, and D can be accounted for by the lost of the c-glide plane (P2₁/c→P1) and doubling of the c lattice parameter. Additionally precipitates of the 1:2 ordered polymorph nucleated in the 1:3 ordered matrix are seen in b (indicated by arrows).