Tilting structures in perovskites

Thirty five low-symmetry tilting phases of the octahedra in which the atoms located at the initial octahedral position remain equivalent are derived for the perovskite structure at the k10(X), k11(M), and k13(R) points of the Brillouin zone. For each low-symmetry phase, structural data are presented and a relationship between the atomic displacements and the order parameters is deduced. All the low-symmetry phases can be obtained by considering only one or two order parameters.