In transition metal oxides, preferential occupation of specific d orbitals on the transition metal ion can lead to the development of a long-range ordered pattern of occupied orbitals. This phenomenon, referred to as orbital ordering, is usually observed indirectly from the cooperative Jahn-Teller distortions (CJTDs) that result as a consequence of the orbital ordering. This paper examines the interplay between orbital ordering, octahedral tilting and cation ordering in perovskites. Both ternary AMX3 perovskites containing an active Jahn-Teller (J-T) ion on the octahedral site and quaternary A2MM'X6 perovskites containing a J-T ion on one-half of the octahedral sites have been examined. In AMX3 perovskites, the tendency is for the occupied 3d3x2-r2 and 3d3z2-r2 orbitals to order in the ac plane, as exemplified by the crystal structures of LaMnO3 and KCuF3. This arrangement maintains a favorable coordination environment for the anion sites. In AMX3 perovskites, octahedral tilting tends to enhance the magnitude of the J-T distortions. In A2MM'X6 perovskites, the tendency is for the occupied 3d3z2-r2 orbitals to align parallel to the c axis. This pattern maintains a favorable coordination environment about the symmetric M'-cation site. The orbital ordering found in rock-salt ordered A2MM'X6 perovskites is compatible with octahedral rotations about the c axis (Glazer tilt system a0a0c-) but appears to be incompatible with GdFeO3-type octahedral tilting (tilt system a-b+a-).
Lufaso, Michael W. and Woodward, Patrick M., "Jahn-Teller Distortions, Cation Ordering and Octahedral Tilting in Perovskites" (2004). Chemistry Faculty Publications. Paper 3.