Figure 3. A/A′ cation ordering and octahedral tilting in the n=1 RPs for NCS materials design.

(a) High-symmetry aristotype structure (φ, I4/mmm). (b) One of the A/A′ cation ordering schemes (irrep: (η₁); space group (s.g.): P4/nmm). (c) Out-of-phase octahedral tilting (oxygen displacements indicated using arrows) (irrep: (η₁,η₁); s.g.: P4₂/ncm) and lattice constants a and b are of equal length. (d) Out-of-phase octahedral tilting (irrep: (η₁,η₂); s.g.: Pccn) and lattice constant a≠b. (e) Coupled distortions (irrep: ⊕ (0,η₁;η₂,0); s.g.: Pbca), where (0,η₁) and (η₂,0) represent Jahn–Teller-like out-of-plane compression and out-of-phase octahedral tilting, respectively.