Design of noncentrosymmetric perovskites from centric and acentric basic building units

We present a detailed crystal-chemistry approach to lift inversion symmetry in inorganic crystals. By considering the ordering of centric and acentric basic building units in one and two dimensional systems, we review the structural "features" necessary to break spatial parity. We then extend this model to three dimensional materials, focusing on the family of ABX₃ perovskites with corner-connected metal-anion BX₆ octahedra and A-site cations filling the interstices (forming AX₁₂ cuboctahedra). Although this extended BX₆ network can tilt and rotate in space, these complex distortions preserve inversion symmetry; however, previous work has shown that certain rotational patterns of the octahedral units in combination with A-site cation ordering are able to lift inversion symmetry in perovskites. Herein, we extend this framework by comprehensively determining and describing the combinations of A- and B-site cation ordering schemes and BX₆ octahedral rotation patterns that will produce noncentrosymmetric crystal structures independent of the chemical makeup. Although no combinations of simple B-site ordering lifts inversion, we find that a wide variety of polar, chiral, and second harmonic active structures can be realized with A-site and mixed A- and B-site cation ordering. We then show that the ability of such combinations to lift inversion symmetry depends on whether a given rotation pattern of the octahedral units distorts the A-site environment into centric or acentric polyhedra, as well as whether the cation ordering scheme aligns them in the proper orientation. Finally, we discuss the chemical factors stabilizing the various tilt patterns and ordering schemes, such as the tolerance factor and global instability index. The guidelines described here offer new insights into this vast family of materials, and detail a useful way to think about the design of noncentrosymmetric materials from basic building units.