Hybrid Perovskite at Full Tilt: Structure and Symmetry Relations of the Incommensurately Modulated Phase of Methylammonium Lead Bromide, MAPbBr₃

As energy-conversion materials, organic–inorganic hybrid perovskites remain a research- and finance-intensive topic. However, even for the arguably most iconic representatives, methyl­ammonium and form­amid­inium lead halides, the crystal structures of several polymorphs have remained undetermined. Herein, we describe the incommensurately modulated structure of MAPbBr₃ in (3+1)­D superspace, as deduced from single-crystal X-ray diffractometry despite systematic twinning. Affirming the published average space group, we determined the superspace group Imma(00γ)s00 with cell parameters of a = 8.4657(9), b = 11.7303(12), c = 8.2388(8) Å, and q = 0.2022(8)c*. Via group–subgroup and mode analyses using irreducible representations, we establish symmetry relationships to the well-known cubic and orthorhombic polymorphs and break down distortions into the average tilt system a^–b⁰a^– and modulated contributions to tilt and deformation of the PbBr₆ coordination polyhedra. Not only does our model fill a long-standing gap in structural knowledge, but it may also serve as a starting point for elucidating other modulated structures within this substance class.