Superspace

Physics

Organic chemistry

Formamidinium

Mathematics

X-ray crystallography

Crystal twinning

Crystallography

Crystal structure

Supersymmetry

Optics

Perovskite (structure)

Halide

Diffraction

Space group

Inorganic chemistry

Chemistry

Materials science

Octahedron

Geometry

Group (periodic table)

Tilt (camera)

Orthorhombic crystal system

Quantum mechanics

Microstructure

The Journal of Physical Chemistry Letters

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.

Hybrid Perovskite at Full Tilt: Structure and Symmetry Relations of the Incommensurately Modulated Phase of Methylammonium Lead Bromide, MAPbBr<sub>3</sub>

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

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