  We present a comprehensive review of the structural chemistry of hybrid lead
halides of stoichiometry APbX4, A2PbX4 or AAPbX4, where A and A are organic
ammonium cations and X = Cl, Br or I. These compounds may be considered as
layered perovskites, containing isolated, infinite layers of corner-sharing
PbX4 octahedra separated by the organic species. We first extract over 250
crystal structures from the CCDC and classify them in terms of unit cell
metrics and crystal symmetry. Symmetry mode analysis is then used to identify
the nature of key structural distortions of the [PbX4] layers. Two generic
types of distortion are prevalent in this family: tilting of the octahedral
units and shifts of the inorganic layers relative to each other. Although the
octahedral tilting modes are well-known in the crystallography of purely
inorganic perovskites, the additional layer shift modes are shown to enrich
enormously the structural options available in layered hybrid perovskites. Some
examples and trends are discussed in more detail in order to show how the
nature of the interlayer organic species can influence the overall structural
architecture, although the main aim of the paper is to encourage workers in the
field to make use of the systematic crystallographic methods used here to
further understand and rationalise their own compounds, and perhaps to be able
to design-in particular structural features in future work.
