Evolutionary exploration of polytypism in lead halide perovskites

The regular ABX₃ cubic perovskite structure is composed of close-packed AX₃ layers stacked along the 〈111〉 axis. An equivalent hexagonal close-packed network can also be formed, in addition to a series of intermediate polytype sequences. Internally, these correspond to combinations of face- and corner-sharing octahedral chains that can dramatically alter the physical properties of the material. Here, we assess the thermodynamics of polytypism in CsPbI₃ and CsPbBr₃. The total energies obtained from density functional theory are used to paramaterize an axial Ising-type model Hamiltonian that includes linear and cubic correlation terms of the pseudo-spin. A genetic algorithm is built to explore the polytype phase space that grows exponentially with the number of layers. The ground-state structures of CsPbX₃ polytypes are analysed to identify features of polytypism such as the distinct arrangements of layers and symmetry forbidden sequences. A number of polytypes with low ordering energies (around thermal energy at room temperature) are predicted, which could form distinct phases or appear as stacking faults within perovskite grains.