Crystal Structures

A hybrid perovskite expressed as ABX 3 is a unique form of crystal consisting of a monovalent organic A-site cation (A = CH 3 NH 3 + and HC(NH 2 ) 2 + ), divalent B-site group-IV cations (B = Pb 2+ and Sn 2+ ), and X-site halide anions (X = I − , Br − , and Cl − ). When a perovskite crystal has a cubic symmetry, its structure is straightforward. In hybrid perovskites, however, depending on the choices of the A, B, and X atoms, BX 6 octahedra are tilted (distorted) and the B−X−B angle deviates from an ideal 180 ° (Section Equilibrium in Other Finite Element Formulations ). A perovskite structural parameter, Goldschmidt's tolerance factor, is a critical value, enabling us to discuss overall perovskite stability (Section Equilibrium in Other Finite Element Formulations ). Hybrid perovskite crystals exhibit strong phase variation with temperature (Section Equilibrium in Other Finite Element Formulations ). Moreover, the organic cations in hybrid perovskites reorient rapidly in a picosecond timescale, while interacting with the BX 3 − scaffold through hydrogen bonding (Section Equilibrium in Other Finite Element Formulations ). An understanding of the detailed perovskite structures described in this chapter is critical to interpret the physical properties and stability of hybrid perovskite crystals.