On the thermal expansion of the tetragonal phase of MAPbI₃ and MAPbBr₃

Abstract

Based on previously published research, the structural response of the tetragonal hybrid perovskite crystal structure of MAPbX3 [MA: [CH3NH3]+, methylammonium; X = I, Br] to thermal expansion is reviewed here. From an averaged crystal structure perspective, the tetragonal perovskite structure of MAPbI3 and MAPbBr3, based on diffraction data, shows apparent Pb-X bond length shortening and apparent shrinkage of the [PbX6] octahedra with increasing temperature. At the same time, these apparent observations, and hence the thermal expansion, are related to the progressive phase transformation towards the cubic structure, as the lattice parameters respond to a shear stress that couples to the order parameters, and this coupling is predicted by group theory and thus aims to explain precisely the apparent negative thermal expansion-like effects. A different picture emerges for the thermal expansion when considering the very localized structure, since neither a shortening of the Pb-X bond lengths nor a shrinking of the [PbX6] octahedra is observed with pair distribution function analysis, and the presence of orthorhombic short-range order in the tetragonal and cubic perovskite structures is assumed in published studies. The compared extended X-ray absorption fine structure studies, which also map the local structure and provide the “true” bond distance, show no lead-halide bond length shortening with temperature. The perpendicular mean square relative displacement has been determined. Therefore, a comparison of the tension and bond expansion effects in both perovskites can be made. In the orthorhombic phase of MAPbI3 and MAPbBr3, positive expansion and negative tension of the lead-halide bond are almost balanced. After transitioning to the tetragonal phase, the equilibrium shifts toward negative tension. This suggests that both hybrid perovskites have tighter lead-halide bonds and less rigid [PbX6] octahedra in the tetragonal phase than in the low temperature perovskite crystal structure.