Dual lattice incommensurabilities and enhanced lattice perfection by low-temperature thermal annealing in photoelectric (CH₃NH₃)PbBr₃

The coupling between the organic CH₃NH₃⁺ cations and inorganic perovskite PbBr3- framework in a large single crystal of (CH₃NH₃)PbBr₃ weighing 13 g was studied using neutron diffraction and inelastic neutron scattering. Two lattice incommensurate (ICM) phases were found; one at higher temperatures, marked ICM_HT, appeared between 150 and 134 K. The second one, marked ICM_LT, developed below 143 K and remained at 75 K. The transition from the ICM_LT to ICM_HT phase upon warming gave rise to extremely large lattice shrinking, followed by extremely large lattice expansion of the tetragonal basal plane of the PbBr₃ lattice. There was a progressive decrease in the width of the diffuse peak at the Bragg position from the PbBr₃^- lattice upon warming, which can be described using a critical exponent to show complete ordering of the atoms into a (CH₃NH₃)PbBr₃ lattice at 200 K. (CH₃NH₃)PbBr₃ exhibits six definitive acousticlike phonon branches at 75 K. The six branches reconstruct into two at 200 K, with the frequencies of both the transverse and longitudinal modes greatly enhanced. The asymmetric structure of the CH3NH3 ions together with the indirect interactions between the CH₃NH₃ ions mediated through the Br ions are used to understand the observed behaviors.