Local structure, bonding, and asymmetry of ((NH2)2CH)PbBr3, CsPbBr3, and (CH3NH3)PbBr3

We report local structure measurements for CsPbBr3 and ((NH2)2CH)PbBr3 (FAPbBr3) and compare them with recent results for (CH3NH3)PbBr3 (MAPbBr3). The Pb-Br bonding is similar for all three systems; the effective spring constants, kappa, are comparable (ranging from 1.20 to 1.95 eV/angstrom 2), but small in magnitude indicating very soft materials. However, there are also important differences between the three systems. Static disorder is very small for CsPbBr3 but increases somewhat with the size of the organic molecular ions MA+ and FA+. At room temperature, dynamic disorder dominates in all compounds. The thermal disorder of the Pb-Br pair distribution function (PDF), i.e., the Debye-Waller factor sigma 2 follows a correlated Debye or Einstein model up to 300 K in CsPbBr3 (orthorhombic phase), but for FAPbBr3 and MAPbBr3, there is a break in the sigma 2(T) curve at the orthorhombic-tetragonal transition (o-t) near 150 K, indicating a small change in the spring constant kappa. kappa increases for MAPbBr3 but decreases in FAPbBr3 at this transition. These changes are attributed to changes in the H-bonding between Br- and MA+ or FA+ at this transition, as a result of librations or rotations of these molecular cations. In addition, the Pb-Br PDF becomes asymmetric at a relatively low temperature for FAPbBr3 and MAPbBr3, while this effect is significantly smaller for CsPbBr3. Finally, we address the question of a model to explain the asymmetric PDF. Two main models are discussed in the literature, an anharmonic pair potential and a split-pair distribution, possibly driven by the presence of a lone pair on the Pb ion. We show that the fourth cumulant C4 can differentiate between these two models and other possible models. Experimentally C4 is positive at 250 K and above, for all three systems and that is inconsistent with a split-peak model, for which C4 is negative for splittings larger than 0.12 angstrom.