Static and Dynamic Disorder in Formamidinium Lead Bromide Single Crystals

Abstract

We show that formamidinium-based crystals are distinct from methylammonium-based halide perovskite crystals because their inorganic sublattice exhibits intrinsic local static disorder that coexists with a well-defined average crystal structure. Our study combines terahertz-range Raman scattering with single-crystal X-ray diffraction and first-principles calculations to probe the evolution of inorganic sublattice dynamics with temperature in the range of 10-300 K. The temperature evolution of the Raman spectra shows that low-temperature, local static disorder strongly affects the crystal structural dynamics and phase transitions at higher temperatures.

Figure 1

(a) Raman-scattering spectra of FAPbBr₃ (red) and MAPbBr₃ (black) single crystals at 10 K. The spectra are offset for the sake of clarity. Vibrational density of states (vDOS) as well as decomposition of the vDOS for the organic and inorganic sublattices of (b) FAPbBr₃ and (c) MAPbBr₃, as calculated by density functional theory. The gray-shaded area marks the frequency range in which the vDOS predominantly features vibrations of the PbBr₆ framework rather than the organic cation. Note that the vDOS also includes contributions from Raman-inactive modes and that it is shown for a selected frequency region that does not, e.g., show contributions from imaginary modes and higher-frequency molecular modes.

Figure 2

FAPbBr₃ crystallography through polarization–orientation Raman scattering and single-crystal X-ray diffraction. (a) False-color polarization–orientation Raman plot of FAPbBr₃ at 10 K. The top panel shows the unpolarized Raman spectrum (as depicted in Figure 1a), and the right panel shows the cross section of the 44 cm^–1 peak (marked by a white dashed line), presenting its polarization-dependent intensity. Spectra were normalized to the highest peak; their intensities are represented by the color scale. (b) Precession image of FAPbBr₃ at 100 K [Immm space group, (10–1) projection]. Red arrows point at some non-indexed satellite reflections of very low intensity, corresponding to a larger (likely doubled) supercell. Bright reflections correspond to the indexed reflections of the Immm space group (#71). (c) Schematic representation of the 100 K crystal structure of FAPbBr₃ obtained from single-crystal X-ray diffraction measurements. Gray, brown, blue, black, and pink spheres denote Pb, Br, N, C, and H atoms, respectively.

Figure 3

(a) Temperature-dependent Raman spectra from 10 to 300 K, measured at 10 K intervals, of FAPbBr₃ (left) and MAPbBr₃ (right). All spectra were normalized to the highest peak, represented by brighter colors according to the color scale. White arrows point to observed phase transitions. (b) Raman spectra of the two crystals at 300 K. The shaded area highlights the intensity difference.