Fig. 2: Transmission electron microscopy (TEM) images and density functional theory (DFT) calculations.

a–d In situ TEM images of the δ-FAPbI₃ film annealed at the phase conversion temperature for different times. The relatively bright spots are the cubic phase nuclei transformed from the hexagonal phase. High-resolution TEM images of FAPbI₃ films incorporated with 3.33 mol% FPEA₂PbI₄ e, f, before and h, i after the phase conversion process. f, i Magnified TEM images of the regions highlighted with yellow dashed boxes in (e) and (h), respectively. g, j Corresponding fast Fourier transform (FFT) analysis of images (f) and (i), respectively. Figure 2e–j are from samples prepared by scratching off the films from the substrate. k DFT-calculated free energy barriers (ΔG_cs) for phase conversion from cubic to hexagonal (α → δ), from hexagonal to cubic (δ → α), and formation enthalpy of the cubic phase (ΔH) with respect to that of the hexagonal phase. Dashed lines and solid lines indicate ΔG_c without and with strain, respectively. The interlayer spacing of the strain-free hexagonal phase, layered perovskite and cubic phase are indicated with gray colored dashed vertical lines (d-spacings of DFT optimized structures). l Schematic free energy diagrams for the hexagonal and cubic phased FAPbI₃ at different temperatures and strain condition. T is temperature and T_c is the temperature for phase conversion.