Wide-Angle X-ray Diffraction Evidence of Structural Coherence in CsPbBr3 Nanocrystal Superlattices

Abstract

Films made of colloidal CsPbBr₃ nanocrystals packed in isolated or densely-packed superlattices display a remarkably high degree of structural coherence. The structural coherence is revealed by the presence of satellite peaks accompanying Bragg reflections in wide-angle X-ray diffraction experiments in parallel-beam reflection geometry. The satellite peaks, also called "superlattice reflections", arise from the interference of X-rays diffracted by the atomic planes of the orthorhombic perovskite lattice. The interference is due to the precise spatial periodicity of the nanocrystals separated by organic ligands in the superlattice. The presence of satellite peaks is a fingerprint of the high crystallinity and long-range order of nanocrystals, comparable to those of multilayer superlattices prepared by physical methods. The angular separation between satellite peaks is highly sensitive to changes in the superlattice periodicity. These characteristics of the satellite peaks are exploited to track the superlattice compression under vacuum, as well as to observe the superlattice growth in situ from colloidal solutions by slow solvent evaporation.

Figure 1

XRD patterns of (a) a film of densely packed CsPbBr₃ NC SLs measured in the out-of-plane reflection geometry. The splitting of the 2θ ∼ 15° peak (highlighted by the magenta box) is due to the SL effect. (b) The same sample measured in the in-plane geometry (a relatively sharp reflection at ∼47.2° is assigned to the silicon substrate). (c) Randomly oriented NCs mixed with amorphous silica (the reference pattern is based on the lattice parameters from Rietveld refinement: a = 8.2248 Å, b = 8.2741 Å, c = 11.7748 Å; Miller indices are provided for the six most intense reflections). (d) Optical microscopy images of the isolated SLs and a film of densely packed SLs of CsPbBr₃ NCs. Note that the peak splitting is observed in both types of samples (Figure S3). (e) Sketch of the film of densely-packed CsPbBr₃ NC SLs featuring domains with a coherent structure.

Figure 2

Closer look at the peak profile at 2θ ∼ 15°. A section of the out-of-plane XRD data shown in Figure 1a was replotted on a logarithmic intensity scale vs scattering vector [q (nm^–1)]. The circles are experimental data, and the continuous red line is a fit. The vertical drop lines indicate the position of the five satellite peaks originating from the SL. The inset shows the best linear fit of the centers of satellite peaks in q vs n, starting from n = 19 (corresponding to the SL wavelength, Λ ∼ 12.2 nm).

Figure 3

(a) Time evolution of the satellite peaks in the 2θ ∼ 15° region (q ∼ 10.6 nm^–1) in the XRD pattern of the film of densely packed CsPbBr₃ NC SLs under static vacuum. (b) Corresponding contraction of the SL wavelength, Λ, as a function of time (red circles).

Figure 4

Emergence of the satellite peaks in the 2θ ∼ 15° region during the growth of a film of densely-packed CsPbBr₃ NC SLs from tetrachloroethylene solution. The figure reports a series of XRD patterns collected over 10 h at 30 min intervals. The inset is a sketch of the actually 3D-printed solvent evaporation chamber sealed with X-ray transparent Kapton and equipped with a sliding window on the side (blue-grey rectangle) to allow the placement of the sample.