Structural Diversity in Multicomponent Nanocrystal Superlattices Comprising Lead Halide Perovskite Nanocubes

Abstract

Nanocrystal (NC) self-assembly is a versatile platform for materials engineering at the mesoscale. The NC shape anisotropy leads to structures not observed with spherical NCs. This work presents a broad structural diversity in multicomponent, long-range ordered superlattices (SLs) comprising highly luminescent cubic CsPbBr₃ NCs (and FAPbBr₃ NCs) coassembled with the spherical, truncated cuboid, and disk-shaped NC building blocks. CsPbBr₃ nanocubes combined with Fe₃O₄ or NaGdF₄ spheres and truncated cuboid PbS NCs form binary SLs of six structure types with high packing density; namely, AB₂, quasi-ternary ABO₃, and ABO₆ types as well as previously known NaCl, AlB₂, and CuAu types. In these structures, nanocubes preserve orientational coherence. Combining nanocubes with large and thick NaGdF₄ nanodisks results in the orthorhombic SL resembling CaC₂ structure with pairs of CsPbBr₃ NCs on one lattice site. Also, we implement two substrate-free methods of SL formation. Oil-in-oil templated assembly results in the formation of binary supraparticles. Self-assembly at the liquid-air interface from the drying solution cast over the glyceryl triacetate as subphase yields extended thin films of SLs. Collective electronic states arise at low temperatures from the dense, periodic packing of NCs, observed as sharp red-shifted bands at 6 K in the photoluminescence and absorption spectra and persisting up to 200 K.

Keywords: binary superlattice; collective properties; colloidal nanocrystals; electron microscopy; lead halide perovskites; nanocrystal shape; self-assembly.

Figure 1

Diversity of binary and ternary SLs obtained from 5.3 and 8.6 nm CsPbBr₃ nanocubes combined with 11.2–25.1 nm spherical Fe₃O₄ and NaGdF₄ NCs, 10.7–11.7 nm truncated cuboid PbS NCs, thick NaGdF₄ disks (31.5 nm in diameter and 18.5 nm thick), and 6.5–28.4 nm disk-shaped LaF₃ NCs. Structures in solid and dashed frames were obtained with 8.6 and 5.3 nm CsPbBr₃ NCs, respectively. HAADF-STEM image illustrates a sharp shape of a CsPbBr₃ nanocube. The graph is a space-filling analysis within a hard-particle model for NaCl-, AlB₂-, and AB₂- and within OTM for ABO₃- and ABO₆-type SLs comprising larger spherical and smaller cubic NCs; the dashed line corresponds to the density of fcc packing of spherical NCs.

Figure 2

Binary NaCl-type SL. (a) TEM image, (upper right inset) HAADF-STEM image, along with the corresponding (bottom inset) small-angle and (b) wide-angle ED patterns of a SL domain in [001]_SL orientation assembled from 8.6 nm CsPbBr₃ cubes and 18.6 nm NaGdF₄ NCs. The upper left inset in (a) represents the NaCl-type unit cell according to the preferential cube’s orientation.

Figure 3

Binary and ternary ABO₃-type SLs. (a) TEM image along with (b) HAADF-STEM image, (c) the corresponding wide-angle ED pattern, and (d) SEM images of the [001]_SL-oriented b-ABO₃-type domains assembled from 8.6 nm CsPbBr₃ cubes and 16.5 nm NaGdF₄ spheres. (e, h) AFM height images of spheres- and cubes-terminated b-ABO₃-type domains, respectively, along with (f, i) the height analysis of the profiles indicated in (e, h), (g, j) AFM three-dimensional images with the respective models. (k) TEM image along with (l) HAADF-STEM image, (m) the corresponding wide-angle ED pattern, and (n) SEM image of the [001]_SL-oriented b-ABO₃-type domains assembled from 8.6 nm CsPbBr₃ cubes and 19.8 nm Fe₃O₄ spheres. (o) TEM image along with (p) HAADF-STEM image and (q) the corresponding wide-angle ED pattern of the [001]-oriented t-ABO₃-type SL domains assembled from 8.6 nm CsPbBr₃ cubes, 11.7 nm PbS truncated cuboids, and 21.5 nm Fe₃O₄ spheres. (r) HAADF-STEM image of a t-ABO₃-type SL domain in [111]_SL orientation assembled from 8.6 nm CsPbBr₃, 11.7 nm PbS, and 25.1 nm Fe₃O₄ NCs; upper inset shows the model of [111]_SL-oriented t-ABO₃ unit cell, and lower inset shows small-angle ED pattern. Insets in (a, k, o) represent binary and ternary ABO₃-type lattices according to the preferential NCs orientations, with Fe₃O₄ shown as gray spheres, NaGdF₄ as yellowish spheres, CsPbBr₃ as blue cubes, and PbS as red truncated cubes. The origin of wide-angle ED reflections in (c, m, q) is color-coded to match the NCs in insets.

Figure 4

Binary AlB₂-type SLs obtained combining 8.6 nm CsPbBr₃ with (a–e) 19.8 nm Fe₃O₄ and (f–j) 16.5 nm NaGdF₄ NCs. (a, b) TEM and (c) HAADF-STEM images of a single domain in [120]_SL orientation, along with the corresponding (d) small-angle and (e) wide-angle ED patterns. (f, g) TEM and (h) HAADF-STEM images of a single domain in [001]_SL orientation, along with the corresponding (i) small-angle and (j) wide-angle ED patterns. Insets in (e, j) show the orientations of CsPbBr₃ NCs in the SL domains with respect to the electron beam (normal to the image plane).

Figure 5

Structural characterization of a binary AlB₂-type SL comprising 5.3 nm CsPbBr₃ and 12.5 nm Fe₃O₄ NCs. (a) TEM image of [120]_SL-oriented domain; inset is the image at higher magnification. (b) Wide-angle ED pattern of a single SL domain in (a). (c) Two-dimensional GISAX scattering pattern, showing long-range order in AlB₂-type binary domains. (d) The unit cell of AlB₂-type SL. (e) Small-angle ED pattern of a domain shown in (a). (f) HAADF-STEM image of the [120]_SL-oriented domain. (g) EDX-STEM maps for Fe (gray, K-line) and Pb (blue, L-line) of the [120]_SL-oriented domain. (h, k, n) Crystallographic models of [120]_SL, [001]_SL, and [010]_SL-oriented AlB₂ lattice, respectively. (i, j) Low- and high-magnification TEM images of an [001]_SL-oriented domain. (l, m) Low- and high-magnification TEM images of a [010]_SL-oriented domain; insets in (i, l) are images obtained by template-matching analysis of corresponding TEM images.

Figure 6

Possible relative orientations of CsPbBr₃ nanocubes within AlB₂-type SL and packing fractions predicted by OPM packing analysis according to the hard-particle model. In both orientations, the body-diagonal of the cubes is parallel to the c-axis of the hexagonal SL unit cell, that is, [001]_SL. In orientation “O1”, the cubes are mutually rotated by 60°, whereas in orientation “O2”, they are identically aligned. A significant increase in the packing fraction can be achieved if the B-cubes in orientation “O2” are not locked in the 2d Wyckoff positions, that is, are allowed to slide along the [001]_SL (“O2 S3”). Wide-angle ED patterns from [120]_SL- (see, for instance, Figures 4e and 5b) and [001]_SL-oriented domains (Figure 5j) point to the alignment of all cubes with one body diagonal parallel to [001]_SL and (110) CsPbBr₃ planes are orthogonal to [010]_SL. Hence these two orientations can be proposed. Experimentally, however, there exists no evidence to differentiate between these two structures, and hence both were considered for the analysis of lattice parameters and packing densities. Excluded is also a substantial orientational disorder in any dimension.

Figure 7

An AB₂-type binary SL assembled from CsPbBr₃ nanocubes and Fe₃O₄ nanospheres. (a) TEM image of a SL assembled by 8.6 nm CsPbBr₃ and 19.8 nm Fe₃O₄ NCs (γ = 0.414), along with the corresponding (inset) small-angle ED pattern, (b) HAADF-STEM image, and (c) wide-angle ED pattern. (d) Comparison of AlB₂ (taken as orientation “O2”, see Figure 6) and AB₂ structures. Red and green lines show the normals to (111) and (110) CsPbBr₃ lattice planes, respectively, and indicate the directions of reflections in wide-angle ED patterns. (e) HAADF-STEM image showing grain boundary between AlB₂ and AB₂ binary SL domains. (f) Modeled crystallographic projections of cubic and spherical NCs in AB₂ structure. (g) EDX-STEM elemental maps of an AB₂-type binary SL assembled from 5.3 nm CsPbBr₃ and 14.5 nm Fe₃O₄ NCs for Pb (blue, L-line) and Fe (red, K-line).

Figure 8

Binary ABO₆-type SLs obtained from 5.3 nm CsPbBr₃ and 16.9 nm Fe₃O₄ NCs (γ = 0.315). (a) Wide-angle and (inset) small-angle ED patterns of [001]_SL-oriented domain. (b) Space-filling analysis for b-ABO₆-type SLs comprising larger spherical and smaller cubic (solid line) or spherical (blue dashed line) NCs within the hard-particle model, except for the indicated OTM branch. (c) Structural model of a b-ABO₆-type unit cell and a slice through (002)_SL. (d–f) HAADF-STEM images of [001]_SL-, [111]_SL-, and [101]_SL-oriented domains and (g) the corresponding structural models of SL projections.

Figure 9

Binary SLs self-assembled from the mixtures of 5.3 nm CsPbBr₃ and 15.2 nm NaGdF₄ NCs. Increasing the relative concentration of CsPbBr₃ NCs changes the experiment outcome from (a–d) NaCl-type to (e–h) AlB₂-type with (i–l) AB₂-type and then to (m, n) ABO₃-type SLs, as illustrated by (o) the scheme. (a, e, i, m) TEM images of [001]_SL projections, along with the corresponding (bottom insets) small-angle ED and (b, f, j, n) wide-angle ED patterns; the respective high-magnification HAADF-STEM images are shown as upper insets. (c, d) HAADF images of [001]_SL- and [111]_SL-oriented domains. (g) TEM image of [120]_SL-oriented domain, along with the corresponding (upper inset) HAADF-STEM image, (bottom inset) small-angle ED, and (h) wide-angle ED patterns. (k) Bright-field and (l) HAADF-STEM images of [001]_SL-oriented domain.

Figure 10

Characterization of b-ABO₃-type SL assembled from 8.6 nm CsPbBr₃ and 10.7–11.7 nm PbS. (a) HAADF-STEM image of a single [001]_SL-oriented binary ABO₃ domain comprising of 8.6 nm CsPbBr₃ NCs and 11.7 nm PbS NCs. (b) TEM image of a single b-ABO₃ domain in [001]_SL orientation assembled from 8.6 nm CsPbBr₃ NCs and 10.7 nm PbS NCs, together with the respective (c) small-angle and (d) wide-angle ED patterns. Diffraction arcs are colored to show their origin from CsPbBr₃ and PbS NCs presented as insets. Inset in (a) shows the binary ABO₃ lattice and illustrates the relative position and orientation of NCs. (e) Crystallographic model of a [001]_SL-oriented ABO₃ lattice, along with HAADF-STEM image and respective EDX-STEM maps for S (red, K-line), Pb (blue, L-line), Cs (green, L-line), and Br (yellow, K-line).

Figure 11

NaCl-type binary SLs from 8.6 nm CsPbBr₃ NCs combined with truncated cuboid PbS NCs. (a) TEM image of a monolayer domain. (b, c) HAADF-STEM images of SL domains with an increasing number of layers. (e, f) TEM images of [001]_SL-oriented SL domains at different magnification, along with the (g) wide-angle and (h) small-angle ED patterns measured from the domain shown in (f); the reflections from CsPbBr₃ and PbS NCs are colored to match the NCs in the structural model (d). Images from (a, c, f–h) were obtained with 10.7 nm PbS NCs (γ = 0.778) and from (b, e) with 11.7 nm PbS NCs (γ = 0.720).

Figure 12

CuAu- and AlB₂-type binary SLs assembled from truncated cuboid 10.7 nm PbS NCs and, respectively, 8.6 and 5.3 nm CsPbBr₃ cubes. (a) TEM image of a single CuAu-type SL domain in [101]_SL orientation, along with the corresponding (inset) small-angle ED and (b) wide-angle ED patterns (the origin of the reflections is color-coded to match the NCs in the model shown as inset). (c) CuAu unit cell and crystallographic model of [101]_SL-oriented lattice assuming preferable orientations of NCs in agreement with ED. (d) HAADF-STEM images of a SL domain taken at 0° and 45° tilting angles around [010]_SL that correspond to [101]_SL and [001]_SL orientations, respectively; crystallographic model of [001]_SL-oriented CuAu-type lattice is depicted in the inset of (e). (f) EDX-STEM elemental maps recorded from a [001]_SL-oriented domain shown in (e). (g) TEM image of AlB₂-type SL with twist grain boundaries between [001]_SL- (magnified in upper inset) and [010]_SL-oriented (magnified in bottom inset) domains. (h) HAADF-STEM, high-magnification TEM image (upper inset), and crystallographic model (bottom inset) along with (i) wide-angle ED pattern of [120]_SL-oriented AlB₂-type SL. Bottom and upper ([120]_SL orientation) insets in (i) represent the unit cell of AlB₂-type SL with orientations of NCs that result in the most intense wide-angle ED spots marked in red (PbS) and blue (CsPbBr₃).

Figure 13

CaC₂-like SL assembled from 8.6 nm CsPbBr₃ nanocubes and 31.5 nm NaGdF₄ thick nanodisks, featuring sets of two cubes on one lattice site. (a) TEM image and the SL models are shown as insets. (b) HAADF-STEM images at different magnifications, along with the corresponding (c) wide-angle ED and (inset) small-angle ED patterns. (d, e) SEM images at different magnifications.

Figure 14

Binary SLs obtained from FAPbBr₃ nanocubes. (a) TEM and HAADF-STEM (top right panel) images of a b-ABO₃-type SL assembled from 9 nm FAPbBr₃ and 19.5 nm NaGdF₄ NCs; SL model is shown in the bottom right panel. (b, c) Bright-field STEM images of, respectively, an [120]-oriented AlB₂-type and [001]_SL-oriented AB₂-type SL domains comprising 9 nm FAPbBr₃ and 15.1 nm NaGdF₄ NCs. (d) HAADF-STEM image of an [111]-oriented NaCl-type SL domain comprising 5.7 nm FAPbBr₃ and 15.1 nm NaGdF₄ NCs. (e) Bright-field STEM image of a columnar AB-type SL domain obtained from 5.7 nm FAPbBr₃ NCs and 12.5 nm LaF₃ nanodisks. (f) TEM and (g) HAADF-STEM images of lamellar SL obtained from 5.7 nm FAPbBr₃ NCs and 12.5 nm LaF₃ nanodisks; EDX-STEM elemental maps for La (magenta, L-line) and Pb (blue, L-line) are shown in the inset in (g). Insets in (b–d) are SL models.

Figure 15

Self-assembly of perovskite NCs at the liquid–air interface. (a) Illustration of the assembly process: NCs dispersed in nonpolar solvents are cast onto the surface of glyceryl triacetate in a Teflon well or Petri dish, which is then covered with glass or larger Petri dish, respectively; ordered SL film floating on the subphase is formed upon evaporation the solvent. (b–d) TEM images of 9 nm CsPbBr₃ NC monolayer obtained from octane on glyceryl triacetate. (e–g) TEM images of AB-type monolayer (obtained from dodecane) and NaCl- and AlB₂-type films (obtained from decane), respectively, comprising 8.6 nm CsPbBr₃ and 19.8 nm Fe₃O₄ NCs.

Figure 16

Oil-in-oil templated assembly of binary SLs comprising perovskite NCs. (a) Illustration of the assembly process: NCs dispersed in toluene are mixed with a fluorinated solvent (FC-40) containing surfactant (008-FS) that is capable of stabilizing droplets with NCs. Slow evaporation of toluene from the droplets during stirring results in the formation of ordered binary supraparticles. (b) SEM and HAADF-STEM (right panel) images of supraparticles with b-ABO₃ structure obtained from 8.6 nm CsPbBr₃ cubic and 18.6 nm NaGdF₄ spherical NCs. (c) SEM images of supraparticles with CaC₂-like structure assembled from 8.6 nm CsPbBr₃ nanocubes and 31.5 nm NaGdF₄ thick nanodisks. Insets in (b, c) show the SL models.

Figure 17

PL properties of ABO₃-type binary SLs at 6 K. (a) PL spectra of binary ABO₃-type SLs assembled by employing 8.6 nm CsPbBr₃ and 19.5 nm (top) or 14.5 nm (bottom) Fe₃O₄ NCs. The PL spectra (black solid lines) are fitted to a doubled Lorentzian function (red and blue lines are the individual functions, while the gray lines are the cumulative fits to the experimental data). (b) Measured coupled vs uncoupled splitting energy for several samples with different distances between O-site and B-site NCs. Error bars denote the standard deviation obtained by measuring several PL spectra on different locations on the same sample.

Figure 18

Impact of the temperature on the PL band from coupled NCs in AlB₂-type binary SLs (5.3 nm CsPbBr₃ NCs + 12.5 nm Fe₃O₄ NCs). (a) Normalized PL spectra for the AlB₂-type SLs at 6 and 100 K. The inset reports a zoom-in PL spectrum for a nominally similar sample where much narrower emission peaks are resolved (full width at half-maximum of about 3 meV, dashed line). (b) Two-dimensional colored plot of normalized PL spectra obtained at different temperatures. (c) The relative amplitude of the two emission bands as a function of temperature (black open circles). The red solid line is the best fit to an Arrhenius plot returning activation energy of 14 meV, very close to the LO-phonon energy of CsPbBr₃ crystal (17 meV). (d) Extracted splitting energy is plotted vs the squared root of the red-shifted peak area, exhibiting a linear dependence (solid red line).

Figure 19

PL and absorbance spectra of binary ABO₃-type SLs comprising 8.8 nm CsPbBr₃ cubes and 18.2 nm (top panel) or 15.1 nm (middle panel) NaGdF₄ spherical NCs, measured at 10 K (top and middle panel) and 200 K (bottom panel).