Shape-Directed Co-Assembly of Lead Halide Perovskite Nanocubes with Dielectric Nanodisks into Binary Nanocrystal Superlattices

Abstract

Self-assembly of colloidal nanocrystals (NCs) holds great promise in the multiscale engineering of solid-state materials, whereby atomically engineered NC building blocks are arranged into long-range ordered structures—superlattices (SLs)—with synergistic physical and chemical properties. Thus far, the reports have by far focused on single-component and binary systems of spherical NCs, yielding SLs isostructural with the known atomic lattices. Far greater structural space, beyond the realm of known lattices, is anticipated from combining NCs of various shapes. Here, we report on the co-assembly of steric-stabilized CsPbBr₃ nanocubes (5.3 nm) with disk-shaped LaF₃ NCs (9.2–28.4 nm in diameter, 1.6 nm in thickness) into binary SLs, yielding six columnar structures with AB, AB₂, AB₄, and AB₆ stoichiometry, not observed before and in our reference experiments with NC systems comprising spheres and disks. This striking effect of the cubic shape is rationalized herein using packing-density calculations. Furthermore, in the systems with comparable dimensions of nanocubes (8.6 nm) and nanodisks (6.5 nm, 9.0 nm, 12.5 nm), other, noncolumnar structures are observed, such as ReO₃-type SL, featuring intimate intermixing and face-to-face alignment of disks and cubes, face-centered cubic or simple cubic sublattice of nanocubes, and two or three disks per one lattice site. Lamellar and ReO₃-type SLs, employing large 8.6 nm CsPbBr₃ NCs, exhibit characteristic features of the collective ultrafast light emission—superfluorescence—originating from the coherent coupling of emission dipoles in the excited state.

Inorganic nanocrystals (NCs) bridge the gap between bulk solids and atoms or molecules due to their size- and morphology-dependent properties, such as optical, plasmonic, and magnetic properties.^1,2 Self-assembly of NCs into long-range ordered superlattices (SLs), comprising one or more kinds of NCs, holds great promise for creating metamaterials with functionalities, which arise from the addition or synergy of the properties of individual building blocks (i.e., electronic, plasmonic or magnetic coupling, etc.).^3,4 Collective properties could be tunable through the interparticle distance, relative NC orientation, and interparticle medium, as it was demonstrated for band-like charge transport in SLs of semiconductor NCs,⁵⁻⁷ dipolar interactions in arrays of magnetic NCs,⁸⁻¹⁰ or near-field couplings in SLs of plasmonic NCs.¹¹⁻¹³ Although dozens of periodic and quasicrystalline SL structures were reported for binary mixtures of spherical NCs, examples of multicomponent SLs comprising nonspherical NCs were reported only for mixtures of spherical NCs with triangular nanoplates,¹⁴ nanorods,¹⁵ octapods¹⁶ and nanocubes,¹⁷ rhombic nanoplates with tripodal nanoplates,¹⁸ nanodisks with nanorods,¹⁹ and nanocubes with triangular nanoplates.²⁰ To this end, a range of shape-engineered and size-uniform NCs are synthetically accessible as building blocks for SLs;²¹ for instance, rod-shaped or polyhedral metallic NCs,²² faceted lanthanide fluoride nanoplates,²³ rod- and prism-shaped lanthanide-doped fluoride NCs,²⁴ diverse Cd chalcogenide morphologies (nanotetrahedra,²⁵ nanorods,^26,27 nanoplatelets^28,29), and lead halide perovskite nanocubes.^30,31

NC self-assembly into SLs is driven by both energetic interactions and entropic contributions.³²⁻³⁴ The former include dipole–dipole,³⁵ Coulombic,³⁶ magnetic,³⁷ and van der Waals forces between inorganic cores and capping ligands,³⁸ whereas relevant entropic factors comprise free volume entropy gain,³³ depletion attraction interactions,³⁹ and entropy associated with ligand configurations.⁴⁰ In the case of entropy-driven crystallization of binary mixtures of spheres, the binary SLs of NaCl-, AlB₂-, and NaZn₁₃-type are known for hard-sphere systems of micrometer-sized colloidal beads characterized by only a steep steric repulsion term in their interparticle potential,^41,42 as they maximize the packing fraction (η) at a given size ratio (γ = d_B/d_A ≤ 1), exceeding that of single-component densest lattices of spheres (face-centered cubic or hexagonal closed packed; fcc and hcp). Much smaller spherical NCs (3–20 nm) stabilized by flexible hydrocarbon ligand chains depart from such purely hard-sphere behavior and yield more than 20 different binary SL structures isostructural with known atomic lattices. Most of these SLs are of much lower packing density if the latter is estimated, assuming the unaltered and uniform thickness of the surface ligand shell.⁴ Note that the packing density in this context is the volume fraction occupied by the NC core and ligand shell. Much higher packing densities can be estimated, thereby rationalizing the observation of such structural diversity, taking into account deformability of the ligand shell. Specifically, hydrocarbon chains of the ligands can bend away from the axis of contact between NCs (Figure 1a) in a structure-specific manner, as captured by the recently introduced orbifold topological model (OTM).⁴³ OTM-corrected packing densities agree well with the experimental observations.^44,45 Sharper NC shapes will favor the formation of vortices by ligand bending in specific mutual geometries of two kinds of NCs upon the “sharp contacts” between these NCs (Figure 1a), thereby favoring denser structures. Hence, the possibilities for obtaining NC SLs are anticipated to be gigantic for multicomponent assemblies of nonspherical NCs. In this context, we have recently reported on the co-assembly of cubic CsPbBr₃ NCs (8.6 nm) and larger spherical NCs (NaGdF₄, Fe₃O₄) into perovskite ABO₃-type binary SLs (with cubes occupying B and O sites).¹⁷ Emergence of ligand vortices on cube vertices (Figure 1a) densifies the lattice and hence explains the high propensity for crystallizing in an ABO₃-type SL within a broad γ-range and also the unformability of this specific SL-type in all-sphere mixtures. Notably, CsPbBr₃ NCs, besides being of great interest for their compelling luminescent properties,^17,46−49 represent a rare, if not a single, example of sub-10 nm NCs with a nontruncated, sharp cuboid shape.

Figure 1.

(a) Ligand deformation in NC SLs comprising sphere–sphere (left), disk–cube edge (middle), and cube edge–cube edge (right) contacts. According to the OTM model, ligand bending affords smaller interparticle separation for anisotropic NCs interacting through sharp contacts. (b) Packing analysis of columnar AB₂(II)-type structures with nanodisks as A-component and spherical NCs (dashed line) or cubic NCs (solid line) as B-component, within the hard particle approximation, except for an indicated OTM branch. The black arrow indicates the size ratio at which the structure was observed experimentally; the black dashed line marks the limit of the close-packed hexagonal disk lattice. (c) Visualization of contacts between NCs in AB₂(II)-type SL according to hard particle and OTM models; lighter blue and gray regions denote the ligand shells around inorganic cores. (d) Didodecyldimethylammonium is the shortest ligand (1.71 nm) that still renders CsPbBr₃ NCs colloidally robust. Smaller ligand size reduces the structural softness of these NCs and maintains an effective cubic shape.

A further avenue for mesoscale assembly of nanocubes is to combine them with nonspherical NCs, since the anisotropic or even complementary shape of the second component can further promote long-range positional and orientational order of both constituent building blocks.¹⁴⁻²⁰ Toward this end, we have targeted assemblies with LaF₃ nanodisks,¹⁹ owing to their well-defined, ensemble-uniform morphology and facile and reproducible synthetic tuning of their dimensions (∼1.6 nm in thickness, 6.5–28.4 nm in diameter), as well as proven utility as building blocks in NC assembly (see columnar assemblies with nanorods in ref (19)). We note that there exist no reports on successful co-assembly of nanodisks and spherical NCs, and also our trials have not led to such assemblies, which we rationalize by comparatively low packing densities for various disk-sphere SL structures. On the contrary, CsPbBr₃ nanocubes combined with LaF₃ nanodisks yield a variety of columnar (periodic intermixing in two dimensions) and structurally three-dimensional SLs. An overarching effect of switching from spheres to cubes of the same size, namely, an increase in space-filling, is illustrated in Figure 1b by plotting hard-particle packing densities for one observed columnar structure [in the following termed as AB₂(II)]. We further assessed the effect of ligand deformability upon the approach between the cube edge and a rim of a disk (Figure 1c). In particular, for the case of an AB₂(II) structure that is observed at γ = 0.430, an OTM calculation suggests considerable densification upon ligand bending (η = 0.915 vs η = 0.878), exceeding the density values for hexagonal columnar packing of disks as a separate competing phase (η = 0.907).

Overall, we report the formation of six columnar SLs by combining 5.3 nm CsPbBr₃ nanocubes with LaF₃ nanodisks (9.2–28.4 nm in diameter). In these structures, stacked face-to-face disks and cubes form pillars, which assemble into two-dimensional long-range ordered, periodic lattices. Transmission electron microscopy (TEM) and selected area electron diffraction (ED) characterization reveal that nanocubes in AB(I)-, AB₂(I)-, and AB₂(II)-type SLs lose orientational freedom and are aligned in one direction, whereas in AB₄- and AB₆-type SLs, cubes may have different orientations. Closely related are binary lamellar SLs, with chains of stacked cubes and disks lying flat with the substrate surface. In the mixtures of 8.6 nm CsPbBr₃ NCs and comparably sized LaF₃ nanodisks (6.5–12.5 nm), we observe a range of highly dense SL structures, wherein disks and cubes alternate in each of the three dimensions. Peculiarly, one lattice site can be occupied by several nanodisks. These findings indicate that a vast structural diversity of long-range ordered mesostructures is at reach through entropy-driven crystallization when two (or more) kinds of nonspherical, shape-engineered NC building blocks are employed.

Photoluminescence studies of lamellar and ReO₃-type SLs, employing large 8.6 nm CsPbBr₃ NCs, reveal collective emission properties at cryogenic temperatures. In particular, excitation at high fluences gives rise to a drastic superradiant acceleration of the radiative rates, along with ringing behavior in the time-resolved traces—signatures of superfluorescence (SF).

Results and Discussion

Monodisperse oleate-capped LaF₃ nanodisks of various sizes, namely, 6.5, 9.0, 9.2, 12.5, 13.3, 16.6, 18.5, 21.0, 26.5, and 28.4 nm in diameter (all being ∼1.6 nm in thickness), were synthesized by thermal decomposition of lanthanum trifluoroacetate in a high-boiling solvent in the presence of long-chain capping ligands.¹⁹ These nanodisks readily stack in a face-to-face manner, lying both flat and perpendicular to the substrate, forming, respectively, hexagonal close-packed columnar or lamellar structures (see TEM characterization in Figure S1). A wide-angle ED pattern from a columnar assembly shows intense (110) and (300) reflections, in agreement with the trigonal crystal structure and basal surface termination by (001) lattice planes. In ED, due to a small electron wavelength, only reflections from lattice planes that are nearly parallel to the incident electron beam are observed; this is why (111) planes of LaF₃ do not contribute to the ED pattern of flat-lying disks, but peaks that originate from these planes are intense in the pattern from vertically stacked disks (see, for instance, Figure 8c). CsPbBr₃ nanocubes of two sizes (5.3 and 8.6 nm) were synthesized by the hot-injection method,^50,51 followed by surface treatment with a didodecyldimethylammonium bromide (DDAB) ligand for rendering them colloidally stable; see schematic in Figure 1d and Figure S2 for optical characterization. Narrow arcs in a wide-angle ED from an ordered monolayer indicate the alignment of cubes with the [001] zone axis parallel to the electron beam (Figure S1). CsPbBr₃ NCs exhibit an orthorhombic Pnma structure with six facets terminated by two {010} and four {101} planes.⁵² For simplicity of the ED analysis and peak assignment, the structure of CsPbBr₃ NCs is treated as pseudocubic with six facets terminated by {100} pseudocubic planes, as the d-spacing between {010} and between {101} planes of the orthorhombic structure are very similar. Self-assembly experiments were carried out utilizing the slow solvent evaporation method over a tilted substrate with the use of octane or toluene as a solvent; see the Experimental Section for the NC synthesis and assembly details.

Figure 8.

Lamellar binary AB(I)-type SLs self-assembled from 8.6 nm CsPbBr₃ nanocubes and 18.5 nm LaF₃ nanodisks. (a) TEM images at different magnifications; the small-angle ED pattern is shown as a bottom inset. (b) HAADF-STEM image along with (c) the corresponding wide-angle ED pattern. (d) Structural model of lamellar AB(I)-type SL illustrating the preferred orientation of NCs revealed by ED perspective and top views. (e) Low magnification HAADF-STEM image. (f) SEM image capturing the surface of the lamellar SL domain with rows of cubes and disks. (g) AFM height image revealing the topology of lamellar domains. (h) Height analysis of the profile indicated in g. (i) AFM 3D image of the top right area in g; the alternating chains of disks and cubes are resolved.

Co-assembly of 5.3 nm cubes with nanodisks yielded six binary columnar structures [two AB, two AB₂, AB₄, and AB₆, Figures S3–S6, domain areas up to 15 μm² for AB(I), 0.5 μm² for AB(II), 2 μm² for AB₂(I), 1 μm² for AB₂(II), 0.8 μm² for AB₄, 4 μm² for AB₆] depending on NC size and concentration ratios. The 5.3 nm CsPbBr₃ NCs with 12.5, 13.3, 16.6, and 18.5 nm LaF₃ nanodisks (γ = 0.430, 0.408, 0.337, and 0.306) form an AB(I)-type lattice. Therein, stacks of nanodisks oriented vertically to the substrate form a simple square columnar lattice with p4mm plane group symmetry (see also ref (53)), while pillars of nanocubes fill the interstitial sites, as confirmed by TEM, high-angle annular dark-field scanning TEM (HAADF-STEM, wherein heavy-element containing CsPbBr₃ NCs have higher contrast), and energy-dispersive X-ray spectroscopy (EDX-STEM) elemental maps (Figures 2a–e and S7a–e).

Figure 2.

Columnar binary AB(I)- and AB₂(I)-type SLs assembled from 5.3 nm CsPbBr₃ NCs and LaF₃ nanodisks. (a) Low and (b) high magnification TEM images, (c and inset in a) structural models, (d) a HAADF-STEM image with an outlined unit cell, and (e) EDX-STEM maps (La, red; Pb, blue; both, L-line) of an AB(I)-type SL obtained with 16.6 nm LaF₃ nanodisks. (f) Low and (g) high magnification TEM images, (h and inset in f) structural models (showing D_2h and C_2v configurations), (i) a HAADF-STEM image with outlined unit cell and (j) EDX-STEM maps (La, red; Pb, blue; both, L-line) of an AB₂(I)-type SL obtained with 26.5 nm LaF₃ nanodisks.

With 26.5 nm nanodisks (γ = 0.221), centered rectangular AB₂(I)-type binary SL with a c2mm symmetry forms, in which each void between the four nanodisk columns is occupied by two pillars of nanocubes, in agreement with EDX-STEM maps (Figures 2f–j and S7h–j). Similarly to AB₂(I)-type SL comprising disks and rods,¹⁹ there are also two possible configurations owing to the different alignment of four nanocube sets around each nanodisk column: one with four sets aligned in the same directions and hence D_2h point group symmetry and another one with a 79° angle between two sets of nanocubes, possessing C_2v symmetry (Figure 2g,h). The presence of both configurations within one domain induces twin boundaries (Figure S7i) and indicates a minor difference in their formation energies.^19,54 Wide-angle ED patterns of AB(I) and AB₂(I) domains (Figure S7c,j) display four weak and broad arcs corresponding to (200) reflections of the CsPbBr₃ nanocubes (contrary to continuous rings originating from randomly rotated LaF₃ disks) which implies the vast prevalence of nanocube face–nanodisk contacts (Figure 2c,h) over nanocube edge–nanodisk contacts. The absence of (111) reflections from perovskite and LaF₃ may indicate the alignment of their [001] zone axis with the out-of-plane z-direction of the SL. A higher degree of orientational coherence, evident from distinct peaks in the ED pattern, is observed in AB(I)-type SLs assembled from larger cubes and disks maintaining a similar size ratio (8.6 nm CsPbBr₃ nanocubes, 26.5 nm LaF₃ nanodisks, γ = 0.335, Figure S7f,g) and can be attributed to a sharper shape of these larger cubes because of their reduced softness.^45,55

Another AB₂(II)-type, centered rectangular lattice with AB₂ stoichiometry and c2mm symmetry forms when combining 5.3 nm cubes with 12.5 nm disks (γ = 0.430, Figure 3). In this structure, the parent hexagonal close-packed disk lattice expands in one direction due to the inclusion of cubes into each interstitial site (at 0.121 < γ < 0.707, Figures 3c and S3e–i). Each disk column is surrounded by two disk and six cube pillars; each cube orients its two faces and one edge to three neighboring disks, as illustrated in Figure 3c, in agreement with the ED pattern of a single SL domain (Figure 3f). As with the AB₂(I) structure, the different relative positioning of eight adjacent NCs around one disk leads to twin boundaries between two possible configurations (Figure 3c): the dominant one with neighboring disks separated from both sides by three nearest cubes (D_2h symmetry) and the second one with four (from one side) and two (from another side) cubes between two adjacent disks and about a 140° angle (C_2v symmetry with mirror plane intersecting the disks). The presence of nine adjacent nanodisk columns belonging to C_2v moieties may lead to a nonagonal flower-like assembly (Figure 3d).

Figure 3.

Columnar AB₂(II)-type binary SL assembled from 5.3 nm CsPbBr₃ NCs and 12.5 nm LaF₃ nanodisks. (a) TEM image and (b) HAADF-STEM images with outlined unit cell. (c) Structural models (showing D_2h and C_2v configurations), (d) TEM image of nonagonally assembled SL domain. (e) Low-magnification TEM image along with (bottom inset) small-angle ED and (f) wide-angle ED patterns measured from the area shown as an upper inset in e.

Increasing the concentration of 5.3 nm CsPbBr₃ NCs relative to the same nanodisks (γ = 0.430) favors the formation of an AB₄-type SL (Figures 4 and S8a–c). Such a lattice has not been reported or predicted for binary mixtures of disks or for combinations of disks with spheres or other shapes. In this structure, columns of nanodisks which form a simple hexagonal lattice are uniformly surrounded by nanocubes. The columns of cubes, however, are not resolvable, which precludes the exact determination of their vertical stacking. Following the analysis of the intensity distribution in HAADF-STEM images (Figure 4c), a plausible stacking of AB₄ layers is such that they are shifted by 60° above one another (Figure 4d). This would yield the observed intensity maxima originating from cubes in the middle of the lines connecting adjacent disks and in the center of the triangles from neighboring disks. Having all of these sites occupied by one layer of cubes is physically infeasible and would result in an AB₅-type SL with resolvable pillars of cubes.

Figure 4.

Columnar AB₄-type binary SL assembled from 5.3 nm CsPbBr₃ and 12.5 nm LaF₃ NCs. (a) TEM image showing the grain boundary between AB₂(II)- and AB₄-type SL domains at an intermediate particle ratio. (b) TEM image along with (c) HAADF-STEM image and (d) structural models of AB₄-type binary SL. Inset in b shows respective small-angle ED pattern. Unit cells are outlined in c and d.

Hexagonal AB₆-type SL with 12 distinct pillars of nanocubes, dedecagonally arranged around columns of nanodisks, was obtained with 21.0 and 28.4 nm LaF₃ NCs (γ = 0.273 and 0.207, Figures 5 and S8d–g). Continuous rings in wide-angle ED patterns (Figures 5c and S8c,f) originating from CsPbBr₃ lattice planes agree with the diversity of in-plane orientations of cubes in the AB₄-type and AB₆-type SLs, while hexagonal arcs from LaF₃ imply slight hexagonal faceting of nanodisks. Nanodisks of 9.2 nm with 5.3 nm CsPbBr₃ NCs (γ = 0.555) form a centered rectangular AB(II)-type lattice where sets of two columns of cubes fill interstitial sites formed by six columns of contacting disks (Figures 6 and S4d–g). Here, the translational order is distorted by a different alignment of nanocube sets: parallel or at an angle of about 102°.

Figure 5.

Columnar AB₆-type binary SL assembled from 5.3 nm CsPbBr₃ and 21.0 nm LaF₃ NCs. (a) Low- and (b) high-magnification TEM images along with the corresponding small-angle ED pattern. (c) HAADF-STEM image with wide-angle ED pattern shown as an inset; a unit cell is outlined. (d) Structural models of AB₆-type binary SL.

Figure 6.

Centered rectangular columnar binary AB(II)-type SL assembled from 5.3 nm CsPbBr₃ NCs and 9.2 nm LaF₃ nanodisks. (a, b) TEM images at different magnifications. (c) And the inset in a shows a perspective and top view of the AB(II) structure; the unit cell is outlined. The lattice can be considered as liquid crystalline, columnar packing, owing to its in-plane disorder and ill-defined vertical order.

In order to rationalize the outcome of crystallization by controlling the size ratio, we analyzed packing densities of the observed structures depending on the effective size ratio defined as γ = l_c/d_d ≤ 1, where l_c (effective cube edge length) and d_d (effective disk diameter) are treated within the hard-particle model. Assuming the preferable orientation of nanocubes (corroborated with ED data), the results are presented in Figure 7a and discussed in Supplementary Note 1. At magic size ratios [γ = 0.272 for AB₂(I), 0.289 for AB₆, 0.414 for AB(I), 0.545 for AB(II), 0.561 for AB₂(II)], the columns of disks still retain the close packing (direct contact), while cubes are large enough to fill the space in between tightly (without rattling). In the vicinity of these size ratios, the packing densities of the structures are close to or exceed the value for the hexagonal close-packed lattice of disk columns (η = 0.907), thus explaining their formability. The experimental lattice parameters (from the analysis of TEM data) generally agree with the calculated values, with a typical divergence of ca. 0.5 nm (see Table S2 and Supplementary Note 1 for details). Our trials to obtain these columnar structures from the mixtures of nanodisks and spherical NCs have not been successful (Figure S9). The results can be explained by low packing densities (Figure 7b) of the structures comprising columns of spheres which occupy only 2/3 of the space within the pillar projection, unlike columns of cubes, rods, or disks which fully occupy the space and form columnar structures with larger disks as shown in this work and ref (19).

Figure 7.

Packing analysis of columnar structures. (a) Calculated packing densities for binary columnar SLs within the hard-disk (A-particle) and hard-cube (B-particle) models. Points on the plots correspond to the SLs obtained in this work. (b) Calculated packing densities for binary columnar SLs within the hard-disk (A-particle) and hard-sphere (B-particle) models; the black arrows indicate experimentally tested size ratios. The dashed lines mark the limit of the close-packed hexagonal disk lattice.

Larger 8.6 nm CsPbBr₃ nanocubes do not assemble with nanodisks into columnar SLs. Instead, extended lamellar ordering (domain areas of 15–30 μm²) was observed with 18.5 nm LaF₃ (γ = 0.463, Figure 8). Similar to layered architectures obtained from the systems of rhombic and tripodal nanoplates,¹⁸ nanoplates and nanospheres,⁵⁶ nanodisks and nanorods,¹⁹ the smectic liquid crystalline lamellar structure consists of alternating one-dimensional strings of nanodisks and nanocubes stacked face-to-face and lying on the substrate. Nanodisk strings of the next layer stand above the nanocube strings of the previous layer, emulating a columnar AB(I)-type structure. Interestingly, the strings in different layers can be rotationally aligned in a nonparallel yet regular manner (see Figure S10 for the structure formed from 5.3 nm CsPbBr₃ and 18.5 nm LaF₃). The distance between two cube chains within the same layer (l ≈ 31.0 nm, see Figure 8b) corresponds to the sum of cube edge length and nanodisk diameter (l_c + d_d = 30.7 nm), in agreement with the cube face–disk edge contacts in the AB(I)-type lamellar SL. The orientational coherence of nanocubes and nanodisks was further confirmed by ED, wherein the presence of (002) LaF₃ reflection indicates vertical orientation of nanodisks with flat facets pointing along the string direction (Figure 8c). The topology of binary domains was visualized by scanning electron microscopy (SEM, Figure 8f) and atomic force microscopy (AFM, Figure 8g–i), revealing alternating chains of stacked disks and cubes.

Extended long-range ordered binary lamellar SL domains (domain areas up to 30 μm²) of different types can be obtained from the mixture of 5.3 nm CsPbBr₃ and 6.5 nm LaF₃ NCs (Figure 9). Template matching and averaging of a homogeneous area of the HAADF-STEM image results in the image with an improved signal-to-noise ratio (Figure 9b). The observed images can originate from an A₂B-type structure (Figure 9c) in which chains of cubes are surrounded by six chains of disks. The interdisk separation of about 2.9 nm indicates that face-to-face contacts within stacks of disks are preserved, while the top view of the model still resembles “interdigitated” columns of disks observed in TEM as a result of the out-of-plane shift of adjacent disk chains also shifted in-plane. The proposed ordering is also in agreement with the distance between neighboring cubes’ projections (l ≈ 13.0 nm); the sum of disk diameter and half of the cube face diagonal is 13.3 nm.

Figure 9.

Lamellar binary SL self-assembled from 5.3 nm CsPbBr₃ nanocubes and 6.5 nm LaF₃ nanodisks. (a) Low-magnification TEM image showing a large single SL domain. (b) HAADF-STEM image; inset is the image obtained by template-matching analysis of the corresponding HAADF-STEM image. (c) Perspective and top views of A₂B-type SL structure that are in agreement with TEM images.

Combining disks and cubes of similar size gives rise to vastly different SL structural space—structures with noncolumnar but three-dimensional intermixing and periodicity. For instance, 8.6 nm CsPbBr₃ nanocubes combined with 12.5 nm nanodisks yield a lattice that can be described as a NaCl type, in which clusters of three disks occupy individual lattice sites in the fcc sublattice (Figure 10a–d). The ED pattern comprises horizontally oriented disks [see (110) and (300) rings from yellow disks, Figure 10c] and two sets of vertically oriented nanodisks with faces aligned along with two in-plane SL directions [(002) and (111) reflections, red and green disks]. The orientation of cubes is locked with faces pointing along with three <100>_SL directions. TEM images also suggest self-substitutional point defects,⁵⁷ seen as several neighboring lattice sites occupied by stacks of disks.

Figure 10.

Binary SLs self-assembled from 8.6 nm CsPbBr₃ nanocubes and LaF₃ nanodisks. (a) SEM and (inset) low-magnification TEM images, (b) TEM image with the corresponding (inset) small-angle ED and (c) wide-angle ED patterns, (d) HAADF-STEM image of a NaCl-type SL self-assembled with 12.5 nm nanodisks; model of a NaCl-type SL unit cell assuming preferable orientation of NCs is shown as an inset. (e) TEM image of a ReO₃-type monolayer binary domain comprising 12.5 nm LaF₃ NCs along with (f) the corresponding wide-angle ED pattern. (g) TEM image and (h) the respective wide-angle ED pattern of a ReO₃-type binary domain assembled from 9.0 nm LaF₃ NCs; structural model of ReO₃-type unit cell and the SL projection are depicted as an inset in g. Small-angle ED pattern is shown as an inset in h. (i) TEM image of a binary ReO₃-type related SL domain assembled from 6.5 nm LaF₃ nanodisks, along with the corresponding (j) wide-angle and (j, inset) small-angle ED patterns. The upper inset in i is a TEM image of a thin SL domain, and the structural model of a unit cell and SL projection is depicted as a lower inset in i. (k) TEM images taken at different magnifications of a columnar binary SL domain assembled from 6.5 nm LaF₃ nanodisks, along with (i) the corresponding wide-angle ED pattern. The NCs that contribute to particular wide-angle ED reflections are depicted in corresponding colors in insets (c, f, h, j, l).

Another observed and very distinct SL motif is a structure which can be described as a ReO₃-type SL (Figures 10e–h, S11d–f), and its appearance is favored when the disk diameter is further reduced to about equal to the edge of the cube (9 nm vs 8.6 nm; 12.5 nm disks are too large to form an ordered three-dimensional ReO₃-type structure, see Figures 10e,f and S11a–c). Nanocubes reside in the primitive positions of the unit cell (forming simple cubic packing), whereas disks interlayer the cubes in a face-to-face manner in all three dimensions (O sites in the ReO₃ lattice). ED confirms the orientations of cubes and disks within the lattice as depicted in the inset in Figure 10g. Similar packing, driven by the strong face-to-face interactions, has been reported for LaF₃ triangular plates sandwiched between PbTe cubes.²⁰

With the smallest LaF₃ disks (6.5 nm), the space-filling in the ReO₃ lattice is compromised. Additional voids that emerge in the ReO₃-lattice can be occupied by the additional disks (Figures 10i,j and S11g-i). Alternatively, another three-dimensional structure emerges, featuring both single disks and their pairs (Figure 10k,l). CsPbBr₃ cubes form columns, in which cubes are interlayered with single disks [contributing to (110) and (300) rings in wide-angle ED] in the vertical direction. Pairs of disks occupy single lattice sites, and these sites form columns as well, in which the in-plane orientation of disks alternates. The top-view onto the resulting structure reveals a checkerboard lattice formed by both NC components.

Lamellar and ReO₃-type SLs, employing large 8.6 nm CsPbBr₃ NCs, can be assembled as large and phase-pure domains on Si₃N₄ grids. The use of such transparent dielectric support membranes instead of carbon films was previously found as decisive for the observation of SF from thin-film SLs comprising perovskite NCs.¹⁷ Lamellar and ReO₃-type SLs feature a high volume fraction of CsPbBr₃ NCs of 0.136 (concentration 2.1 × 10⁵ NCs/μm³) and 0.188 (concentration 2.9 × 10⁵ NCs/μm³), respectively. These values are close to the volume fraction obtained in ABO₃ SLs, which were shown to exhibit SF,¹⁷ and a factor of 2 higher than for NaCl-type SLs, which could not be driven into the SF regime. In the ReO₃-type SL, the occurrence of SF is manifested by the appearance of a red-shifted emission band (of about 30 meV), while in the lamellar-type SL, the SF is almost resonant to the excitonic emission (Figure 11a,c). In both cases, a continuous shortening of the radiative lifetimes down to a few tens of picoseconds has been observed by increasing the excitation fluences (Figure 11b,d). These results further suggest that the number of coherently coupled dipoles (oscillators) per volume is pivotal for the radiative lifetime speed-up, in addition to low energetic disorder, the mutual alignment among the dipoles, and a long coherence time.

Figure 11.

Optical properties of binary SLs at cryogenic temperature (6 K). (a) Emission spectrum of ReO₃-type SLs employing 8.6 nm CsPbBr₃ NCs and 9 nm LaF₃ disks (on Si₃N₄ membranes), featuring, at high excitation fluences, two emission bands separated by ca. 28 meV. (b) Time-resolved emission traces at low (10 μJ cm^–2), medium (40 μJ cm^–2), and high (320 μJ cm^–2) excitation fluences. Shortening of the radiative lifetime and ringing behavior, typical of SF, are observed. The emission spectrum and the time-resolved photoluminescence traces obtained for lamellar SLs (on Si₃N₄ membranes) are reported in c and d. In this case, characteristic SF emission features can be observed that are almost resonant with the NC excitonic emission. (e) Emission spectrum of lamellar SLs employing small 5.3 nm CsPbBr₃ NCs (on carbon membranes). (f) A red-shifted band attributed to incoherently coupled NC emission is observed with typical 80 to 100 meV splitting.

As recently predicted by theoretical calculations based on non-Hermitian radiative Hamiltonians for simple cubic packing of CsPbBr₃ nanocubes,⁵⁸ smaller NCs should yield stronger coupling and stronger superradiant emission rate enhancement and overall a more facile emergence of SF as compared to larger NCs. Thus far, our studies with such densely packed SLs of 5.3 nm NCs (unpublished) and with ABO₃-type SLs¹⁷ comprising these small NCs have not yielded spectroscopic features of SF. Here, we extended the search for SF to lamellar SLs and do not find evidence of SF characteristics as well. While we could not find strongly accelerated luminescence decay, A₂B-type lamellar SLs comprising 5.3 nm CsPbBr₃ NCs and 6.5 nm LaF₃ disks feature a strongly red-shifted band from coupled NCs, with typical shifts ranging from 80 to 100 meV (Figure 11e,f). The emission of coupled NCs is still far from the expected bulk emission (ca. 2.3 eV, 535–540 nm) and strongly varies from spot to spot on the same sample because of differently sized, coupled domains (Figure 11f), thus contrasting the hypothesis that the red-shifted emission band would emerge from merged, bulk-like microcrystals.⁵⁹ Such large photoluminescence red shifts might originate from the shorter NC-to-NC distance, which enhances the NC coupling, irrespective of whether being mediated by a near-field effect with wave function tunneling, a partial necking involving the NC corners, or dipolar coupling. The apparent absence of coherent coupling and SF in thus far studied NC assemblies of small CsPbBr₃ NCs can be attributed to the higher static energetic disorder in the ensemble. Despite the comparably narrow NC size distribution as for larger NCs, the energetic disorder increases due to quantum confinement, as exemplified by the larger photoluminescence line-broadening in small NCs (ca. 45 meV) compared to larger NCs (ca. 25 meV). Furthermore, all atomistic inhomogeneities can strongly add up to the energetic disorder, including the morphological dissimilarity of NCs (deviations in surface terminations and NC truncation), variation in the inter-NC distance, or various degrees of possible NC necking. Furthermore, in the case of thin-film superlattices comprising 5 nm NCs, presented herein, the use of carbon-coated Cu grids may inhibit the onset of SF (Figure S12).

Conclusions

This study contributed to the exploration of the structural space of multicomponent SLs derived from nonspherical, shape-engineered NC building blocks. Specifically, co-assembly of lead halide perovskite NCs of sharp, nontruncated cubic morphology (5.3 and 8.6 nm edge length) and size-tunable LaF₃ nanodisks yielded a number of columnar and three-dimensional structures, which are not common for mixtures of spherical NCs. Most of the obtained assemblies are characterized by not only positional but also orientational order of constituent building blocks. Columnar and lamellar lattices are characterized by alternating pillars of disks and cubes, forming long-range ordered patterns in two dimensions. All columnar structures were observed at cube edge length-to-disk diameter ratios γ ≤ 0.555. When the sizes of disks and cubes become similar, three-dimensional lattices form, wherein cubes interact with disks through flat faces in all three directions. Besides maximizing the packing density, the observed propensity to maximize the surface of contact by aligning nanodisks to cube facets agrees well with the increased interaction potential between flat surfaces of anisotropic NCs.⁶⁰ Explicit free energy calculations are required to rationalize the formation of the observed structures and to guide further work in this arena.

Lamellar and ReO₃-type SLs employing large 8.6 nm CsPbBr₃ NCs were shown to emit ultrafast superfluorescent bursts of light, with excitation-fluence-dependent radiative lifetimes as short as 25 and 7 ps (defined as the 1/e lifetime), respectively. Characteristic ringing behavior in the time-resolved decay traces, a hallmark feature of SF emission, was also observed. SLs with smaller 5.3 nm CsPbBr₃ NCs exhibit a much red-shifted emission band, evidencing (incoherent) coupling between NCs. Yet, no spectroscopic evidence of SF could be observed with these constituent NCs being in the strong quantum confinement regime. Future work should focus on delineating the factors governing the emergence of coherent coupling in the excited state, including both the mesoscopic aspects (the SL packing geometry, NC shape, NC size-distribution, etc.) and the structural inhomogeneities down to the atomistic level (crystallographic alignment of NCs with SL, structural coherence of the SL, variations in the inter-NC distance etc.).

Experimental Section

Synthesis of Cesium Oleate Stock Solution

Cs₂CO₃ (0.2 g, Sigma-Aldrich, 99.9%), oleic acid (0.6 mL, OA, Sigma-Aldrich, 90%, vacuum-dried at 100 °C), and 1-octadecene (7.5 mL, ODE, Sigma-Aldrich, 90%, distilled) were loaded into a 25 mL flask and dried under a vacuum for 20 min at 100 °C, and then heated under N₂ to 120 °C until all Cs₂CO₃ reacted with OA.

Synthesis of CsPbBr₃ NCs

The 8.6 nm NCs were synthesized following the method reported in ref (51). In a 25 mL three-neck flask, PbBr₂ (55 mg, ABCR, 98%) was degassed three times, suspended in 5 mL of ODE, and degassed again three times at room temperature. The suspension was fast heated up to 180 °C, when the temperature reached 120 °C; 0.5 mL of OA and oleylamine (0.5 mL, OLA, Strem, 97%, distilled) was injected. At 180 °C, preheated to about 100 °C cesium oleate solution in ODE (0.6 mL) was injected. The reaction mixture was cooled immediately to room temperature with an ice bath. The crude solution was centrifuged at 20 130 relative centrifugal force (rcf) for 5 min. The supernatant was discarded, and the precipitate was dispersed in hexane (0.3 mL, Sigma-Aldrich, anhydrous, 95%). The solution was centrifuged again at 13 750 rcf for 3 min, and the precipitate was discarded. Then, OLA/OA ligands were exchanged by didodecyldimethylammonium bromide (DDAB) treatment. Then, 0.3 mL of hexane, toluene (0.6 mL, Sigma-Aldrich, anhydrous, 99.8%), and DDAB (0.14 mL, 0.05 M in toluene, Sigma-Aldrich, 98%) were added to the supernatant and stirred for 1 h, followed by destabilization with ethyl acetate (1.8 mL, Sigma-Aldrich, 99.9%), centrifuging at 20 130 rcf for 3 min and redispersion in 0.6 mL of toluene. Synthesis of 5.3 nm CsPbBr₃ NCs was adopted from ref (50) followed by DDAB treatment.

Synthesis of LaF₃ Nanodisks Was Adopted from Ref (19)

In a typical synthesis of 6.5 nm NCs, 192 mg of lanthanum trifluoroacetate, LiF (31.2 mg, Sigma-Aldrich, 99.99%), 6 mL of OA, and 6 mL of ODE were degassed in a 25 mL three-neck flask at 125 °C for 2 h. Then, the solution was heated to 295 °C at 15 °C/min under nitrogen and kept at this temperature for 32 min. The reaction mixture was cooled to room temperature, and 3 mL of hexane along with ethanol (30 mL, Merck, 99.8%) was added to destabilize the colloidal solution. The NCs were precipitated by centrifugation at 2200 rcf for 2 min and washed two additional times with hexane (along with 10–30 uL OA) and ethanol (1 to 1 by volume). After purification, NCs were dispersed in 3 mL of hexane, and residual LiF, which is not soluble in nonpolar solvents, was separated by centrifugation at 2200 rcf for 2 min. For the synthesis of bigger NCs, a longer reaction time and a higher temperature were used; for example, 21.0 nm LaF₃ NCs were synthesized at 300 °C for 86 min. Lanthanum trifluoroacetate was synthesized by reaction of La₂O₃ (3.24 g, Sigma-Aldrich, 99.999%) with trifluoroacetic acid (16 mL, Sigma-Aldrich, 99%) and 16 mL of water under reflux (93 °C) for 1 h. A white product was isolated by evaporation of the unreacted acid and water under a vacuum at 60 °C and dried overnight under a vacuum.

Synthesis of 6.0 nm PbS NCs Was Adopted from Ref (61)

Lead(II) acetate trihydrate (379 mg, Sigma-Aldrich, 99.99%) along with 6.9 mL of OA and 3.1 mL of ODE were loaded in a three-neck flask and dried under a vacuum at 105 °C for 1 h. The atmosphere was changed to nitrogen, and the solution was heated up to 145 °C. Then, the heating mantle was removed, and hexamethyldisilathiane solution (0.105 mL, Sigma-Aldrich, synthesis grade, in 5 mL ODE) was swiftly injected. After 3 min of stirring the reaction was quenched with an ice–water bath. The NCs were purified by rinsing with 10 mL of hexane and destabilization with 10 mL of ethanol. The washing was repeated twice with hexane (10 mL along with 15 μL OA) and ethanol (5 mL) as a solvent–antisolvent pair, and the NCs were dispersed in 4 mL of hexane.

Preparation of Multicomponent SLs

NC SLs were prepared using a drying-mediated self-assembly method on carbon-coated TEM grids (carbon type B, Ted Pella, Formvar protective layer removed by immersing the grid in toluene for 10 s) as substrates. A mixture of NCs in octane or anhydrous toluene had an overall particle concentration of 0.5–2.5 μM and NC number ratios (CsPbBr₃ to LaF₃ NCs) in the range of 0.5–20. A total of 30–35 μL of NC mixture was transferred into a tilted 2 mL glass vial with a substrate inside. The solvent was evaporated under 0.45 atm pressure at room temperature. For example, AB₂(II)-type SL with high yield was obtained from the solution prepared by mixing 12.5 nm LaF₃ NCs (0.6 μL, 18 mg/mL), 5.3 nm CsPbBr₃ NCs (5.0 μL, 7.0 μM), and 25 μL toluene. AB₆-type SL: 21.0 nm LaF₃ NCs (2.2 μL, 10 mg/mL), 5.3 nm CsPbBr₃ NCs (7.5 μL, 7.4 μM), and 25 μL toluene. Lamellar AB(I)-type SL: 18.5 nm LaF₃ NCs (1.5 μL, 17 mg/mL), 8.6 nm CsPbBr₃ NCs (2 μL, 5.1 μM), and 25 μL toluene. ReO₃-type SL: 9.0 nm LaF₃ NCs (0.9 μL, 9 mg/mL), 8.6 nm CsPbBr₃ NCs (1.8 μL, 5.9 μM), and 25 μL toluene.

Optical Measurements

Optical absorption spectra of NCs dispersed in toluene were measured with a Jasco V770 spectrometer in transmission mode. Photoluminescence (PL) spectra were measured in a 90° configuration using Horiba Fluoromax-4P+ equipped with a photomultiplier tube and a monochromatized 150 W xenon lamp as an excitation source. For PL and time-resolved PL of SLs (Figure 11a–d), the sample was mounted in a helium exchange-gas cryostat at 6 K. A frequency-doubled regenerative amplifier seeded with a mode-locked Ti:sapphire laser with a pulse duration of 100–200 fs and a repetition rate of 1 kHz at 3.1 eV photon energy was used as an excitation source after passing through short-pass filters (442 nm cutoff wavelength). For both excitation and detection, we used the same focusing lens with 100 mm focal length, resulting in an excitation spot radius of about 60 μm. The recorded PL was long-pass filtered (480 nm cutoff wavelength) and then dispersed via a grating with 150 lines per mm in a 0.3-m-long monochromator and detected with a streak camera with a nominal time resolution of 2 ps and instrument response function fwhm of 4 ps. The time-integrated PL spectra were recorded with a 0.5-m-long spectrograph with a grating with 300 lines per millimeter and a nitrogen-cooled CCD camera.

For the PL spectra presented in Figure 11e,f, the sample was mounted in a closed-loop, coldfinger cryostat on an x–y–z positioning stage and cooled down to a temperature of 5 K. The sample was excited with a fiber-coupled excitation laser at an energy of 3.06 eV, in pulsed mode with a 10 MHz repetition rate (pulse duration 50 ps). The excitation laser output was filtered with a short-pass filter and directed toward the long-working-distance 100× microscope objective (numerical aperture NA = 0.85) using a dichroic beam splitter, resulting in a nearly Gaussian-shaped excitation spot with a 1/e² radius of 1.5 μm. The emission was collected via the same microscope objective. For PL measurements, the collected light was then dispersed via a 300-lines-per-millimeter grating inside a 0.5-m-long monochromator and detected by an EMCCD camera.

Electron Microscopy Characterization

Transmission electron microscopy (TEM) and high-angle annular dark-field scanning TEM (HAADF-STEM) images as well as wide- and small-angle electron diffraction (ED) patterns were collected with the use of JEOL JEM2200FS microscope operating at a 200 kV accelerating voltage. Energy-dispersive X-ray (EDX-STEM) maps and HAADF-STEM were recorded using an FEI Titan Themis microscope operated at 300 kV. SEM images were obtained on a FEI Helios 660 operated at 3 kV using immersion mode.

Atomic Force Microscopy

ScanAsyst-AiIR probes were used to analyze the topography of the SLs on the Bruker Icon 3 Atomic Force Microscope.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.1c06047.

• Packing analysis of columnar SLs comprising disks with cubes and disks with spheres; optical characterization of CsPbBr₃ NCs and TEM images of NC building blocks used for self-assembly; TEM characterization of columnar, lamellar, three-dimensional SLs; and results on the assembly of LaF₃ nanodisks with spherical PbS NCs (PDF)

The authors declare no competing financial interest.