Structural Diversity in Multicomponent Nanocrystal Superlattices Comprising Lead Halide Perovskite Nanocubes.

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.

Assembly of monodisperse nanocrystals (NCs) into long-range ordered superlattices (SLs) makes an ideal platform for creating materials with controlled and programmed functionalities that result not only from the combination and enhancement of size-dependent properties of constituent building blocks but also from synergistic effects and emergent interactions between neighboring NCs.[1,2] Early examples include conductivity enhancement in binary SLs of Ag2Te with PbTe NCs,[3] exchange coupling effects in assemblies of magnetic NCs,[4] and near-field plasmonic-plasmonic resonance in the SL comprising gold NCs.[5] Various strategies have been developed for the fabrication of single and multicomponent SL structures with desired dimensionality and geometry, including colloid destabilization by nonsolvent diffusion,[6] drying-induced assembly over tilted substrate,[7,8] or at a liquid–air interface[9−11] and microemulsion-templated assembly.[12,13] Self-organization of NCs may be further governed by the external electric and magnetic fields.[14,15] The assembly of steric-stabilized colloidal NCs coated with hydrocarbon ligand chains relies on relatively weak (van der Waals, dipole–dipole, magnetic, Coulombic) interactions between NCs[1,16] with the considerable role of entropic contributions.[7] For example, the gain in free volume entropy upon self-assembly of monodisperse spherical NCs favors the formation of the densest possible structures with face-centered cubic (fcc) or hexagonal close packing.[1,17] For binary mixtures of spherical NCs, over 20 structures analogous to known atomic lattices were reported. Typically, the observed structure is the one having higher packing density (η) for a given NC size ratio, γ = dB/dA, where dB is the diameter of a smaller B-component and dA is the diameter of a larger A-component, both computed taking into account the dimensions of the core and ligand shell.[2,18−20] In the simple optimal packing model (OPM),[21] the effective diameter of steric-stabilized NCs is calculated assuming that the ligand shell is space-filling along the axis connecting neighboring NCs. Commonly observed are those binary SL structures, whose hard-particle packing densities are close to or exceed the packing density of fcc packing of spheres (η = 0.74).

Advancements in NC synthesis methodologies with exquisite NC size- and shape-engineering motivate the exploration of different SL structures.[22−24] The phase behavior of assemblies from shape-anisotropic NCs can be explained by the presence of directional entropic forces, which lead to dense local packing.[25] Already with single-component SLs of nonspherical NCs, minor differences in NC shape were reported to change the resulting structure; for instance, in the case of cubes vs truncated cubes such as Pt, PbS, or iron oxide.[26−29] A plethora of different binary SLs had been observed combining spherical NCs with several nonspherical NCs such as triangular nanoplates (columnar and three-dimensional structures),[18] nanowires and rhombic nanoplates (wherein chains of nanowires or stacked face-to-face plates template the assembly of spheres into ordered one-dimensional arrays),[30−32] nanorods (forming three-dimensional superstructures with the positional and orientational ordering of building blocks),[33,34] and branched octapod NCs.[35] Very little work has been reported for mixtures of exclusively nonspherical, anisotropic NCs. These are binary lamellar SL of shape-complementary nanoplates,[33] several columnar SLs from the mixtures of nanodisks and nanorods,[36,37] and, very recently, thin-film SLs from PbTe cubes coassembled with triangular nanoplates.[38]

Lead halide perovskite NCs—the latest generation of semiconductor quantum dots introduced in 2015[39]—have attracted much attention for their enhanced properties as narrow-band, bright light emitters[40−42] and are intensely investigated for both classical light generation (light-emitting diodes, down-conversion in LCDs)[43,44] and as single-photon sources.[45,46] Being synthetically available as sharp, monodisperse cubes with edge-length tunable in 5–20 nm,[47−49] perovskite NCs are attractive highly uniform, shape-engineered building blocks for SLs. Since 2017, CsPbBr3 NCs had been reported to form superstructures with simple-cubic packing (scp).[50−57] At cryogenic temperatures, single-component CsPbBr3 NC SLs were found to exhibit superfluorescence. There, in contrast to spontaneous emission where the individual NCs emit photons randomly and independently, a coherent coupling among several NCs in superfluorescent domains leads to collective emission, resulting in ultrafast (few tens of picoseconds) bursts of photons.[53] These findings stimulated exploration of multicomponent SLs with perovskite NCs, as a means of attaining programmable positional and orientational order of these coherent light emitters.[58,59] Fundamentally important is that these were the original trials to coassemble cubic NCs with other shapes, and the outcome was vastly different from the results of the all-sphere NC self-assembly. Specifically, when CsPbBr3 nanocubes are coassembled with spherical dielectric NaGdF4 NCs, the binary perovskite b-ABO3-type SL forms, with cubes occupying B and O sites. Perovskite-type SL had not been reported, and not observed in our reference experiments, for all-sphere mixtures, which can be rationalized by much higher computed packing densities of this lattice when using cubes on B/O-sites. We then utilized the nonequivalence of B and O sites to incorporate the third component, truncated cubic PbS NCs, on a slightly larger B-site, yielding a ternary ABO3-type SL.[58] In the subsequent work, CsPbBr3 cubes were combined with thin LaF3 disks (1.6 nm in thickness, 6.5–28.4 nm in diameter), yielding six columnar structures, wherein columns of disks and cubes form a two-dimensional periodic pattern, and four three-dimensional structures that feature face-to-face contacts between cubes and disks of comparable size.[59]

Here, we present a detailed survey and comprehensive discussion of all multicomponent SL structures (Figure ) obtained by combining cubic CsPbBr3 NCs (and FAPbBr3 NCs) with diverse spherical and nonspherical NCs into multicomponent SLs. Beyond refs (58 and 59), a broader selection of building blocks was utilized (truncated cuboids and thick disks), additional structure types are presented (AB2, b-ABO6, CaC2), and their formation was rationalized using space-filling calculations. Generally, cubic shape and facile ligand-deformability at the vertices and edges yield denser packing compared to spheres. In total, six structures were found in small cube-large sphere and small cube-large truncated cube mixtures, of which three are identical to those commonplace in all-sphere assemblies (NaCl, AlB2, and CuAu types) and the other three are exclusive to the use of cubes as smaller component (AB2, b-ABO3, b-ABO6). Unlike columnar structures with thin LaF3 disks, thick NaGdF4 nanodisks (18.5 nm thick, 31.5 nm in diameter) yield a CaC2-like lattice with clusters of two 8.6 nm cubes. In all presented structures, cubic NCs are orientationally locked. While the screening of SL formation in this work and in our earlier reports (refs (58 and 59)) were conducted by drying the colloids directly on the microscopy substrates, we also present the adaptation of the on-liquid formation of SLs as free-floating membranes for perovskite NCs, wherein a suited subphase solvent such as glyceryl triacetate is proposed. This polar solvent does not disperse apolar NC colloids drop-casted atop nor chemically damages the perovskite NCs. We also present the utility of the microemulsion-based method for the formation of multicomponent SLs comprising perovskite NCs. These SLs give rise to collective electronic states across perovskite NCs at low temperatures, as is evidenced by their photoluminescence (PL) and absorption spectra containing sharp red-shifted bands persisting up to 200 K.

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.

Results and Discussion

Due to rather ionic bonding and specifics of surface termination with a high propensity of lead atoms to maintain octahedral coordination, perovskite NCs tend to expose nonreconstructed, CsBr-terminated facets [(100) in pseudocubic notation], essentially without truncation.[60] Sharp nanocubes CsPbBr3 with the edge lengths of 5.3 and 8.6 nm were synthesized by the hot-injection method (see respective luminescence and absorption spectra in Figure S1).[61,62] The NCs were coated by didodecyldimethylammonium bromide (DDAB), which is the shortest ligand still rendering these NCs colloidally stable. As manifested by the distinct diffraction arcs in the wide-angle selected-area electron diffraction (ED) pattern from the assembled monolayer (see Figure S2), nanocubes align face-to-face with the [001] zone axis parallel to the electron beam. CsPbBr3 nanocubes crystallize in orthorhombic Pnma structure with six facets terminated by four {101} and two {010} planes.[60] Since the d-spacing between {010} and {101} planes is nearly identical, in the ED analysis we treat the structure of CsPbBr3 NCs as pseudocubic with six facets terminated by {100} pseudocubic planes. 10.7 and 11.7 nm oleate-capped PbS nanocubes with truncated vertices possess rock-salt crystal structure and are terminated by {100} lattice planes. Due to similar PbS and CsPbBr3 lattice constants, their diffraction patterns overlap; however, because of the higher symmetry of the PbS structure, the {100} and {110} reflections are absent. The 11.2–25.1 nm Fe3O4 spherical NCs possessing inverse spinel cubic structure were synthesized by thermally decomposing iron oleate.[63] Spherical, 15.1–19.5 nm hexagonal-phase β-NaGdF4 NCs were synthesized by thermal decomposition of gadolinium trifluoroacetate.[31] Six arcs originating from {100} lattice planes imply slight hexagonal faceting of nanospheres. The decreased sodium-to-gadolinium ratio in the precursor solution and increased reaction time lead to NaGdF4 nanodisks (31.5 nm in diameter and 18.5 nm in thickness). The size distribution of NCs used in experiments was in the range from 2.9 to 7.7% [standard size deviation based on 200 particles, see transmission electron microscopy (TEM) characterization in Figure S2]. In most experiments, SLs were grown as polycrystalline films on a range of substrates (carbon-coated copper-grids and Si3N4 membranes on Si grids) by drying the NC mixtures in toluene.

Coassembly of CsPbBr3 Cubes with Spheres

First, we will discuss the systems of cubic 8.6 and 5.3 nm CsPbBr3 NCs with spherical Fe3O4 and NaGdF4 NCs. 8.6 nm CsPbBr3 nanocubes with spherical NCs can form NaCl-, AlB2- (along with AB2-), and b-ABO3-type SLs, depending on particle number ratio. Figure a shows NaCl-type SL obtained as a dominant product at a low CsPbBr3-to-NaGdF4 particle number ratio (ca. 1.2:1 and γ = 0.439). Wide-angle ED measured from a single SL domain reveals the orientation of CsPbBr3 cubes with ⟨100⟩ directions coinciding with ⟨100⟩SL, that is, each cube interacts with six spheres through flat facets; subscript “SL” denotes Miller indices of an SL. At high cube-to-sphere particle ratios (ca. 4.2:1), a b-ABO3-type SL is the sole product (Figure a–n). In this structure, spherical Fe3O4 or NaGdF4 NCs reside on the A site (1a position of Pm3̅m perovskite structure), while cubes occupy two crystallographically different sites, 1b (B site) and 3c (O sites). Distinct features of CsPbBr3 in the wide-angle ED reveal the orientation of O- and B-positioned cubes: CsPbBr3 NCs on faces (O-sites) interact with four spheres through facets and have two of ⟨110⟩ aligned with ⟨100⟩SL, while the cube in the center of the unit cell (B-site) is 45° rotated with respect to O-cubes and has all ⟨100⟩ aligned with ⟨100⟩SL (Figure c,m). Scanning electron microscopy (SEM, Figure d,n) and atomic force microscopy (AFM, Figure e–j) illustrate the surface topology of b-ABO3-type SLs. Precise height profile AFM measurement resolves two distinct surface terminations in [001]SL-oriented domains: (i) spheres terminated (Figure e–g) and (ii) B-site cubes terminated, as evident from sharper and higher maxima in Figure h–j.

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.

The formation of NaCl and b-ABO3 SLs with cubic NCs can be rationalized by their high packing densities, exceeding those of fcc packing of spheres (Figure ).[58] The coordination environment of B- and O-positioned cubes in b-ABO3-type structure is different, for example, at γ ≥ 0.414, O-cubes interact through vertices, while B-cubes are rattlers. Targeted incorporation of larger (compared to perovskite cubes) truncated cuboidal PbS NCs (11.7 nm) on B-sites leads to a three-component t-ABO3-type SL with higher packing density than that of b-ABO3 lattice comprising the same sizes of spheres (21.5 and 25.1 nm) and perovskite cubes (8.6 nm), Figure o–r. Wide-angle ED confirms the same orientation of O-site perovskite cubes as in the binary lattice, and PbS truncated cubes preserving the orientation of B-site perovskite cube. The PbS incorporation into the structure is apparent from high contrast in high-angle annular dark-field scanning TEM (HAADF-STEM) images (Figure p,r). The completeness of the substitution of CsPbBr3 cubes on B site by PbS NCs is evident from the absence of (110) reflection (“1” in Figure q) expected from the center perovskite cube, while the (220) reflection originating from PbS (“2” in Figure q) is intensely diffracting in the analogous direction. These structures are also described in our previous work, ref (58).

At the intermediate particle number ratios (ca. 2.2:1, cubes-to-spheres), the dominant product is an AlB2-type SL. Figure a–e shows TEM characterization of [120]SL-oriented domain assembled from 8.6 nm CsPbBr3 and 19.8 nm Fe3O4 NCs, while Figure f–j presents [001]SL-oriented domain obtained from 8.6 nm CsPbBr3 combined with 16.5 nm NaGdF4 NCs. In this lattice, nanocubes occupy each trigonal prismatic void in a simple hexagonal lattice of spheres. Wide-angle ED pattern from [120]SL-oriented domain (Figure e) comprises narrow arcs originating from (110) and (111) CsPbBr3 lattice planes that run in perpendicular directions, while the ED pattern from [001]SL projection (Figure j) features six (110) CsPbBr3 arcs at 60° angles. This is reflective of the preferential orientation of CsPbBr3 nanocubes in the SL: one of their [111] directions is aligned with [001]SL (6-fold axis) and [110] with [010]SL, that is, cubes interact with three spheres from one side of the trigonal prismatic void via facets and with three spheres from another side via edges.

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).

Smaller, 5.3 nm CsPbBr3 nanocubes with Fe3O4 NCs readily form NaCl- (Figure S3) and AlB2-type SLs, in which, similar to larger cubes, a high degree of orientational order is observed. AlB2-type binary SLs are obtained with iron oxide NCs (11.2–15.6 nm, γ = 0.443, 0.405, 0.368, 0.336, Figure and Figure S4). Structural peculiarities of the AlB2 binary SL are detailed here for the case of 12.5 nm Fe3O4 NCs (Figure ). The grazing-incidence small-angle X-ray scattering (GISAXS) pattern shows strong, periodic reflections (Figure c) owing to long-range order and complex, base-centered orthorhombic symmetry (C222), resulting from the stacking of hexagonal CsPbBr3 and Fe3O4 layers, with an in-plane A–B–A–B packing direction, as also confirmed by energy-dispersive X-ray spectroscopy (EDX-STEM, on Figure g). See Supplementary Note 1 and Figure S5 for further details on GISAXS SL characterization. TEM tilting series readily differentiate the predominantly observed [120]SL projection of the AlB2-type from the similar [100]SL projection of CuAu-type SL (Figure S6). The AlB2-type structure was additionally confirmed by electron tomography of [001]SL-oriented domain (see Supplementary Video 1). Figure i–n displays occasionally observed [001]SL and [010]SL projections of AlB2-type SL. The signal-to-noise ratio was improved upon template matching and averaging of large homogeneous areas of TEM images (insets in Figure i,l). Small-angle ED and wide-angle ED patterns (for [120]SL-orientation) confirm the preferential orientation of nanocubes analogously to AlB2-lattices with larger CsPbBr3 NCs, albeit with much weaker intensities of perovskite reflections due to reduced scattering factor of small NCs. The broader arcs indicate a higher orientational freedom of smaller nanocubes within the SL. The (111) and (110) lattice planes of CsPbBr3 are normal to [001]SL and [010]SL, respectively, as in the binary SLs with larger cubes. However, there are three sets of {110} CsPbBr3 lattice planes with a common [111] zone axis that is parallel to [001]SL. Therefore, 60° rotation around [001]SL does not change the position of diffraction spots. Consequently, there are two possible relative orientations of nanocubes: half of the cubes being 60° rotated about [001]SL (“O1”) or all having the same orientation (“O2”, Figure a). We would also note that ambiguity in this rotational orientation around [001]SL, as well as the possibility of the partial rattling of cubes along the same direction (not resolvable with TEM images), complicates the packing density analysis (Figure b). Our analysis shows that a combined effect of the “O2”-orientation and cube displacement along [001]SL direction can lead to the hard-particle packing densities of 0.7–0.8 in the γ range of 0.35–0.70 (see detailed discussion and calculations in the Supplementary Note 2).

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 e and 5b) and [001]SL-oriented domains (Figure j) 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.

Next to AlB2-type binary SLs and for both sizes of nanocubes combined with Fe3O4 spheres, another AB2 structure belonging to the tetragonal crystal system, namely the P42/mmc space group, concomitantly forms (Figure and Figures S8−S10). This structure can be viewed as derived from the AlB2 structure with a small modification: Shifting of each fourth (100) lattice plane along [011] vector, the corresponding lattice plane and the direction of shifting are marked in Figure d. This AB2-type packing is characterized by spherical NCs forming trigonal prisms, highlighted in Figure d, alternating in two perpendicular directions normal to the out-of-plane [001]SL, with cubic NCs occupying each void orienting in the same way as in the trigonal prismatic void of AlB2-type lattice, hence retaining the AB2 stoichiometry. Such ordering is in agreement with the contrast differences in TEM, HAADF-STEM images, EDX elemental mapping, and wide-angle ED patterns of [001]SL projection (Figure and Figures S9 and S10). Its wide-angle ED displays reflections originating from (110) and (111) CsPbBr3 lattice planes (four arcs of each kind) running normal to [100]SL and [010]SL, which implies two relative orientations of nanocubes with a 90° angle between [111] directions because reflections from (110) and (111) planes of one nanocube cannot appear in the same direction. The higher yield of AlB2-type SLs indicates its lower formation energy barrier compared to AB2 SLs, while the calculated packing densities of both structures coincide up to γ ≤ 0.435 (see for details Supplementary Note 3 and Figure and Figure S8).

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 ) 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).

At γ = 0.315 (5.3 nm CsPbBr3 and 16.9 nm Fe3O4 NCs) and high cube-to-sphere particle number ratio (ca. 12:1), binary b-ABO6-type SL forms (Figure ). It possesses a Pm3̅m space group with cubic NCs occupying one B-site (1b Wyckoff position) and six O-sites (6f Wyckoff position). This structure can also be viewed as ABO3-like, where each of three O-sites (3c Wyckoff position) are occupied by two small cubes. O-positioned cubes are well resolved in HAADF-STEM images of [111]SL-, [101]SL-, and, especially, [001]SL-oriented domains (Figure d–g). Higher intensity of four {110} CsPbBr3 arcs in the wide-angle ED is in agreement with the alignment of the majority of cubes (O-sites) with two of ⟨110⟩ crystallographic directions pointing along with two ⟨100⟩SL; however, their broadening may indicate lower orientational order. Space-filling analysis within the hard-particle model revealed a narrow maximum which is still below the fcc limit (Figure b). Consideration of the deformability of ligand shell on cubic NCs contacting through vertices, within orbifold topological model[64] (OTM, see calculations in the Supplementary Note 4), results in the densification of the lattice and may explain its formation within a narrow size ratio range as such lattice was not observed with 19.8 and 15.6 nm Fe3O4 NCs.

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.

The usage of 15.2 nm NaGdF4 NCs as spherical building blocks in coassembly with 5.3 nm CsPbBr3 nanocubes (γ = 0.344) results in the formation of NaCl-, AlB2-, and AB2-type SLs with orientationally aligned perovskite nanocubes (Figure a–l), analogously to the case of Fe3O4 spheres. We also observed the formation of b-ABO3-type SL at a high cube-to-sphere particle number ratio in the solution (Figure m,n). Interestingly, as evident from distinct arcs in wide-angle ED, a high degree of orientational ordering of A-site NCs was observed in all these structures, especially in AlB2- and AB2-types featuring hexagonal motifs, further pointing to the hexagonal faceting of NaGdF4 NCs. Specifically, in NaCl-type SL, the (100) lattice planes tend to align normally to the in-plane ⟨110⟩SL. At γ < 0.414, NaCl-type SL is defined by the fcc sublattice of A-particles with cubes rattling in the voids and neighboring NaGdF4 NCs prefer to interact through the surfaces faceted by (100) and (001) planes. Interestingly, at γ > 0.414 (see Figure a,b for γ = 0.439), when A-particles contact O-cubes, the preferred orientation of NaGdF4 NCs is different, they orient faceted surfaces toward cube facets, as manifested by a higher intensity of (100) and (002) wide-angle ED reflections along ⟨100⟩SL. In AlB2-type SL, NaGdF4 NCs within one hexagonal layer contact each other predominantly through the surfaces terminated by (100) planes and contact A-particles from other layers by (001) terminated surfaces, as is evident from six sharp (100) diffraction spots measured from [001]SL-oriented domain and from the sets of (100) and (002) narrow arcs originating along [010]SL and [001]SL directions, respectively, measured from [120]SL-oriented domain (Figure f,h). The wide-angle ED pattern measured from [001]SL-oriented AB2-type domain (Figure j) consists of two sets of the NaGdF4 reflections present in the pattern of [120]SL-oriented AlB2-type domain (Figure h) rotated by 90°, completely in agreement with the proposed AB2 structure in Figures d and 9o. The formation of b-ABO3-type SL can benefit from the patchiness of NaGdF4 NCs,[65] as in this structure, which at γ < 0.414 is governed by contacts between A-particles in scp, NaGdF4 NCs orient their surfaces faceted by (100) and (001) planes along [100]SL and [110]SL in-plane directions.

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.

Coassembly of CsPbBr3 Cubes with Truncated Cuboids

We then studied the assembly behavior of the system comprising CsPbBr3 cubes and truncated cuboid PbS NCs. Intriguingly, truncated cubes can behave similarly to spheres and occupy A-sites in binary ABO3- and NaCl-type SLs, albeit losing orientational freedom. The b-ABO3-type SLs form from the mixtures of 8.6 nm CsPbBr3 nanocubes with 10.7–11.7 nm truncated cubic PbS NCs (Figure ). The corresponding size ratios (γ = 0.72–0.78) are much higher compared to the systems with spherical NCs as an A-component wherein b-ABO3-type SL forms up to γ = 0.54. EDX-STEM maps confirm that PbS NCs occupy only A-sites. Eight (100) and (110) maxima which appear in the directions normal to ⟨100⟩SL and ⟨110⟩SL together with eight (111) maxima with a splitting angle of 19.5° in wide-angle ED pattern indicate the presence of B- and O-positioned CsPbBr3 cubes with the same orientations as in the b-ABO3-type SLs comprising spheres on A-sites. Moreover, as can be seen from TEM image and wide-angle ED analysis, namely the higher intensity of the reflections “2” and “3” which originate mainly from strongly diffracting PbS NCs compared to the intensity of the reflections “1” and “4” which are produced only by CsPbBr3 NCs, the orientation of PbS NCs is not random and matches the orientation of O-site CsPbBr3 nanocubes residing on the unit cell faces parallel to the substrate. Such PbS orientation implies contacts between PbS vertices and faces of the other O-site cubes residing on perpendicular to the substrate facets of ABO3 lattice (see insets in Figure a,d), making the truncated shape of larger cubes beneficial for the formation of b-ABO3 structure. For example, such a structure could not be obtained from the binary mixtures of sharp cubic CsPbBr3 NCs of two sizes.

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).

At lower CsPbBr3 loading, the dominant product is NaCl-type SL which is characterized by the alignment of ⟨100⟩ directions of both CsPbBr3 and PbS NCs coinciding with ⟨100⟩SL, as is evident from ED. Figure a–c shows TEM and HAADF-STEM images of binary domains with gradually increasing thickness, in agreement with the vanishing difference in intensities of neighboring SL site projections of NaCl-type SL. A much higher wide-angle ED intensity of (200) and (220) peaks compared to that of (100) and (110) results from stronger scattering on PbS lattice planes, which contribute only to the former set of reflections and do not to the latter due to higher Fm3̅m symmetry of the PbS lattice; furthermore, (200) and (220) reflections from PbS and CsPbBr3 add up due to similar lattice constants (Figure g and Figure S11).

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).

The 8.6 nm CsPbBr3 cubes with 10.7 nm PbS truncated cubes also form a CuAu-type SL (Figure a–f). Typically observed is the [101]SL orientation (Figure a). The site occupancies are confirmed by recording HAADF-STEM images of [101]SL-oriented domains at 0° and 45° tilting angles and comparing them with the modeled CuAu projections (Figure d,e). Complex wide-angle ED pattern (Figure b), contrary to b-ABO3- and NaCl-type SLs, reveals several different orientations of PbS cuboids that reside on equivalent lattice sites. Similar orientational behavior of PbS NCs is observed in AlB2-type SL assembled from 5.3 nm CsPbBr3 NCs (Figure g–i). The [010]SL and [001]SL orientations that are common to AlB2-type SLs from all-sphere systems were observed (Figure g), while the dominant one was [120]SL. In this lattice, the majority of PbS NCs are aligned with [110] along [120]SL and [100] along [010]SL; however, several distinct peaks remain undefined. Weak CsPbBr3 (110) arcs indicate that perovskite cubes orient one edge along [010]SL, yet the intense (111) reflections from PbS NCs hinder the determination of CsPbBr3 (111) peaks, and, consequently, the conclusion whether cube orientation is the same as in the AlB2-type SL with spherical NCs on the A-site.

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).

Coassembly of CsPbBr3 Cubes with Thick Nanodisks

Combining 8.6 nm perovskite nanocubes with larger NaGdF4 disks (31.5 nm in diameter and 18.5 nm in thickness) resulted in the formation of an SL structure featuring the periodic clustering of two CsPbBr3 NCs, which we interpret as a CaC2-like SL (Figure ), albeit with an orthogonal unit cell metric due to anisotropic shape of the NaGdF4 NCs. SEM images of the surface of SL domains (Figure d,e) show the occupancy of one lattice site by pairs of cubes with face-to-face alignment. Within one layer, cubes are surrounded by four vertically oriented disks, two of which approach cubes by flat faces and the other two by their rims. Nanodisks from the next layer assemble on top of cubes from the previous layer, emulating the CaC2-like packing. Such ordering is in agreement with the contrast observed in TEM of the monolayer domain (Figure S12) and TEM and HAADF-STEM image of multilayer (Figure a,b) and was unambiguously confirmed by electron tomography reconstruction of ordered SL domains (see Supplementary Video 2). Four narrow arcs from (100) and (110) CsPbBr3 lattice planes in the wide-angle ED reveal the orientation of perovskite cubes, pointing their faces along three lattice vectors (Figure c). However, the more pronounced (100) peak along the shortest lattice vector may indicate some tilt of the cubes around this direction.

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.

Multicomponent SLs Comprising FAPbBr3 Nanocubes

Apart from cuboid CsPbBr3 NCs, also hybrid organic–inorganic perovskite NCs, namely formamidinium lead bromide (FAPbBr3) NCs can serve as versatile building blocks for NC SLs. For example, 9 nm FAPbBr3 cubes with larger spherical 15.1–19.5 nm NaGdF4 NCs form b-ABO3-, AlB2-, and AB2-type structures (Figure a–c). The 5.7 nm FAPbBr3 nanocubes, in analogy to 5.3 nm CsPbBr3 NCs,[58,59] form the NaCl-type SL with 15.1 nm NaGdF4 spheres (Figure d) and columnar AB-type or lamellar (which is the dominant product) SLs with 12.5 nm LaF3 nanodisks (Figure e–g).

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.

Self-assembly of Perovskite NCs on Liquid Subphase

Thus, far, the presented SLs were obtained by casting the small volume of the mixture of NCs (ca. 28–35 μL in toluene) over the substrates located in the tilted vial. This simple approach allows for facile screening of the SL formation yet has its drawbacks too. For instance, the range of suitable substrates is rather limited to hydrophobic surfaces. The obtained films usually are characterized by cracks between SL domains that reduce surface coverage. Moreover, adhesion of the SL domain to the substrate, while it still contains solvent, may result in additional crack formation within the domain.[20] Drying-mediated assembly on the surface of an immiscible liquid, usually a polar solvent such as ethylene glycols and acetonitrile, used as support was introduced to overcome these issues, allows for obtaining centimeter-scale SL membranes transferable to the arbitrary substrate, enabling integration of thin-film SLs into devices.[9] This method is, however, difficult to extend to perovskite NCs as even a small but finite solubility in the subphase polar solvent compromises their structural integrity.

After the extensive screening of possible alternatives, we find that glyceryl triacetate is both immiscible with nonpolar solvents such as toluene and hydrocarbons and also does not disperse or chemically harm perovskite NCs and can be utilized as a support in the liquid–air interfacial assembly (see Figure a). We also note that fluorinated solvents, such as FC-40, satisfy the aforementioned requirements, but the nonpolar solvents have a low tendency to spread into a needed thin liquid layer on this fluorinated subphase due to limited wettability. Noteworthy, perfluorodecalin featuring partial miscibility with hexane was successfully used as a substrate for obtaining three-dimensional nearly isotropic perovskite SLs.[54] The self-assembly on glyceryl triacetate occurs within several minutes to several hours depending upon solvent evaporation rate (hexane, octane, decane, or dodecane). Figure b–d shows an extended monolayer of CsPbBr3 NCs assembled on the surface of glyceryl triacetate from the solution of NCs in octane. Mixtures of NCs yield ordered binary mono- and multilayers with different structures depending on the concentration, particle number, and size ratios (Figure e–g).

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.

Self-Assembly of Binary Supraparticles Comprising Perovskite NCs

Microemulsion-templated self-assembly is another method enabling the control over the superstructure dimensionality and allows for the formation of three-dimensional supraparticles upon the assembly in spherical confinement of the “oil” droplet (colloid) stabilized in an immiscible solvent with the aid of a surfactant.[66,67] Potentially, such ordered multicomponent supraparticles can serve as building blocks for mesoscale materials with hierarchical order, wherein the properties could be defined by constituent NCs, their packing within the supraparticles, and finally by the ordering of supraparticles themselves. Furthermore, dispersed individual supraparticles can be, in principle, manipulated and deposited on-demand into desired locations within photonic and other structures. Colloidal spheres of mono- and binary SLs were reported to form from the emulsions of nonpolar solvents in water.[12,68,69] Recently, a carrier solvent–surfactant pair suitable for dispersing perovskite NC colloidal droplets (in toluene) was developed, namely, fluorinated solvents FC-40 or HFE-750 and fluorinated surfactant 008-FS, yielding single-component perovskite supraparticles.[70] Here, we extend the method to binary SLs with perovskite NCs (Figure ). Supraparticles with b-ABO3-type structures can be obtained from the emulsions of 8.6 nm CsPbBr3 and 18.6 nm NaGdF4 NCs (Figure b). Smaller domains appear to be single crystalline, albeit, as revealed by electron tomography reconstruction[71] (see Supplementary Video 3), they may possess structural defects such as nanocube vacancies. The growth inside larger droplets leads to 500–1500 nm supraparticles and is characterized by several nucleation sites resulting in polycrystalline SLs[72] (see SEM images in Figure b). Perovskite cubes with thick NaGdF4 disks form supraparticles with the ordering analogous to the CaC2-like structure (Figure c) presented earlier (Figure ).

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.

Collective Optical Properties of b-ABO3 and AlB2-type SLs

An exceptional emissivity of lead halide perovskite NCs motivates the exploration of their properties at both single-particle and ensemble levels. Here, we focus on the optical properties where, already on the single-NC level, perovskite NCs are standing out because of their exceptionally fast radiative rates and high oscillator strength[73] and long exciton coherence.[45,74] Scalable self-assembly from colloids makes for an attractive path to the controlled aggregate states of these bright emitters. The relationship between the periodic mesostructure and emerging collective luminescent characteristics can then be delineated and rationalized. Collective PL properties had been observed in our earlier work on monocomponent CsPbBr3 NC SLs[53] and binary ABO3-type SLs (CsPbBr3 cubes + NaGdF4 spheres),[58] studied at cryogenic temperatures. Already with cw-excitation, coupling between perovskite NCs is apparent from the sharp PL band, red-shifted with respect to the excitonic PL of uncoupled NCs. Furthermore, for the same samples, pulsed excitation with higher fluencies gives rise to superradiant emission, specifically superfluorescence. Superfluorescence emerges when coherence is established over a number of excited emitters via a common radiation field, forming a giant dipole. This then manifests itself as short (subnanosecond) and intense (proportional to the squared number of coupled emitters) bursts of light.

Herein, we survey the behavior of the red-shifted PL band, as well as concomitant absorption band, from the coupled NCs in relation to the lattice structure and NC size and composition. Such energetically shifted emission and absorption bands are well-known for molecular aggregates, where the coherent coupling in J-/H-aggregates can lead to super/subradiant emission.[75] Hence, we interpret the emergence of this additional emission band next to the excitonic PL band as emission that originates from coupled NC that is induced by the NC assembly into ordered SLs. The energy splitting between these bands may be viewed as a signature of the coupling strength. In Figure a, we show the emission spectra of two b-ABO3 SLs with 8.6 nm CsPbBr3 nanocubes and iron oxide NCs of different sizes. As the A-sphere (Fe3O4) size increases from 14.5 to 19.5 nm, so does also the lattice parameter and hence the B–O sites distance (from 10.2 to 11.8 nm), as seen experimentally by TEM and GISAXS. The PL peak energy splitting between uncoupled NCs and the coupled NCs decreases from 54 ± 7 meV to 37 ± 5 meV (Figure a). In b-ABO3-type SLs, NCs are in very close proximity (the distance between inorganic cores of perovskite NCs is below 1.4 nm), potentially allowing a wave function tunneling. Contrary to the long-range dipole–dipole coupling, which exhibits a characteristic 1/D6 scaling of the coupling strength as a function of the distance D between the dipoles, Dexter-like wave function tunneling is expected to exhibit exponential behavior. The exact determination of the underlying physical mechanism responsible for the NC coupling remains to be further explored; in particular, whether B–O or O–O sites couple by the short-range wave function overlap or whether there exists longer-range B–B (a unit cell apart) dipolar coupling or similar.

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.

In molecular aggregates, the coupling between the constituent molecules and, therefore, the aggregate emission band can exhibit peculiar temperature trends.[75] In order to shed light on the role of such phonon-related processes within the NC aggregates, temperature-dependent measurements were carried out on AlB2 SLs formed by 5.3 nm CsPbBr3 NCs and 12.5 nm iron oxide NCs. We chose this SL structure given the large energetic splitting (ca. 140 meV) observed for this SL type. Although the geometry of the perovskite NC sublattice and crystallographic alignment of NCs is vastly different than in b-ABO3 SLs, thus precluding a trustful comparison, the enhanced red-shift could be assigned to the shorter NC–NC distance (ca. 9.5 nm) and higher quantum confinement obtained with 5.3 nm CsPbBr3 NCs. Figure a shows typical PL spectra at low (6 K) and elevated (100 K) temperatures, whereas complete temperature evolution is shown in Figure b. While the emission band of the uncoupled NCs (near 2.50 eV) shifts only slightly to blue, the emission from the coupled NCs shifts more, reducing the energetic splitting and decreasing in relative intensity while broadening. Spectral substructure of the coupled PL band is occasionally seen (inset of Figure a), which we attribute to several distinct aggregate domains being present within the excitation beam spot of ca. 2 μm2. We note that while a large fraction of studied SLs display the red-shifted emission from coupled NCs, its appearance still varies from sample to sample, probably due to the very short-range nature of the coupling, being it either wave function tunneling or partial necking of the NCs.

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).

The ratio between the coupled (aggregate) and the uncoupled (nonaggregate) NC emission is plotted in Figure c, along with an Arrhenius fit, returning activation energy of about 14 meV, close to the LO-phonon energy in CsPbBr3 NCs (17 meV).[76,77] This suggests that a phonon-driven mechanism similar to that in molecular aggregates reduces the effective number of coupled emitters N with temperature rise. This notion is supported by rather linear correlation obtained when plotting the splitting ΔE between the coupled and the uncoupled emission bands vs the square root of the peak area of the coupled emission (using the temperature-dependent data), which represents the number of coupled emitters (ΔE ∝ √N, Figure d). This dependency and the emission of coupled NCs being far from the expected bulk emission (ca. 2.3 eV, 535–540 nm) as well as a very strong quenching of the red aggregate band already at intermediate temperatures would hardly be reconcilable with an alternative assumption that the red-shifted emission peak could originate from the bulk material forming during the aggregation process.[78] The latter would imply an order of magnitude reduction of bulk emission quantum yield just within this temperature range.

Further evidence for red-shifted PL band originating from coupled NCs is found in the absorption spectra, presented here for b-ABO3-type SLs (8.8 nm CsPbBr3 + NaGdF4 NCs, Figure ). These SLs exhibit two emission bands with a relative energetic splitting (ΔE) scaling with the NC-to-NC distances: on average, 45 and 37 meV for 15.1 and 18.2 nm NaGdF4 NCs, respectively (Figure , top and middle panels). The red-shifted band is also resolved in absorption, similar to our earlier studies on single-component SLs.[53] Similar to the PL behavior, the relative energetic splitting scales with the lattice parameter of the SL. The temperature behavior is analogous too; an additional absorption band vanishes when reaching 200 K (Figure ), being strong evidence that rules out the hypothesis attributing the red-shifted PL band to bulk inclusions.[78] In particular, while a drop of the PL intensity from the bulk inclusions upon heating could be rationalized by the rapidly decaying PL quantum yield, the absorbance must persist.

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).

Conclusions

In summary, we have presented a full survey of multicomponent SLs comprising sharp, sub-10 nm cubic perovskite NCs, obtained thus far in our experiments by combining them with spherical, truncated cubic, and disk-shaped NCs. Three SL structure types are of the kind commonly reported for binary mixtures of spherical NCs (NaCl, AlB2, and CuAu types). Three other binary structures (perovskite ABO3, AB2, ABO6) are related to the cubic shape of perovskite NC building blocks. AB2 can be viewed as derived from AlB2 by slipping each fourth (100)SL in an [011]SL direction. ABO6 can be conceived as the ABO3 lattice, wherein each O-site is occupied by two 5.3 nm CsPbBr3 cubes. When an anisotropic NC counter building block is utilized, namely, thick NaGdF4 nanodisks (18.5 nm thick, 31.5 nm in diameter), a CaC2-like lattice forms, wherein the 8.6 nm cubes occupy the “C2-site”, and the anisotropy of disks reduces tetragonal symmetry of the unit cell into orthogonal. In all studied SLs, cubic NCs are orientationally locked. We also report a substrate-less growth of thin-film SLs by drying colloids atop of an immiscible liquid (glyceryl triacetate) or of SL supraparticles with the aid of emulsion. Low-temperature PL and absorption spectra attest emergence of collective states in these highly dense aggregates of highly luminescent NCs.

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 25 mL flask, dried under vacuum for 20 min at 100 °C, and then heated under N2 to 120 °C until all the Cs2CO3 reacted with OA.

Synthesis of CsPbBr3 NCs

The 8.6 nm NCs were synthesized following the method reported in ref (62). In a 25 mL three-neck flask, PbBr2 (55 mg, ABCR, 98%) was degassed three times, suspended in 5 mL of ODE, and degassed three times again at room temperature. The suspension was quickly heated to 180 °C, when the temperature reached 120 °C, 0.5 mL of OA and oleylamine (0.5 mL, OLA, Strem, 97%, distilled) were 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 12,100 rpm (equivalent to 20,130 relative centrifugal force) 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 10,000 rpm for 3 min, and the precipitate was discarded. Then, OLA/OA ligands were exchanged by DDAB treatment. 0.3 mL 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 12,100 rpm for 3 min and redispersing in 0.6 mL of toluene. Synthesis of 5.3 nm CsPbBr3 NCs was adopted from ref (61) followed by DDAB treatment. The concentration of CsPbBr3 NCs was calculated from the optical absorption at 335 nm using the reported molar extinction coefficient.[79] The concentration of other NCs was determined gravimetrically, accounting for capping ligands with the grafting densities stated in Supplementary Note 2.

Synthesis of NaGdF4 NCs by Thermal Decomposition of Gadolinium Trifluoroacetate[31]

Gadolinium trifluoroacetate (147 mg, 0.267 mmol), NaF (16.1–22.4 mg, 0.383–0.533 mmol, lower loading resulted in larger NCs size, Merk, 99.99%), 4 mL of OA, and 4 mL of ODE were degassed in a three-neck flask at 125 °C for 70 min. Then the solution was heated to 312 °C at 15 °C/min under nitrogen and kept at this temperature for 75 min. The reaction mixture was cooled to room temperature, and 36 mL of ethanol (Merck, 99.8%) was added to destabilize the colloidal solution. The NCs were precipitated by centrifugation at 4000 rpm for 3 min and washed three additional times with hexane (along with 25 μL OA) and ethanol (1 to 1.5 by volume). After purification, NCs were stored in 2 mL of hexane. Gadolinium trifluoroacetate was synthesized by reaction of Gd2O3 (2.159 g, 6 mmol, Sigma-Aldrich, 99.9%) with trifluoroacetic acid (7.4 mL, 95 mmol, Sigma-Aldrich, 99%) and 12.4 mL of water under reflux (93 °C) for 1 h. The white product was isolated by evaporation of the unreacted acid and water under vacuum at 60 °C and dried overnight under vacuum.

For the synthesis of NaGdF4 disks, gadolinium trifluoroacetate (221 mg, 0.4 mmol), NaF (29.5 mg, 0.7 mmol), 6 mL of OA, and 6 mL of ODE were degassed in a three-neck flask at 125 °C for 90 min. Then the solution was heated to 312 °C at 15 °C/min under nitrogen and kept at this temperature for 83 min. The reaction mixture was cooled to room temperature, then 2 mL of hexane and 36 mL of ethanol were added to destabilize the colloidal solution. The NCs were precipitated by centrifugation at 5000 rpm for 2 min and washed additionally twice with hexane (along with 40 μL of OA) and ethanol (1:2.5 by volume). After purification, NCs were stored in 2 mL of toluene.

Synthesis of Truncated Cubic PbS NCs[80]

For a synthesis of 10.7 nm PbS NCs, PbO (278.8 mg, 1.25 mmol, Aldrich, 99%), OA (3.125 mL, 9.88 mmol), and 6.25 mL of ODE were degassed in a three-neck flask for 30 min at room temperature and 30 min at 100 °C. Then the solution was flushed with nitrogen and heated to 200 °C. At this temperature, sulfur (40 mg, 1.25 mmol, Fluka, 99.5%) dissolved in OLA (1.25 mL 3.8 mmol) was swiftly injected. The reaction mixture was cooled to room temperature with a water bath after 5 min of stirring. The NCs were washed four times with hexane (along with 25 μL OA) and ethanol (3:1 by volume) and stored in hexane. For the synthesis of 11.7 nm PbS NCs, the mixture of 2.2 mL of OA with 7.2 mL of ODE was used as a solvent, and the reaction temperature was increased to 205 °C.

Synthesis of Fe3O4 NCs by Thermal Decomposition of Iron Oleate[63]

For the synthesis of iron oleate complex, FeCl3 (1.658 g, 10 mmol, Alfa-Aesar, 98%) and sodium oleate (9.125 g, 30 mmol, TCI, 97%) were dissolved in a mixture of 35 mL of hexane, 20 mL of ethanol, and 15 mL of distilled water. After stirring under nitrogen at 65 °C for 5 h, the upper organic layer was separated and washed five times with warm water, followed by centrifugation and isolation in a separatory funnel. The waxy solid product was isolated using a rotary evaporator and dissolved in ODE to form 0.4 mol/kg solution. In a typical synthesis of 15.6 nm Fe3O4 NCs, iron oleate complex in ODE (5 mL), OA (0.8 mL, 2.53 mmol), and 5 mL of ODE were loaded into a three-neck flask and vacuum dried at 110 °C for 90 min. The reaction mixture was then heated under nitrogen from 200 to 312 °C with a constant heating rate of 2 °C/min and maintained at this temperature for 30 min after the initiation took place. The solution was cooled to room temperature and washed with 3 mL of hexane and 12 mL of acetone, followed by centrifugation at 8000 rpm for 3 min. The precipitate was dissolved in 3 mL of hexane with 25 μL of OA. After two additional rounds of purification with hexane and acetone (2:1 by volume), the NCs were dispersed in 3 mL hexane. The size of NCs was controlled by varying the concentration of OA (higher for larger NCs) and reaction temperature (higher for larger NCs).

Synthesis of 12.5 nm LaF3 Nanodisks by Thermal Decomposition of Lanthanum Trifluoroacetate[37]

Lanthanum trifluoroacetate (192 mg), 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 300 °C at 15 °C/min under nitrogen and kept at this temperature for 70 min. The reaction mixture was cooled to room temperature, and 3 mL of hexane along with ethanol (30 mL) was added to destabilize the colloidal solution. The NCs were precipitated by centrifugation at 4000 rpm for 2 min and washed two additional times with hexane (along with 10–30 μL of OA) and ethanol (1:1 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 4000 rpm for 2 min. Lanthanum trifluoroacetate was synthesized by reaction of La2O3 (3.24 g, Sigma-Aldrich, 99.999%) with trifluoroacetic acid (16 mL) and 16 mL of water under reflux (93 °C) for 1 h. The white product was isolated by evaporation of the unreacted acid and water under vacuum at 60 °C and dried overnight under vacuum.

Preparation of Multicomponent SLs

Self-assembly of NCs was carried out using a drying-mediated method on carbon-coated TEM grids (carbon type B, Ted Pella, Formvar protective layer was removed by immersing the grid in toluene for 10 s), HF-treated silicon, and silicon nitride TEM windows (Agar Scientific, Norcada). A mixture of NCs in anhydrous toluene had an overall particle concentration of 0.5–2 μM and NC number ratios in the range of 0.5–20. 28–35 μL of NC mixture was transferred into a tilted 2 mL glass vial with a substrate inside. The solvent was evaporated under 0.5 atm pressure at room temperature. For example, binary ABO3-, AlB2-, and NaCl-type SLs were obtained with high yields on TEM grids upon slow drying of the solutions prepared by mixing 15.2 nm NaGdF4 NCs (29 mg/mL, 1.8, 2.0, and 2.4 μL, respectively) and 5.3 nm CsPbBr3 NCs (7.5 μM; 4.7, 2.6, and 1.7 μL, respectively) with anhydrous toluene (25 μL); binary ABO3-type SL, 11.7 nm PbS NCs (1.8 μM, 3 μL), 8.6 nm CsPbBr3 NCs (5.0 μM, 7 μL) and 25 μL of toluene; binary NaCl-type SL, 11.7 nm PbS NCs (1.8 μM, 2.8 μL), 8.6 nm CsPbBr3 NCs (3.9 μM, 3 μL) and 25 μL of toluene.

For the assembly of single-component CsPbBr3 NCs film at the liquid–air interface, a 1 × 1 cm2 Teflon well was filled with 0.5 mL of glyceryl triacetate (Sigma-Aldrich, 99%), CsPbBr3 NCs in octane (0.4 μM, 20 μL) were dropped onto the surface, and then the well was covered by glass slide and octane slowly evaporated. After drying was completed, the film was transferred to a carbon-coated TEM grid, and the substrate was further dried under vacuum to get rid of the residual subphase. For the assembly of NaCl-type film, the mixture of 8.6 nm CsPbBr3 NCs (4.3 μM, 2.5 μL, in toluene), 19.5 nm Fe3O4 NCs (39 mg/mL, 2.5 μL, in toluene), and 10 μL of decane was dropped onto the surface of glyceryl triacetate in Teflon well following the aforementioned procedure. For the assembly of the AlB2-type film, the mixture of 8.6 nm CsPbBr3 NCs (4.3 μM, 9 μL, in toluene), 19.5 nm Fe3O4 NCs (39 mg/mL, 6 μL, in toluene), and 100 μL of decane was dropped onto the surface of glyceryl triacetate (1.5 mL) in Petri dish (3 cm in diameter), covered by glass slide following the aforementioned procedure.

For the typical microemulsion-templated self-assembly, solution 1 (CsPbBr3 and NaGdF4 NCs in toluene with the total NCs concentration about 5 mg/mL) was added into solution 2 (fluorosurfactant 008-FS in fluorinated solvent FC-40). Then, the resulting suspension was mixed with a vortex mixer or a homogenizer. Emulsified solution was slowly stirred for 24–48 h until the toluene was evaporated. For the assembly of a b-ABO3-type micelle, the mixture of 8.6 nm CsPbBr3 NCs (1.7 μM, 25 μL, in toluene), 18.6 nm NaGdF4 NCs (9 mg/mL, 82 μL, in toluene), and 60 μL of toluene was added to the solution of 5 wt % 008-FS in FC-40 (50 μL, RAN Biotechnologies) and FC-40 (283 μL, abcr) following the aforementioned procedure. For the assembly of an orthorhombic CaC2-like micelle, the mixture of 8.6 nm CsPbBr3 NCs (1.3 μM, 45 μL, in toluene), 31.5 nm NaGdF4 NCs (2 mg/mL, 90 μL, in toluene), and 32 μL of toluene was added to the solution of 5 wt % 008-FS in FC-40 (50 μL) and FC-40 (283 μL) following the aforementioned procedure.

Electron Microscopy Characterization

TEM and HAADF-STEM images as well as ED and small-angle ED patterns were collected with the use of JEOL JEM2200FS microscope operating at 200 kV accelerating voltage. EDX-STEM maps and HAADF-STEM images at different tilt angles were recorded using an FEI Titan Themis microscope operated at 300 kV equipped with a SuperEDX detector, with the aid of a motorized dual-axis tomography holder. Captured TEM and electron diffraction images were compared with the ones simulated in Crystal Maker 10.4.5 and Single Crystal 3.1.5 software, purchased from CrystalMaker Software Ltd. Electron tomography was carried out in HAADF-STEM mode at 300 kV using a small beam semiconvergence angle of 2.5 mrad, to increase the depth of field. Images were recorded over a tilt angle range ± (57–72)° and interval 2–3°. Reconstruction was done using IMOD with a Back Projection algorithm and SIRT-like radial filter.[81] The tomograms were recorded on SLs self-assembled on carbon-coated TEM grids as continuous films or via a microemulsion technique. SEM images were obtained on a FEI Helios 660 operated at 3–7 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.

GISAXS Characterization

GISAXS measurements were performed at the Austrian SAXS beamline of the electron storage ring ELETTRA using a photon energy of 8 keV.[82] The beamline setup was adjusted to a sample to detector distance of 1961.43 mm to result in an accessible horizontal scattering vector q-range of −1.2 nm–1 < qH < 1.8 nm–1 and vertical scattering vector q-range of −0.1 nm–1 < qV < 2.9 nm–1. The X-ray beam was collimated to a spot size at the sample of approximately 200 μm × 200 μm. The images were recorded using the Pilatus 1 M detector (Dectris, Switzerland) with an exposure time of 10 s per image. Reference patterns to calibrate the q-scale were collected of silver-behenate (d-spacings of 5.838 nm). Samples were mounted on a 2-axis goniometer stage with 0.001° angular precision, allowing us to ensure an incidence angle of 0.04° for the measurements (determined by alignment of the specular reflection on the detector). The presented data were corrected for fluctuations of the primary intensity. Data treatment was done using the NIKA2D[83] (geometry correction and calibration) as well as GIXSGUI[84] (lattice indexing) software packages.

Optical Spectroscopy

For the PL measurements, the sample was mounted on an XYZ nanopositioning stage inside an evacuated liquid-helium coldfinger cryostat and cooled to 6 K. Nanocrystals were excited with a fiber-coupled excitation laser at a photon energy of 3.06 eV with pulses of 50 ps duration. A long working-distance, 100×, microscope objective with a numerical aperture of 0.7 was used for both excitation and detection, leading to a Gaussian excitation spot with a 1/e2 diameter of 1.4 μm. The emission was then dispersed in a 750 mm monochromator by a 3000 lines per mm grating and detected with a back-illuminated, cooled EMCCD camera.

For absorption and PL experiments reported in Figure , a custom-made setup, enabling both experiments to probe the same sample area, was used. The samples were placed on the coldfinger of a Janis CCS-150 closed-cycle optical refrigerator, allowing temperature variation within the 10–300 K range. Steady-state PL was excited by a 405 nm diode laser, focused onto a ∼2 μm diameter spot, via a Mitutoyo long working distance objective with 50× magnification and 0.55 numerical aperture. The emission was detected via the same objective, using a long-pass filter to block the excitation laser, while spectrally analyzed by a 0.75 m Acton750i Princeton spectrometer equipped with a 1024 × 256 pixels PIXIS charge-coupled device (CCD) camera. For absorption measurements, a tungsten-halogen white light source was coupled into a 600 μm core multimode fiber, and the output beam was focused onto the sample via the same microscope objective described above. The transmitted beam was coaxially collected and analyzed via the same combination of spectrometer and CCD described above.

Optical Properties of CsPbBr3 NCs in Toluene

Optical absorption spectra were measured with Jasco V770 spectrometer in transmission mode. 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.