Gold-Cage Perovskites: A Three-Dimensional AuIII-X Framework Encasing Isolated MX63- Octahedra (MIII = In, Sb, Bi; X = Cl-, Br-, I-).

The Cs8AuIII4MIIIX23 (M = In3+, Sb3+, Bi3+; X = Cl-, Br-, I-) perovskites are composed of corner-sharing Au-X octahedra that trace the edges of a cube containing an isolated M-X octahedron at its body center. This structure, unique within the halide perovskite family, may be derived from the doubled cubic perovskite unit cell by removing the metals at the cube faces. To our knowledge, these are the only halide perovskites where the octahedral sites do not bear an average 2+ charge. Charge compensation in these materials requires a stoichiometric halide vacancy, which is disordered around the Au atom at the unit-cell corner and orders when the crystallization is slowed. Using X-ray crystallography, X-ray absorption spectroscopy, and pair distribution function analysis, we elucidate the structure of this unusual perovskite. Metal-site alloying produces further intricacies in this structure, which our model explains. Compared to other halide perovskites, this class of materials shows unusually low absorption onset energies ranging between ca. 1.0 and 2.4 eV. Partial reduction of Au3+ to Au+ affords an intervalence charge-transfer band, which redshifts the absorption onset of Cs8Au4InCl23 from 2.4 to 1.5 eV. With connected Au-X octahedra and isolated M-X octahedra, this structure type combines zero- and three-dimensional metal-halide sublattices in a single material and stands out among halide perovskites for its ordering of homovalent metals, ordering of halide vacancies, and incorporation of purely trivalent metals at the octahedral sites.

Binary Assembly of PbS and Au Nanocrystals: Patchy PbS Surface Ligand Coverage Stabilizes the CuAu Superlattice.

Self-assembly of two sizes of nearly spherical colloidal nanocrystals (NCs) capped with hydrocarbon surface ligands has been shown to produce more than 20 distinct phases of binary nanocrystal superlattices (BNSLs). Such structural diversity, in striking contrast to binary systems of micron-sized colloidal beads, cannot be rationalized by models assuming entropy-driven crystallization of simple spheres. In this work, we show that the PbS ligand binding equilibrium controls the relative stability of two closely related BNSL structures featuring alternating layers of PbS and Au NCs. At an intermediate size ratio, as-prepared PbS NCs assemble with Au NCs into CuAu BNSLs featuring orientational coherence of PbS NCs across the lattice. Measurement of interparticle separations within CuAu and modeling of the structure reveal that PbS inorganic cores are nearly in contact through (100) NC surfaces in the square tiling of the CuAu basal plane. On the other hand, AlB2 BNSLs with PbS NCs packed in random orientations were found to be the dominant self-assembly product when the same binary NC solution was evaporated in the presence of added oleic acid (OAH). Solution nuclear magnetic resonance titration experiments confirmed that added OAH binds to PbS NCs, implicating ligand surface coverage as an important factor influencing the relative stability of CuAu and AlB2 BNSLs at the experimental size ratio. From these results, we conclude that as-prepared PbS NCs feature sparsely covered (100) surfaces and thus effectively flat patches along NC x-, y-, and z-directions. Such anisotropic PbS-PbS interactions can be efficiently screened by restoring effectively spherical NC shape via addition of OAH to the binary assembly solution. Our findings underscore the important contribution of NC surfaces to superlattice phase stability and offer a strategy for targeted BNSL assembly.

Systematic Mapping of Binary Nanocrystal Superlattices: The Role of Topology in Phase Selection.

The self-assembly of two sizes of spherical nanocrystals has revealed a surprisingly diverse library of structures. To date, at least 15 distinct binary nanocrystal superlattice (BNSL) structures have been identified. The stability of these binary phases cannot be fully explained using the traditional conceptual framework treating the assembly process as entropy-driven crystallization of rigid spherical particles. Such deviation from hard sphere behavior may be explained by the soft and deformable layer of ligands that envelops the nanocrystals, which contributes significantly to the overall size and shape of assembling particles. In this work, we describe a set of experiments designed to elucidate the role of the ligand corona in shaping the thermodynamics and kinetics of BNSL assembly. Using hydrocarbon-capped Au and PbS nanocrystals as a model binary system, we systematically tuned the core radius ( R) and ligand chain length ( L) of particles and subsequently assembled them into binary superlattices. The resulting database of binary structures enabled a detailed analysis of the role of effective nanocrystal size ratio, as well as softness expressed as L/ R, in directing the assembly of binary structures. This catalog of superlattices allowed us to not only study the frequency of different phases but to also systematically measure the geometric parameters of the BNSLs. This analysis allowed us to evaluate new theoretical models treating the cocrystallization of deformable spheres and to formulate new hypotheses about the factors affecting the nucleation and growth of the binary superlattices. Among other insights, our results suggest that the relative abundance of the binary phases observed may be explained not only by considerations of thermodynamic stability, but also by a postulated preordering of the binary fluid into local structures with icosahedral or polytetrahedral symmetry prior to nucleation.

Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials.

Chemical methods developed over the past two decades enable preparation of colloidal nanocrystals with uniform size and shape. These Brownian objects readily order into superlattices. Recently, the range of accessible inorganic cores and tunable surface chemistries dramatically increased, expanding the set of nanocrystal arrangements experimentally attainable. In this review, we discuss efforts to create next-generation materials via bottom-up organization of nanocrystals with preprogrammed functionality and self-assembly instructions. This process is often driven by both interparticle interactions and the influence of the assembly environment. The introduction provides the reader with a practical overview of nanocrystal synthesis, self-assembly, and superlattice characterization. We then summarize the theory of nanocrystal interactions and examine fundamental principles governing nanocrystal self-assembly from hard and soft particle perspectives borrowed from the comparatively established fields of micrometer colloids and block copolymer assembly. We outline the extensive catalog of superlattices prepared to date using hydrocarbon-capped nanocrystals with spherical, polyhedral, rod, plate, and branched inorganic core shapes, as well as those obtained by mixing combinations thereof. We also provide an overview of structural defects in nanocrystal superlattices. We then explore the unique possibilities offered by leveraging nontraditional surface chemistries and assembly environments to control superlattice structure and produce nonbulk assemblies. We end with a discussion of the unique optical, magnetic, electronic, and catalytic properties of ordered nanocrystal superlattices, and the coming advances required to make use of this new class of solids.

The surface science of nanocrystals.

All nanomaterials share a common feature of large surface-to-volume ratio, making their surfaces the dominant player in many physical and chemical processes. Surface ligands - molecules that bind to the surface - are an essential component of nanomaterial synthesis, processing and application. Understanding the structure and properties of nanoscale interfaces requires an intricate mix of concepts and techniques borrowed from surface science and coordination chemistry. Our Review elaborates these connections and discusses the bonding, electronic structure and chemical transformations at nanomaterial surfaces. We specifically focus on the role of surface ligands in tuning and rationally designing properties of functional nanomaterials. Given their importance for biomedical (imaging, diagnostics and therapeutics) and optoelectronic (light-emitting devices, transistors, solar cells) applications, we end with an assessment of application-targeted surface engineering.

Many-body effects in nanocrystal superlattices: departure from sphere packing explains stability of binary phases.

This work analyzes the role of hydrocarbon ligands in the self-assembly of nanocrystal (NC) superlattices. Typical NCs, composed of an inorganic core of radius R and a layer of capping ligands with length L, can be described as soft spheres with softness parameter L/R. Using particle tracking measurements of transmission electron microscopy images, we find that close-packed NCs, like their hard-sphere counterparts, fill space at approximately 74% density independent of softness. We uncover deformability of the ligand capping layer that leads to variable effective NC size in response to the coordination environment. This effect plays an important role in the packing of particles in binary nanocrystal superlattices (BNSLs). Measurements on BNSLs composed of NCs of varying softness in several coordination geometries indicate that NCs deform to produce dense BNSLs that would otherwise be low-density arrangements if the particles remained spherical. Consequently, rationalizing the mixing of two NC species during BNSL self-assembly need not employ complex energetic interactions. We summarize our analysis in a set of packing rules. These findings contribute to a general understanding of entropic effects during crystallization of deformable objects (e.g., nanoparticles, micelles, globular proteins) that can adapt their shape to the local coordination environment.

Self-assembly of tetrahedral CdSe nanocrystals: effective "patchiness" via anisotropic steric interaction.

Controlling the spontaneous organization of nanoscale objects remains a fundamental challenge of materials design. Here we present the first characterization of self-assembled superlattices (SLs) comprised of tetrahedral nanocrystal (NCs). We observe self-assembly of CdSe nanotetrahedra into an open structure (estimated space-filling fraction φ ≈ 0.59) which has not been anticipated by many recent theoretical studies and simulations of tetrahedron packings. This finding highlights a gap in the understanding of the hierarchy of energy scales acting on colloidal NCs during self-assembly. We propose a strong dependence of ligand-ligand interaction potential on NC surface curvature. This effect favors spatial proximity of vertices in the dense colloidal crystal and may be considered an emergent "patchiness" acting through chemically identical ligand molecules.