Letter pubs.acs.org/NanoLett
An Obtuse Rhombohedral Superlattice Assembled by Pt Nanocubes Ruipeng Li,† Kaifu Bian,‡ Yuxuan Wang,§ Hongwu Xu,∥ Jennifer A. Hollingsworth,⊥ Tobias Hanrath,‡ Jiye Fang,§ and Zhongwu Wang*,† †
Cornell High Energy Synchrotron Source and ‡School of Chemical and Bimolecular Engineering, Cornell University, Ithaca, New York 14853, United States § Department of Chemistry, State University of New York at Binghamton, Binghamton, New York 13902, United States ∥ Earth and Environmental Sciences Division and ⊥Materials Physics and Applications Division: Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States S Supporting Information *
ABSTRACT: We grew large single three-dimensional supercrystals from colloidal Pt nanocubes (NCs) suspended in hexane. A synchrotron-based two circle diffractometer was used to obtain an unprecedented level of detail from full sets of small/wide-angle X-ray scattering (SAXS/WAXS) patterns. Automatic indexing and simulations of X-ray patterns enabled detailed reconstruction of NC translation and shape orientation within the supercrystals from atomic to mesometric levels. The supercrystal has an obtuse rhombohedral (Rh) superlattice with space group R3m and a trigonal cell angle of 106.2°. Individual NCs orient themselves in a manner of atomic Pt[111] parallel to superlattice Rh[111]. We analyzed the superlattice structure in context of three spatial relationships of proximate NCs including face-to-face, edge-toedge, and corner-to-corner configurations. Detailed analysis of supercrystal structure reveals nearly direct corner-to-corner contacts and a tight interlocking NC structure. We employed the correlations between strain and lattice distortion and established the first structural correlating mechanism between five superlattice polymorphs to elucidate the superlattice transformations and associated developing pathways. Together, the experimental and modeling results provide comprehensive structural information toward controlling design and efficient materials-processing for large fabrication of nanobased functional materials with tailored structures and desired properties. KEYWORDS: Pt nanocube, self-assembly, obtuse rhombohedral, superlattice, SAXS and WAXS, supercrystallography
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surface properties to nanocrystal assembly.4,24−26 Remarkably, despite their simple shape, NCs yield a rich and complex phase behavior of self-assembled superlattices. Recent experiments of NC assembly reveal a series of superlattice polymorphs upon changing the assembly environment: (1) fast evaporation of NC-dispersed solutions causes formation of either a simple cubic (SC) or a body-centered-cubic (BCC) superlattice or both in thin film-based NC assembly;26,27 (2) drying-induced compression subjected to thin film develops numerous intermediate superlattices with various magnitudes of lattice distortion;28,29 (3) control of solvent evaporation results in the nucleation and growth of three-dimensional (3D) supercrystals that mostly have a face-center-cubic (FCC) superlattice.30−32 To explore the intrinsic structural correlations with capable reconstruction of transformation pathway, synchrotron-based in situ solution SAXS experiments were conducted, revealing a ligand-induced structural switch between SC and FCC
anocrystal assemblies can retain the size-dependent properties of the individual nanocrystals from which they are built, and they can also manifest enhanced or novel collective properties from near-field coupling.1−5 Understanding and controlling nanocrystal assembly, as well as discovering new superlattice phases, will underpin our ability to control structure−property relations toward creation of useful properties for practical applications in this emerging class of complex nanomaterials.6−15 One “knob” for controlling nanocrystal− superlattice assembly is that of nanocrystal shape. Recent progress and advances in the synthesis of anisotropically shaped nanocrystals provide an opportunity to exploit geometrydependent superlattices with enhanced electronic coupling between parallel surface facets of aligned shaped nanocrystals,4,16−23 which cannot be accessed and realized using only spherical nanocrystal building blocks. A nanocube (NC) with surface termination of six identical crystallographic facets serves as the most basic polyhedral building block 20−22 and provides additional but easily manipulated parameters to investigate and understand the structural response of interplay between geometrical effects and © XXXX American Chemical Society
Received: July 21, 2015 Revised: August 13, 2015
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Nano Letters superlattices.33 To implement the shape-dependent consequence, molecular dynamics and theoretical modeling were recently performed, providing a basic energy landscape of shape-directed superlattice phase diagram.34−37 However, very few experiments have been performed to demonstrate how NCs take advantage of shape-dependent surface properties and interact with environments to develop particular crystallographic orientations in periodically ordered superlattices. Lack of close linkage between experiment and simulation impedes the use of proposed design principles or guiding rules to make reliable prediction and feasible synthesis of nanocrystal superlattices with desired crystallographic symmetry and shape orientation for technological applications. Fundamental knowledge gaps persist in our understanding of the detailed translational and orientational order of NCs in selfassembled superlattices. Currently, two major limitations prevent detailed feasible reconstruction of the superlattice: (1) difficulty of growing large single supercrystals; (2) lack of powerful structure characterization techniques with sufficient in-depth penetrating ability and enough high spatial resolution. In this Letter, we show how we have overcome such technical obstacles to achieve significant scientific progress by (1) developing an efficient protocol to grow submillimeter grains of single supercrystals from NC dispersions in hexane; (2) collecting high-resolution synchrotron-based single supercrystal small/wide-angle X-ray scattering (SAXS/WAXS) patterns using a homemade two-circle diffractometer; (3) implementing a reliable structure refinement approach, which we call “supercrystallography” that allows for accurate determination of translational and orientational orderings of NCs in supercrystal. This approach provides an unprecedented level of detail into the structure of the supercrystal. Upon decoding the obtuse rhombohedral (Rh) superlattice of Pt NC selfassembled supercrystal from atomic to mesometric length scales, we employed the correlations of lattice distortion with developed strain in supercrystal and constructed a primary scheme of various superlattice polymorphs and their structural correlations, which offers decent illustration of the nucleation and growth as well as superlattice transformation of NC supercrystals under various environments. Experimental Section. Synthesis of Pt NCs. Platinum NCs were synthesized using a high-temperature organic solution approach.38 Briefly, 0.020 g of platinum acetylacetonate (0.05 mmol) with 8.0 mL of oleylamine and 2.0 mL of oleic acid (OA) was loaded into a three-neck flask, and the system was heated to 160 °C under an argon flowing stream. Under vigorously stirring, 0.050 g of tungsten hexacarbonyl was subsequently introduced into the solution, and the temperature controlled by digit heating system was then increased to 200 °C. The reaction system was maintained at 200 °C for additional 30 s before the heating mantle was promptly removed. The resultant products were collected by centrifugation after adding a certain amount of absolute ethanol and washing with anhydrous hexane. With two cycles of such treatment, most of the surfactants such as oleylamine were removed, and the final products were dispersed in 5 mL of hexane for additional processing and characterization. Nanocube Assembly. NC supercrystals were grown from Pt NC suspensions of hexane in a glass vial. The vial was sealed properly to maintain a slow solvent evaporation. After complete evaporation of solvents, large grains of NC supercrystals were formed and then preserved in the glass vial.
Electron Microscopy Characterization. Dilute Pt NC suspensions in hexane were drop cast onto a carbon-coated 200 mesh copper grid for transmission electron microscopic (TEM) characterization. TEM images were taken on an FEI Tecnai T12 microscope operated at 120 kV. NC supercrystals were transferred from the vial to a Si wafer for scanning electron microscopic (SEM) characterization. SEM images with variable magnifications were recorded on a LEO 1550 FESEM microscope operated at 5−10 kV. Synchrotron-Based SAXS and WAXS. Both SAXS and WAXS images were collected from NC supercrystals at the B1 station of CHESS, Cornell University.39,40 Incident white Xrays were converted to monochromatic beam at a fixed X-ray energy of 25.514 keV, equivalent to a wavelength of 0.485946 Å. A double circular pinhole aligned tube was used to reduce monochromatic X-rays to a small X-ray beam of 100 μm in diameter. Two powder standards of Ag behenate and CeO2 were used to calibrate the sample-to-detector distances for analysis of SAXS and WAXS data, respectively. One supercrystal was carefully transferred onto a MiTeGen mesh grid, which was then mounted on the two-circle diffractometer. Upon X-ray illumination, both SAXS and WAXS images were collected from the same volume of supercrystal at each of rotated angles. Briefly, the supercrystal was initially aligned with one typical crystallographic orientation parallel to Φ axis. Then, the comprehensive sets of SAXS/WAXS images were collected from supercrystal upon rotation of Φ from 0 to 180° at an angular step of 1°. Results and Discussion. By carefully controlling the solvent evaporation rate, we were able to grow very large three-dimensional single supercrystals. This enabled us to perform unprecedented structural studies to determine not only the overall superlattice structure but also the orientation and relative positioning of the constituent NCs. As effective NC stabilizers in solution and also acting as artificial bonds to tighten NCs together in supercrystals, OA molecules were passivated at surfaces of the synthesized Pt NCs. A typical TEM image (Figure 1a) shows that NCs have an average edge length of 9.5 nm (Figure S1). Figure 1b and c shows that the supercrystals have grain size over 50 μm (Figure 1b and c). High-resolution SEM image and the corresponding fast Fourier transform (FFT) pattern (Figure 1d and inset) reveal the single crystal nature of individual supercrystal grains. To fully reconstruct the structure of NC assembled supercrystal from atomic through molecular and nanometric to mesoscopic scale, we developed a synchrotron-based X-ray scattering approach, called “supercrystallography”, at the B1 station of CHESS. The supercrystal was initially aligned with one typical superlattice orientation of SL[100], SL[110], or SL[11̅0] parallel to the rotation axis of Φ (Figure S2). Consequently, the comprehensive sets of SAXS/WAXS images were collected from the same volume of supercrystal upon rotation of the sample from Φ = 0 to 180° in an angular step of 1°. Adapting to the single crystal indexing procedure widely used in protein crystallography, single supercrystal SAXS images were automatically indexed with positional match to several candidate space groups and then refined into the best matched superlattice symmetry. To confirm the indexed structure, the full sets of SAXS patterns were simulated to compare scattering spots in position with experimentally collected SAXS data sets. Figure 2 and Movie S1 show several sets of collected and simulated SAXS patterns of single supercrystal projected at B
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Figure 2. Typical SAXS patterns collected from one supercrystal upon rotation of (a−d) SL[100] at Φ = 0°, 67°, 130°, and 156° and (e−h) SL[110] at Φ = 0°, 24°, 54°, and 90°. Each panel includes both collected (left) and simulated (right) SAXS images with insets showing the matched crystallographic orientations of rhombohedral superlattice. The angular difference between SL[100] and SL[110] is 30° at Φ = 0°.
Figure 1. Characterization of Pt nanocubes (NCs) and assembled supercrystals: (a) TEM image of individual NCs; (b) optical image of one typical supercrystal grain circled in red and mounted on 25 μm mesh grid; (c and d) SEM images of one typical supercrystal at lower and higher resolutions; (e) experimental setup for “supercrystallography” SAXS/WAXS analysis of single supercrystal structure.
several typical crystallographic orientations upon rotation of the supercrystal along SL[100], SL[110], and SL[11̅0]. Experiments and simulations consistently agree that NC supercrystal has an obtuse Rh superlattice with space group R3̅m. The unit cell parameters are refined as a = b = 19.78 nm, c = 14.26 nm, and γ = 120° in a hexagonal lattice, which can be alternatively represented by an equivalent Rh lattice with a = 12.37 nm and α = 106.2° (Figure S3). For the latter description, we use the Rh cell setting to clearly illustrate the typical 3-fold symmetry as schematically shown in Figure 3b. The primitive obtuse Rh cell consists of 8 NCs situated in corners, which accordingly form six rhombic planes. Three rhombuses share one vortex by their obtuse angle end points so that each Rh cell includes only two vertexes in which all three side angles from one vortex are obtuse (Figure 3a). The connection of the two vertexes forms the 3̅m symmetrical axis of the obtuse Rh cell. Unlike the common acute Rh cell in which the two typical vertexes with intersection of the 3̅m symmetrical axis have all three side angles to be acute (Figure 3b), the obtuse Rh superlattice is observed and fully resolved for the first time among a large variety of NC-assembled supercrystals.25,26,32
Figure 3. Comparison of (a) obtuse and (b) acute rhombohedral (Rh) superlattices, in which the dots represent the positions of nanocubes in superlattice for better visualization. Each panel shows: (top) primitive cells with the 3̅m symmetry, and bottom) net geometries of Rh superlattices showing how the vertexes with the various trigonal angles meet together and form 3-fold symmetric axis. Note: Each Rh includes only two vertexes in which three side angles are identical, but the difference between two typical Rhs is either obtuse or acute for all the three side angles. In net geometry, the mirrored planes in superlattice are marked by the same color.
Simultaneous acquisition of scattering data at wide angles allows for identification of the orientation of NCs within the superlattice sites. In combination with the full sets of WAXS C
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Nano Letters images collected and simulated from the same single supercrystal grain at identically SAXS-controlled conditions, this integrative approach provides rich information toward ultimate determination of orientational ordering of NCs in obtuse Rh superlattice. Figure 4 shows four panels of WAXS images
Figure 5. Structural reconstruction of Pt NC assembled supercrystal at orientations of (a) Φ = 0°, (b) Φ = 146°, and (c) Φ = 56°, in which Xrays are parallel to Pt[111], Pt[110] and Pt[100], respectively. Each panel shows: (top) obtuse Rh superlattice at typical orientation and (bottom) corresponding ordering of NC orientations in the superlattice.
display three types of packing geometries (Figure 6): (1) faceto-face (F−F) configuration along SLRh[100] in which two
Figure 4. Representative WAXS patterns collected upon rotation of SL[100] at (a) Φ = 2°, (b) Φ = 56°, (c) Φ = 110°, and (d) Φ = 146°. In each pattern, the marked spots represent one typical group of scattering spots along the orientation given in inset, which match well with simulations at the same atomic crystallographic orientation. It is noted that additional spots can be seen in patterns, which originate from either small crystallites or large mosaicity of the supercrystal.
collected and indexed from a single supercrystal at several typical orientations of Φ = 2°, 56°, 110°, and 146°. These WAXS images correspond to the X-ray scattering patterns of Pt crystal projected at orientations of Pt[111], Pt[001], Pt[1̅1̅1], and Pt[1̅1̅0], respectively. In conjunction of the cubic structure of Pt with the above-defined atomic orientations of NCs, the four WAXS images can be equivalently obtained upon rotation of supercrystal along Pt[1̅10] from Pt[100] orientation with angular variations of −54.7°, 0°, 54.7° and 90°. With full analysis of collected and simulated X-ray scattering data sets, we can precisely determine the orientational ordering of NCs in obtuse Rh superlattice. Figure 5 summarizes the relationships between NC orientation and Rh superlattice directions: (1) all NCs in supercrystal orient identically; (2) integration of the cube shape symmetry in lattice refinement reduces superlattice symmetry from R3̅m to R3m; (3) the atomic Pt[111] direction of the NC is parallel to SLRh[111]; (4) other low-index atomic planes have a slight degree of misorientation with respect to the high-symmetry superlattice axis. However, taking account of the angular rotation resolution of 1°, the angular mismatch of 1.3° defined between Pt[111] and superlattice SLRh[111] can be reasonably considered as a systematic error. Beyond providing the translational and orientational ordering information on NCs in superlattice, our “supercrystallography” approach is capable to give insights into shape-related structural anisotropy of NCs. In obtuse Rh superlattice, neighboring NCs
Figure 6. NC packing configurations and a series of defined parameters of neighboring NCs in obtuse Rh superlattice: (a) faceto-face, (b) edge-to-edge, and (c) corner-to-corner configurations.
NCs are parallel by Pt{100} facet (Figure 6a and S6); (2) edgeto-edge (E-E) configuration in which two NCs approach in SLRh[110] by edge [i.e., Pt(110)] (Figure 6b and S7); and (3) corner-to-corner (C−C) configuration in which two NCs approach in SLRh[111] by corner [i.e., Pt(111)] (Figure 6c and S8). The first two types of configurations appear in 2D rhombic plane (Figure S6), whereas the third orients along the 3-fold symmetric axis. NCs with face-to-face configurations in SLRh[100] and SLRh[010] directions are slightly different. However, if taking consideration of the angular rotating resolution of 1° in data collection, the defined angular mismatch of 1.3° between SLRh[111] and Pt[111] can be regarded as a systematic error to D
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Figure 7a shows the superlattice developing sequence along with the change of α from 120° to 60°. SC has a simple
be neglected (Figures 6a and S6). Two tilting NCs slide slightly and yield a surface mismatch of 1.15 nm (i.e., equivalent to a surface facet overlapping area of ∼76%) and a Pt[100]∧SLRh[100] angle of 7.5°. The inter-NC separation between two neighboring NCs is estimated to be about 2.8 nm, roughly equivalent to 1.5 times of one free OA molecule length (i.e., ∼2 nm). In the case of edge-to-edge configuration (Figures 6b and S7), NCs seated diagonally in SLRh[110] and SLRh[11̅0] of one rhombic plane display different inter-NC distances. In SLRh[110], the inter-NC distance and the Pt[110]∧SLRh[110] angle are 14.78 nm and 14.35°, respectively, yielding a smaller inter-NC separation of 0.95 nm. By contrast, NCs in SLRh[11̅0] display a much greater inter-NC separation of 10.78 nm. There two types of separating spaces between NCs are interconnectively merged into a wavy-shape tunnel over the entire supercrystal which confines soft OA ligands inside. Unlike other superlattice symmetries observed in NC assembles,27,30,31,33 the corner-to-corner configuration appears to be a unique structural feature that exists only in the obtuse Rh superlattice. The resultant interlocking structure dramatically reduces the freedom of NC migration, making the obtuse Rh superlattice as one tighten and mechanically stable structure. NCs with a C−C configuration develop the SLRh[111]-oriented 3-fold symmetric axis (Figures 3c and S8), which coincidently overlaps with both SLRh[111] and Pt[111]. The inter-NC distance of 14.26 nm was found about 2 nm shorter than the diagonal NC length of 16.26 nm. Such an unrealistic shortage of diagonal length implies the existence of slight surface truncation at NC corners. To avoid direct touch or fusion of NCs through their corners, the magnitude of surface truncation should be at least ∼1.2 nm to compensate for half the shortage of diagonal length (i.e., 1 nm) plus one Pt monolayer [i.e., Pt(111) = 0.2 nm]. There are three possible mechanisms to produce a surface truncation of 1.2 nm at NC corner: (1) Pt(111) truncation only at NC corner; (2) Pt(110) truncation only at NC edge; (3) coexistence of both Pt(111) and Pt(110) truncations at corner and edge. Recent in situ TEM imaging reveals that Pt nanocrystals are terminated at surfaces by three low-index facets of Pt(111) and Pt(100) and Pt(110).41 Therefore, the coexistence of surface truncations at both corner and edge is probably one of the most favorable truncation cases (Figure S9). The surface truncation is estimated to be at least on the order of three Pt monolayers. To understand the nucleation and growth route of NC supercrystal under various conditions, we took advantage of the reconstructed translational and orientational orderings of NCs in obtuse Rh superlattice and thus explored further about characteristics of superlattice polymorphs and associated transformation pathway. Simple cubic (SC) appears as the simplest superlattice that displays a direct face-to-face arrangement of NCs and often forms in thin film-based NC assembly.25 Upon the increase of the film thickness, numerous superlattices emerge at different evolution stages of NC assembly. At controlled conditions of NC concentration or solvent evaporation, the nucleation and growth of supercrystal are often associated with simultaneous development of surface stress and internal strain of both NC and supercrystal, which accordingly causes certain magnitude of superlattice distortion. The superlattice angle of α given in lattice parameters on the Rh cell setting is used as a variable to quantify the structural distortion and superlattice variation and thus to manifest the structural transformation consequence.
Figure 7. Structural comparisons between obtuse, acute Rh and simple cubic superlattices: (a) superlattice variation as a function of α; (b−d) NP interactions in (b) obtuse Rh superlattice, (c) simple cubic, and (d) acute Rh superlattices. Three panels from top to bottom represent the SLRh(100), SLRh(11̅0), and SLRh(111) planes, showing the space occupation around the edge-to-edge configuration along SLRh[110], corner-to-corner configuration along SLRh[111], and the 3-fold axis, respectively.
primitive lattice in which α equals 90°, so we begin with the simplest lattice of SC to discuss the superlattice transformation and associated pathway. Upon increase of α by SC[111]directed compression (Figure S10, left), SC undergoes a Rh lattice distortion that accordingly develops a series of obtuse Rh superlattices along with increase of the obtuse angle. Once the compression drives α to reach 120°, obtuse Rh transforms to a 2D hexagonal lattice. For instance, the honeycomb-like hexagonal lattice nucleated at air−liquid interface represents one significant example in which the building block can be considered as a modified NC but has relatively an increased ratio of surface truncations.42 On the contrary, upon the decrease of α by SC[111]-directed tension (Figure S10, right), SC transforms to an acute Rh lattice. When the tension drives α to reach 60°, a perfect FCC lattice is fully developed. The structural switch between SC and FCC along with development of intermediate Rh lattices in the range of α from 90 to 60° represents one common cubic-to-Rh distortion pathway, which has been widely observed in a large variety of crystals made up of nanocrystals and atoms.33,43,44 E
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superlattice transformation. At the final stage of supercrystal growth, the evaporation-induced increase of molecules in solvent through enhanced osmotic force and resultant drying of nucleated supercrystals develop surface stress and strain on supercrystal grains, which leads to superlattice transformation from either SC or FCC to an intermediate Rh lattice. In the case of superlattice transformation from either SC or FCC to BCC, the transformation pathway is different from the case discussed above. The latter superlattice transformation does not involve significant rotation and tilting of NCs. Instead, NCs simply chase the well-known Bain deformation route12,45,46 and slide relatively to each other. While the relative sliding of NCs in SL[110] direction transforms BCC to SC, stretching of NCs in SL[100] direction transforms BCC to FCC. Before completion of the above structural transformations, a series of intermediate lattices form and display various degrees of tetragonal distortion. Conclusion. In summary, through controlling the solvent evaporation, we have grown large single supercrystal grains from Pt NC suspensions in hexane. Based on newly developed “supercrystallography” approach that combines synchrotronbased SAXS/WAXS data collection with automatic indexing and simulations of single supercrystal X-ray scattering patterns, we fully reconstructed the anisotropic structure of Pt NCassembled supercrystal at an unprecedented level from atomic to mesometric scale. The supercrystal crystallizes in an Rh superlattice with space group R3m and an obtuse angle of 106.2°. Neighboring NCs are packed into three types of configurations: (1) face-to-face, (2) edge-to-edge, and (3) corner-to-corner. Both the face-to-face and corner-to-corner configurations play a governing role in the coupling and interactions between NCs and surface ligands toward maximization of both packing density and configuration entropy and structural enhancement of obtuse Rh superlattice. By correlating the surface strain and resultant lattice distortion, we have developed a scheme for various superlattice polymorphs of NC assembled supercrystals and clarified the stress-driven transformation pathways. These results not only allow one to understand the nucleation and growth and superlattice transformation of NC supercrystals but also help find ways in directed design of materials processing toward fabrication of transformative materials with desired mesostructures and tailored properties for real applications.
Taking a close look at the three superlattices of SC and obtuse and acute Rh’s, we can find that both the acute and obtuse Rh lattice can be assembled by six identical rhombuses but through completely different processes (Figure 3, bottom); in SC, six rhombuses are simply replaced by six identical squares. Adding another constraint factor, three superlattices can be manifested by the differences in superlattice angle α. When α changes from acute through right to obtuse angle, the superlattice changes as a consequence from acute Rh through SC to obtuse Rh. Figure 7b−d shows the packing configurations of NCs in three typical superlattice planes of SLRh(100), SLRh(110̅ ), and SLRh(111) and that three typical superlattices are the obtuse Rh, SC and acute Rh at α = 106.2°, 90°, and 73.8°, respectively. It is obvious that identical rhombus frames in SLRh(100) plane of both acute and obtuse Rh are arranged in a perpendicular manner. If analyzing superlattice locally, the transformation can be understood from development of rhombuses in Rh by distortion of squares in SC. As one additional feature, the void space in the frame center is significantly minimized, indicative of an increased packing density of hard NC cores. However, if looking at both SLRh(11̅0) and SLRh(111) planes, the NC arrangement and packing frame are similar, but the magnitude of void space in frame center displays completely opposite tendencies of variation. In SLRh(11̅0) plane, NCs in obtuse Rh are arranged tighter than those in SC and acute Rh, whereas in SLRH(111) the trend is reverse. To comprehend the superlattice formation and growth from a thermodynamic point of view, we calculated the superlattice volume and the NC packing density (see methods in SI). Figure 8 shows the variations of both superlattice volume and
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Figure 8. Packing densities of several typical superlattices in the plot of superlattice angle α varying from 120° to 60°. The red, blue, and black dots represent the observed obtuse Rh and calculated SC and acute Rh, respectively.
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b02879. Additional data sets include calculating and analyzing methods of X-ray scattering patterns and packing densities, experimental setups, single crystal X-ray scattering simulations, experimental details, figures, table, and superlattice information (PDF) Collected and simulated SAXS patterns in typical orientations with rotations of the supercrystal along SLHex[100], SLHex[110], and SLHex[11̅0] axis (MP4)
NC packing density as a function of α ranging from 120° to 60°. Among the superlattices as shown in Figure 8, SC has the largest cell volume of 1892.8 nm3 but the smallest packing density of 45.3%, while FCC with α = 60° has an intermediate volume of 1338.22 nm3 but the highest packing density of 64.07% (Table S1). A higher NC packing density is indicative of higher configuration entropy. Therefore, SC and FCC represent the least and most favorable superlattice, respectively, when the NC assembly process is maintained under thermodynamic conditions. Recent experiments with control of solvent evaporation reveal the formation of large FCC supercrystals that display long-range ordering coherence of NC translation and atom orientation.32 At the early stage of NC assembly, thermal perturbation always occurs in the system, and accordingly breaks the thermodynamic balance and thus causes
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. F
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The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We appreciate technical support from many CHESS staff and invaluable discussions with many colleagues at Cornell University. Particular thanks go to Marian Szebenyi and Tiit Lukk for crystallographic programming indexing and Sol Gruner and Bill Bassett for scientific inspiration. This work is partially supported by the Laboratory Directed Research and Development (LDRD) program of Los Alamos National Laboratory, which is operated by Los Alamos National Security LLC, under DOE Contract DE-AC52-06NA25396. CHESS is supported by the NSF award DMR-1332208.
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DOI: 10.1021/acs.nanolett.5b02879 Nano Lett. XXXX, XXX, XXX−XXX
