Understanding Fe3O4 Nanocube Assembly with ... - ACS Publications

Subscriber access provided by UNIV OF LOUISIANA

Article

Understanding Fe3O4 Nanocube Assembly with Reconstruction of a Consistent Superlattice Phase Diagram Zhongwu Wang, Xin Huang, Jinlong Zhu, Binghui Ge, Kerong Deng, Xiaotong Wu, Tianyuan Xiao, Tian Jiang, Zewei Quan, and Y Charles Cao J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b13082 • Publication Date (Web): 28 Jan 2019 Downloaded from http://pubs.acs.org on January 28, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Journal of the American Chemical Society

Understanding Fe3O4 Nanocube Assembly with Reconstruction of a Consistent Superlattice Phase Diagram Xin Huang+, Jinlong Zhu⊥, Binghui Ge§, Kerong Deng±, Xiaotong Wu±, Tianyun Xiao‡, Tian Jiang‡, Zewei Quan±, Y. Charles Cao‡, Zhongwu Wang+,* +,

Cornell High Energy Synchrotron Source, Cornell University, Ithaca, New York 14853, United States; ⊥, Center for High Pressure Science and Technology Advanced Research (HPSTAR), Beijing, 100090, P. R. China; §, Institute of Physical Science and Information Technology, Anhui University, Hefei, 230601, Anhui, P. R. China; ±, Department of Chemistry, Southern University of Science and Technology (SUSTech), Shenzhen, Guangdong 518055, P. R. China; ‡, Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States.

ABSTRACT: Nanocube (NC) assemblies display complex superlattice behaviors, which require a systematic understanding of their nucleation and growth as well transformation towards construction of a consistent superlattice phase diagram. This work made use of Fe3O4 NCs with controlled environments, and assembled NCs into three dimensional (3D) superlattices of simple cubic (sc), body-centered cubic (bcc) and facecentered cubic (fcc), acute and obtuse rhombohedral (rh) polymorphs and 2D superlattices of square and hexagon. Controlled experiments and computations of in-situ and static small angle x-ray scattering (SAXS) as well as electron microscopic imaging revealed that the fcc and bcc polymorphs preferred a primary nucleation at the early stage of NC assembly, which started from the high packing planes of fcc(111) and bcc(110), respectively, in both 3D and 2D case. Upon continuous growth of superlattice grain (or domain), a confinement stress appeared and distorted fcc and bcc into acute and obtuse rh polymorph, respectively. The variable magnitudes of competitive interactions between configurational and directional entropy determine the primary superlattice polymorph of either an fcc or a bcc, while emergent enhancement of confinement effect on enlarged grains attributes to lately developed superlattice transformations. Differently, the formation of a sc requires a strong driving force which is either emergent simultaneously or applied externally so that one easy case of the sc formation can be achieved in 2D thin films. Unlike the traditional Bath deformation pathway that involves an intermediate body-centred tetragonal lattice, the observed superlattice transformations in NC assembly underwent a simple rhombohedral distortion, which was driven by a growth-induced inplane compressive stress. Establishment of a consistent phase diagram of NC-based superlattices and reconstruction of their assembly pathways provide critical insight and solid base for controlled design and scalable fabrication of nano-based functional materials with desired superlattices and collective properties for real-world applications.

resultant superlattices of simple shaped nanocrystals, such as sphere, rod and plate. 3, 4 Upon discovery of enhanced flat facetto-facet coupling between neighboring shaped nanocrystals and recent advance of wet synthetic chemistry, 5, 6 both experiments and simulations are rapidly switched to explore the selfassembly and structural development as well as underlying mechanism over a rich variety of complex anisotropic

INTRODUCTION Nanocrystal assembly leads to a broad spectrum of supercrystals with various ordered superlattices, which make promise for designable control and scalable fabrication of novel materials with desired properties and functionalities.1, 2 Previous studies focus largely on the self-assembly and

1 ACS Paragon Plus Environment

Journal of the American Chemical Society 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 11

much distinct assembly pathways between the two observed rh superlattice polymorphs. To resolve puzzles among superlattice polymorphs such as one highlighted above, it is obviously required to develop an in-situ/real time characterization technique with enough time and spatial resolutions, capable of truly capturing the structure and variations of NC assembly over the whole process from the early nucleation through subsequent growth and transformation to the final superlattice polymorph. In this work, we made use of monodispersive Fe3O4 NCs and delicately designed various control experiments to obtain a series of typical superlattice polymorphs. In parallel, we combined both static and in-situ/real time synchrotron-based small angle x-ray scattering (SAXS) characterization with electron microscopy imaging, and carried out systematic explorations on the nucleation and growth as well as transformation of NC assembly into several stable superlattice polymorphs. Besides achievement of experimental and technical progresses and controlled growth of superlattice polymorphs, we also implemented computational approach to make precise indexing of collected SAXS patterns and reliable computation of SAXS-based superlattice variations towards reconstruction of convincing superlattice transformation pathways between fcc, bcc and sc polymorphs, which are linked by a series of low-symmetry superlattice intermediates. Combining both experiments and computations with careful analysis and reasonable correlation, we stepped a bit further and explored the competitive interactions between positional (configurational) and directional entropic forces, thus providing insights into the nucleation and growth and transformation of NC-based superlattice polymorphs.

nanocrystals and their superlattice phase behaviors upon variation of size, surface coating molecule and composition of nanocrystals. 7~13 Among a large diversity of anisotropic shapes, nanocube (NC) appears as the simplest shape with surface termination of six identically cubic facets. 1, 8 Unlike spherical nanocrystals that mostly self-assemble into a close packing superlattice of either a face-centred cubic (fcc) or hexagonal close packing (hcp) with a packing density of 74%, 2, 14~17 NCs embrace only such a very simple anisotropic feature, but surprisingly, the emergence of directional interactions between parallel aligned facets lead NCs to manifest a rich superlattice phase behaviors.18~43 Control of the interaction strength between NCs can be achieved by delicate tuning of assembly environments, and thus enables feasible modification of the structural symmetry of assembled superlattice. 18~43 Upon drop-casting of dilute NC suspension solutions towards self-assembly of two dimensional (2D) thin films, NCs can nucleate into superlattices with either a monolayer or multiple layers. 18~30 While the monolayers are often dominated by hexagonal and square lattices, 18~22 the multiple layers turn a bit complex, showing various superlattices of simple cubic (sc), body-centred cubic (bcc) and fcc superlattices. 18, 22-30 Once a fast drying comes up to mediate the assembly process, a stress emerges to confine the superlattice grains, accordingly driving gradual deformation of original cubic superlattices into low symmetry polymorphs. 18, 28-30 Upon increase of NC concentration with control of solvent evaporation at a slow rate, NCs interact with surface-coating ligands and surrounding solvent molecules, and self-assemble into ordered 3D superlattices with subsequent growth over a large length scale. 31-43 Such 3D superlattice crystals (called supercrystals) not only display long-range translational ordering of NCs, 31-42 but also orientationally align atomically crystallographic planes across NCs. 31~33 Once the assembly environments are perturbed, a certain degree of thermal fluctuation appears to make influence of the whole assembly system. Among the variety of complex interaction forces, the contributing magnitude changes relatively from one to another, certainly modifying the ways of NC assembly. As a consequence, various superlattice polymorphs are developed to minimize the total free energy of the assembly system. As witnessed by a rapid expansion of NC-based superlattice library, NC assembles not only produce the well-recognized high symmetry superlattice polymorphs of sc, bcc and fcc, 34-42 but also give rise to a series of superlattice intermediates with reduced symmetries, such as tetragonal, orthorhombic, rhombohedral (rh) and so on. 18, 31-33, 42 Without use of in-situ/real time structural identification, the above-determined superlattices represent only a series of finally achieved structural polymorphs with achievement of the certain thermodynamic stability, which may not truly reflect the primary superlattice polymorphs nucleated at the early stage of NC assembly. Therefore, the question comes up with how one superlattice initially nucleates, grows and eventually develops into another thermodynamically stable polymorph as named above. As an example, recent studies observed the two typical rh superlattices in large 3D NC assembles, 32, 33, 42, in which the lattice angles of defined primitive rhombus cell inside are acute and obtuse, respectively. Such an angular difference implies

EXPERIMENTAL Synthesis of Fe3O4 NCs: The iron oxide (Fe3O4) NCs with surface coating molecules of oleic acid (OA) were synthesized by decomposition of iron (III) oleates, following slightly modified literature approach. 31 Typically, 1 mmol of iron oleate, 0.5 mmol of sodium oleate and 0.5 mmol of oleic acid were dissolved in 5 g of 1-octadecene. Therefore, the solutions were heated up to 320 ℃ and refluxed for 1 hour. The synthesized NCs were purified using a solvent/non-solvent pair of n-hexane/ethanol for three times. The NCs were collected and stored in toluene for additional characterization and assembly processing. Assembly of Fe3O4 NCs: NC assembles were made by two major approaches, including 1) drop casting of NC suspension solution of toluene on substrates of silicon, Kapton tape and copper grid, and 2) diffusion-mediated evaporation and saturation of NC suspensions in toluene by varied volumetric ratios of ethanol either in a glass capillary or in a nuclear magnetic resonance tube. Briefly, Fe3O4 NCs were dissolved in toluene and controlled at a fixed NC concentration of approximately 10 mg/ml. For the drop casting assembly, 2 μl of NC suspension solution was drop cast on a substrate to guide NC assembly at a fast rate of solvent evaporation. For the capillary-based assembly, 2 μl of NC solution was quickly injected into a glass capillary (1 mm in diameter), and then about 6 ~ 10 μl of ethanol was filled into the glass capillary. An air separation between toluene and ethanol was set to avoid a direct contact between the two different types of solvents. After


Page 3 of 11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Journal of the American Chemical Society RESULTS AND DISCUSSIONS

sealing the two openings of the capillary, a slow evaporation of ethanol across the air separation space with a sluggish diffusion into toluene was made to trigger the self-assembly of NCs in a diffusion-developed anti-solvent environment. Synchrotron-based x-ray scattering characterization: The NC assembles were characterized by synchrotron-based small/wide angle x-ray scattering (SAXS/WAXS) at the B1 station of Cornell High Energy Synchrotron Source (CHESS). 44, 45 Briefly, the incident white x-ray beam was collimated by a pair of single silicon crystals with (111) orientation into a monochromatic beam with an energy of 25.514 keV, equilibrant to the wavelength of 0.485946 Å. The monochromatic x-ray beam was reduced by a circular tube to a small beam with 100 µm in diameter to illuminate the samples. A large area detector of Mar345 was used to record the scattered x-rays from assembled samples. The sample-to-detector distance and other detector-sitting parameters were calibrated by the two standards of CeO2 and Ag-behenate. The NC assembles made by drop casting were first loaded either onto a Kapton tape or into a stainless gasket hole. After mounting the samples on the stage of the B1 station at the CHESS, both SAXS and WAXS images were simultaneously collected from the same volume of the samples. The in-situ/real time experiments were performed only on SAXS, in which a long sample-to-director distance was set to improve the spatial resolution. Using a Fit2D software package, the SAXS images collected from the samples were reduced into 1D plots of intensity against either two theta (°) or inverse nanometer (nm1) for structural analysis. Electron microscopic characterizations: The assemble samples were also characterized by scanning and transmission electron microscopy (SEM and TEM). The TEM characterizations were conducted on Hitachi H-7000 TEM operating at 100 KV, while high resolution TEM (HRTEM) and selected area electron diffraction (SAED) were conducted on FEI Tecnai F20 S/TEM operating at 200 KV. The monolayer TEM samples were prepared by dropping ~1 mg/ml of NC suspended chloroform solutions on a copper grid, whereas the superlattice TEM samples were prepared by dropping ~10 mg/ml NC-suspended toluene solutions on a copper grid. The samples were both dried under air conditions. Additional TEM and scanning TEM (STEM) images were also performed, including high-angle annular dark field (HAADF), annular bright field and secondary electron modes, as well as energy dispersive x-ray spectroscopy element mapping using a JEOL ARM 200 equipped with a probe corrector and an image corrector. Similarly, the samples were prepared by dropping ~10 mg/ml NC-suspended toluene solutions on a copper grid and dried under air conditions. Indexing and computation of SAXS Images: The analysis and indexing as well as computation of SAXS images were made using Matlab with partial adaption and modification from GIXSUI 1.6.2 package. 46 Briefly, several cubic superlattices were used to start with, and the rhombus was defined as equivalent primitive cell from each superlattice polymorph for SAXS-based reconstruction of the transformation pathways. Upon gradual change of the rhombus angle, a series of SAXS patterns were computed to determine intermediate superlattice polymorphs with reduced symmetries.

Characterization of Fe3O4 NCs: The quality of iron oxide (Fe3O4) NCs plays significant role for the nucleation and growth of NC self-assembled superlattice under controlled environments. A typical TEM image (Figure 1a) revealed the monodispersity of synthesized Fe3O4 NCs. Both SAED (Figure 1b) and WAXS patterns (Figure 1c) consistently identified the crystallization of individual NCs in an atomic cubic structure (Fd3m), which has lattice constants of a = 8.442 Å and V = 601.6 Å3. One typical high resolution HAADF image revealed slight truncations of individual NCs with surface termination of six (100) and eight (111) facets (Figure 1d and inset). Based on the HAADF-defined fringe number of cubic lattice and the WAXS-determined d-spacing of (400) planes (see Table S1), the side length of NC was accurately calculated to be 12.5 nm (Figures 1d and S1).

FIGURE 1 Electron microscopy and x-ray scattering characterizations of iron oxide (Fe3O4) nanocubes (NCs): a) low resolution transmission electron microscopic (TEM) image; b) selected area electron diffraction (SAED) pattern; c) wide angle xray scattering (WAXS) pattern; and d) high resolution high-angle annular dark field (HAADF) image with inset of cartoon illustration on the shape of one typical NC.

Finally harvested superlattices under control environments: Previous studies observed several superlattice polymorphs from NC assembles, but random control of assembly environments and extensive use of NCs with variable compositions and sizes hindered direct comparison and reliable correlation between various superlattice polymorphs towards construction of a consistent superlattice phase diagram. 18~43 To circumvent from such a severe issue, the experiments were designed to start with Fe3O4 NCs suspended in toluene at a fixed NC concentration of ~10 mg/mol. Through delicate control of assembly environments, the self-assembly of NCs was tuned into various periodically ordered superlattice polymorphs. Starting with thin film assembly, drop casting of NC solution on Kapton tape resulted in ultimate collection of a bcc superlattice (Figure 2a, and also see the detailed analysis at SI and Figures S2, S3), whereas interface-mediated diffusion of ethanol into toluene caused the early and primary nucleation of



Page 4 of 11

polymorph with reasonable achievement of a thermodynamically stable state. In-situ SAXS for the formation of the acute rhombohedral superlattice: In order to capture the initial nucleation of one superlattice and also uncover its continuous growth with subsequent development into a final superlattice polymorph, one realistic in-situ/real time experiment was designed with fair control of overall assembly time for reasonable access of synchrotron x-ray to make simultaneous monitoring of the NC assembly pathway. As a result, one unique control of the diffusion rate of ethanol in toluene through a separation space between the two solvents was designed to make NC assembly measurable within the time and spatial resolutions of synchrotron-based SAXS technique.

an fcc superlattice (Figure 2b). The bcc and fcc superlattices have a unit cell parameter of a = 23.0 nm and a = 26.2 nm, respectively. Apparently, these two high symmetry cubic superlattice polymorphs underwent different ways of the nucleation and growth, but one common feature was shown as that the NC assembly was completed in a fast fashion. Practically, the bcc was controlled by a fast evaporation of solvent, whereas the fcc was made through a quick saturation of NCs under a diffusion-induced anti-solvent environment (e.g. a mixture of toluene and ethanol). Thus, both bcc and fcc can be reasonably considered as the early nucleated superlattices under two typical but different environments.

FIGURE 3 Configuration of in-situ/real time SAXS experimental setup (a) and several typical SAXS images (b~f) collected in real time at several points over the course of NC assembly.

FIGURE 2 Small angle x-ray scattering (SAXS) patterns of (a) body-centred cubic (bcc), (b) face-centered cubic (fcc), (c) acute and (d) obtuse rhombohedral (rh) superlattices. The acute and obtuse angles of inside rhombus are 66.1° (c) and 106° (d), respectively. Note: inset marks in color represent the indexed peak positions (or spots) of corresponding superlattices.

Figure 3a shows the experimental setup of in-situ/real time SAXS measurements with reasonable control of the diffusion rate to form an anti-solvent environment and with x-ray illumination on the upper boundary of the capillary. Upon slow diffusion of ethanol into NC-suspended toluene (see SI for the details), SAXS images from one portion of NC-suspended solvents were simultaneously and continuously collected as a function of time (Figure 3b-3f and Videos S1). The SAXS images initially displayed a strong diffusion feature of x-ray scattering, indicative of a random/disorder state of NCs in toluene dominant anti-solvents (Figure 3b). Upon continuous diffusion of ethanol in toluene, the solubility of NCs in antisolvents decreased gradually (Figure 3c). Once NCs were saturated in solvents, the nucleation of fcc superlattice with a strong (111) orientation was emerged on the capillary wall (Figure 3d and Figure S4). Upon continuous growth, there was a noticeable decrease in d-spacing of fcc(111) and lattice volume (Figures 3d-f and S5). An overall analysis of d-spacing at different orientations indicated that a much stronger compressive stress were developed within in-plane of fcc(111) in the direction parallel to the capillary wall. Continuous enhancement of in-plane compression gradually distorted the initially formed fcc into an acute rh superlattice polymorph with a (001) orientation (Figure 3f and Figure S6, Video S2). Note that the fcc could be alternatively treated as a rh as well, with the lattice angle of 60°, and under this newly defined configuration, the (111) plane of fcc is the (001) plane of the asconstructed acute rh.

Aimed at growing large supercrystal, a slow solvent processing of NC-suspensions was designed to control the selfassembly of Fe3O4 NCs. While the sluggish diffusion of vapored ethanol into toluene over a course of one week enabled the final harvest of an acute rh superlattice (Figure 2c), the evaporation of toluene at a very slow rate allowed one to eventually obtain an obtuse rh superlattice (Figure 2d). The acute rh has lattice constants of a = 17.1 nm and α = 66.1°, whereas the obtuse rh has a = 17.1 nm and α = 106°. Such experimental observations implied a dramatic difference of the nucleation and growth pathway between acute and obtuse rh superlattice polymorphs. Besides the fcc that was characterized during the intermediate process of NC assembly, all other three superlattice polymorphs were determined after a complete drying of NC assembly. It is thus indicated that these three superlattice polymorphs represent the thermodynamically stable structural states achieved at the final stage under individually controlled environments. Therefore, the question comes up with whether each of these superlattice polymorphs could also reflect the initial structure nucleated at the early stage, and if not, what is exactly the truly initial superlattice and how it continues to grow and thus develop into the finally observed superlattice


Page 5 of 11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4 presented the time-dependent variation of x-ray scattering intensity of both solution and superlattice at the two selected spots on SAXS image (Figure S7). Apparently, the whole process of NC assembly from the nucleation of fcc through its growth to the final formation of an acute rh superlattice polymorph was accomplished over the course of approximately 100 minutes (e.g. t = 240 – 140 = 100 minutes). At this typical stage, the anti-solvents became completely transparent, and then, the acute rh polymorph remained almost constant of both scattering intensity (Figure 4a) and rhombus angle (Figure 4b), but very slightly decrease of lattice constant (Figure S5).

toluene environments truly favors the primary formation of a bcc superlattice polymorph at the early stage. This allows us to reasonably conclude that the obtuse rh superlattice was developed from the early formed bcc superlattice polymorph (Figures 2a, 2d).

FIGURE 5 Structural correlations between face-centred cubic (fcc), simple cubic (sc) and body-centred cubic (bcc) superlattices through a gradual angular development of equivalently defined rhombus inside: a) fcc, an acute angle of 60° and a lattice constant of 𝑎(fcc)/√2); b) sc, an angle of 90° and no change of a; c) bcc, an obtuse angle of 109.5° and a lattice constant of 𝑎(bcc)√3/2). Note: upon a rhombohedral (rh) distortion, the planes of fcc(111) and bcc(110) are correspondingly developed into the (001) plane of resultant rh lattice.

FIGURE 4 Normalized scattering intensity of two selected SAXS spots as a function of time, representing changes of NC concentration in solvent and growing superlattice, respectively (Top); and the change of rhombus angle as a function of time (Bottom).

After removal of remaining solutions and complete drying of NC assembly, the rhombus angle of acute rh superlattice did not show a continuous increase towards achievement of an expected sc, or even an obtuse rh superlattice. Thus, it was understandable that the observed obtuse rh superlattice actually underwent a different assembly pathway, rather than a large magnitude of structural distortion directly from the fcc superlattice. Our previous results on the assembly of Pt and Pt3Co NCs also revealed that the obtuse rh superlattice underwent a very sluggish formation process, 32, 33 which normally took time over the period of a week or a month. Therefore, instead of an unrealistic conduction of synchrotronbased in-situ experiment, a feasible control experiment was alternatively designed. In a simple way, a drop casting of NC suspensions with similar control of assembly environments was allowed to make rapid quenching and preservation of the primary superlattice nucleated at the early stage for ex-situ structural determination. As shown in Figures 2a, S2 and S3 on the fast quenching superlattices, NC assembly under single

FIGURE 6 Several computed SAXS patterns of superlattices upon variation of the superlattice angle from 90° to 117°, corresponding to the rhombus angle from 60 to 109.5°, including (a) fcc, (b, c) fccbased acute rh, (d) sc, (e) bcc-based obtuse rh, and (f) bcc. Note: the computations are based on the fcc(111) orientation.

Computational simulation of SAXS: In order to justify the reliability of above derived pathway of the nucleation and transformation, the SAXS patterns of NC-based superlattices were computed against the variation of superlattice angle upon



transformation from one to another. Figure 5 shows the structural correlations between superlattice polymorphs of fcc, sc and bcc. The blue bonds represent the unit cell of fcc and bcc, whereas the red bonds represent that the primitive unit cells of fcc and bcc are converted into the rhombus lattices with the lattice angle of 60° and 109.5°, respectively. Thus, the superlattice transformation pathway can be easily understood through the angular change of inside defined rhombus primitive unit cell. Based on the deformation pathway, we began with computation from the fcc with a (111) orientation [treated as (001) oriented rh with rhombus angle of 60°], which was commonly observed in this and previous studies, 29, 30, 42 and then continuous increase of the lattice angle of rh maintains the (001) orientation. The SAXS patterns were generated and presented in Video S3 and Figure 6 and Figures S8~S10. The computed SAXS series (Figure 6a~b, and Videos S1 and S2) are in an excellent match with in-situ SAXS measurements of the fcc-to-acute rh transformation (Figure 3), confirming the reliability of the computation-based transition model. The reliability of the model indicates its feasibility to compute and reconstruct the pathways of other superlattice transformations. As for the obtuse rh superlattice, there are two possible transformation pathways (Videos S3, S4), depending on whether it starts from either a sc (Figure 6d), or a bcc (Figure 6f). Taking into account the enhancement of emergent stress upon growth of superlattice grain, the lattice was expected to reduce from the starting superlattice through a transformation process towards the formation of high-density obtuse rh polymorph. Figure 7 presents the calculated packing density of various superlattice polymorphs as a function of rhombus angle from 60° to 109.5° (see the calculation details in SI). Among superlattice polymorphs involved, the sc has the highest packing density, excluding the possibility for a compressive stress-induced sc-to-obtuse rh transformation pathway. Therefore, the only pathway is the bcc-to-obtuse rh transformation. This is not only consistent with a compressioninduced increase of packing density, but also supported by the in-situ observed fcc-to-acute rh pathway that is similarly involved by a stress-induced change from lower to higher packing density (Figures 2, 3, 7).

Page 6 of 11

Previous studies mostly employed the well-known Bath deformation route to interpret the stress-induced structural distortion and associated phase transformation, such as the fccto-bcc transition (Figure S11) and some low symmetry intermediate lattices. Basically, the Bath-based transformation mechanism involves a body-centred tetragonal phase, which changes in lattice ratio of a/c, and remains constant in lattice angle. Taking into account these parameters, we computed a series of SAXS patterns as shown in Figure S12 and Video S5, which are in apparent disagreement with our experimental observations (Figures S13, S14). This allows one to exclude the Bath deformation pathway, thus confirming the novelty of the transformation pathway observed in NC assembly. Formation of simple cubic (sc) under strong confinement: In principle, a higher packing density is indicative of a greater configurational entropy and a lower free energy. 8, 47 Therefore, the sc represents the most stable superlattice and is expected to be formed at the final stage of NC assembly. Based on the orientational development upon superlattice transformation (Figure 6), the superlattice transformation from either bcc or fcc to sc polymorph certainly requires a shear force, which should be strong enough to completely change the stacking sequence of NCs from ABABAB in bcc(110) and ABCABC in fcc(111) to AAAAAA of sc(100). In the cases of thick 2D and large 3D supercrystals, the inter-NC distances are observed in a narrow range of 2.6~3.1 nm. 14, 17, 47 Correlating the double OA length of ~4 nm, it is suggested that OA intercalations exist inside superlattice to form a strong OA-NC interface. To break down the intercalated OAs and thus drive NCs with a great magnitude of movement, the driving forces are certainly much larger than the solvent-based weak interaction forces as observed in NC assembles. Therefore, the formation possibility of sc superlattice can be made by a reasonable control and treatment of thin film assembly, which does not require strong forces to trigger a less heavy NC rearrangement. To test this assumption, thin film assembly with a 2D structural feature was treated heavily by multiple washing of ethanol and acetone (at least 10 times), which truly resulted in the formation of sc superlattice (Figure 8a, b). As one additional example, the drying-induced strong confinement surrounding individual solvent drops on solid substrate often resulted in the formation of square lattice at the edge of monolayer-dominated coffer ring (Figure 8c).

FIGURE 7 Calculated variation of packing density as a function of rhombus angle from 60 to 109.5°, equivalent to the superlattice angle from 90 to 117°.


Page 7 of 11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Journal of the American Chemical Society polymorph. 51 Upon continuous growth of superlattice grain, the confinement stress starts to play a similar role as that in fcc, and drives the bcc distorting into an obtuse rh superlattice. Taking into account the two relatively changed ranges of the rhombus angle of 19.5 (bcc-sc) and 30° (fcc-sc) (see Figure 7), the distorting magnitude of 3.5° as observed in transformation from the bcc to obtuse rh is relatively compatible to the magnitude of 6.1° as deformed from the fcc to acute rh. In a different case of thin film, as the NC concentration reduces dramatically, the assembly stimulus of 2D superlattice appears to be the same as that in 3D superlattice and is dominated by the positional (configurational) entropy, which prefers an in-plane hexagonal (or quasi-hexagonal) close packing of NCs at the early stage. 17, 52, 53, 54 However, once a strong confinement appears under insitu assembly environments (such as the reduction of drop size) or a heavy treatment of solvent is lately applied, a great magnitude of NC movement is enabled to rearrange NCs into a closer packing superlattice. This typical processing eventually causes the formation of a sc (or square) superlattice, which maximizes both the positional (configurational) and directional entropies towards dramatic minimization of total free energy (Figure 9, Lower Panel).

FIGURE 8 Typical electron microscopic images of two dimensional (2D) thin films with slight and with strong flushing of ethanol and acetone solvents (a, b) and drop-confined assembly (c).

Competitive interactions between driving forces and correlations between NC-based superlattice polymorphs: Careful analysis and reasonable correlation of in-situ and static (ex-situ) SAXS experiments and large computations as well as electron microscopy imaging of controlled NC assembles allow one to understand the dominant play of certain driving forces under typically controlled environments and reconstruct the transformation pathways between NC-based superlattice polymorphs (Figure 9). Controlled of NCs with a low concentration in a good solvent such as toluene, the surface coating molecules have a large magnitude of freedom, so NCs behave like a series of spherical nanoparticles, capable of moving around in solvent. Without direct core-core interactions, NC assembly makes effort to maximize the positional (configurational) entropy towards a rational minimization of total free energy. 14, 17, 47, 48 As a result, the positional (configurational) entropy dominates the interactions, thus causing the primary formation of an fcc superlattice. 49 Upon controlled diffusion of ethanol into toluene, the resultant anti-solvents cause a dramatic reduction of NC solubility and accordingly enable a quick saturation of NCs in solvents. Like the fast quenching of high temperature phase towards its well preservation under ambient conditions , such an anti-solvent tuned fast processing allows for a rapid preservation of the primary fcc in the growing grain without significant change of superlattice. As a consequence, continuous development of compressive stress upon superlattice growth is only capable of causing an acute rh distortion, rather than a large rearrangement of stacking sequence into a sc superlattice polymorph. Without diffusion of ethanol, the slow evaporation of single toluene gradually increases the NC concentration, and the assembly environment still maintains a thermodynamic state. In order to improve the stability of the whole assembly system, the shape effect starts to play a significant role and thus causes an increase of directional entropy. Similar to the self-assembly of nanoplates or nanorods, 11, 50 a preferred facet-to-facet alignment between neighboring NCs is developed to increase the directional entropy, which thus drives the primary nucleation of an orientationally ordered bcc superlattice

FIGURE 9 Construction of NC-based superlattice polymorphs and their pathways of the nucleation, growth and transformation. Note: Lower and Upper Panels show the two dimensional (2D) and three dimensional (3D) superlattice, respectively.

CONCLUSIONS Control experiments have been delicately designed to assemble Fe3O4 NCs into periodically ordered superlattice polymorphs of sc, fcc, bcc, acute and obtuse rh. In-situ and static experiments and computations of SAXS as well as electron microscopic imaging allowed one to determine the superlattice polymorphs and their nucleation and growth and transformation. Careful analysis and close correlations enabled feasible construction of a consistent phase diagram of NC-based superlattices. Upon control of assembly environments, diffusion-mediated saturation of anti-solvents and slow evaporation of single toluene resulted in the primary nucleation of fcc or bcc, respectively, and the emergent confining effect



associated with the growth of superlattice grains causes subsequent transformation of fcc and bcc to the acute and obtuse rh polymorph, respectively. At the early nucleation stage, the configurational entropy dominates the interactions, and NC assembly favors an fcc; once the directional entropy starts to dominate the play, a bcc forms accordingly. Lately, the polymorph types of developed superlattice depend on the magnitude of emergent stress as applied on the growing grain. Lack of external stimulus, the emergent weak stress is only able to drive a rhombohedral distortion of the primary superlattice, but differently, given of an external force, the dramatically enhanced stress is strong enough to cause the formation of a high density sc superlattice polymorph. Unlike the well-known Bath deformation, the two superlattice transformations observed in this work undergoes only a simple rhombohedral distortion caused by a growth-associated in-plane compressional stress. These results not only provide significant insights into the nucleation and growth as well as transformation of various superlattice polymorphs, but also open up a window for controlled design and fabrication of nanobased novel materials with desired structures and properties for future applications.

3. 4.

5.

6.

7. 8. 9.

10.

ASSOCIATED CONTENT Supporting Information

11.

The Supporting Information is available free of charge on the ACS Publications website. Additional data sets include figures, 2D SAXS images and integrated 1D SAXS patterns, TEM images, SEM images, in-situ experimental and computational SAXS Videos with superlattice indexing and associated change of packing density and superlattice information (PDF)

12.

13.

AUTHOR INFORMATION 14.

Corresponding Author * [email protected].

Notes

15.

The authors declare no competing financial interest.

16.

ACKNOWLEDGMENT We thank all CHESS staff members for technical support and several colleagues across Cornell campus for constructive discussions. CHESS is supported by the NSF award DMR1332208.

17.

18.

REFERENCES 1. 2.

19.

Boles, M. A.; Engel, M.; Talapin, D. V. Self-assembly of colloidal nanocrystals: from intricate structures to functional materials. Chem. Rev. 2016, 116, 11220–11289. Murray, C. B.; Kagan, C. R.; Bawendi, M. G. Synthesis and characterization of monodisperse nanocrystals and close-

20.

Page 8 of 11

packed nanocrystal assemblies. Annu. Rev. Mater. Sci. 2000, 30, 545–610. Onsager, L. The effects of shape on the interaction of colloidal particles. Ann. N. Y. Acad. Sci. 1949, 51, 627–659. Ye, X.; Collins, J. E.; Kang, Y.; Chen, J.; Chen, D. T. N.; Yodh, A. G.; Murray, C. B. Morphologically controlled synthesis of colloidal upconversion nanophosphors and their shape-directed self-assembly. Proc. Natl. Acad. Sci. U. S. A. 2010, 107, 22430–22435. Liljeroth, P.; Overgaag, K.; Urbieta, A.; Grandidier, B.; Hickery, S. G.; Vanmaekelbergh, D. Variable orbital coupling in a two-dimensional quantum-dot solid probed on a local scale. Phys. Rev. Lett. 2006, 97 (9), 096803. Xia, Y.; Xiong, Y.; Lim, B.; Skrabalak, S. E. Shapecontrolled synthesis of metal nanocrystals: simple chemistry meets complex physics? Angew. Chem. Inter. Edit. 2009, 48, 60–103. Quan, Z.; Fang, J. Superlattices with non-spherical building blocks. Nano Today 2010, 5, 390−411. Damasceno, P. F., Engel, M.; Glotzer, S. C. Predictive selfassembly of polyhedra into complex structures. Science 2012, 337, 453–457. Bouju, X.; Duguet, É.; Gauffre, F.; Henry, C. R.; Kahn, M. L.; Mélinon, P.; Ravaine, S. Nonisotropic self-assembly of nanoparticles: from compact packing to functional aggregates. Adv. Mater. 2018, 30, 1706558. Yu, Y.; Lu, X.; Guillaussier, A.; Voggu, V. R.; Pineros, W.; Mata, M. d. l.; Arbiol J.; Smilgies, D.-M.; Truskett, T. M.; Korgel, B. A. Orientationally ordered silicon nanocrystal cuboctahedra in superlattices. Nano Lett. 2016, 16, 7814– 7821. Wang, T.; Zhuang, J.; Lynch, J.; Chen, O.; Wang, Z.; Wang, X.; LaMontagne, D.; Wu, H.; Wang, Z.; Cao, Y. C. Selfassembled colloidal superparticles from nanorods. Science 2012, 338, 358–363. Nagaoka, Y. Tan, T.; Li, R.; Zhu, H.; Eggert, D.; Wu, Y. A.; Liu, Y.; Wang, Z.; Chen, O. Superstructures generated from truncated tetrahedral quantum dots. Nature 2018, 561, 378– 382. Henzie, J.; Grunwald, M.; Widmer-Cooper, A.; Geissler, P. L.; Yang, P. Self-assembly of uniform polyhedral silver nanocrystals into densest packings and exotic superlattices. Nat. Mater. 2012, 11, 131–137. Wang, Z.; Schliehe, C.; Bian, K.; Dale, D.; Bassett, W. A.; Hanrath, T.; Klinke, C.; Weller, H. Correlating superlattice polymorphs to internanoparticle distance, packing density, and surface lattice in assemblies of PbS nanoparticles. Nano Lett. 2013, 13 (3), 1303–1311. Nagaoka, Y.; Chen, O.; Wang, Z.; Cao, Y. W. Structural control of nanocrystal superlattices using organic guest molecules. J. Am. Chem. Soc. 2012, 134 (6), 2868–2871. Weidman, M. C.; Yager, K. G.; Tisdale, W. A. Interparticle spacing and structural ordering in superlattice PbS nanocrystal solids undergoing ligand exchange. Chem. Mater. 2015, 27, 474–482. Wang, Z.; Bian, K.; Nagaoka, Y.; Fan, H.; Cao, Y. C. Regulating multiple variables to understand the nucleation and growth and transformation of PbS nanocrystal superlattices. J. Am. Chem. Soc. 2017, 139, 14476–14482. Quan, Z.; Xu, H.; Wang, C.; Wen, X.; Wang, Y.; Zhu, J.; Li, R.; Sheehan, C. J.; Wang, Z.; Smilgies, D.-M.; Luo, Z.; Fang, J. Solvent-mediated self-assembly of nanocube superlattices. J. Am. Chem. Soc. 2014, 136, 1352–1359. Chan, H.; Demortière, A.; Vukovic, Král, P.; L.; Petit, C. Colloidal nanocube supercrystals stabilized by multipolar coulombic coupling. ACS Nano 2012, 6 (5), 4203–4213. Tao, A.; Sinsermsuksakul, P.; Yang, P. Tunable plasmonic


Page 9 of 11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


21.

22.

23.

24.

25.

26. 27.

28. 29.

30.

31.

32.

33.

34.

35.

36.

lattices of silver nanocrystals. Nat. Nanotechnol. 2007, 2, 435–440. Choi, J. J.; Bian, K.; Baumgardner, W. J.; Smilgies, D.-M.; Hanrath, T. Interface-induced nucleation, orientational alignment and symmetry transformations in nanocube superlattices. Nano Lett. 2012, 12, 4791-4798. Wetterskog, E.; Agthe, M.; Mayence, A.; Grins, J.; Wang, D.; Rana, S.; Ahniyaz, A.; Salazaar-Alvarez, G.; Bergstrom, L. Precise control over shape and size of iron oxide nanocrystals suitable for assembly into ordered particle arrays. Adv. Mater. 2014, 15, 055010. Yang, Y.; Lee, Y. H.; Phang, I. Y.; Jiang, R.; Sim, H. Y. F.; Wang, J. F.; Ling, X. Y. A chemical approach to break the planar configuration of Ag nanocubes into tunable twodimensional metasurfaces. Nano Lett. 2016, 16, 3872-3878. Dang, F.; Kato, K.; Imai, H.; Wada, S.; Haneda, H.; Kuwabara, M. Characteristics of multilayered nanostructures of CeO2 nanocrystals self-assembled on an enlarged liquid-gas interface. Cryst. Growth Des. 2011, 11, 4129-4134. Kato, K.; Dang, F.; Mimura, K.; Kinemuchi, Y.; Imai, H.; Wada, S.; Osada, M.; Haneda, H.; Kuwabara, M. Nano-sized cube-shaped single crystalline oxides and their potentials; composition, assembly and functions. Adv. Powder Tech. 2014, 25, 1401-1414. Soligno, G.; Dijkstra, M.; Roij, R. V. Self-assembly of cubes into 2D hexagonal and honeycomb lattices by hexapolar capillary interactions. Phys. Rev. Lett. 2016, 116, 258001. Disch, S.; Wetterskog, E.; Hermann, R. P.; Salazar-Alvarez, G.; Busch, P.; Brückel, T.; Bergström, L.; Kamali, S. Shape induced symmetry in self-assembled mesocrystals of iron oxide nanocubes. Nano Lett. 2011, 11, 1651-1656. Singh, G.; Cha, H.; Baskin, A.; Gelman, E.; Repnin, N.; Kral, P.; Klajn, R. Self-assembly of magnetite nanocubes into helical superstructures. Science 2014, 345, 1149-1153. Yang, H. J.; He, S. Y.; Chen, H. L.; Tuan, H. Y. Monodisperse copper nanocubes: synthesis, self-assembly, and large-area dense-packed films. Chem. Mater. 2014, 26, 1785-1793. Eggiman, B. W.; Tate, M. P.; Hillhouse, H. W. Rhombohedral structure of highly ordered and oriented selfassembled nanoporous silica thin films. Chem. Mater. 2006, 18, 723-730. Wang, T.; Wang, X.; LaMontagne, D.; Wang, Z.; Wang, Z.; Cao, Y. C. Shape-controlled synthesis of colloidal superparticles from nanocubes. J. Am. Chem. Soc. 2012, 134, 18225-18228. Li, R.; Bian, K.; Wang, Y.; Xu, H.; Hollingsworth, J. A.; Hanrath, T.; Fang, J.; Wang, Z. An obtuse rhombohedral superlattice assembled by Pt nanocubes. Nano Lett. 2015, 15, 6254-6260. Zhang, J.; Zhu, J.; Li, R.; Fang, J.; Wang, Z. Entropy-driven Pt3Co nanocube assembles and thermally mediated electrical conductivity with anisotropic variation of the rhombohedral superlattice. Nano Lett. 2017, 17, 362-367. Agthe, M.; Plivelic T. S.; Labrador, A.; Bergstrom L.; Salazar-Alvarez, G. Following in real time the two-step assembly of nanoparticles into mesocrystals in levitating drops. Nano Lett. 2016, 16, 6838-6843. Meijer, J. M.; Byelov, D. V.; Rossi, L.; Snigirev, A.; Snigireva, I.; Philipse A. P.; Petukhov, A. V. Self-assembly of colloidal hematite cubes: a microradian X-ray diffraction exploration of sedimentary crystals. Soft Matter 2013, 9, 10729-10738. Yang, P. W.; Thoka, S.; Lin, P. C.; Su, C. J.; Sheu, H. S.; Huang, M. H.; Jeng, U. S. Tracing the surfactant-mediated nucleation, growth, and superpacking of gold supercrystals

37.

38.

39.

40.

41.

42. 43.

44.

45.

46.

47.

48.

49.

50.

51.

using time and spatially resolved x-ray scattering. Langmuir 2017, 33, 3253-3261. Wang, B.; Wang, X.; Zou, J.; Yan, Y.; Xie, S.; Hu, G.; Li, Y.; Dong A. Simple-cubic carbon frameworks with atomically dispersed iron dopants toward high-efficiency oxygen reduction. Nano Lett. 2017, 17, 2003-2009. Li, F.; Delo, S. A.; Sterin, A. Disassembly and selfreassembly in periodic nanostructures: a face-centered-tosimple-cubic transformation. Angew. Chem. Int. Ed. 2007, 46, 6666-6669. Meijer, J. M.; Pal, A.; Ouhajji, S.; Lekkerkerker, H. N. W.; Philipse, A. P.; Petukhov, A. V. Observation of solid–solid transitions in 3D crystals of colloidal superballs. Nat. Comm. 2017, 14352. Quan, Z.; Loc, W. S.; Lin, C.; Luo, Z.; Yang, K.; Wang, Y.; Wang, H.; Wang, Z.; Fang, J. Tilted face-centered-cubic supercrystals of PbS nanocubes. Nano Lett. 2012, 12, 44094413. Wang, T.; Li, R.; Quan, Z.; Loc, W. S.; Bassett, W. A.; Xu, H.; Cao, Y. C.; Fang, J.; Wang, Z. Pressure processing of nanocube assemblies toward harvesting of a metastable PbS phase. Adv. Mater. 2015, 27, 4544-4549. Zhang, Y.; Lu, F.; van der Lelie, D.; Gang, O. Continuous phase transformation in nanocube assemblies. Phys. Rev. Lett. 2011, 107, 135701. Wang, D.; Hermes, M.; Kotni, R.; Wu, Y.; Tasios, N.; Liu, Y.; Nijs, B. d.; Van der Wee, E. B.; Murray, C. B.; Dijkstra, M.; van Blaaderen, A. Interplay between spherical confinement and particle shape on the self-assembly of rounded cubes. Nat. Comm. 2018, 9, 2228. Wang, Z.; Chen, O.; Cao, C. Y.; Finkelstein, K.; Smilgies, D.-M.; Lu, X.; Bassett, W. A. Integrating in situ high pressure small and wide angle synchrotron x-ray scattering for exploiting new physics of nanoparticle supercrystals. Rev. Sci. Instrum. 2010, 81, 093902. Bian, K.; Wang, Z.; Hanrath, T. Comparing the structural stability of PbS nanocrystals assembled in fcc and bcc superlattice allotropes. J. Am. Chem. Soc. 2012, 134, 10787−10790. Jiang, Z. GIXSGUI: a MATLAB toolbox for grazingincidence x-ray scattering data visualization and reduction, and indexing of buried three-dimensional periodic nanostructured films. J. Appl. Crystal. 2015, 48, 917-926. Li, R.; Bian, K.; Hanrath, T.; Bassett, W. A.; Wang, Z. Decoding the superlattice and interface structure of truncate PbS nanocrystal-assembled supercrystal and associated interaction forces. J. Am. Chem. Soc. 2014, 136, 1204712055. Lu, C.; Akey, A. J.; Dahlman, C. J.; Zhang, D.; Herman, I. P. Resolving the growth of 3D colloidal nanoparticle superlattices by real-time small-angle x-ray scattering. J. Am. Chem. Soc. 2012, 134, 18732-18738. Montanarella, F.; Geuchies, J. J.; Dasgupta, T.; Prins, P. T.; van Overbeek, C.; Dattani, R.; Baesjou, P.; Dijkstra, M.; Petukhov, A. V.; van Blaaderen, A.; Vanmaekelbergh, D. Crystallization of nanocrystals in spherical confinement probed by in situ x-ray scattering. Nano Lett. 2018, 18 (6), 3675–3681. Wang, Z.; Wen, X.-D.; Hoffmann, R.; Son, J. S.; Li, R.; Fang, C.-C.; Smilgies, D.-M.; Hyeon, T. Reconstructing a solid-solid phase transformation pathway in CdSe nanosheets with associated soft ligands. Proc. Natl. Acad. Sci. U. S. A. 2010, 107 (40) 17119–17124. Li, R.; Zhang, J.; Tan, R.; Gerdes, F.; Luo, Z.; Xu, H.; Hollingsworth, J. A.; Klinke, C.; Chen, O.; Wang, Z. Competing interactions between various entropic forces toward assembly of Pt3Ni octahedra into a body-centered cubic superlattice. Nano Lett. 2016, 16 (4), 2792–2799.



52. Maiti, S.; André, A.; Banerjee, R.; Hagenlocher, J.; Konovalov, O.; Schreiber, F.; Scheele, M. Monitoring selfassembly and ligand exchange of PbS nanocrystal superlattices at the liquid/air interface in real time. J. Phys. Chem. Lett. 2018, 9, 739–744. 53. Zhang, D.; Lu, C.; Hu, J.; Lee, S. W.; Ye, F.; Herman, I. P. Small angle x-ray scattering of iron oxide nanoparticle monolayers formed on a liquid surface. J. Phys. Chem. C. 2015, 119, 10727–10733.

54.

Page 10 of 11

Geuchies, J. J.; van Overbeek, C.; Evers, W. H.; Goris, B.; Backer, A.; Gantapara, A. P.; Rabouw, F. T.; Hilhorst, J.; Peters, J. L.; Konovalov, O.; Petukhov, A. V.; Dijkstra, M.; Siebbeles, L. D. A.; van Aert, S.; Bals, S.; Vanmaekelbergh, D. In situ study of the formation mechanism of twodimensional superlattices from PbSe nanocrystals. Nat. Mater. 2016, 15, 1248–1254.


Page 11 of 11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table of Contents (TOC)

11 Environment ACS Paragon Plus

Understanding Fe3O4 Nanocube Assembly with ... - ACS Publications

Recommend Documents