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Symmetry-Driven Spontaneous Self-Assembly of Nanoscale Ceria Building Blocks to Fractal Superoctahedra Satyanarayana V. N. T. Kuchibhatla,*,†,‡ A. S. Karakoti,‡ D. C. Sayle,§ H. Heinrich,‡ and S. Seal*,‡

CRYSTAL GROWTH & DESIGN 2009 VOL. 9, NO. 3 1614–1620

EMSL, Pacific Northwest National Laboratory, Richland, Washington 99354, AdVanced Materials Processing and Analysis Center, UniVersity of Central Florida, Orlando, Florida 32816, Department of Applied Science Security and Resilience, Cranfield Defence and Security, Defence Academy of the United Kingdom, Swindon, UK SN6 8LA, and Nanoscience and Technology Center, UniVersity of Central Florida, Orlando, Florida 32816 ReceiVed December 14, 2008

ABSTRACT: A combination of long-term aging studies and molecular dynamics (MD) simulations has been successfully used to explain the time-dependent hierarchical assembly of ceria nanoparticles (CNPs). When the CNPs were aged in as-synthesized condition at room temperature in water, it was observed that the individual 3-5 nm CNPs result in octahedral superstructures through a fractal assembly. This hierarchical fractal self-assembly was observed despite the absence of any surfactant, at room temperature, and under atmospheric pressure. High resolution transmission electron microscopy (HRTEM) and fast Fourier transform (FFT) analysis have been used to explore the assembly of the individual nanoparticles into fractal superoctahedra. Both experimental work and theoretical analysis showed that the initial octahedral and truncated octahedral seeds symmetrically assemble and result in the superoctahedra with intermediate transformation steps. Introduction The quest for improving the performance of materials in various functional applications and the enthusiasm to mimic the nature to produce ultrastrong, highly versatile, low-cost materials have been driving forces behind the past decade of materials research. During the course of this development, it has been realized that the assembly of nanoparticles can lead to entirely different frontiers in research and development.1 Researchers across the globe have achieved a significant control over the size, shape, self-assembly, and properties of semiconductor and metallic materials.1,2 Similar levels of knowledge and control are required for functional oxides such as cerium, titanium, zinc, and zirconium oxides. Use of fluorite-structured oxides (such as ceria, zirconia) for fast ion conduction in solid oxide fuel cells (SOFCs), as catalyst support and, lately, in solar cells and biomedical applications makes the understanding of their size, shape, and structural evolution of paramount importance.3-6 It is well established that energetically and topologically favored structures are needed to selectively utilize various properties of these materials.7 In order to meet the demands of material requirements and explore the complexities, Billinge and Levin8 have recently emphasized the need for a “complex modeling” paradigm combining theory and experiment in a self-consistent computational framework. This approach is expected to provide a comprehensive solution for the complex nanostructural problem, which is beyond the reach of a conventional materials analysis approach. In an effort to address this challenging issue, we have recently presented a systematic enumeration of nanostructural building blocks into complex crystalline structures.9 In addition to the conventional colloidal crystallization aspects, researchers have reported significantly important and consistently evolving approaches for “superstructure” formation from individual building blocks, namely, the “oriented attach* Corresponding author. E-mail: [email protected] (S.V.N.T.K.); sseal@ mail.ucf.edu (S.S.). † Pacific Northwest National Laboratory. ‡ Advanced Materials Processing and Analysis Center. § Defence Academy of the United Kingdom.

Figure 1. (a) TEM images of as-synthesized CNPs showing 15-20 nm agglomerates (inset); SAED pattern confirms the ceria fluorite structure.

ment” pioneered by Penn, Banfield et al.,10-12 and the mesocrystal formation through the so-called “non-classical crystallization” approach analyzed by Colfen et al.13,14 It is interesting to note that often the leads for understanding the behavior of nanoscale materials and their superstructures were obtained from the biomolecules and the mineral structures.15 Ceramic oxides (such as ceria, titania, and zirconia) with their close structural proximity to the minerals have already seen some benefit from this approach. Hence, we take a similar approach and elucidate the behavior of “superstructure” evolution in nanoscale cerium oxide (ceria). Ceria nanoparticles (CNPs) have gained a significant attention from chemists, physicists, and materials scientists due to their fundamental and technologically interesting redox chemistry.6 CNPs can efficiently switch between 3+ and 4+ oxidation states depending on the ambient conditions. The increased defect concentration at the surface of ultrasmall particles (smaller than 10 nm) can improve their performance in catalysis, solar cells, and disease treatment/prevention.16 Soft chemistry routes have been widely used to synthesize CNPs. Several research groups, including our group, showed that the individual CNPs have octahedral and truncated octahedral shapes with {111} and

10.1021/cg801358z CCC: $40.75  2009 American Chemical Society Published on Web 02/04/2009

Nanoscale Ceria Building Blocks to Fractal Superoctahedra

Crystal Growth & Design, Vol. 9, No. 3, 2009 1615

Figure 2. (a) TEM images of CNPs aged for one week or longer showing polyhedral agglomerates with about 50 nm diameter (inset); SAED pattern confirms the ceria fluorite structure; (b) high-resolution micrograph of a portion of the superoctahedron (inset) FFT pattern.

Figure 3. Different regions identified in (a) and (b) indicate the individual (representative) nanoparticle building blocks with octahedral symmetry enclosed by the low energy {111} and {200} planes. A schematic depiction of an octahedron in a cubic cell is given in (c), while (d) shows a possible truncation plane in the octahedron that appears as a hexagon in top view. Various planes and directions of interest are identified in a cube.

{100} surface terminations. While Sayle and co-workers have used molecular dynamics (MD) simulations to examine this fact, Gunter’s group used electron tomography to confirm the octahedral morphology of the CNPs.17-20 Yan et al.21 have reported synthesis of ceria nanorods and octahedral particles through a template-free, hydrothermal approach. Evidently, most of the experimental and theoretical studies have been confined to “single crystal” ceria particles synthesized through relatively high-energy conditions. In contrast, we have synthesized the CNPs at room temperature and aged for relatively long periods (several days to weeks). The observed spontaneous selfassembly and the effect of temperature and synthesis medium on the nanoparticle behavior were described previously.22 After a systematic analysis, we have proposed a possible model for the template free, hierarchical assembly of CNPs at room

Figure 4. (a) An agglomerate of ∼20 nm consisting of various smaller particles. The inset (b) is a FFT pattern of the image indicating the polycrystalline nature of the agglomerate. The (1) white dotted circle indicates two different particles coming together at an angle. This kind of interaction between two particles will result in a high-energy interface and interfacial defects (shown with a dotted white arrow in the picture). As shown in panel (c) the particles may undergo intra-agglomerate rotation and align the planes to attain a low-energy interface (3). The black dotted circle indicates the ∼3 nm size of individual constituents in the agglomerate (2), the white dotted circle shows the joining of two particles with similar planes with coherent interface, and the arrow indicates an interfacial dislocation.

temperature and when aged under frozen conditions.23 The truncated octahedral seeds of ceria preferentially assemble into secondary and tertiary structures, while retaining the octahedral symmetry through close packing similar to the growth of fractal structures. Earlier, Alvarez24 systematically explained the significance of various polyhedral morphologies in inorganic chemistry. It was quoted “despite the small recognition, the ‘superoctahedron’ (an octahedron made of a number of octahedra) does exist in chemistry”. However, most of these reported instances were with metallic clusters or at the atomic bonding level. For the first time, we report “superoctahedra” in oxide nanostructures. Here, we present a 2-fold approach to understand the evolution of superoctahedra from individual CNPs. In this manuscript, our template-free, time-dependent, hierarchical selfassembly model of CNPs leading to the formation of a fractal like superoctahera is critically examined with the help of highresolution transmission electron microscopy (HRTEM) analysis.

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Kuchibhatla et al.

Figure 5. Representations of the atomic position comprising the CNPs after (a) 1 ns, (b) 1.5 ns, and (c) 6 ns. Left: the atomic positions are shown as large spheres to enable one to visualize and appreciate the 3D “shape” and right: the spheres are smaller to better communicate the epitaxy between agglomerated CNPs. The colors for the atom positions are blue and white to better distinguish individual CNPs. Oxygen is not shown to improve clarity of the figures.

Figure 6. (a) HRTEM image of the ceria nanoparticle agglomerates; the white circle shows at least three different smaller agglomerates forming a larger agglomerate and the inset is a FFT of the region marked with red-dots. (b) Fourier filtered image formed by selectively masking the {111} planes, applying inverse Fourier transform. Various interfacial defects and interparticle boundaries are identified.

We support the experimental findings with molecular dynamics (MD) simulations. The simulations have successfully predicted the formation of single crystal octahedral and truncated octa-

hedral seeds of ceria, in collusion with the experimental findings,17,25 which further lead to the formation of fractal superoctahedra.



sin(bπV) ( sin(aπu) πu πV )

L(u, V) ) δ(u, V) + 4σ2φ2(u, V) sin2 γ

2

where a, b present the dimensions of the area in which the micrograph is collected. δ is the delta function in two dimensions, φ(u,V) is the Fourier transform of φ(x, y) - the phase change, u, V are the coordinates of the diffraction plane, σ is the interaction constant, and γ is the phase shift of the electron waves at the focal plane. The WPOA may not be valid in the case of the small particles that result in inelastic scattering and even in some cases with refraction effects. However, JoseYacaman et al.2 have shown that the fast-Fourier transform (FFT) can also be used for crystallographic analysis under dynamic scattering conditions. Although the intensities of the diffraction spots may not be equal to those obtained in the FFT, the distance between the spots in FFT is still equal to g. The most significant advantage offered by the FFT analysis results from the ability to choose the area of interest. Even very small sizes can be chosen within an image and processed to obtain the crystallographic information of individual nanoparticles, as shown in the Supporting Information, Figures SI-1, SI-2, and SI-3. Figure 7. Representations of the atom positions comprising the model CNP after attachment. (a) Three CNPs attached at {100}; the coherent interfaces are shown more clearly in (b) and a schematic detailing the behavior in (c). In (d) an enlarged interfacial region is shown, revealing the considerable transport of ions (highlighted by the gray rectangle) to the interfacial region during the simulation to facilitate a coherent interface.

Details about the synthesis of CNPs and their time-dependent morphological evolution can be found in a previous publication.22 Detailed methodologies of the MD simulations used in this manuscript are described in a recent publication.26 The HRTEM images were collected using an FEI-TECNAI F-30 system at 300 kV with a point-to-point resolution of 0.2 nm. Image analysis was done using the GATAN digital micrograph software. TEM images of the CNPs were collected in assynthesized condition and at different aging times. The TEM samples were prepared by dipping a holey-carbon coated copper grid in the nanoparticles’ suspension. These grids were dried at room temperature in anaerobic conditions and used for imaging. Purpose and Significance of FFT in HRTEM Analysis. HRTEM is an indispensable technique for understanding the internal structural and morphological aspects of nanoscale materials.8 Bright-field imaging coupled with diffraction analysis is often used to achieve this. However, even in a perfectly aligned microscope, the images acquired often suffer from a significant amount of unwanted noise either from crystalline or amorphous supports used to hold the samples.27,28 This noise may create problems while analyzing the structures of nanoparticles. Furthermore, it may be very tedious to work with ultrasmall particles to attain their individual diffraction pattern. Even with the smallest possible selected-area aperture, the area under selection may contain a number of particles contributing to the diffraction pattern and may result in features not true for an individual particle. Hence, use of image processing techniques to analyze the individual nanoparticles and smaller agglomerates is an effective alternative. Image processing in the Fourier space and the inverse Fourier transforms eliminate the unwanted noise from the images. Fourier transforms of the image are similar to diffraction patterns for the imaging done under weak phase object approximation (WPOA).2,29 The intensity of the transform was calculated by Tomita et al.29 as

Discussion In as-synthesized condition, CNPs were found to form 15-20 nm agglomerates constituted with 3-5 nm individual particles as shown in Figure 1a. The selected-area electron diffraction pattern (SAEDP) is consistent with the ceria fluorite structure (PDF# - 034 - 0394) Figure 1a, inset. The high-magnification micrograph clearly shows that most of the lattice fringes correspond to the {111} lattice planes with a majority of the surface planes in Bragg condition (image not shown here). It should be noted that the agglomerates do not have any specific morphology in the as-synthesized condition. When the solutions are aged for three weeks or more,22 polyhedral structures in the size range of 50-70 nm are observed (Figure 2a). The size of these polyhedral structures increases up to 150 nm with further aging. Despite the larger agglomerate size, the individual building blocks remain 3-5 nm in size (Figure 2b). The crystallinity of the polyhedra is confirmed by SAED patterns (inset Figure 2a) and FFT (inset Figure 2b), respectively. Having observed the consistent evolution of the polyhedral superstructures, we have compared this morphology with existing platonic solids, and it was clear from the images taken at different tilt angles (not shown here) that the morphology matches the “octahedral” shape. Following is an in-depth analysis on the formation mechanism of the “superoctahedra” formed from the individual octahedral building blocks supported by theoretical investigations. The time-dependent formation of fractal superoctahedra represents a two-stage agglomeration behavior of nanoparticles. (1) Instantaneous agglomeration of initial individual nanoparticles into primary agglomerates. (2) Preferred or oriented agglomeration of primary agglomerates into superoctahedra. We have analyzed the characteristics of the individual particles followed by primary agglomerates and then the agglomeration of the individual agglomerates to the final structure. The observations are reconfirmed by the results from MD simulations. Morphological Evolution of Ceria Nanoparticles into Superoctahedron. The formation of a particular shape is based on the arrangement of different planes and their conformation in energetically favorable orientations. The reason for time dependence of these shapes can be readily understood by the fact that the growing planes of the ceria crystallites are the close


Kuchibhatla et al.

Figure 8. (a) Image showing corners, faces, and edges of the octahedron (colors in a BF TEM image were reversed to enhance the clarity); (b) HRTEM image of a corner of the octahedron with individual building blocks of ∼5 nm identified with circles; the inset is an FFT confirming the crystallinity of the structure.

Figure 9. Fractal self-assembly: Schematic describing the proposed mechanism underlying the self-assembly of CNPs into fractal superoctahedra: Truncated octahedral CNPs, (a), self-assemble at {100}, (b), and {111}, (c), to facilitate an octahedral superstructure, (d). These superstructures then assemble to form superoctahedra, (e); successive generations (f) and (g) all facilitate octahedral shapes.

packed {111} planes, constituting the facets of the individual building blocks following the Wulff criterion.14 If the growth process is not complete, the octahedron will end up as a truncated octahedron with both {100} and {111} facets constituting the surface. Individual ceria nanoparticles with {111}

and {100} facets and the schematic models of the octahedral and truncated octahedral facets are shown in Figure 3. During the course of agglomeration, particles align planes with similar interplanar spacing at the interface to attain coherency. Confluence of two particles with similar planes at an angle (no specific alignment) results in incoherent interfaces and interfacial defects. However, the planes spontaneously align themselves to form a low-energy interface. This can be achieved by intra-agglomerate rotation as presented in Figure 4(1c). The nature of the interface between two particles with aligned and misaligned planes is also shown in Figure 4. The dotted lines help the reader visualize as a top view image of an octahedron, with the basal plane normal to the electron beam. The visualization of different planes in an individual particle constituting the agglomerates and their relative orientation could be achieved through FFT analysis. The spontaneous assembly and the final morphological evolution are highly dependent on the nature of the interfacial plane. Whether the individual nanoparticles are octahedra or truncated octahedra plays a major role in deciding the orientation of the planes at the interface through either {100} or {111}. A clear description of the rearrangement of nanoparticles is observed through MD simulations as well. By introducing four (evenly spaced) model CNPs (each comprising about 16 000 atoms) into a cubic simulation cell with dimensions 18 × 18 × 18 nm3 and allowing the nanoparticles to agglomerate, we obtain similar agglomeration and orientation relationships of particles. In Figure 5, snapshots of the atomic positions comprising the model CNPs, as a function of time, are shown. Inspection of animations depicting the agglomeration reveal that the nanoparticles are strongly attractive and move closer together and attach. An animation showing the attachment and realignment of two CNP is provided as part of Supporting Information. The initial attachment results in a misalignment of lattice planes (Figure 5a). However, as the simulation continues, the CNPs rearrange to facilitate a coherent alignment (Figure 5b,c). Further attachment of two smaller agglomerates to form a secondary structure (while evolving as octahedron) will proceed with the incorporation of defects. The strain at the interface is often relieved through formation of interfacial defects as shown in the Figure 6. It is very difficult to visualize any features or defects from the as-obtained micrograph. However, when planes corresponding to {111} are selectively masked and a filtered


image is acquired the features become evident as shown in Figure 6b. Within the agglomerate, nanoparticles are found to form twin and twist boundaries to accommodate interfacial strain. Similar incorporation and elimination of defects was observed through MD simulations. As the time progresses the MD simulation becomes more consistent with the experimental observations. Continuation of nanoparticles in Figure 5 shows that after 6 ns, three CNPs have rearranged to attach at {100} planes (Figure 7a). The interface is coherent as evidenced from Figure 7b; a schematic of the self-assembly is shown in Figure 7c. Attachment at {100} is perhaps not surprising because the surface is less stable compared with {111} surfaces.17 Accordingly, CNPs, attached at {100} planes, would not expose such (unstable) surfaces. Indeed, fluorite {100} surfaces are inherently dipolar,30 although we note that during crystallization of the nanoparticle, the process is able to quench the dipole.7 The simulations also reveal (Figure 7d) that there is significant transport of ions (comprising the CNPs) to interfacial regions presumably to facilitate a coherent (and therefore energetically more stable) interface between neighboring CNPs. Features similar to this can be expected but may not be categorically proved by HRTEM analysis; hence the simulations prove vital. So far, we have seen the characteristics of the individual particles and the agglomerates. The next and most important aspect of interest is the nature of the final superoctahedron. While the low magnification micrograph (colors inverted to enhance the features) shows the 8 faces (similar to the {111} facets in single crystal octahedron), 6 corners, and 12 edges; the high resolution images confirm the presence of 3-5 nm individual particles in the 50-70 nm agglomerates (Figure 8). Occasionally, we have seen the final octahedra with a different contrast at the center. The differences in effective thickness of the structure being imaged might be the reason for such an observation. Based on the HRTEM observations, Figures 8 and 9 and the MD simulations we propose that some of the final octahedra may contain a cavity at the center, Figure SI-4, Supporting Information. The exact mechanism through which the cavity is created is not clear at this point. However, the MD simulations indicate that the possible reason for the cavity is the self-assembly with the {100} planes at the interface. Formation of hollow cubes of ceria has been reported very recently31 wherein Chen et al. reported the oriented agglomeration of individual nanoparticles into cubes which further leads to formation of hollow nanocubes due to Ostwald ripening effects. In contrast to what we have observed in this manuscript, Chen et al. did not observe individual nanoparticles in the presence of H2O2. We believe that the aging is a key factor that contributed to the superoctahedral structures and various aspects reported by other researchers along with the role of precursors will be the focus of future studies. In a manner analogous to the one proposed by Chen et al.31 we predict that a similar mechanism may be contributing to the formation of hollow at the center in ceria superoctahedra. While the room temperature conditions in our work has retained the polycrystalline nature of particle, very high energy provided by the hydrothermal conditions might have contributed to the singlecrystal-like structure. As proposed earlier in the manuscript, whether the starting building unit of a ceria nanoparticle is an octahedron or truncated octahedron may decide whether the attachment of nanoparticles is through {100} or {111} planes. To clarify this aspect, in a second set of simulations, we positioned four CNPs (each comprising 16 000 atoms) into a simulation cell: a ) b ) c )


13 nm; R ) β ) γ ) 90° with CNPs located at face-centered positions and performed constant pressure MD simulation at 253 K (-20 °C as synthesized) and at 3400 K for 1.5 ns. Periodic boundary conditions were imposed throughout. The final atomistic structures of the superlattices are shown in Figure SI-5 [Figure SI 5a,b, Supporting Information for 253 and 3400 K, respectively]. In both cases the CNPs agglomerate together and attach at {111} faces to facilitate close packed superstructures. Final lattice parameters are Low temperature: a ) 10.5 nm b ) 11.1 nm c ) 11.1 nm R ) 95.4° β ) 87.2° γ ) 85.6° High temperature: a ) 9.6 nm b ) 9.8 nm c ) 11.3 nm R ) 98.8° β ) 86.2° γ ) 88.0° At low temperature, the CNPs approximate to a (cubic) close packed structure. Conversely, for the high-temperature system, there is significant elongation of the c-parameter (compared with a and b) together with an increased angle (R ) 98.8°). Projections along each of the three axes of Figure SI 5b, Supporting Information are shown in Figure SI 5c-e, Supporting Information. The images reveal that the CNPs are packed tightly (via {111}) in “octahedral” fashion. Accordingly, based upon experimental evidence supported by simulation we theorize that the CNPs self-assemble into fractal octahedral superlattices. A schematic detailing of the proposed mechanism is shown in Figure 9. Specifically, CNPs, 9(a), attract one another and move closer together. However, initially, the CNP are misoriented with respect to one another. The CNPs then reorient to facilitate coherent (energetically stable) interfaces. Specifically, the nanoparticles can attach at {100} interfaces, Figure 9b. Attachment may be improved by substantial transport of ions (comprising the CNP) to interfacial regions. To facilitate an octahedral structure, six CNPs attach at {100} and {111} planes, Figure 9c. These octahedral superlattices can then self-assemble into superoctahedra in successive fractal-like steps, Figure 9(d-e), (e-f), (f-g). The reason for simulating the systems at (artificially) high temperature is to equip the atoms comprising the CNPs with sufficient energy to enable them to overcome activation energy barriers. This strategy enables one to offset, in part, the low (nanosecond) durations accessible using molecular dynamical simulation. Also the fact that our simulations were performed in vaccuo is not entirely an actual representation of true experimental conditions. However, we note that the effect of solvent plays a significant role in CNPs self-assembly, and therefore we advocate that water be introduced into future simulations. At present this is computationally prohibitive because it would require 1-2 orders of magnitude more CPU. Most of the previous experimental studies on the CNPs or, in general, on nanoparticles25,32-35 were confined to very short time periods. Except for the work reported by Matijevic,36 the assembly of CNPs was often induced by the use of surfactants and templates.37 Matijevic reported the formation of 2-d hexagonal arrays and rodlike structures of CNPs in a waterbased environment and attributed different morphologies to the reactant concentration and type of anions. Deshpande et al.38 have reported the mesoscale assembly of monodispersed ceria nanoparticles in the presence of surfactants. While both these studies are significant, the role of long-term aging and a detailed analysis of the 3-d superstructures observed in our studies stand unique. We, for the first time, studied the aging characteristics of the CNPs in as-synthesized condition for more than 300 days at room temperature. The realization of these fractal structures in ceria and the unique morphology was only possible because of the long-term aging studies undertaken by our group. With


the increasing use of the nanoparticles in multiple applications, where they are often supplied in suspension, these findings are significant as they predict the time-dependent agglomeration tendency of nanoparticles at room temperature in the absence of any surfactants. Conclusion With HRTEM and FFT analysis, we have shown that the individual building blocks of CNPs spontaneously assemble to form superoctahedral structures supported well by the outcome of the MD simulations. The simulation results have proven to be vital in confirming the formation of superoctahedra as a result of the fractal agglomeration of nanoscale octahedral building blocks of ceria. With the help of FFT, the orientation of the nanoparticles within the agglomerates and their interfacial defects are analyzed. The nanoparticles undergo an intraagglomerate rotation to align in a preferred direction while forming the final morphology. Acknowledgment. Authors would like to acknowledge the partial funding support from NSF under the Grants NSF NIRT CBET-0708172 and NSF CMMI: -0629080 and CambridgeCranfield HPC facility. A portion of the research was performed using EMSL, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research located at Pacific Northwest National Laboratory (PNNL). PNNL is a multiprogram national laboratory operated for the U.S. DOE by Battelle Memorial Institute under Contract No. DE-AC06-76RLO 1830. Supporting Information Available: HRTEM images, FFTs, SAED patterns, TEM images, atomistic structures of CNPs and MD simulations. This material is available free of charge via the Internet at http:// pubs.acs.org.

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