Is Geometric Frustration-Induced Disorder a Recipe for High Ionic Conductivity?

Ionic conductivity is ubiquitous to many industrially important applications such as fuel cells, batteries, sensors, and catalysis. Tunable conductivity in these systems is therefore key to their commercial viability. Here, we show that geometric frustration can be exploited as a vehicle for conductivity tuning. In particular, we imposed geometric frustration upon a prototypical system, CaF2, by ball milling it with BaF2, to create nanostructured Ba1-xCaxF2 solid solutions and increased its ionic conductivity by over 5 orders of magnitude. By mirroring each experiment with MD simulation, including "simulating synthesis", we reveal that geometric frustration confers, on a system at ambient temperature, structural and dynamical attributes that are typically associated with heating a material above its superionic transition temperature. These include structural disorder, excess volume, pseudovacancy arrays, and collective transport mechanisms; we show that the excess volume correlates with ionic conductivity for the Ba1-xCaxF2 system. We also present evidence that geometric frustration-induced conductivity is a general phenomenon, which may help explain the high ionic conductivity in doped fluorite-structured oxides such as ceria and zirconia, with application for solid oxide fuel cells. A review on geometric frustration [ Nature 2015 , 521 , 303 ] remarks that classical crystallography is inadequate to describe systems with correlated disorder, but that correlated disorder has clear crystallographic signatures. Here, we identify two possible crystallographic signatures of geometric frustration: excess volume and correlated "snake-like" ionic transport; the latter infers correlated disorder. In particular, as one ion in the chain moves, all the other (correlated) ions in the chain move simultaneously. Critically, our simulations reveal snake-like chains, over 40 Å in length, which indicates long-range correlation in our disordered systems. Similarly, collective transport in glassy materials is well documented [for example, J. Chem. Phys. 2013 , 138 , 12A538 ]. Possible crystallographic nomenclatures, to be used to describe long-range order in disordered systems, may include, for example, the shape, length, and branching of the "snake" arrays. Such characterizations may ultimately provide insight and differences between long-range order in disordered, amorphous, or liquid states and processes such as ionic conductivity, melting, and crystallization.

Liquid crystal seed nucleates liquid-solid phase change in ceria nanoparticles.

Molecular dynamics (MD) simulation was used to explore the liquid-solid (crystal) phase change of a ceria nanoparticle. The simulations reveal that the crystalline seed, which spontaneously evolves and nucleates crystallisation, is a liquid rather than a solid. Evidence supporting this concept includes: (a) only 3% of the total latent heat of solidification had been liberated after 25% of the nanoparticle had (visibly) crystallised. (b) Cerium ions, comprising the (liquid) crystal seed had the same mobility as cerium ions comprising the amorphous regions. (c) Cerium ion mobility only started to reduce (indicative of solidification) after 25% of the nanoparticle had crystallised. (d) Calculated radial distribution functions (RDF) revealed no long-range structure when 25% of the nanoparticle had (visibly) crystallised. We present evidence that the concept of a liquid crystal seed is more general phenomenon rather than applicable only to nanoceria.

Visualizing the enhanced chemical reactivity of mesoporous ceria; simulating templated crystallization in silica scaffolds at the atomic level.

Unique physical, chemical, and mechanical properties can be engineered into functional nanomaterials via structural control. However, as the hierarchical structural complexity of a nanomaterial increases, so do the challenges associated with generating atomistic models, which are sufficiently realistic that they can be interrogated to reliably predict properties and processes. The structural complexity of a functional nanomaterial necessarily emanates during synthesis. Accordingly, to capture such complexity, we have simulated each step in the synthetic protocol. Specifically, atomistic models of mesoporous ceria were generated by simulating the infusion and confined crystallization of ceria in a mesoporous silica scaffold. After removing the scaffold, the chemical reactivity of the templated mesoporous ceria was calculated and predicted to be more reactive compared to mesoporous ceria generated without template; visual "reactivity fingerprints" are presented. The strategy affords a general method for generating atomistic models, with hierarchical structural complexity, which can be used to predict a variety of properties and processes enabling the nanoscale design of functional materials.

Mechanical properties of mesoporous ceria nanoarchitectures.

Architectural constructs are engineered to impart desirable mechanical properties facilitating bridges spanning a thousand meters and buildings nearly 1 km in height. However, do the same 'engineering-rules' translate to the nanoscale, where the architectural features are less than 0.0001 mm in size? Here, we calculate the mechanical properties of a porous ceramic functional material, ceria, as a function of its nanoarchitecture using molecular dynamics simulation and predict its yield strength to be almost two orders of magnitude higher than the parent bulk material. In particular, we generate models of nanoporous ceria with either a hexagonal or cubic array of one-dimensional pores and simulate their responses to mechanical load. We find that the mechanical properties are critically dependent upon the orientation between the crystal structure (symmetry, direction) and the pore structure (symmetry, direction).

Amorphization and recrystallization study of lithium insertion into manganese dioxide.

Various polymorphs of MnO(2) are widely used as electrode materials in Li/MnO(2) batteries. Electrolytic manganese dioxide (EMD) is the most electrochemically active form of MnO(2) and is very difficult to characterize. Their structural details are still largely unknown owing to the poor quality of X-ray diffraction (XRD) patterns obtained from most MnO(2) samples. Simulated amorphisation and crystallization technique was used to derive microstructural models for Li-MnO(2) which included most microstructural details that one would expect to find in the real material. Specifically, pyrolusite-MnO(2), comprising about 25,000 atoms, was amorphised (strain-induced) under molecular dynamics (MD) and different concentrations of lithium ions were inserted. Each system was then crystallized under MD simulation. The resulting models conformed to the pyrolusite polymorph, with microstructural features including: extensive micro-twinning and more general grain-boundaries, stacking faults, dislocations and isolated point defects and defect clusters. Molecular graphical images, showing the atom positions for the microstructural features together with simulated XRD patterns they give rise to, are presented and compared with measured XRD. The calculated XRD are in accord with experiment thus validating the structural models.

Predicting the electrochemical properties of MnO2 nanomaterials used in rechargeable li batteries: simulating nanostructure at the atomistic level.

Nanoporous beta-MnO2 can act as a host lattice for the insertion and deinsertion of Li with application in rechargeable lithium batteries. We predict that, to maximize its electrochemical properties, the beta-MnO2 host should be symmetrically porous and heavily twinned. In addition, we predict that there exists a "critical (wall) thickness" for MnO2 nanomaterials above which the strain associated with Li insertion is accommodated via a plastic, rather than elastic, deformation of the host lattice leading to property fading upon cycling. We predict that this critical thickness lies between 10 and 100 nm for beta-MnO2 and is greater than 100 nm for alpha-MnO2: the latter accommodates 2 x 2 tunnels compared with the smaller 1 x 1 tunnels found in beta-MnO2. This prediction may help explain why certain (nano)forms of MnO2 are electrochemically active, while others are not. Our predictions are based upon atomistic models of beta-MnO2 nanomaterials. In particular, a systematic strategy, analogous to methods widely and routinely used to model crystal structure, was used to generate the nanostructures. Specifically, the (space) symmetry associated with the nanostructure coupled with basis nanoparticles was used to prescribe full atomistic models of nanoparticles (0D), nanorods (1D), nanosheets (2D), and nanoporous (3D) architectures. For the latter, under MD simulation, the amorphous nanoparticles agglomerate together with their periodic neighbors to formulate the walls of the nanomaterial; the particular polymorphic structure was evolved using simulated amorphization and crystallization. We show that our atomistic models are in accord with experiment. Our models reveal that the periodic framework architecture, together with microtwinning, enables insertion of Li anywhere on the (internal) surface and facilitates Li transport in all three spatial directions within the host lattice. Accordingly, the symmetrically porous MnO2 can expand and contract linearly and crucially elastically under charge/discharge. We also suggest tentatively that our predictions for MnO2 are more general in that similar arguments may apply to other nanomaterials, which might expand and contract elastically upon charging/discharging.

Origin of electrochemical activity in nano-Li2MnO3; stabilization via a 'point defect scaffold'.

Molecular dynamics (MD) simulations of the charging of Li2MnO3 reveal that the reason nanocrystalline-Li2MnO3 is electrochemically active, in contrast to the parent bulk-Li2MnO3, is because in the nanomaterial the tunnels, in which the Li ions reside, are held apart by Mn ions, which act as a pseudo 'point defect scaffold'. The Li ions are then able to diffuse, via a vacancy driven mechanism, throughout the nanomaterial in all spatial dimensions while the 'Mn defect scaffold' maintains the structural integrity of the layered structure during charging. Our findings reveal that oxides, which comprise cation disorder, can be potential candidates for electrodes in rechargeable Li-ion batteries. Moreover, we propose that the concept of a 'point defect scaffold' might manifest as a more general phenomenon, which can be exploited to engineer, for example, two or three-dimensional strain within a host material and can be fine-tuned to optimize properties, such as ionic conductivity.

Shape of CeO2 nanoparticles using simulated amorphisation and recrystallisation.

Evolutionary simulation has been used to generate full atomistic models for CeO2 nanoparticles, which comprise [100]-truncated [111] octahedra in accord with experiments.

Environment-mediated structure, surface redox activity and reactivity of ceria nanoparticles.

Nanomaterials, with potential application as bio-medicinal agents, exploit the chemical properties of a solid, with the ability to be transported (like a molecule) to a variety of bodily compartments. However, the chemical environment can change significantly the structure and hence properties of a nanomaterial. Accordingly, its surface reactivity is critically dependent upon the nature of the (biological) environment in which it resides. Here, we use Molecular Dynamics (MD) simulation, Density Functional Theory (DFT) and aberration corrected TEM to predict and rationalise differences in structure and hence surface reactivity of ceria nanoparticles in different environments. In particular we calculate reactivity 'fingerprints' for unreduced and reduced ceria nanoparticles immersed in water and in vacuum. Our simulations predict higher activities of ceria nanoparticles, towards oxygen release, when immersed in water because the water quenches the coordinative unsaturation of surface ions. Conversely, in vacuum, surface ions relax into the body of the nanoparticle to relieve coordinative unsaturation, which increases the energy barriers associated with oxygen release. Our simulations also reveal that reduced ceria nanoparticles are more active towards surface oxygen release compared to unreduced nanoceria. In parallel, experiment is used to explore the activities of ceria nanoparticles that have suffered a change in environment. In particular, we compare the ability of ceria nanoparticles, in an aqueous environment, to scavenge superoxide radicals compared to the same batch of nanoparticles, which have first been dried and then rehydrated. The latter show a distinct reduction in activity, which we correlate to a change in the redox chemistry associated with moving between different environments. The reactivity of ceria nanoparticles is therefore not only environment dependent, but is also influenced by the transport pathway or history required to reach the particular environment in which its reactivity is to be exploited.

Cellular interaction and toxicity depend on physicochemical properties and surface modification of redox-active nanomaterials.

The study of the chemical and biological properties of CeO2 nanoparticles (CNPs) has expanded recently due to its therapeutic potential, and the methods used to synthesize these materials are diverse. Moreover, conflicting reports exist regarding the toxicity of CNPs. To help resolve these discrepancies, we must first determine whether CNPs made by different methods are similar or different in their physicochemical and catalytic properties. In this paper, we have synthesized several forms of CNPs using identical precursors through a wet chemical process but using different oxidizer/reducer; H2O2 (CNP1), NH4OH (CNP2), or hexamethylenetetramine (HMT-CNP1). Physicochemical properties of these CNPs were extensively studied and found to be different depending on the preparation methods. Unlike CNP1 and CNP2, HMT-CNP1 was readily taken into endothelial cells and the aggregation can be visualized using light microscopy. Exposure to HMT-CNP1 also reduced cell viability at a 10-fold lower concentration than CNP1 or CNP2. Surprisingly, exposure to HMT-CNP1 led to substantial decreases in ATP levels. Mechanistic studies revealed that HMT-CNP1 exhibited substantial ATPase (phosphatase) activity. Though CNP2 also exhibits ATPase activity, CNP1 lacked ATPase activity. The difference in catalytic (ATPase) activity of different CNPs preparation may be due to differences in their morphology and oxygen extraction energy. These results suggest that the combination of increased uptake and ATPase activity of HMT-CNP1 may underlie the biomechanism of the toxicity of this preparation of CNPs and may suggest that ATPase activity should be considered when synthesizing CNPs for use in biomedical applications.

Cationic surface reconstructions on cerium oxide nanocrystals: an aberration-corrected HRTEM study.

Instabilities of nanoscale ceria surface facets are examined on the atomic level. The electron beam and its induced atom migration are proposed as a readily available probe to emulate and quantify functional surface activity, which is crucial for, for example, catalytic performance. In situ phase contrast high-resolution transmission electron microscopy with spherical aberration correction is shown to be the ideal tool to analyze cationic reconstruction. Hydrothermally prepared ceria nanoparticles with particularly enhanced {100} surface exposure are explored. Experimental analysis of cationic reconstruction is supported by molecular dynamics simulations where the Madelung energy is shown to be directly related to the binding energy, which enables one to generate a visual representation of the distribution of "reactive" surface oxygen.

The induction of angiogenesis by cerium oxide nanoparticles through the modulation of oxygen in intracellular environments.

Angiogenesis is the formation of new blood vessels from existing blood vessels and is critical for many physiological and pathophysiological processes. In this study we have shown the unique property of cerium oxide nanoparticles (CNPs) to induce angiogenesis, observed using both in vitro and in vivo model systems. In particular, CNPs trigger angiogenesis by modulating the intracellular oxygen environment and stabilizing hypoxia inducing factor 1α endogenously. Furthermore, correlations between angiogenesis induction and CNPs physicochemical properties including: surface Ce(3+)/Ce(4+) ratio, surface charge, size, and shape were also explored. High surface area and increased Ce(3+)/Ce(4+) ratio make CNPs more catalytically active towards regulating intracellular oxygen, which in turn led to more robust induction of angiogenesis. Atomistic simulation was also used, in partnership with in vitro and in vivo experimentation, to reveal that the surface reactivity of CNPs and facile oxygen transport promotes pro-angiogenesis.

Mechanical properties of ceria nanorods and nanochains; the effect of dislocations, grain-boundaries and oriented attachment.

We predict that the presence of extended defects can reduce the mechanical strength of a ceria nanorod by 70%. Conversely, the pristine material can deform near its theoretical strength limit. Specifically, atomistic models of ceria nanorods have been generated with full microstructure, including: growth direction, morphology, surface roughening (steps, edges, corners), point defects, dislocations and grain-boundaries. The models were then used to calculate the mechanical strength as a function of microstructure. Our simulations reveal that the compressive yield strengths of ceria nanorods, ca. 10 nm in diameter and without extended defects, are 46 and 36 GPa for rods oriented along [211] and [110] respectively, which represents almost 10% of the bulk elastic modulus and are associated with yield strains of about 0.09. Tensile yield strengths were calculated to be about 50% lower with associated yield strains of about 0.06. For both nanorods, plastic deformation was found to proceed via slip in the {001} plane with direction <110>--a primary slip system for crystals with the fluorite structure. Dislocation evolution for the nanorod oriented along [110] was nucleated via a cerium vacancy present at the surface. A nanorod oriented along [321] and comprising twin-grain boundaries with {111} interfacial planes was calculated to have a yield strength of about 10 GPa (compression and tension) with the grain boundary providing the vehicle for plastic deformation, which slipped in the plane of the grain boundary, with an associated <110> slip direction. We also predict, using a combination of atomistic simulation and DFT, that rutile-structured ceria is feasible when the crystal is placed under tension. The mechanical properties of nanochains, comprising individual ceria nanoparticles with oriented attachment and generated using simulated self-assembly, were found to be similar to those of the nanorod with grain-boundary. Images of the atom positions during tension and compression are shown, together with animations, revealing the mechanisms underpinning plastic deformation. For the nanochain, our simulations help further our understanding of how a crystallising ice front can be used to 'sculpt' ceria nanoparticles into nanorods via oriented attachment.

Elastic deformation in ceria nanorods via a fluorite-to-rutile phase transition.

Atomistic simulations reveal that ceria nanorods, under uniaxial tension, can accommodate over 6% elastic deformation. Moreover, a reversible fluorite-to-rutile phase change occurs above 6% strain for a ceria nanorod that extends along [110]. We also observe that during unloading the stress increases with decreasing strain as the rutile reverts back to fluorite. Ceria nanorods may find possible application as vehicles for elastic energy storage.

Simulating mechanical deformation in nanomaterials with application for energy storage in nanoporous architectures.

Central to porous nanomaterials, with applications spanning catalysts to fuel cells is their (perceived) "fragile" structure, which must remain structurally intact during application lifespan. Here, we use atomistic simulation to explore the mechanical strength of a porous nanomaterial as a first step to characterizing the structural durability of nanoporous materials. In particular, we simulate the mechanical deformation of mesoporous Li-MnO(2) under stress using molecular dynamics simulation. Specifically, such rechargeable Li-ion battery materials suffer volume changes during charge/discharge cycles as Li ions are repeatedly inserted and extracted from the host beta-MnO(2) causing failure as a result of localized stress. However, mesoporous beta-MnO(2) does not suffer structural collapse during cycling. To explain this behavior, we generate a full atomistic model of mesoporous beta-MnO(2) and simulate localized stress associated with charge/discharge cycles. We calculate that mesoporous beta-MnO(2) undergoes a volume expansion of about 16% when Li is fully intercalated, which can only be sustained without structural collapse, if the nanoarchitecture is symmetrically porous, enabling elastic deformation during intercalation. Conversely, we predict that unsymmetric materials, such as nanoparticulate beta-MnO(2), deform plastically, resulting in structural collapse of (Li) storage sites and blocked transport pathways; animations revealing elastic and plastic deformation mechanisms under mechanical load and crystallization of mesoporous Li-MnO(2) are presented at the atomistic level.

Mapping nanostructure: a systematic enumeration of nanomaterials by assembling nanobuilding blocks at crystallographic positions.

Nanomaterials synthesized from nanobuilding blocks promise size-dependent properties, associated with individual nanoparticles, together with collective properties of ordered arrays. However, one cannot position nanoparticles at specific locations; rather innovative ways of coaxing these particles to self-assemble must be devised. Conversely, model nanoparticles can be placed in any desired position, which enables a systematic enumeration of nanostructure from model nanobuilding blocks. This is desirable because a list of chemically feasible hypothetical structures will help guide the design of strategies leading to their synthesis. Moreover, the models can help characterize nanostructure, calculate (predict) properties, or simulate processes. Here, we start to formulate and use a simulation strategy to generate atomistic models of nanomaterials, which can, potentially, be synthesized from nanobuilding block precursors. Clearly, this represents a formidable task because the number of ways nanoparticles can be arranged into a superlattice is infinite. Nevertheless, numerical tools are available to help build nanoparticle arrays in a systematic way. Here, we exploit the "rules of crystallography" and position nanoparticles, rather than atoms, at crystallographic sites. Specifically, we explore nanoparticle arrays with cubic, tetragonal, and hexagonal symmetries together with primitive, face centered cubic and body centered cubic nanoparticle "packing". We also explore binary nanoparticle superlattices. The resulting nanomaterials, spanning CeO(2), Ti-doped CeO(2), ZnO, ZnS, MgO, CaO, SrO, and BaO, comprise framework architectures, with cavities interconnected by channels traversing (zero), one, two and three dimensions. The final, fully atomistic models comprise three hierarchical levels of structural complexity: crystal structure, microstructure (i.e., grain boundaries, dislocations), and superlattice structure.

Oxygen transport in unreduced, reduced and Rh(III)-doped CeO2 nanocrystals.

Ceria, CeO2, based materials are a major (active) component of exhaust catalysts and promising candidates for solid oxide fuel cells. In this capacity, oxygen transport through the material is pivotal. Here, we explore whether oxygen transport is influenced (desirably increased) compared with transport within the bulk parent material by traversing to the nanoscale. In particular, atomistic models for ceria nanocrystals, including perfect: CeO2; reduced: CeO1.95 and doped: Rh0.1Ce0.9O1.95, have been generated. The nanocrystals were about 8 nm in diameter and each comprised about 16,000 atoms. Oxygen transport can also be influenced, sometimes profoundly, by microstructural features such as dislocations and grain-boundaries. However, these are difficult to generate within an atomistic model using, for example, symmetry operations. Accordingly, we crystallised the nanocrystals from an amorphous precursor, which facilitated the evolution of a variety of microstructures including: twin-boundaries and more general grain-boundaries and grain-junctions, dislocations and epitaxy, isolated and associated point defects. The shapes of the nanocrystals are in accord with HRTEM data and comprise octahedral morphologies with {111} surfaces, truncated by (dipolar) {100} surfaces together with a complex array of steps, edges and corners. Oxygen transport data was then calculated using these models and compared with data calculated previously for CeO1.97/ YSZ thin films and the (bulk) parent material, CeO197. Oxygen transport was calculated to increase in the order: CeO2 nanocrystal < (reduced) CeO1.95 nanocrystal approximately Rh0.1Ce0.9O1.95 nanocrystal < CeO1.97/YSZ thin film < (reduced) CeO1.97 (bulk) parent material; the mechanism was determined to be primarily vacancy driven. Our findings indicate that reducing one- (thin film) or especially three- (nanocrystal) dimensions to the nanoscale may prove deleterious to oxygen transport. Conversely, we observed dynamic evolution and annihilation of surface vacancies via surface oxygens migrating to the bulk of the nanocrystal; the vacancies left are then filled by other oxygens moving to the surface. Coupled with previous simulation studies, in which we calculated that oxygen extraction from the surface of a ceria nanocrystal was energetically easier compared with the bulk surface, our calculations predict that ceria nanocrystals would facilitate effective oxidative catalysis. This study describes framework simulation procedures, which can be used in partnership with experiment, to explore transport in nanocrystalline ionic systems, which include complex microstructures. Such data can provide predictions for experiment or help reduce the number of experiments required.

"Simulating synthesis": ceria nanosphere self-assembly into nanorods and framework architectures.

We predict, from computer modeling and simulation in partnership with experiment, a general strategy for synthesizing spherical oxide nanocrystals via crystallization from melt. In particular we "simulate synthesis" to generate full atomistic models of undoped and Ti-doped CeO2 nanoparticles, nanorods, and nanoporous framework architectures. Our simulations demonstrate, in quantitative agreement with experiment [Science 2006, 312, 1504], that Ti (dopant) ions change the shape of CeO2 nanocrystals from polyhedral to spherical. We rationalize this morphological change by elucidating, at the atomistic level, the mechanism underpinning its synthesis. In particular, CeO2 nanocrystals can be synthesized via crystallization from melt: as a molten (undoped) CeO2 nanoparticle is cooled, nucleating seeds spontaneously evolve at the surface and express energetically stable [111] facets to minimize the energy. As crystallization proceeds, the [111] facets grow, thus facilitating a polyhedral shape. Conversely, when doped with Ti, a (predominantly) TiO2 shell encapsulates the inner CeO2 core. This shell inhibits the evolution of nucleating seeds at the surface thus rendering it amorphous during cooling. Accordingly, crystallization is forced to proceed via the evolution of a nucleating seed in the bulk CeO2 region of the nanoparticle, and as this seed grows, it remains surrounded by amorphous ions, which "wrap" around the core so that the energies for high-index facets are drastically reduced; these amorphous ions adopt a spherical shape to minimize the surface energy. Crystallization emanates radially from the nucleating seed, and because it is encapsulated by an amorphous shell, the crystallization front is not compelled to express energetically favorable surfaces. Accordingly, after the nanoparticle has crystallized it retains this spherical shape. A typical animation showing the crystallization (with atomistic detail) is available as Supporting Information. From this data we predict that spherical oxide nanocrystals can be synthesized via crystallization from melt in general by suppressing nucleating seed evolution at the surface thus forcing the nucleating seed to spontaneously evolve in the bulk. Nanospheres can, similar to zeolitic classifications, constitute Secondary Building Units (SBUs) and can aggregate to form nanorods and nanoporous framework architectures. Here we have attempted to simulate this process to generate models for CeO2 and Ti-doped CeO2 nanorods and framework architectures. In particular, we predict that Ti doping will "smooth" the surfaces: hexagonal prism shaped CeO2 nanorods with [111] and [100] surfaces become cylindrical, and framework architectures change from facetted pores and channels with well-defined [111] and [100] surfaces to "smooth" pores and channels (expressing both concave and convex curvatures). Such structures are difficult to characterize using, for example, Miller indices; rather we suggest that these new structural materials may be better described using minimal surfaces.

Simulating self-assembly of ZnS nanoparticles into mesoporous materials.

Characterization of materials is crucial for the quantification and prediction of their physical, chemical, and mechanical properties. However, as the complexity of a system increases, so do the challenges involved in elucidating its structure. While molecular simulation and modeling have proved invaluable as complements to experiment, such simulations now face serious challenges: new materials are being synthesized with ever increasing structural complexity, and it may soon prove impossible to generate models that are sufficiently realistic to describe them adequately. Perhaps, ultimately, it will only be possible to generate such models by simulating the synthetic process itself. Here, we attempt such a strategy to generate full atomistic models for mesoporous molecular sieves. As in experiment, this is done by allowing nanoparticles to self-assemble at high temperature to form an amorphous mesoporous framework. The temperature is then reduced, and the system is allowed to crystallize. Animations of atomic trajectories, available as Supporting Information, reveal the evolution of multiple seeds which propagate to form a complex framework. The products are polycrystalline mesoporous framework structures containing cavities connected by channels running along "zero", one, two, and three perpendicular directions. We suggest that it is easier to generate these model structures by attempting to simulate the synthetic process rather than by using more conventional techniques. The strategy is illustrated using ZnS as a model system. Further development of the mathematics of minimal surfaces will advance our understanding of these structures.

Converting ceria polyhedral nanoparticles into single-crystal nanospheres.

Ceria nanoparticles are one of the key abrasive materials for chemical-mechanical planarization of advanced integrated circuits. However, ceria nanoparticles synthesized by existing techniques are irregularly faceted, and they scratch the silicon wafers and increase defect concentrations. We developed an approach for large-scale synthesis of single-crystal ceria nanospheres that can reduce the polishing defects by 80% and increase the silica removal rate by 50%, facilitating precise and reliable mass-manufacturing of chips for nanoelectronics. We doped the ceria system with titanium, using flame temperatures that facilitate crystallization of the ceria yet retain the titania in a molten state. In conjunction with molecular dynamics simulation, we show that under these conditions, the inner ceria core evolves in a single-crystal spherical shape without faceting, because throughout the crystallization it is completely encapsulated by a molten 1- to 2-nanometer shell of titania that, in liquid state, minimizes the surface energy. The principle demonstrated here could be applied to other oxide systems.