Clarifying stability, probability and population in nanoparticle ensembles

The Thermal Stability of Asymmetric Separated Configurations inside Alloy Nanoparticles: Atomic-Scale Modeling of Pd-Ir Nanophase Diagrams

Compared to alloy bulk phase diagrams, the experimental determination of phase diagrams for alloy nanoparticles (NPs), which are useful in various nanotechnological applications, involves significant technical difficulties, making theoretical modeling a feasible alternative. Yet, being quite challenging, modeling of separation nanophase diagrams is scarce in the literature. The task of predicting comprehensive nanophase diagrams for Pd-Ir face-centered cubic-based three cuboctahedra is facilitated in this study by combining the computationally efficient statistical-mechanical Free-energy Concentration Expansion Method, which includes short-range order (SRO) with coordination-dependent bond-energy variations as part of the input and with rotationally symmetric site grouping for extra efficiency. This nanosystem has been chosen mainly because of the very small atomic mismatch that simplifies the modeling, e.g., in the assessment of vibrational entropy contributions based in this work on fitting to the Pd-Ir experimental bulk critical temperature. This entropic effect, together with SRO, leads to significant destabilization of low-T Quasi-Janus (QJ) asymmetric configurations of the NP core, which transform to symmetric partially mixed nanophases. First-order and second-order intracore transitions are predicted for dilute and intermediate-range compositions, respectively. Caloric curves computed for the former case yield the NP-size dependent transition latent heat, and in the latter case critical temperatures exhibit a specific scaling behavior. The computed separation diagrams and intracore solubility diagrams reflect enhanced elemental mixing in smaller QJ nanophases. In addition to these diagrams, the revealed near-surface compositional variations are likely to be pertinent to the utilization of Pd-Ir NPs, e.g., in catalysis.

Size-dependent shape distributions of platinum nanoparticles

While it is well established that nanoparticle shape can depend on equilibrium thermodynamics or growth kinetics, recent computational work has suggested the importance of thermal energy in controlling the distribution of shapes in populations of nanoparticles. Here, we used transmission electron microscopy to characterize the shapes of bare platinum nanoparticles and observed a strong dependence of shape distribution on particle size. Specifically, the smallest nanoparticles (<2.5 nm) had a truncated octahedral shape, bound by 〈111〉 and 〈100〉 facets, as predicted by lowest-energy thermodynamics. However, as particle size increased, the higher-energy 〈110〉 facets became increasingly common, leading to a large population of non-equilibrium truncated cuboctahedra. The observed trends were explained by combining atomistic simulations (both molecular dynamics and an empirical square-root bond-cutting model) with Boltzmann statistics. Overall, this study demonstrates experimentally how thermal energy leads to shape variation in populations of metal nanoparticles, and reveals the dependence of shape distributions on particle size. The prevalence of non-equilibrium facets has implications for metal nanoparticles applications from catalysis to solar energy.

Predicting archetypal nanoparticle shapes using a combination of thermodynamic theory and machine learning

Machine learning is a useful way of identifying representative or pure nanoparticle shapes as part of a larger ensemble, but its predictive capabilities can be limited when a large dataset of candidate structures must already exist. Ideally one would like to use machine learning to define the ideal dataset for future, more computationally intensive, studies before a significant amount of resources are consumed. In this work we combine an established analytical phenomenological model and statistical machine learning to predict the archetypes and prototypes of a diverse ensemble of 2380 platinum nanoparticle morphologies developed with less than twenty input electronic structure simulations. By parameterising a size- and shape-dependent thermodynamic model, probabilities are assigned to seventeen different shapes between three and thirty nanometres, which together with structural features such as nanoparticle diameter, surface area, sphericity and facet configuration form the basis for archetypal analysis and K-means clustering. Using this approach we rapidly identify six "pure" archetypes and twelve "representative" prototypes that can be used in future computational studies of properties such as catalysis.

Ensemble averaged structure-function relationship for nanocrystals: effective superparamagnetic Fe clusters with catalytically active Pt skin

Practical applications require the production and usage of metallic nanocrystals (NCs) in large ensembles. Besides, due to their cluster-bulk solid duality, metallic NCs exhibit a large degree of structural diversity. This poses the question as to what atomic-scale basis is to be used when the structure-function relationship for metallic NCs is to be quantified precisely. We address the question by studying bi-functional Fe core-Pt skin type NCs optimized for practical applications. In particular, the cluster-like Fe core and skin-like Pt surface of the NCs exhibit superparamagnetic properties and a superb catalytic activity for the oxygen reduction reaction, respectively. We determine the atomic-scale structure of the NCs by non-traditional resonant high-energy X-ray diffraction coupled to atomic pair distribution function analysis. Using the experimental structure data we explain the observed magnetic and catalytic behavior of the NCs in a quantitative manner. Thus we demonstrate that NC ensemble-averaged 3D positions of atoms obtained by advanced X-ray scattering techniques are a very proper basis for not only establishing but also quantifying the structure-function relationship for the increasingly complex metallic NCs explored for practical applications.

Beyond Magic Numbers: Atomic Scale Equilibrium Nanoparticle Shapes for Any Size

In the pursuit of complete control over morphology in nanoparticle synthesis, knowledge of the thermodynamic equilibrium shapes is a key ingredient. While approaches exist to determine the equilibrium shape in the large size limit (≳10-20 nm) as well as for very small particles (≲2 nm), the experimentally increasingly important intermediate size regime has largely remained elusive. Here, we present an algorithm, based on atomistic simulations in a constrained thermodynamic ensemble, that efficiently predicts equilibrium shapes for any number of atoms in the range from a few tens to many thousands of atoms. We apply the algorithm to Cu, Ag, Au, and Pd particles with diameters between approximately 1 and 7 nm and reveal an energy landscape that is more intricate than previously suggested. The thus obtained particle type distributions demonstrate that the transition from icosahedral particles to decahedral and further into truncated octahedral particles occurs only very gradually, which has implications for the interpretation of experimental data. The approach presented here is extensible to alloys and can in principle also be adapted to represent different chemical environments.

The effect of chemical ordering and lattice mismatch on structural transitions in phase segregating nanoalloys

We elucidate the effect of lattice mismatch and chemical ordering on structural transitions in bimetallic nanoalloys.

Statistics, damned statistics and nanoscience - using data science to meet the challenge of nanomaterial complexity

For many years dealing with the complexity of nanoscale materials, the polydispersivity of individual samples, and the persistent imperfection of individual nanostructures has been secondary to our search for novel properties and promising applications. For our science to translate into technology, however, we will inevitably need to deal with the issue of structural diversity and integrate this feature into the next generation of more realistic structure/property predictions. This is challenging in the field of nanoscience where atomic level precision is typically inaccessible (experimentally), but properties can depend on structural variations at the atomic scale. Fortunately there exists a range of reliable statistical methods that are entirely applicable to nanoscale materials; ideal for navigating and analysing enormous amount of information required to accurately describe realistic samples. Combined with advances in automation and information technology the field of data science can assist us in dealing with our big data, characterising our uncertainties, and more rapidly identifying useful structure/property relationships. Taking greater advantage of data-driven methods involves thinking differently about our research, but applied appropriately these methods can accelerate the discovery of nanomaterials that are optimised to make the transition from science to technology.

Challenges in modelling nanoparticles for drug delivery

Although there have been significant advances in the fields of theoretical condensed matter and computational physics, when confronted with the complexity and diversity of nanoparticles available in conventional laboratories a number of modeling challenges remain. These challenges are generally shared among application domains, but the impacts of the limitations and approximations we make to overcome them (or circumvent them) can be more significant one area than another. In the case of nanoparticles for drug delivery applications some immediate challenges include the incompatibility of length-scales, our ability to model weak interactions and solvation, the complexity of the thermochemical environment surrounding the nanoparticles, and the role of polydispersivity in determining properties and performance. Some of these challenges can be met with existing technologies, others with emerging technologies including the data-driven sciences; some others require new methods to be developed. In this article we will briefly review some simple methods and techniques that can be applied to these (and other) challenges, and demonstrate some results using nanodiamond-based drug delivery platforms as an exemplar.

Effects of surface stability on the morphological transformation of metals and metal oxides as investigated by first-principles calculations

Morphology is a key property of materials. Owing to their precise structure and morphology, crystals and nanocrystals provide excellent model systems for joint experimental and theoretical investigations into surface-related properties. Faceted polyhedral crystals and nanocrystals expose well-defined crystallographic planes depending on the synthesis method, which allow for thoughtful investigations into structure-reactivity relationships under practical conditions. This feature article introduces recent work, based on the combined use of experimental findings and first-principles calculations, to provide deeper knowledge of the electronic, structural, and energetic properties controlling the morphology and the transformation mechanisms of different metals and metal oxides: Ag, anatase TiO2, BaZrO3, and α-Ag2WO4. According to the Wulff theorem, the equilibrium shapes of these systems are obtained from the values of their respective surface energies. These investigations are useful to gain further understanding of how to achieve morphological control of complex three-dimensional crystals by tuning the ratio of the surface energy values of the different facets. This strategy allows the prediction of possible morphologies for a crystal and/or nanocrystal by controlling the relative values of surface energies.

Re-visiting the O/Cu(111) system--when metastable surface oxides could become an issue!

Surface oxidation processes are crucial for the functionality of Cu-based catalytic systems used for methanol synthesis, partial oxidation of methanol or the water-gas shift reaction. We assess the stability and population of the "8"-structure, a [formula, see text:] oxide phase, on the Cu(111) surface. This structure has been observed in X-ray photoelectron spectroscopy and low-energy electron diffraction experiments as a Cu(111) surface reconstruction that can be induced by a hyperthermal oxygen molecular beam. Using density-functional theory calculations in combination with ab initio atomistic thermodynamics and Boltzmann statistical mechanics, we find that the proposed oxide superstructure is indeed metastable and that the population of the "8"-structure is competitive with the known "29" and "44" oxide film structures on Cu(111). We show that the configuration of O and Cu atoms in the first and second layers of the "8"-structure closely resembles the arrangement of atoms in the first two layers of Cu2O(110), where the atoms in the "8"-structure are more constricted. Cu2O(110) has been suggested in the literature as the most active low index facet for reactions such as water splitting under light illumination. If the "8"-structure were to form during a catalytic process, it is therefore likely to be one of the reactive phases.

In silico veritas

Innovations in computational nanoscience have traditionally come in conjunction with experimental innovations, but uncertainty often surrounds the trustworthiness of in silico studies. While the accuracy of simulations has been improving every year, considerably less attention has focused on dealing with increasing complexity, which may be the source of concern. Creating more realistic virtual experiments (without sacrificing theoretical and numerical accuracy) remains challenging, particularly when we are confronted with the polydispersivity characteristic of extra silico samples. Fortunately, there are various theoretical methods that can be used in conjunction with first-principles simulations, not the least of which are the statistical tools and techniques promised by the emerging fields of materials informatics and data-driven sciences.