Metallic nanoparticles meet metadynamics

Charting Nanocluster Structures via Convolutional Neural Networks

A general method to obtain a representation of the structural landscape of nanoparticles in terms of a limited number of variables is proposed. The method is applied to a large data set of parallel tempering molecular dynamics simulations of gold clusters of 90 and 147 atoms, silver clusters of 147 atoms, and copper clusters of 147 atoms, covering a plethora of structures and temperatures. The method leverages convolutional neural networks to learn the radial distribution functions of the nanoclusters and distills a low-dimensional chart of the structural landscape. This strategy is found to give rise to a physically meaningful and differentiable mapping of the atom positions to a low-dimensional manifold in which the main structural motifs are clearly discriminated and meaningfully ordered. Furthermore, unsupervised clustering on the low-dimensional data proved effective at further splitting the motifs into structural subfamilies characterized by very fine and physically relevant differences such as the presence of specific punctual or planar defects or of atoms with particular coordination features. Owing to these peculiarities, the chart also enabled tracking of the complex structural evolution in a reactive trajectory. In addition to visualization and analysis of complex structural landscapes, the presented approach offers a general, low-dimensional set of differentiable variables that has the potential to be used for exploration and enhanced sampling purposes.

Theory of Anisotropic Metal Nanostructures

A significant challenge in the development of functional materials is understanding the growth and transformations of anisotropic colloidal metal nanocrystals. Theory and simulations can aid in the development and understanding of anisotropic nanocrystal syntheses. The focus of this review is on how results from first-principles calculations and classical techniques, such as Monte Carlo and molecular dynamics simulations, have been integrated into multiscale theoretical predictions useful in understanding shape-selective nanocrystal syntheses. Also, examples are discussed in which machine learning has been useful in this field. There are many areas at the frontier in condensed matter theory and simulation that are or could be beneficial in this area and these prospects for future progress are discussed.

Impurity diffusion in magic-size icosahedral clusters

Atomic diffusion is at the basis of chemical ordering transformations in nanoalloys. Understanding the diffusion mechanisms at the atomic level is therefore a key issue in the study of the thermodynamic behavior of these systems and, in particular, of their evolution from out-of-equilibrium chemical ordering types often obtained in the experiments. Here, the diffusion is studied in the case of a single-atom impurity of Ag or Au moving within otherwise pure magic-size icosahedral clusters of Cu or Co by means of two different computational techniques, i.e., molecular dynamics and metadynamics. Our simulations reveal unexpected diffusion pathways, in which the displacement of the impurity is coupled with the creation of vacancies in the central part of the cluster. We show that the observed mechanism is quite different from the vacancy-mediated diffusion processes identified so far, and we demonstrate that it can be related to the presence of non-homogeneous compressive stress in the inner part of the icosahedral structure.

Characterization of amorphous LixSi structures from ReaxFF via accelerated exploration of local minima

Motivated by the abundant experimental work in the area of Li-ion batteries, in the present work we characterize via computer simulations the structure of Si-Li amorphous alloys in a wide range of compositions. Using a reactive force field we propose a novel accelerated exploration of local minima to obtain amorphous structures close to equilibrium. The features of this system analyzed for different alloy compositions are the partial radial distribution functions g(r), the first and second nearest neighbour coordination numbers and the short-order structure. The complex structure of the second peak of the Si-Li g(r) is elucidated using a cluster-connection analysis.

Out-of-Equilibrium Polymorph Selection in Nanoparticle Freezing

The ability to design synthesis processes that are out of equilibrium has opened the possibility of creating nanomaterials with remarkable physicochemical properties, choosing from a much richer palette of possible atomic architectures compared to equilibrium processes in extended systems. In this work, we employ atomistic simulations to demonstrate how to control polymorph selection via the cooling rate during nanoparticle freezing in the case of Ni₃Al, a material with a rich structural landscape. State-of-the-art free-energy calculations allow us to rationalize the complex nucleation process, discovering a switch between two kinetic pathways, yielding the equilibrium structure at room temperature and an alternative metastable one at higher temperature. Our findings address the key challenge in the synthesis of nanoalloys for technological applications, i.e., rationally exploiting the competition between kinetics and thermodynamics by designing a treatment history that forces the system into desirable metastable states.

The transformation of cuboctahedral to icosahedral nanoparticles: atomic structure and dynamics

The rearrangement of transition metal nanoparticles from cuboctahedral to icosahedral structures is studied for up to 923 atoms. The atomic structure and temperature dependence of the transition are investigated with a well-defined collective variable. This collective variable describes the folding of the square fcc(100) facets into two triangular facets through a linear combination of the diagonals of all fcc(100) facets of all shells of the particle. Activation barriers are determined through harmonic transition state theory and constrained molecular dynamics simulations based on force field potentials. These calculations predict an activation entropy larger than 1 meV K^-1, leading to strongly temperature dependent activation barriers. Density functional theory calculations were additionally performed both as single point calculations and as full optimizations. Cu, Ag, Au and Ni clusters show low barriers for concerted, symmetric transition up to the 309-atomic clusters. In contrast, for Pd, Pt, Rh and Ir higher barriers are required, already for the 147-atomic clusters. With increasing barriers, an asymmetric but still concerted rearrangement becomes energetically more favorable than the fully symmetric transformation. The material-dependence of the transition can be correlated with the melting point of the bulk metals.

Correlating Oxygen Reduction Reaction Activity and Structural Rearrangements in MgO-Supported Platinum Nanoparticles

We develop a multi‐scale approach towards the design of metallic nanoparticles with applications as catalysts in electrochemical reactions. The here discussed method exploits the relationship between nanoparticle architecture and electrochemical activity and is applied to study the catalytic properties of MgO(100)‐supported Pt nanosystems undergoing solid‐solid and solid‐liquid transitions. We observe that a major increment in the activity is associated to the reconstruction of the interface layers, supporting the need for a full geometrical characterisation of such structures also when in‐operando.

Structural properties of sub-nanometer metallic clusters

At the nanoscale, the investigation of structural features becomes fundamental as we can establish relationships between cluster geometries and their physicochemical properties. The peculiarity lies in the variety of shapes often unusual and far from any geometrical and crystallographic intuition clusters can assume. In this respect, we should treat and consider nanoparticles as a new form of matter. Nanoparticle structures depend on their size, chemical composition, ordering, as well as external conditions e.g. synthesis method, pressure, temperature, support. On top of that, at finite temperatures nanoparticles can fluctuate among different structures, opening new and exciting horizons for the design of optimal nanoparticles for advanced applications. This article aims to overview geometrical features of transition metal clusters and of their various rearrangements.

Melting of large Pt@MgO(1 0 0) icosahedra

On the basis of ab initio calculations, we present a new parametrisation of the Vervisch-Mottet-Goniakowski (VMG) potential (Vervisch et al 2002 Phys. Rev. B 24 245411) for modelling the oxide-metal interaction. Applying this model to mimic the finite temperature behaviour of large platinum icosahedra deposited on the pristine MgO(1 0 0), we find the nanoparticle undergoes two solid-solid transitions. At 650 K the 'squarisation' of the interface layer, while a full reshaping towards a fcc architecture takes place above 950 K. In between, a quite long-lived intermediate state with a (1 0 0) interface but with an icosahedral cap is observed. Our approach reproduces experimental observations, including wetting behaviour and the lack of surface diffusion.

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.

Controlling Structural Transitions in AuAg Nanoparticles through Precise Compositional Design

We present a study of the transitional pathways between high-symmetry structural motifs for AgAu nanoparticles, with a specific focus on controlling the energetic barriers through chemical design. We show that the barriers can be altered by careful control of the elemental composition and chemical arrangement, with core@shell and vertex-decorated arrangements being specifically influential on the barrier heights. We also highlight the complexity of the potential and free energy landscapes for systems where there are low-symmetry geometric motifs that are energetically competitive to the high-symmetry arrangements. In particular, we highlight that some core@shell arrangements preferentially transition through multistep restructuring of low-symmetry truncated octahedra and rosette-icosahedra, instead of via the more straightforward square-diamond transformations, due to lower energy barriers and competitive energetic minima. Our results have promising implications for the continuing efforts in bespoke nanoparticle design for catalytic and plasmonic applications.

Modeling the atomistic growth behavior of gold nanoparticles in solution

The properties of gold nanoparticles strongly depend on their three-dimensional atomic structure, leading to an increased emphasis on controlling and predicting nanoparticle structural evolution during the synthesis process. In order to provide this atomistic-level insight and establish a link to the experimentally-observed growth behavior, a kinetic Monte Carlo simulation (KMC) approach is developed for capturing Au nanoparticle growth characteristics. The advantage of this approach is that, compared to traditional molecular dynamics simulations, the atomistic nanoparticle structural evolution can be tracked on time scales that approach the actual experiments. This has enabled several different comparisons against experimental benchmarks, and it has helped transition the KMC simulations from a hypothetical toy model into a more experimentally-relevant test-bed. The model is initially parameterized by performing a series of automated comparisons of Au nanoparticle growth curves versus the experimental observations, and then the refined model allows for detailed structural analysis of the nanoparticle growth behavior. Although the Au nanoparticles are roughly spherical, the maximum/minimum dimensions deviate from the average by approximately 12.5%, which is consistent with the corresponding experiments. Also, a surface texture analysis highlights the changes in the surface structure as a function of time. While the nanoparticles show similar surface structures throughout the growth process, there can be some significant differences during the initial growth at different synthesis conditions.