Tetrahedral Clusters Stabilized by Alloying.

A family of nanoclusters of tetrahedral symmetry is proposed. These clusters consist of symmetrically truncated tetrahedra with additional hexagonal islands on the four facets of the starting tetrahedron. The islands are placed in stacking fault positions. The geometric magic numbers of these clusters are derived. Global optimization searches within an atomistic potential model of Pt-Pd show that the tetrahedral structures can be stabilized for intermediate compositions of these nanoalloys, even when they are not the most stable structures of the elemental clusters. These results are also confirmed by density functional theory calculations for the magic sizes 59, 100, and 180. A thermodynamic analysis by the harmonic superposition approximation shows that Pt-Pd tetrahedral nanoalloys can be stable even above room temperature.

Sudden collective atomic rearrangements trigger the growth of defect-free silver icosahedra.

The growth of Ag clusters on amorphous carbon substrates is studied in situ by X-ray scattering experiments, whose final outcome is imaged by electron microscopy. The real-time analysis of the growth process at room temperature shows the formation of a large majority of icosahedral structures by a shell-by-shell growth mode which produces smooth and nearly defect-free structures. Molecular dynamics simulations supported by ab initio calculations reveal that the shell-by-shell mode is possible because of the occurrence of collective displacements which involve the concerted motion of many atoms of the growing shell. These collective processes are a kind of black swan event, as they occur suddenly and rarely, but their occurrence is decisive for the final outcome of the growth. Annealing and ageing experiments show that the as-grown icosahedra are metastable, in agreement with the energetic stability calculations.

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.

Frame-by-frame observations of structure fluctuations in single mass-selected Au clusters using aberration-corrected electron microscopy.

The multi-dimensional potential energy surface (PES) of a nanoparticle, such as a bare cluster of metal atoms, controls both the structure and dynamic behaviour of the particle. These properties are the subject of numerous theoretical simulations. However, quantitative experimental measurements of critical PES parameters are needed to regulate the models employed in the theoretical work. Experimental measurements of parameters are currently few in number, while model parameters taken from bulk systems may not be suitable for nanosystems. Here we describe a new measurement methodology, in which the isomer structures of a single deposited nanocluster are obtained frame-by-frame in an aberration-corrected scanning transmission electron microscope (ac-STEM) in high angle annular dark field (HAADF) mode. Several gold clusters containing 309 ± 15 atoms were analysed individually after deposition from a mass-selected cluster source onto an amorphous carbon film. The main isomers identified are icosahedral (Ih), decahedral (Dh) and face-centred-cubic (fcc) (the bulk structure), alongside many amorphous (glassy) structures. The results, which are broadly consistent with static ac-STEM measurements of an ensemble of such clusters, open the way to dynamic measurements of many different nanoparticles of diverse sizes, shapes and compositions.

Growth pathways of Cu shells on Au and AuCu seeds: interdiffusion, shape transformations, strained shells and patchy surfaces.

The growth of AuCu nanoparticles obtained by depositing Cu atoms on starting seeds of pure Au and on mixed AuCu seeds is studied by molecular dynamics simulations. Depending on the shape of the seed, its composition and the growth temperature, different growth pathways are observed, in which several types of structural transformations take place. The final growth structures comprise Au@Cu core@shell arrangements as well as Janus-like structures with patchy surfaces. The results of the growth simulations are rationalized in terms of the activation of different diffusion processes, both on the surface and inside the growing clusters. These diffusion processes regulate structural transitions between different motifs and the occurrence of dewetting phenomena. The simulation results show that depositon of Cu atoms on pure Au or mixed AuCu seed can be an effective tool for producing clusters with uncommon surface atom arrangements of potential interest for catalysis.

Structural transformations in Cu, Ag, and Au metal nanoclusters.

Finite-temperature structures of Cu, Ag, and Au metal nanoclusters are calculated in the entire temperature range from 0 K to melting using a computational methodology that we proposed recently [M. Settem et al., Nanoscale 14, 939 (2022)]. In this method, Harmonic Superposition Approximation (HSA) and Parallel Tempering Molecular Dynamics (PTMD) are combined in a complementary manner. HSA is accurate at low temperatures and fails at higher temperatures. PTMD, on the other hand, effectively samples the high temperature region and melts. This method is used to study the size- and system-dependent competition between various structural motifs of Cu, Ag, and Au nanoclusters in the size range 1-2 nm. Results show that there are mainly three types of structural changes in metal nanoclusters, depending on whether a solid-solid transformation occurs. In the first type, the global minimum is the dominant motif in the entire temperature range. In contrast, when a solid-solid transformation occurs, the global minimum transforms either completely to a different motif or partially, resulting in the co-existence of multiple motifs. Finally, nanocluster structures are analyzed to highlight the system-specific differences across the three metals.

Machine learning of atomic dynamics and statistical surface identities in gold nanoparticles.

It is known that metal nanoparticles (NPs) may be dynamic and atoms may move within them even at fairly low temperatures. Characterizing such complex dynamics is key for understanding NPs' properties in realistic regimes, but detailed information on, e.g., the stability, survival, and interconversion rates of the atomic environments (AEs) populating them are non-trivial to attain. In this study, we decode the intricate atomic dynamics of metal NPs by using a machine learning approach analyzing high-dimensional data obtained from molecular dynamics simulations. Using different-shape gold NPs as a representative example, an AEs' dictionary allows us to label step-by-step the individual atoms in the NPs, identifying the native and non-native AEs and populating them along the MD simulations at various temperatures. By tracking the emergence, annihilation, lifetime, and dynamic interconversion of the AEs, our approach permits estimating a "statistical equivalent identity" for metal NPs, providing a comprehensive picture of the intrinsic atomic dynamics that shape their properties.

Hydrogen Promotes the Growth of Platinum Pyramidal Nanocrystals by Size-Dependent Symmetry Breaking.

The growth of pyramidal platinum nanocrystals is studied by a combination of synthesis/characterization experiments and density functional theory calculations. It is shown that the growth of pyramidal shapes is due to a peculiar type of symmetry breaking, which is caused by the adsorption of hydrogen on the growing nanocrystals. Specifically, the growth of pyramidal shapes is attributed to the size-dependent adsorption energies of hydrogen atoms on {100} facets, whose growth is hindered only if they are sufficiently large. The crucial role of hydrogen adsorption is further confirmed by the absence of pyramidal nanocrystals in experiments where the reduction process does not involve hydrogen.

Correction: Tempering of Au nanoclusters: capturing the temperature-dependent competition among structural motifs.

Correction for 'Tempering of Au nanoclusters: capturing the temperature-dependent competition among structural motifs' by Manoj Settem et al., Nanoscale, 2022, 14, 939-952, https://doi.org/10.1039/D1NR05078H.

Growth pathways of exotic Cu@Au core@shell structures: the key role of misfit strain.

The CuAu system is characterized by a large lattice mismatch which causes a misfit strain in its core@shell architectures. Here we simulate the formation of Cu@Au core@shell nanoparticles by Au deposition on a preformed seed, and we study the effect of the shape and composition of the starting seed on the growth pathway. Three geometric shapes of the starting seed are considered: truncated octahedra, decahedra and icosahedra. For each shape, we consider two compositions, pure Cu and CuAu, at equicomposition and intermixed chemical ordering. Our results show that the shape and composition of the seed have significant effects on the growth pathways of Cu@Au core@shell nanoparticles. When starting with icosahedral seeds, the growing structure stays in that motif always. When starting with truncated octahedral and decahedral seeds, we have observed that there is a clear difference between the pure and intermixed seeds. For pure seeds, the growth often leads to exotic structures that are obtained after some structural transformations. For mixed seeds, the growth leads to quite regular structures resembling those obtained for pure metals. These growth pathways originate from strain relaxation mechanisms, which are rationalized by calculating the atomic level stress.

Machine Learning Assisted Clustering of Nanoparticle Structures.

We propose a scheme for the automatic separation (i.e., clustering) of data sets composed of several nanoparticle (NP) structures by means of Machine Learning techniques. These data sets originate from atomistic simulations, such as global optimizations searches and molecular dynamics simulations, which can produce large outputs that are often difficult to inspect by hand. By combining a description of NPs based on their local atomic environment with unsupervised learning algorithms, such as K-Means and Gaussian mixture model, we are able to distinguish between different structural motifs (e.g., icosahedra, decahedra, polyicosahedra, fcc fragments, twins, and so on). We show that this method is able to improve over the results obtained previously thanks to the successful implementation of a more detailed description of NPs, especially for systems showing a large variety of structures, including disordered ones.

Two-Steps Versus One-Step Solidification Pathways of Binary Metallic Nanodroplets.

The solidification of AgCo, AgNi, and AgCu nanodroplets is studied by molecular dynamics simulations in the size range of 2-8 nm. All these systems tend to phase separate in the bulk solid with surface segregation of Ag. Despite these similarities, the simulations reveal clear differences in the solidification pathways. AgCo and AgNi already separate in the liquid phase, and they solidify in configurations close to equilibrium. They can show a two-step solidification process in which Co-/Ni-rich parts solidify at higher temperatures than the Ag-rich part. AgCu does not separate in the liquid and solidifies in one step, thereby remaining in a kinetically trapped state down to room temperature. The solidification mechanisms and the size dependence of the solidification temperatures are analyzed, finding qualitatively different behaviors in AgCo/AgNi compared to AgCu. These differences are rationalized by an analytical model.

Combined atomistic simulations to explore metastability and substrate effects in Ag-Co nanoalloy systems.

The Ag/Co nanoalloy system is a model system situated energetically at the limit of stability of the core-shell chemical ordering with respect to a simple phase separation behavior. This makes the system highly susceptible to effects of the environment, such as interaction with a substrate. However, kinetic effects may also be exploited by careful atom-by-atom particle growth that allows to lock in certain out-of-equilibrium configurations, such as off-center, quasi-Janus and even Janus type particles. In this contribution, we explore to what extent out-of-equilibrium structures are due to kinetic effects and the influence of the interaction of the particles with an amorphous carbon substrate by a joint experimental and molecular dynamics study. The simulation set up performed at 300 K and 600 K mimicks the experimental growth process. The substrate deforms the particles, but has also an ordering effect on particle orientation and particle structure. In the case of growth of Ag on Co seeds, particles assume close to equilibrium quasi-Janus structures, while for the deposition of Co on Ag seeds, highly out-of-equilibrium structures with several subsurface Co clusters are obtained.

Interplay between interdiffusion and shape transformations in nanoalloys evolving from core-shell to intermixed structures.

Nanoalloys are often grown or synthesized in non-equilibrium configurations whose further evolution towards equilibrium can take place through complex pathways. In this work, we consider bimetallic systems with tendency towards intermixing, namely AgAu, PtPd and AuCu. We analyze their evolution starting from non-equilibrium initial configurations, such as phase-separated core@shell ones, by means of molecular dynamics (MD) simulations. These systems present some differences, since AuCu bulk alloys make ordered phases at low temperature whereas AgAu and PtPd remain in solid solution. Moreover, Cu, Au and Ag have similar cohesive energies whereas Pt is much more cohesive than Pd. We consider both truncated octahedral and icosahedral initial shapes in the size range between 2 and 3 nm. For each AB system, we consider both A@B and B@A core@shell starting configurations. The evolution is characterized by monitoring the time-dependent degree of intermixing and the evolution of the shape. The simulations are performed up to temperatures close to the melting range. The approach to thermodynamic equilibrium is monitored by MD simulations and compared with the equilibrium chemical configurations obtained by Monte Carlo simulations.

Growth mechanisms from tetrahedral seeds to multiply twinned Au nanoparticles revealed by atomistic simulations.

The growth pathways from tetrahedral to multiply twinned gold nanoparticles in the gas phase are studied by molecular dynamics simulations supported by density functional theory calculations. Our results show that the growth from a tetrahedron to a multiple twin can take place by different pathways: directly from a tetrahedron to a decahedron (Th → Dh pathway), directly from a tetrahedron to an icosahedral fragment (Th → Ih), and from a tetrahedron to an icosahedron passing through an intermediate decahedron (Th → Dh → Ih). The simulations allow to determine the key atomic-level growth mechanism at the origin of twinning in metal nanoparticles. This mechanism is common to all these pathways and starts from the preferential nucleation of faulted atomic islands in the vicinity of facet edges, leading to the formation and stabilization of twin planes and of fivefold symmetry axes.

Tempering of Au nanoclusters: capturing the temperature-dependent competition among structural motifs.

A computational approach to determine the equilibrium structures of nanoclusters in the whole temperature range from 0 K to melting is developed. Our approach relies on Parallel Tempering Molecular Dynamics (PTMD) simulations complemented by Harmonic Superposition Approximation (HSA) calculations and global optimization searches, thus combining the accuracy of global optimization and HSA in describing the low-energy part of configuration space, together with the PTMD thorough sampling of high-energy configurations. This combined methodology is shown to be instrumental towards revealing the temperature-dependent structural motifs in Au nanoclusters of sizes 90, 147, and 201 atoms. The reported phenomenology is particularly rich, displaying a size- and temperature-dependent competition between the global energy minimum and other structural motifs. In the case of Au90 and Au147, the global minimum is also the dominant structure at finite temperatures. In contrast, the Au201 cluster undergoes a solid-solid transformation at low temperature (<200 K). Results indicate that PTMD and HSA very well agree at intermediate temperatures, between 300 and 400 K. For higher temperatures, PTMD gives an accurate description of equilibrium, while HSA fails in describing the melting range. On the other hand, HSA is more efficient in catching low-temperature structural transitions. Finally, we describe the elusive structures close to the melting region which can present complex and defective geometries, that are otherwise difficult to characterize through experimental imaging.

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.