Combining shape-changing with exchange moves in the optimization of nanoalloys

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.

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.

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.

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.

An Improved Self-Adaptive Differential Evolution with the Neighborhood Search Algorithm for Global Optimization of Bimetallic Clusters

Global optimization of multicomponent cluster structures is considerably time-consuming due to the existence of a vast number of isomers. In this work, we proposed an improved self-adaptive differential evolution with the neighborhood search (SaNSDE) algorithm and applied it to the global optimization of bimetallic cluster structures. The cross operation was optimized, and an improved basin hopping module was introduced to enhance the searching efficiency of SaNSDE optimization. Taking (PtNi)_N (N = 38 or 55) bimetallic clusters as examples, their structures were predicted by using this algorithm. The traditional SaNSDE algorithm was carried out for comparison with the improved SaNSDE algorithm. For all the optimized clusters, the excess energy and the second difference of the energy were calculated to examine their relative stabilities. Meanwhile, the bond order parameters were adopted to quantitatively characterize the cluster structures. The results reveal that the improved SaNSDE algorithm possessed significantly higher searching capability and faster convergence speed than the traditional SaNSDE algorithm. Furthermore, the lowest-energy configurations of (PtNi)₃₈ clusters could be classified as the truncated octahedral and disordered structures. In contrast, all the optimal (PtNi)₅₅ clusters were approximately icosahedral. Our work fully demonstrates the high efficiency of the improved algorithm and advances the development of global optimization algorithms and the structural prediction of multicomponent clusters.

Exploring AuRh nanoalloys: a computational perspective on the formation and physical properties

We studied the formation of AuRh nanoalloys (between 20–150 atoms) in the gas phase by means of Molecular Dynamics (MD) calculations, exploring three possible formation processes: one‐by‐one growth, coalescence, and nanodroplets annealing. As a general trend, we recover a predominance of Rh@Au core‐shell ordering over other chemical configurations. We identify new structural motifs with enhanced thermal stabilities. The physical features of those selected systems were studied at the Density Functional Theory (DFT) level, revealing profound correlations between the nanoalloys morphology and properties. Surprisingly, the arrangement of the inner Rh core seems to play a dominant role on nanoclusters’ physical features like the HOMO‐LUMO gap and magnetic moment. Strong charge separations are recovered within the nanoalloys suggesting the existence of charge‐transfer transitions.

Understanding the strain-dependent structure of Cu nanocrystals in Ag-Cu nanoalloys

The structure of octahedral Ag-Cu nanoalloys is investigated by means of basin hopping Monte Carlo (BHMC) searches involving the optimization of shape and chemical ordering. Due to the significant size mismatch between Ag and Cu, the misfit strain plays a key role in determining the structure of Ag-Cu nanoalloys. At all the compositions, segregated chemical ordering is observed. However, the shape of the Cu nanocrystal and the associated defects are significantly different. At lower amounts of Cu (as little as 2 atom %), defects close to the surface are observed leading to a highly non-compact shape of the Cu nanocrystal which is non-trivial. The number of Cu-Cu bonds is relatively lower in the non-compact shape which is contrary to the preference of bulk Ag-Cu alloys to maximize the homo-atomic bonds. Due to the non-compact shape, {100} Ag-Cu interfaces are observed which are not expected. As the amount of Cu increases, the Cu nanocrystal undergoes a shape transition from non-compact to a compact octahedron. The associated defect structure is also modified. The structural changes due to the strain effects have been explained by calculating the atomic pressure maps and the bond length distributions. The trends relating to the structure have also been verified at larger sizes.

Regression and clustering algorithms for AgCu nanoalloys: from mixing energy predictions to structure recognition

The lowest-energy structures of AgCu nanoalloys are searched for by global optimization algorithms for sizes 100 and 200 atoms depending on composition. Even though the AgCu system is very weakly miscible in macroscopic samples, the mixing energy for these nanoalloys turns out to be clearly negative for both sizes, a result which is attributed to the stabilization of non-crystalline Cu@Ag core-shell structures at the nanoscale. The mixing energy is a quantity nowadays unknown in its functional form, so that its prediction may take advantage of machine learning techniques. A support vector regressor is then implemented to successfully predict the mixing energy of AgCu nanoalloys of both sizes. Moreover, with the help of unsupervised learning algorithms, it is shown that the automatic classification of such nanoalloys into different physically meaningful structural families is indeed possible. Finally, thanks to the harmonic superposition approximation, the temperature-dependent probabilities of such structural families are calculated.

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.

Core-shell vs. multi-shell formation in nanoalloy evolution from disordered configurations

The evolution towards equilibrium of AuCo, AgNi and AgCu nanoparticles is studied by molecular dynamics simulations. Nanoparticle sizes of about 2.5 nm are considered, in the temperature range from 300 to 700 K. The simulations reveal complex equilibration pathways, in which geometric structure and chemical ordering change with time. These nanoparticles present the same type of strong tendency to phase separation and to surface segregation of either Au or Ag, which lead to the same type of core@shell equilibrium structures. In spite of these similarities, the equilibration pathways of these nanoparticles from chemically disordered configurations present both quantitative and qualitative differences. Quantitative differences are found in the equilibration time scale, which is much longer in AgCu than in AgNi and AuCo. Qualitative differences are found in the presence or absence of geometric structure transformations, and in the formation of different types of three-shell metastable chemical ordering during evolution. It is also shown that surface segregation depends on the geometric structure, being faster in icosahedra than in fcc nanoparticles.

Site-Specific Wetting of Iron Nanocubes by Gold Atoms in Gas-Phase Synthesis

A key challenge in nanotechnology is the rational design of multicomponent materials that beat the properties of their elemental counterparts. At the same time, when considering the material composition of such hybrid nanostructures and the fabrication process to obtain them, one should favor the use of nontoxic, abundant elements in view of the limited availability of critical metals and sustainability. Cluster beam deposition offers a solvent- and, therefore, effluent-free physical synthesis method to achieve nanomaterials with tailored characteristics. However, the simultaneous control of size, shape, and elemental distribution within a single nanoparticle in a small-size regime (sub-10 nm) is still a major challenge, equally limiting physical and chemical approaches. Here, a single-step nanoparticle fabrication method based on magnetron-sputtering inert-gas condensation is reported, which relies on selective wetting of specific surface sites on precondensed iron nanocubes by gold atoms. Using a newly developed Fe-Au interatomic potential, the growth mechanism is decomposed into a multistage model implemented in a molecular dynamics simulation framework. The importance of growth kinetics is emphasized through differences between structures obtained either experimentally or computationally, and thermodynamically favorable configurations determined via global optimization techniques. These results provide a roadmap for engineering complex nanoalloys toward targeted applications.

Effect of applied force and atomic organization of copper on its adhesion to a graphene substrate

Copper/graphene composites are lightweight and possess many attractive properties such as improved mechanical, electrical, and thermal properties.