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

Kinetically Trapped Nanocrystals with Symmetry-Preserving Shapes

The shape of nanocrystals is crucial in determining their surface area, reactivity, optical properties, and self-assembly behavior. Traditionally, shape control has been achieved through empirical methods, highlighting the need for a more refined theoretical framework. A comprehensive model should account for the kinetic factors at distinct stages of the shape formation process to identify the key determinants of nanocrystal morphology. By modulating kinetics at terraces, ledges, and kinks, we reveal that the primary factors are the adatom nucleation energies and the geometry of growth islands. Transient sites dominate the growth process, leading to kinetically trapped, metastable shapes. We illustrate these concepts with face-centered cubic nanocrystals, demonstrating diverse shape evolutions, including surface roughening and the preservation of crystal symmetry in cubes, octahedra, rhombic dodecahedra, and their truncated variants. This study reveals the mechanisms driving the formation of cubic nanocrystal shapes and offers guidance for their precise synthesis.

Strain release by 3D atomic misfit in fivefold twinned icosahedral nanoparticles with amorphization and dislocations

Multiple twinning to form fivefold twinned nanoparticles in crystal growth is common and has attracted broad attention ranging from crystallography research to physical chemistry and materials science. Lattice-misfit strain and defects in multiple twinned nanoparticles (MTP) are key to understand and tailor their electronic properties. However, the structural defects and related strain distributions in MTPs are poorly understood in three dimensions (3D). Here, we show the 3D atomic misfit and strain relief mechanism in fivefold twinned icosahedral nanoparticles with amorphization and dislocations by using atomic resolution electron tomography. We discover a two-sided heterogeneity in variety of structural characteristics. A nearly ideal crystallographic fivefold face is always found opposite to a less ordered face, forming Janus-like icosahedral nanoparticles with two distinct hemispheres. The disordered amorphous domains release a large amount of strain. Molecular dynamics simulations further reveal the Janus-like icosahedral nanoparticles are prevalent in the MTPs formed in liquid-solid phase transition. This work provides insights on the atomistic models for the modelling of formation mechanisms of fivefold twinned structures and computational simulations of lattice distortions and defects. We anticipate it will inspire future studies on fundamental problems such as twin boundary migration and kinetics of structures in 3D at atomic level.

Experimental High-Resolution Observation of the Truncated Double-Icosahedron Structure: A Stable Twinned Shell in Alloyed Au-Ag Core@Shell Nanoparticles

Given the binary nature of nanoalloy systems, their properties are dependent on their size, shape, structure, composition, and chemical ordering. When energy and entropic factors for shapes and structure variations are considered in nanoparticle growth, the spectra of shapes become so vast that even metastable arrangements have been reported under ambient conditions. Experimental and theoretical variations of multiply twinned particles have been observed, from the Ino and Marks decahedra to polyicosahedra and polydecahedra with comparable energetic stability among them. Herein, we report the experimental production of a stable doubly truncated double-icosahedron structure (TdIh) in Au-Ag nanoparticles, in which a twinned Ag-rich alloyed shell is reconstructed on a Au-Ag alloyed Ino-decahedral core. The structure, chemical composition, and growth pathway are proposed on the basis of high-angle annular dark-field scanning transmission electron microscopy analysis and excess energy calculations, while its structural stability is estimated by large-scale atomic molecular dynamics simulations. This novel nanostructure differs from other structures previously reported.

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.

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.

Development of nanoparticle bulk morphology analysis: a multidomain XRD approach

The appearance of twin/stacking faults in nanoparticles creates strains affecting the catalytic, optical, and electrical properties of nanomaterials. Currently, there is a lack of experimental tools for a numeric characterization of these defects in samples. Therefore, many structure-property correlations are poorly understood. Here, we report the exploration of the twinning effect on the XRD pattern and its practical application. We developed a new approach focused on the special mutual orientation of periodic fcc segments, domains. Using computational simulations, we found that the more domains, the smaller the height ratio of 220 to 111 diffraction peaks. Knowing this correlation, we performed the XRD bulk morphology and size analysis of Au and AuPt samples. The obtained results were compared with the results of TEM and SAXS analyses. In a broader context, our multidomain XRD method is a simple alternative to TEM which enables unraveling the structure-property correlations in NP studies.

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.

Spiers Memorial Lecture: Nanoalloys of multiple components; the road to advance the field and experimental and theoretical challenges

The field of nanoalloys has been advancing at a rapid pace in the last two decades. Many new characterization methods and theoretical advances have produced a substantial knowledge of the nanoalloys' properties and structure. Most of the work has been limited to binary alloys. A path forward for the field will be the study of nanoalloys with three or more metals. Adding new components will produce new properties and possibly more fabrication controls. In this paper, we will discuss the challenges that will arise in multi-metallic nanoalloys. We will show that entropy and twin boundaries play a dominant role in multi-metallic alloys.

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.

Insight into the Role of Nanoparticles Shape Factors and Diameter on the Dynamics of Rotating Water-Based Fluid

This article addresses the dynamic of three-dimensional rotating flow of Maxwell nanofluid across a linearly stretched sheet subject to a water-based fluid containing copper nanoparticles. Nanoparticles are used due to their fascinating features, such as exceptional thermal conductivity, which is crucial in modern nanotechnology and electronics. The primary goal of this comprehensive study is to examine the nanoparticles size and shape factors effect on the base fluid temperature. The mathematical model contains the governing equations in three dimensional partial differential equations form, and these equations transformed into dimensionless ordinary dimensional equations via suitable similarity transformation. The bvp4c technique is harnessed and coded in Matlab script to obtain a numerical solution of the coupled non-linear ordinary differential problem. It is observed that the greater input of rotating, Deborah number, and magnetic parameters caused a decline in the fluid primary and secondary velocities, but the nanoparticles concentration enhanced the fluid temperature. Further, a substantial increment in the nanofluid temperature is achieved for the higher nanoparticle's diameter and shape factors.