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Synthetic two-dimensional (2D) materials have no bulk counterparts and typically exist as single atomic layers due to substrate-stabilized growth. Multilayer formation, although broadly sought for structure and property tuning, has not yet been achieved in the case of synthetic 2D boron: that is, borophene 1 , 2 . Here, we experimentally demonstrate the synthesis of an atomically well-defined borophene polymorph beyond the single-atomic-layer (SL) limit. The structure of this bilayer (BL) borophene is consistent with two covalently bonded α-phase layers (termed BL-α borophene) as evidenced from bond-resolved scanning tunnelling microscopy, non-contact atomic force microscopy and density functional theory calculations. While the electronic density of states near the Fermi level of BL-α borophene is similar to SL borophene polymorphs, field-emission resonance spectroscopy reveals distinct interfacial charge transfer doping and a heightened local work function exceeding 5 eV. The extension of borophene polymorphs beyond the SL limit significantly expands the phase space for boron-based nanomaterials. A borophene polymorph with two covalently bonded boron monolayers was synthesized, expanding the physical properties of borophene and filling the gap between monolayer borophene and icosahedron-based bulk boron.

We study quotients of projective and affine spaces by various actions of the icosahedral group. Basically we concentrate on the rationality questions.

We study quotients of projective and affine spaces by various actions of the icosahedral group. Basically we concentrate on the rationality questions.

The study of the electrochemical catalyst conversion of renewable electricity and carbon oxides into chemical fuels attracts a great deal of attention by different researchers. The main role of this process is in mitigating the worldwide energy crisis through a closed technological carbon cycle, where chemical fuels, such as hydrogen, are stored and reconverted to electricity via electrochemical reaction processes in fuel cells. The scientific community focuses its efforts on the development of high-performance polymeric membranes together with nanomaterials with high catalytic activity and stability in order to reduce the platinum group metal applied as a cathode to build stacks of proton exchange membrane fuel cells (PEMFCs) to work at low and moderate temperatures. The design of new conductive membranes and nanoparticles (NPs) whose morphology directly affects their catalytic properties is of utmost importance. Nanoparticle morphologies, like cubes, octahedrons, icosahedrons, bipyramids, plates, and polyhedrons, among others, are widely studied for catalysis applications. The recent progress around the high catalytic activity has focused on the stabilizing agents and their potential impact on nanomaterial synthesis to induce changes in the morphology of NPs.

Significance This work demonstrates a structure–property correlation in metallic glasses for the community of amorphous solids. It associates geometrically unfavored motifs, i.e., those most disordered local polyhedral packing structures in a metallic glass, with the soft spots defined from the vibrational modes and correlates them with shear transformation zones composed of atoms with large nonaffine displacements. The statistical correlation established thus ties together the heterogeneity inherent in the amorphous structure with the spatial heterogeneity in the mechanical (elastic and plastic) properties of a metallic glass. In a 3D model mimicking realistic Cu ₆₄Zr ₃₆ metallic glass, we uncovered a direct link between the quasi-localized low-frequency vibrational modes and the local atomic packing structure. We also demonstrate that quasi-localized soft modes correlate strongly with fertile sites for shear transformations: geometrically unfavored motifs constitute the most flexible local environments that encourage soft modes and high propensity for shear transformations, whereas local configurations preferred in this alloy, i.e., the full icosahedra (around Cu) and Z16 Kasper polyhedra (around Zr), contribute the least.

Liquids and solids are two fundamental states of matter. However, our understanding of their three-dimensional atomic structure is mostly based on physical models. Here we use atomic electron tomography to experimentally determine the three-dimensional atomic positions of monatomic amorphous solids, namely a Ta thin film and two Pd nanoparticles. We observe that pentagonal bipyramids are the most abundant atomic motifs in these amorphous materials. Instead of forming icosahedra, the majority of pentagonal bipyramids arrange into pentagonal bipyramid networks with medium-range order. Molecular dynamics simulations further reveal that pentagonal bipyramid networks are prevalent in monatomic metallic liquids, which rapidly grow in size and form more icosahedra during the quench from the liquid to the glass state. These results expand our understanding of the atomic structures of amorphous solids and will encourage future studies on amorphous–crystalline phase and glass transitions in non-crystalline materials with three-dimensional atomic resolution. Atomic electron tomography is used to determine the three-dimensional atomic structure of monatomic amorphous solids with liquid-like structure, which is characterized by the existence of pentagonal bipyramid networks with medium-range order.

Surface organic ligands are critical in determining the formation and properties of atomically precise metal nanoclusters. In contrast to the conventionally used thiolate, phosphine and alkynyl ligands, the amine ligand dipyridylamine is applied here as a protecting agent in the synthesis of atomically precise metal nanoclusters. We report two homoleptic amido-protected Ag nanoclusters as examples of all-nitrogen-donor-protected metal nanoclusters: [Ag 21 (dpa) 12 ]SbF 6 ( Ag 21 ) and [Ag 22 (dpa) 12 ](SbF 6 ) 2 ( Ag 22 ) (dpa = dipyridylamido). Single crystal X-ray structural analysis reveals that both clusters consist of a centered-icosahedron Ag 13 core wrapped by 12 dpa ligands. The flexible arrangement of the N donors in dpa facilitates the solvent-triggered reversible interconversion between Ag 21 and Ag 22 due to their very different solubility. The successful use of dpa in the synthesis of well-defined silver nanoclusters may motivate more studies on metal nanoclusters protected by amido type ligands. Noble metal nanoclusters are commonly protected by thiolate, phosphine, or alkynyl ligands. Here, the authors synthesize two homoleptic amido-protected silver clusters, whose structures interconvert easily with changes of solvent due to the coordination flexibility and diverse binding modes of the nitrogen-donor ligands.

The question of whether all materials can solidify into the glassy form proposed by Turnbull half a century ago remains unsolved. Some of the simplest systems of monatomic metals have not been vitrified, especially the close-packed face-centred cubic metals. Here we report the vitrification of gold, which is notoriously difficult to be vitrified, and several similar close-packed face-centred cubic and hexagonal metals using a method of picosecond pulsed laser ablation in a liquid medium. The vitrification occurs through the rapid cooling during laser ablation and the inhibition of nucleation by the liquid medium. Using this method, a large number of atomic configurations, including glassy configurations, can be generated simultaneously, from which a stable glass state can be sampled. Simulations demonstrate that the favourable stability of monatomic metals stems from the strong topological frustration of icosahedra-like clusters. Our work breaks the limitation of the glass-forming ability of matter, indicating that vitrification is an intrinsic property of matter and providing a strategy for the preparation and design of metallic glasses from an atomic configuration perspective. It is shown that gold and several similar close-packed face-centred cubic and hexagonal metals can be vitrified, which breaks the limitation of the glass-forming ability of matter.

The dynamics of glass-forming systems shows a multitude of features that are absent in normal liquids, such as non-exponential relaxation and a strong temperature-dependence of the relaxation time. Connecting these dynamic properties to the microscopic structure of the system is challenging because of the presence of the structural disorder. Here we use computer simulations of a metallic glass-former to establish such a connection. By probing the temperature and wave-vector dependence of the intermediate scattering function we find that the relaxation dynamics of the glassy melt is directly related to the local arrangement of icosahedral structures: Isolated icosahedra give rise to a liquid-like stretched exponential relaxation whereas clusters of icosahedra lead to a compressed exponential relaxation that is reminiscent to the one found in a solid. Our results show that in metallic glass-formers these two types of relaxation processes can coexist and give rise to a dynamics that is surprisingly complex. Glasses show peculiar relaxation dynamics below glass transition temperature, yet a deeper understanding of this phenomenon is still lacking. Wu et al. show the coexistence of stretched and compressed relaxation in a metallic glass system and attribute their origins to different local cluster structures.

Multi-component aggregates are being intensively researched in various fields because of their highly tunable properties and wide applications. Due to the complex configurational space of these systems, research would greatly benefit from a general theoretical framework for the prediction of stable structures, which, however, is largely incomplete at present. Here we propose a general theory for the construction of multi-component icosahedral structures by assembling concentric shells of different chiral and achiral types, consisting of particles of different sizes. By mapping shell sequences into paths in the hexagonal lattice, we establish simple and general rules for designing a wide variety of magic icosahedral structures, and we evaluate the optimal size-mismatch between particles in the different shells. The predictions of our design strategy are confirmed by molecular dynamics simulations and density functional theory calculations for several multi-component atomic clusters and nanoparticles. The icosahedron is the most symmetrical solid structure and is found in metal clusters, colloidal aggregates, viruses and organelles. Here, the authors propose a general theory for the design of multi-component icosahedral aggregates by packing shells of different types.