Two-dimensional (2D) materials, such as graphene and boron nitride, have specific lattice structures independent of external conditions. In contrast, the structure of 2D boron sensitively depends on metal substrate, as we show herein using the cluster expansion method and a newly developed surface structure-search method, both based on first-principles calculations. The preferred 2D boron on weaker interacting Au is nonplanar with significant buckling and numerous polymorphs as in vacuum, whereas on more reactive Ag, Cu, and Ni, the polymorphic energy degeneracy is lifted and a particular planar structure is found to be most stable. We also show that a layer composed of icosahedral B12 is unfavorable on Cu and Ni but unexpectedly becomes a possible minimum on Au and Ag. The substrate-dependent 2D boron choices originate from a competition between the strain energy of buckling and chemical energy of electronic hybridization between boron and metal.

ABSTRACT:We study the mechanical properties of two-dimensional (2D) boron-borophenes -by first-principles calculations. The recently synthesized borophene with 1/6 concentration of hollow hexagons (HH) is shown to have in-plane modulus C up to 210 N/m and bending stiffness as low as D = 0.39 eV. Thus, its Foppl-von Karman number per unit area, defined as C/D, reaches 568 nm -2 , over twofold higher than graphene's value, establishing the borophene as one of the most flexible materials. Yet, the borophene has a specific modulus of 346 m 2 /s 2 and ideal strengths of 16 N/m, rivaling those (453 m 2 /s 2 and 34 N/m) of graphene. In particular, its structural fluxionality enabled by delocalized multi-center chemical bonding favors structural phase transitions under tension, which result in exceptionally small breaking strains yet highly ductile breaking behavior. These mechanical properties can be further tailored by varying the HH concentration, and the boron sheet without HHs can even be stiffer than graphene against tension. The record high flexibility combined with excellent elasticity in boron sheets can be utilized for designing composites and flexible systems.

Hexagonal boron nitride (h-BN) sheet is a structural analogue of graphene, yet its growth mechanism has been rarely studied, as complicated by its binary composition. Here, we reveal an atomistic growth mechanism for the h-BN islands by combining crystal growth theory with comprehensive first-principles calculations. The island shapes preferred by edge equilibrium are found to be inconsistent with experimental facts, which is in contrast to previous common views. Then the growth kinetics is explored by analyzing the diffusion and docking of boron and nitrogen atoms at the edges in a step-by-step manner of the nanoreactor approach. The determined sequence of atom-by-atom accretion reveals a strong kinetic anisotropy of growth. Depending on the chemical potential of constituent elements, it yields the h-BN shapes as equilateral triangles or hexagons, explaining a number of experimental observations and opening a way for the synthesis of quality h-BN with controlled morphology. The richer growth kinetics of h-BN compared to graphene is further extendable to other binary two-dimensional materials, notably metal dichalcogenides.

Recently synthesized graphitic honeycomb structures, consisting of sp 2-bonded graphene nanoribbons connected by sp 3-bonded "hinges" are investigated theoretically. Honeycombs of different "wall-chiralities" (armchair and zigzag) and sizes are studied. Simulation of the reconstruction of the hinges shows that zigzag honeycombs spontaneously rearrange, resulting in a new structure. Elastic mechanical simulations show that the Young's modulus of the structures is determined solely by the density of the hinges, regardless of the structural orientation or regularity. Compression tests display a distinct behavior of self-localized deformation, similar to that of macroscopic honeycombs. Interestingly, the failure strain of the honeycomb structure is affected significantly by its lattice size and geometrical regularity. Electronic band structures of different types of honeycombs are calculated, showing that the conductivity of armchair honeycombs follows the well-known "3n"-dependency, while zigzag honeycombs are always metallic.

1wileyonlinelibrary.com to fully understand the GBs in terms of structures and properties. While the GBs in graphene have been confi rmed to be strings of pear-shaped pentagonheptagon (5|7) edge dislocations, [ 30,31 ] the fl exible organization of dislocations gives rise to diverse GB shapes, e.g., straight lines, loops [ 32 ] and sinuous shapes. Energetically, identical edge dislocations should favor a vertical alignment, [ 17 ] and the formed GB will bisect the tilt angle of the misoriented grains. The energetically favored bisector GBs are indeed observed in highly oriented pyrolytic graphite as linear periodic superstructures, [33][34][35] in line with recent theoretical models. [ 17,31,36 ] However, the situation becomes quite different in CVD-grown graphene, wherein the grain sizes become much smaller than those in exfoliated samples and the GB shapes turn into sinuous. [7][8][9][10][11] Atomic scale characterizations revealed that the sinuous GBs usually do not bisect the misorientation (tilt) angle of domains over a nanometer length, [ 8,10 ] thus belonging to asymmetric (or nonbisector) type. Considering the abundance of asymmetric GBs in CVD-grown samples, determining their structures and their infl uence on electronic behavior is hence particularly important for designing graphene devices with desired performance. Despite extensive theoretical effort on the nonbisector GBs, [19][20][21]37,38 ] little is know about their preferred structures and even less about the modifi cation of properties that they cause. What is more, no physical rule is proposed for elucidating the formation mechanism of sinuous grain boundaries prevalent in experimental observations.Here, we perform an analytical study of asymmetric GBs in graphene and reveal a universal rule for reaching their ground state structures. In contrast to the commonly used linear models, we fi nd that the nonbisector GBs are preferably composed of slant bisector segments that form a sinuous shape, which closely resembles recent experimental images. The orientation, geometry and atomic structures of the bisector segments in the sinuous grain boundaries ( s -GBs) can be well quantifi ed by the domains' matching vectors and are verifi ed by extensive atomistic calculations. Further, the s-GBs are distinct in showing enhanced mechanical strength and semiconducting transport behavior. These fi ndings not only serve as a general guidance for understanding the morphology of GBs in two-dimensional atomic crystals but also offer a new insight into their structure-property relationships. Unraveling the Sinuous Grain Boundaries in GrapheneZhuhua Zhang , Yang Yang , Fangbo Xu , Luqing Wang , and Boris I. Yakobson * Grain boundaries (GBs) in graphene are stable strings of pentagon-heptagon dislocations. The GBs have been believed to favor an alignment of dislocations, but increasing number of experiments reveal diversely sinuous GB structures whose origins have long been elusive. Based on dislocation theory and fi rst-principles calculations, an extensive analysi...

We report a comprehensive first-principles study of the structural and chemical properties of the recently discovered B cage. It is found to be highly reactive and can exothermically dimerize, regardless of the orientation, by overcoming a small energy barrier ≃0.06 eV. The energy gap of the system varies widely with the aggregation of the increasing number of B cages, from 3.14 eV in a single B, to 1.54 eV in the dimer, to 1.25 eV in the trimer. We also explore a recipe for protecting the B cage by sheathing it within a carbon shell and identify carbon nanotubes with a radius of ∼6 Å as optimal hosts for an isolated cage. It is demonstrated that B can be unfolded into a planar 'molecule' that tessellates the plane. The corresponding 2D boron sheet constitutes a structural precursor foldable into this unique boron cage structure of current interest.

One can utilize the folding of paper to build fascinating 3D origami architectures with extraordinary mechanical properties and surface area. Inspired by the same, the morphology of 2D graphene can be tuned by addition of magnetite (FeO) nanoparticles in the presence of a magnetic field. The innovative 3D architecture with enhanced mechanical properties also shows a high surface area (∼2500 m g) which is utilized for oil absorption. Detailed microscopy and spectroscopy reveal rolling of graphene oxide (GO) sheets due to the magnetic field driven action of magnetite particles, which is further supported by molecular dynamics (MD) simulations. The macroscopic and local deformation resulting from in situ mechanical loading inside a scanning electron microscope reveals a change in the mechanical response due to a change internal morphology, which is further supported by MD simulation.

Here we report a unique method to locally determine the mechanical response of individual covalent junctions between carbon nanotubes (CNTs), in various configurations such as "X", "Y", and "Λ"-like. The setup is based on in situ indentation using a picoindenter integrated within a scanning electron microscope. This allows for precise mapping between junction geometry and mechanical behavior and uncovers geometry-regulated junction stiffening. Molecular dynamics simulations reveal that the dominant contribution to the nanoindentation response is due to the CNT walls stretching at the junction. Targeted synthesis of desired junction geometries can therefore provide a "structural alphabet" for construction of macroscopic CNT networks with tunable mechanical response.