Kinetically Determined Shapes of Grain Boundaries in Graphene.

A large-scale chemical synthesis of graphene produces a polycrystalline material with grain boundaries (GBs) that disturb the lattice structure and drastically affect material properties. An uncontrollable formation of GB can be detrimental, yet precise GB engineering can impart added functionalities onto graphene-and its noncarbon two-dimensional "cousins." While the importance of growth kinetics in shaping single-crystalline graphene islands has lately been appreciated, kinetics' role in determining a GB structure remains unaddressed. Here we report on the analysis of the GB formation as captured by kinetic Monte Carlo simulations in contrast with global minimum guided GB structures considered previously. We identified a key parameter-edge misorientation angle-that describes the initial geometry of merging grains and unambiguously defines the resulting GB structure, while a commonly used lattice tilt angle corresponds to several qualitatively different GB structures. A provided systematic analysis of GB structures formed from a full range of edge misorientation angles reveals conditions that result in straight and periodic GBs as well as conditions responsible for meandering and disordered GBs. Additionally, we address the special case of translational GBs, where lattices of merging grains are aligned but shifted compared to each other. Collected data can be used for deliberate GB structural engineering, for example, by a three-dimensional patterning of the substrate surface to introduce disclinations creating a graphene lattice tilt.

Flexoelectricity and Charge Separation in Carbon Nanotubes.

The effect of flexoelectric voltage on the electronic and optical properties of single- and double-wall carbon nanotubes is evaluated by the first-principles calculations. The voltage between the inner channel of curved sp2 carbon nanostructures and their surroundings scales linearly with nanotube wall curvature and can be boosted/reversed by appropriate outer wall functionalization. We predict and verify computationally that in double-wall nanotubes, flexoelectricity causes a straddling to staggered band gap transition. Accurate band structure calculations taking into account quasiparticle corrections and excitonic effects lead to an estimated critical diameter of ∼24 Šfor this transition. Double-wall nanotubes above this diameter have staggered band alignment and could be potentially used for charge separation in photovoltaic devices.

A jellium model of a catalyst particle in carbon nanotube growth.

We show how a jellium model can represent a catalyst particle within the density-functional theory based approaches to the growth mechanism of carbon nanotubes (CNTs). The advantage of jellium is an abridged, less computationally taxing description of the multi-atom metal particle, while at the same time in avoiding the uncertainty of selecting a particular atomic geometry of either a solid or ever-changing liquid catalyst particle. A careful choice of jellium sphere size and its electron density as a descriptive parameter allows one to calculate the CNT-metal interface energies close to explicit full atomistic models. Further, we show that using jellium permits computing and comparing the formation of topological defects (sole pentagons or heptagons, the culprits of growth termination) as well as pentagon-heptagon pairs 5|7 (known as chirality-switching dislocation).

Mechanochemistry of One-Dimensional Boron: Structural and Electronic Transitions.

Recent production of long carbyne chains, concurrent with advances in the synthesis of pure boron fullerenes and atom-thin layers, motivates an exploration of possible one-dimensional boron. By means of first-principles calculations, we find two isomers, two-atom wide ribbon and single-atom chain, linked by a tension-driven (negative-pressure) transformation. We explore the stability and unusual properties of both phases, demonstrating mechanical stiffness on par with the highest-performing known nanomaterials, and a phase transition between stable 1D metal and an antiferromagnetic semiconductor, with the phase boundary effectively forming a stretchable 1D Schottky junction. In addition, the two-phase system can serve as a constant-tension nanospring with a well-calibrated tension defined by enthalpic balance of the phases. Progress in the synthesis of boron nanostructures suggests that the predicted unusual behaviors of 1D boron may find powerful applications in nanoscale electronics and/or mechanical devices.

Carbonization with Misfusion: Fundamental Limits of Carbon-Fiber Strength Revisited.

D-loops, a new type of structural defect in carbon fibers, are presented, which have highly detrimental effect on their mechanical properties and can define a new fundamental upper limit to their strength. These defects form exclusively during polyacrylonitrile carbonization, act as stress concentrators in the graphitic basal plane, and cannot be removed by local annealing.

Topochemistry of Bowtie- and Star-Shaped Metal Dichalcogenide Nanoisland Formation.

A large number of experimental studies over the past few years observed the formation of unusual highly symmetric polycrystalline twinned nanoislands of transition metal dichalcogenides, resembling bowties or stars. Here, we analyze their morphology in terms of equilibrium and growth shapes. We propose a mechanism for these complex shapes' formation via collision of concurrently growing islands and validate the theory with phase-field simulations that demonstrate how highly symmetric structures can actually emerge from arbitrary starting conditions. Finally, we use first-principles calculations to propose an explanation of the predominance of high-symmetry polycrystals with 60° lattice misorientation angles.

Breaking of symmetry in graphene growth on metal substrates.

In graphene growth, island symmetry can become lower than the intrinsic symmetries of both graphene and the substrate. First-principles calculations and Monte Carlo modeling explain the shapes observed in our experiments and earlier studies for various metal surface symmetries. For equilibrium shape, edge energy variations δE manifest in distorted hexagons with different ground-state edge structures. In growth or nucleation, energy variation enters exponentially as ∼e(δE/k(B)T), strongly amplifying the symmetry breaking, up to completely changing the shapes to triangular, ribbonlike, or rhombic.

Defect-detriment to graphene strength is concealed by local probe: the topological and geometrical effects.

Defects in solids commonly limit mechanical performance of materials by reducing their rigidity and strength. However, topological defects also induce a prominent geometrical effect in addition to local stress buildup, which is especially pronounced in two-dimensional crystals. These dual roles of defects modulate mechanical responses of the material under local and global probes in very different ways. We demonstrate through atomistic simulations and theoretical analysis that local response of two-dimensional crystals can even be stiffened and strengthened by topological defects as the structure under indentation features a positive Gaussian curvature, while softened and weakened mechanical responses are measured at locations with negative Gaussian curvatures. These findings shed lights on mechanical characterization of two-dimensional materials in general. The geometrical effect of topological defects also adds a new dimension to material design, in the scenario of geometrical and topological engineering.

Why nanotubes grow chiral.

Carbon nanotubes hold enormous technological promise. It can only be harnessed if one controls their chirality, the feature of the tubular carbon topology that governs all the properties of nanotubes-electronic, optical, mechanical. Experiments in catalytic growth over the last decade have repeatedly revealed a puzzling strong preference towards minimally chiral (near-armchair) tubes, challenging any existing hypotheses and making chirality control ever more tantalizing, yet leaving its understanding elusive. Here we combine the nanotube/catalyst interface thermodynamics with the kinetic growth theory to show that the unusual near-armchair peaks emerge from the two antagonistic trends at the interface: energetic preference towards achiral versus the faster growth kinetics of chiral nanotubes. This narrow distribution is inherently related to the peaked behaviour of a simple function, xe(-x).

Mechanically induced metal-insulator transition in carbyne.

First-principles calculations for carbyne under strain predict that the Peierls transition from symmetric cumulene to broken-symmetry polyyne structure is enhanced as the material is stretched. Interpretation within a simple and instructive analytical model suggests that this behavior is valid for arbitrary 1D metals. Further, numerical calculations of the anharmonic quantum vibrational structure of carbyne show that zero-point atomic vibrations eliminate the Peierls distortion in the mechanically free chain, preserving the cumulene symmetry. The emergence and increase of Peierls dimerization under tension then implies a qualitative transition between the two forms, which our computations place around 3% strain. Thus, the competition between the zero-point vibrations and mechanical strain determines a switch in symmetry resulting in the transition from metallic state to a dielectric, with a small effective mass and a high carrier mobility. In any practical realization, it is important that the effect is also chemically modulated by the choice of terminating groups. These findings are promising for applications such as electromechanical switching and band gap tuning via strain, and besides carbyne itself, they directly extend to numerous other systems that show Peierls distortion.

Can xenon in water inhibit ice growth? Molecular dynamics of phase transitions in water-Xe system.

Motivated by recent experiments showing the promise of noble gases as cryoprotectants, we perform molecular dynamics modeling of phase transitions in water with xenon under cooling. We follow the structure and dynamics of xenon water solution as a function of temperature. Homogeneous nucleation of clathrate hydrate phase is observed and characterized. As the temperature is further reduced we observe hints of dissociation of clathrate due to stronger hydrophobic hydration, pointing towards a possible instability of clathrate at cryogenic temperatures and conversion to an amorphous phase comprised of "xenon + hydration shell" Xe·(H2O)21.5 clusters. Simulations of ice-xenon solution interface in equilibrium and during ice growth reveal the effects of xenon on the ice-liquid interface, where adsorbed xenon causes roughening of ice surface but does not preferentially form clathrate. These results provide evidence against the ice-blocker mechanism of xenon cryoprotection.

Extensive energy landscape sampling of nanotube end-caps reveals no chiral-angle bias for their nucleation.

In the formation of a carbon nanotube (CNT) nucleus, a hemispherical fullerene end-cap, a specific pattern of six pentagons encodes what unique (n,m) chirality a nascent CNT would inherit, with many possible pentagon patterns corresponding to a single chirality. This configurational variety and its potential role in the initial stages of CNT catalytic growth remain essentially unexplored. Here we present large-scale calculations designed to evaluate the intrinsic energies of all possible CNT caps for selected chiralities corresponding to tube diameters d ≲ 1 nm. Our quantitative analysis reveals that for all chiral angles χ the energy scale variability associated with the CNT caps is small, compared to that of the CNT/catalyst interface. Such a flat energy landscape cannot therefore be a dominant factor for chiral distribution and lends further credibility to interface-controlled scenarios for selective growth of single-walled CNT of desired chirality.

Large hexagonal bi- and trilayer graphene single crystals with varied interlayer rotations.

Bi- and trilayer graphene have attracted intensive interest due to their rich electronic and optical properties, which are dependent on interlayer rotations. However, the synthesis of high-quality large-size bi- and trilayer graphene single crystals still remains a challenge. Here, the synthesis of 100 µm pyramid-like hexagonal bi- and trilayer graphene single-crystal domains on Cu foils using chemical vapor deposition is reported. The as-produced graphene domains show almost exclusively either 0° or 30° interlayer rotations. Raman spectroscopy, transmission electron microscopy, and Fourier-transformed infrared spectroscopy were used to demonstrate that bilayer graphene domains with 0° interlayer stacking angles were Bernal stacked. Based on first-principle calculations, it is proposed that rotations originate from the graphene nucleation at the Cu step, which explains the origin of the interlayer rotations and agrees well with the experimental observations.

New insights into the properties and interactions of carbon chains as revealed by HRTEM and DFT analysis.

Atomic carbon chains have raised interest for their possible applications as graphene interconnectors as the thinnest nanowires; however, they are hard to synthesize and subsequently to study. We present here a reproducible method to synthesize carbon chains in situ TEM. Moreover, we present a direct observation of the bond length alternation in a pure carbon chain by aberration corrected TEM. Also, cross bonding between two carbon chains, 5 nm long, is observed experimentally and confirmed by DFT calculations. Finally, while free standing carbon chains were observed to be straight due to tensile loading, a carbon chain inside the walls of a carbon nanotube showed high flexibility.

Carbyne from first principles: chain of C atoms, a nanorod or a nanorope.

We report an extensive study of the properties of carbyne using first-principles calculations. We investigate carbyne's mechanical response to tension, bending, and torsion deformations. Under tension, carbyne is about twice as stiff as the stiffest known materials and has an unrivaled specific strength of up to 7.5 × 10(7) N·m/kg, requiring a force of ∼10 nN to break a single atomic chain. Carbyne has a fairly large room-temperature persistence length of about 14 nm. Surprisingly, the torsional stiffness of carbyne can be zero but can be "switched on" by appropriate functional groups at the ends. Further, under appropriate termination, carbyne can be switched into a magnetic semiconductor state by mechanical twisting. We reconstruct the equivalent continuum elasticity representation, providing the full set of elastic moduli for carbyne, showing its extreme mechanical performance (e.g., a nominal Young's modulus of 32.7 TPa with an effective mechanical thickness of 0.772 Å). We also find an interesting coupling between strain and band gap of carbyne, which is strongly increased under tension, from 2.6 to 4.7 eV under a 10% strain. Finally, we study the performance of carbyne as a nanoscale electrical cable and estimate its chemical stability against self-aggregation, finding an activation barrier of 0.6 eV for the carbyne-carbyne cross-linking reaction and an equilibrium cross-link density for two parallel carbyne chains of 1 cross-link per 17 C atoms (2.2 nm).

Pseudo Hall-Petch strength reduction in polycrystalline graphene.

The fracture of polycrystalline graphene is explored by performing molecular dynamics simulations with realistic finite-grain-size models, emphasizing the role of grain boundary ends and junctions. The simulations reveal a ~50% or more strength reduction due to the presence of the network of boundaries between polygonal grains, with cracks preferentially starting at the junctions. With a larger grain size, a surprising systematic decrease of tensile strength and failure strain is observed, while the elastic modulus rises. The observed crack localization and strength behavior are well-explained by a dislocation-pileup model, reminiscent of the Hall-Petch effect but coming from different underlying physics.

Feasibility of Lithium Storage on Graphene and Its Derivatives.

Nanomaterials are anticipated to be promising storage media, owing to their high surface-to-mass ratio. The high hydrogen capacity achieved by using graphene has reinforced this opinion and motivated investigations of the possibility to use it to store another important energy carrier - lithium (Li). While the first-principles computations show that the Li capacity of pristine graphene, limited by Li clustering and phase separation, is lower than that offered by Li intercalation in graphite, we explore the feasibility of modifying graphene for better Li storage. It is found that certain structural defects in graphene can bind Li stably, yet a more efficacious approach is through substitution doping with boron (B). In particular, the layered C3B compound stands out as a promising Li storage medium. The monolayer C3B has a capacity of 714 mAh/g (as Li1.25C3B), and the capacity of stacked C3B is 857 mAh/g (as Li1.5C3B), which is about twice as large as graphite's 372 mAh/g (as LiC6). Our results help clarify the mechanism of Li storage in low-dimensional materials, and shed light on the rational design of nanoarchitectures for energy storage.

Equilibrium at the edge and atomistic mechanisms of graphene growth.

The morphology of graphene is crucial for its applications, yet an adequate theory of its growth is lacking: It is either simplified to a phenomenological-continuum level or is overly detailed in atomistic simulations, which are often intractable. Here we put forward a comprehensive picture dubbed nanoreactor, which draws from ideas of step-flow crystal growth augmented by detailed first-principles calculations. As the carbon atoms migrate from the feedstock to catalyst to final graphene lattice, they go through a sequence of states whose energy levels can be computed and arranged into a step-by-step map. Analysis begins with the structure and energies of arbitrary edges to yield equilibrium island shapes. Then, it elucidates how the atoms dock at the edges and how they avoid forming defects. The sequence of atomic row assembly determines the kinetic anisotropy of growth, and consequently, graphene island morphology, explaining a number of experimental facts and suggesting how the growth product can further be improved. Finally, this analysis adds a useful perspective on the synthesis of carbon nanotubes and its essential distinction from graphene.

Unfolding the fullerene: nanotubes, graphene and poly-elemental varieties by simulations.

Recent research progress in nanostructured carbon has built upon and yet advanced far from the studies of more conventional carbon forms such as diamond, graphite, and perhaps coals. To some extent, the great attention to nano-carbons has been ignited by the discovery of the structurally least obvious, counterintuitive, small strained fullerene cages. Carbon nanotubes, discovered soon thereafter, and recently, the great interest in graphene, ignited by its extraordinary physics, are all interconnected in a blend of cross-fertilizing fields. Here we review the theoretical and computational models development in our group at Rice University, towards understanding the key structures and behaviors in the immense diversity of carbon allotropes. Our particular emphasis is on the role of certain transcending concepts (like elastic instabilities, dislocations, edges, etc.) which serve so well across the scales and for chemically various compositions.