Stability and dynamics of the tetravacancy in graphene

The Formation and Transformation of Low-Dimensional Carbon Nanomaterials by Electron Irradiation

Low-dimensional materials based on graphene or graphite show a large variety of phenomena when they are subjected to irradiation with energetic electrons. Since the 1990s, electron microscopy studies, where a certain irradiation dose is unavoidable, have witnessed unexpected structural transformations of graphitic nanoparticles. It is recognized that electron irradiation is not only detrimental but also bears considerable potential in the formation of new graphitic structures. With the availability of aberration-corrected electron microscopes and the discovery of techniques to produce monolayers of graphene, detailed insight into the atomic processes occurring during electron irradiation became possible. Threshold energies for atom displacements are determined and models of different types of lattice vacancies are confirmed experimentally. However, experimental evidence for the configuration of interstitial atoms in graphite or adatoms on graphene remained indirect, and the understanding of defect dynamics still depends on theoretical concepts. This article reviews irradiation phenomena in graphene- or graphite-based nanomaterials from the scale of single atoms to tens of nanometers. Observations from the 1990s can now be explained on the basis of new results. The evolution of the understanding during three decades of research is presented, and the remaining problems are pointed out.

The Adsorption Mechanism of Hydrogen on FeO Crystal Surfaces: A Density Functional Theory Study

The hydrogen-based direct reduction of iron ores is a disruptive routine used to mitigate the large amount of CO₂ emissions produced by the steel industry. The reduction of iron oxides by H₂ involves a variety of physicochemical phenomena from macroscopic to atomistic scales. Particularly at the atomistic scale, the underlying mechanisms of the interaction of hydrogen and iron oxides is not yet fully understood. In this study, density functional theory (DFT) was employed to investigate the adsorption behavior of hydrogen atoms and H₂ on different crystal FeO surfaces to gain a fundamental understanding of the associated interfacial adsorption mechanisms. It was found that H₂ molecules tend to be physically adsorbed on the top site of Fe atoms, while Fe atoms on the FeO surface act as active sites to catalyze H₂ dissociation. The dissociated H atoms were found to prefer to be chemically bonded with surface O atoms. These results provide a new insight into the catalytic effect of the studied FeO surfaces, by showing that both Fe (catalytic site) and O (binding site) atoms contribute to the interaction between H₂ and FeO surfaces.

Insights into the Electrochemical Production of Hydrogen Peroxide over Single-Atom Co-N-C Catalysts with the Introduction of Carbon Vacancy Defect near the Co-N4 Site

With the introduction of carbon divacancy, trivacancy, and tetravacancy defects near the Co-N₄ site, we have explored the 2e^- ORR activity at the Co-N₄ site from the perspective of spatial structure and the atomic orbital by DFT calculations. We demonstrate the hybridization strength between Co 3dyz (3dxz) and O 2py (2px) orbitals is the origin of 2e^- ORR activity at the Co-N₄ site and the hybridization strength relates to the height of the Co 3d projected orbital in the Z direction. The bond length (L_Co-O, L_O-O), the charge transfer from the Co site to the *OOH adsorbate (ΔQ_Co-O), the d-band center of the Co site (ε_d), and the ICOHP value between Co 3d and O 2p orbitals as descriptors can well predict the 2e^- ORR activity at the Co-N₄ site. This work provides original insights into the 2e^- ORR activity over the single-atom Co-N-C catalysts.

Visualizing defect dynamics by assembling the colloidal graphene lattice

Graphene has been under intense scientific interest because of its remarkable optical, mechanical and electronic properties. Its honeycomb structure makes it an archetypical two-dimensional material exhibiting a photonic and phononic band gap with topologically protected states. Here, we assemble colloidal graphene, the analogue of atomic graphene using pseudo-trivalent patchy particles, allowing particle-scale insight into crystal growth and defect dynamics. We directly observe the formation and healing of common defects, like grain boundaries and vacancies using confocal microscopy. We identify a pentagonal defect motif that is kinetically favoured in the early stages of growth, and acts as seed for more extended defects in the later stages. We determine the conformational energy of the crystal from the bond saturation and bond angle distortions, and follow its evolution through the energy landscape upon defect rearrangement and healing. These direct observations reveal that the origins of the most common defects lie in the early stages of graphene assembly, where pentagons are kinetically favoured over the equilibrium hexagons of the honeycomb lattice, subsequently stabilized during further growth. Our results open the door to the assembly of complex 2D colloidal materials and investigation of their dynamical, mechanical and optical properties.

Ab Initio Investigation of the Adsorption of CO2 Molecules on Defect Sites of Graphene Surfaces: Role of Local Vacancy Structures

An in-depth investigation into the adsorption of CO₂ on graphene vacancies is essential for the understanding of their applications in various industries. Herein, we report an investigation of the effects of vacancy defects on CO₂ gas adsorption behavior on graphene surfaces using the density functional theory. The results show that the formation of vacancies leads to various deformations of local carbon structures, resulting in different adsorption capabilities. Even though most carbon atoms studied can only trigger physisorption, there are also carbon sites that are energetically favored for chemisorption. The general order of the adsorption capabilities of the local carbon atoms is as follows: carbon atoms with dangling bonds > carbon atoms shared by five- and six-membered rings and a vacancy > carbon atoms shared by two six-membered rings and a vacancy. A stronger interaction in the adsorption process generally corresponds to more obvious changes in the partial density of states and a larger amount of transferred charge.

Probing Electron Beam Induced Transformations on a Single-Defect Level via Automated Scanning Transmission Electron Microscopy

A robust approach for real-time analysis of the scanning transmission electron microscopy (STEM) data streams, based on ensemble learning and iterative training (ELIT) of deep convolutional neural networks, is implemented on an operational microscope, enabling the exploration of the dynamics of specific atomic configurations under electron beam irradiation via an automated experiment in STEM. Combined with beam control, this approach allows studying beam effects on selected atomic groups and chemical bonds in a fully automated mode. Here, we demonstrate atomically precise engineering of single vacancy lines in transition metal dichalcogenides and the creation and identification of topological defects in graphene. The ELIT-based approach facilitates direct on-the-fly analysis of the STEM data and engenders real-time feedback schemes for probing electron beam chemistry, atomic manipulation, and atom by atom assembly.

A density functional theory study on the adsorption reaction mechanism of double CO2 on the surface of graphene defects

Much research has been done on reactions of a single CO₂ molecule with a graphene surface. In this paper, density functional theory calculations are used to investigate the adsorption and reaction of double CO₂ on the surface of single vacancy (SV) and divacancy (DV) defect graphene. The study found that due to the mutual repulsion between CO₂ and the size of the SV defect, it is difficult for two CO₂ molecular to be adsorbed directly above the SV defect at the same time. Regardless of SV or DV, the adsorption of the first CO₂ in the defect center will have a beneficial effect on the adsorption of the second CO₂. In addition, the transition state calculation of the CO₂ reaction on the DV plane was carried out, and the adsorption behavior was analyzed and studied. This in-depth study is helpful to the understanding of the reaction behavior of CO₂ on graphene, and further exploration in the direction of the effective application of graphene to the reaction and adsorption of CO₂. Our work explores the adsorption behavior of CO₂ on graphene surfaces, the physical and chemical adsorption of double CO₂ at the defect was studied and analyzed.

Exploring order parameters and dynamic processes in disordered systems via variational autoencoders

We suggest and implement an approach for the bottom-up description of systems undergoing large-scale structural changes and chemical transformations from dynamic atomically resolved imaging data, where only partial or uncertain data on atomic positions are available. This approach is predicated on the synergy of two concepts, the parsimony of physical descriptors and general rotational invariance of noncrystalline solids, and is implemented using a rotationally invariant extension of the variational autoencoder applied to semantically segmented atom-resolved data seeking the most effective reduced representation for the system that still contains the maximum amount of original information. This approach allowed us to explore the dynamic evolution of electron beam-induced processes in a silicon-doped graphene system, but it can be also applied for a much broader range of atomic scale and mesoscopic phenomena to introduce the bottom-up order parameters and explore their dynamics with time and in response to external stimuli.

Direct observation and catalytic role of mediator atom in 2D materials

The structural transformations of graphene defects have been extensively researched through aberration-corrected transmission electron microscopy (AC-TEM) and theoretical calculations. For a long time, a core concept in understanding the structural evolution of graphene defects has been the Stone-Thrower-Wales (STW)-type bond rotation. In this study, we show that undercoordinated atoms induce bond formation and breaking, with much lower energy barriers than the STW-type bond rotation. We refer to them as mediator atoms due to their mediating role in the breaking and forming of bonds. Here, we report the direct observation of mediator atoms in graphene defect structures using AC-TEM and annular dark-field scanning TEM (ADF-STEM) and explain their catalytic role by tight-binding molecular dynamics (TBMD) simulations and image simulations based on density functional theory (DFT) calculations. The study of mediator atoms will pave a new way for understanding not only defect transformation but also the growth mechanisms in two-dimensional materials.

Effect of Structural Disorders on the Li Storage Capacity of Graphene Nanomaterials: A First-Principles Study

We employed first-principles calculations to investigate the effect of structural disorders on the Li storage capacity of graphene nanomaterials. Our calculations first revealed that the Li storage capacity of a graphene monolayer does not necessarily increase with the size of a C vacancy created but is largely determined by the local geometry of the defect sites. Our electronic structure analysis further revealed that the enhanced Li storage capacity by the C vacancy defect is mainly attributed to the increased number of the unoccupied electronic density of states lying near the Fermi level, which can be substantially increased by raising the number of bond rotations within the vacancy sites. Furthermore, it was also found that the Li storage capacity of graphene can be effectively enhanced by increasing the degree of local ring disorders without the presence of any vacancy defect. The amorphous graphene structure was shown to possess a relatively higher Li storage capacity compared to pristine graphene, primarily owing to the presence of many nonhexagonal rings randomly distributed in the graphene lattice. These nonhexagonal rings can create many electron-deficient regions on the graphene surface to effectively accommodate more electrons from Li, thereby substantially enhancing the Li storage capacity of graphene nanomaterials.

Atomic Structure and Dynamics of Defects and Grain Boundaries in 2D Pd2Se3 Monolayers

We study the atomic structure and dynamics of defects and grain boundaries in monolayer Pd₂Se₃ using annular dark field scanning transmission electron microscopy. The Pd₂Se₃ monolayers are reproducibly created by thermally induced phase transformation of few-layered PdSe₂ films in an in situ heating holder in the TEM to promote Se loss. A variety of point vacancies, one-dimensional defects, grain boundaries (GBs), and defect ring complexes are directly observed in monolayer Pd₂Se₃, which show a series of dynamics triggered by electron beam irradiation. High mobility of vacancies leads to self-healing of point vacancies by migration to the edge and subsequent edge etching under beam irradiation. Specific defects for Pd₂Se₃ are stabilized by the formation of Se-Se bonds, which can shift in a staggered way to buffer strain, forming a wave-like one-dimensional defect. Bond rotations are also observed and play an important role in defect and grain boundary dynamics in Pd₂Se₃ during vacancy production. The GBs form in a meandering pathway and migrate by a sequence of Se-Se bond rotations without large-scale vacancy formation. In the GB corners and tilted GBs, other highly symmetric vacancy defects also occur to adapt to the orientation change. These results give atomic level insights into the defects and grain boundaries in Pd₂Se₃ 2D monolayers.

Nanocrystalline graphene at high temperatures: insight into nanoscale processes

During high temperature pyrolysis of polymer thin films, nanocrystalline graphene with a high defect density, active edges and various nanostructures is formed. The catalyst-free synthesis is based on the temperature assisted transformation of a polymer precursor. The processing conditions have a strong influence on the final thin film properties. However, the precise elemental processes that govern the polymer pyrolysis at high temperatures are unknown. By means of time resolved in situ transmission electron microscopy investigations we reveal that the reactivity of defects and unsaturated edges plays an integral role in the structural dynamics. Both mobile and stationary structures with varying size, shape and dynamics have been observed. During high temperature experiments, small graphene fragments (nanoflakes) are highly unstable and tend to lose atoms or small groups of atoms, while adjacent larger domains grow by addition of atoms, indicating an Ostwald-like ripening in these 2D materials, besides the mechanism of lateral merging of nanoflakes with edges. These processes are also observed in low-dose experiments with negligible electron beam influence. Based on energy barrier calculations, we propose several inherent temperature-driven mechanisms of atom rearrangement, partially involving catalyzing unsaturated sites. Our results show that the fundamentally different high temperature behavior and stability of nanocrystalline graphene in contrast to pristine graphene is caused by its reactive nature. The detailed analysis of the observed dynamics provides a pioneering overview of the relevant processes during ncg heating.

Evolution of Glassy Carbon Microstructure: In Situ Transmission Electron Microscopy of the Pyrolysis Process

Glassy carbon is a graphene-rich form of elemental carbon obtained from pyrolysis of polymers, which is composed of three-dimensionally arranged, curved graphene fragments alongside fractions of disordered carbon and voids. Pyrolysis encompasses gradual heating of polymers at ≥ 900 °C under inert atmosphere, followed by cooling to room temperature. Here we report on an experimental method to perform in situ high-resolution transmission electron microscopy (HR-TEM) for the direct visualization of microstructural evolution in a pyrolyzing polymer in the 500-1200 °C temperature range. The results are compared with the existing microstructural models of glassy carbon. Reported experiments are performed at 80 kV acceleration voltage using MEMS-based heating chips as sample substrates to minimize any undesired beam-damage or sample preparation induced transformations. The outcome suggests that the geometry, expansion and atomic arrangement within the resulting graphene fragments constantly change, and that the intermediate structures provide important cues on the evolution of glassy carbon. A complete understanding of the pyrolysis process will allow for a general process tuning specific to the precursor polymer for obtaining glassy carbon with pre-defined properties.

Building Structures Atom by Atom via Electron Beam Manipulation

Building materials from the atom up is the pinnacle of materials fabrication. Until recently the only platform that offered single-atom manipulation was scanning tunneling microscopy. Here controlled manipulation and assembly of a few atom structures are demonstrated by bringing together single atoms using a scanning transmission electron microscope. An atomically focused electron beam is used to introduce Si substitutional defects and defect clusters in graphene with spatial control of a few nanometers and enable controlled motion of Si atoms. The Si substitutional defects are then further manipulated to form dimers, trimers, and more complex structures. The dynamics of a beam-induced atomic-scale chemical process is captured in a time-series of images at atomic resolution. These studies suggest that control of the e-beam-induced local processes offers the next step toward atom-by-atom nanofabrication, providing an enabling tool for the study of atomic-scale chemistry in 2D materials and fabrication of predefined structures and defects with atomic specificity.

Anomalous strength characteristics of Stone-Thrower-Wales defects in graphene sheets - a molecular dynamics study

Graphene, viz., the one-atom-thick sheet of carbon, exhibits outstanding mechanical properties, but defects, which are inevitable at the time of synthesis, may strongly affect these properties. In this study, the effects of two types of Stone-Thrower-Wales (namely, STW-1 and STW-2) defects on the mechanical properties of graphene sheets at different temperatures and strain rates were investigated on the basis of molecular dynamics simulations. The authors also investigated the effect of the strain rate and defect concentration on the failure morphology of STW-1 and STW-2 defected graphene sheets. It was observed that, irrespective of the strain rate, the fracture strengths of STW-1 and STW-2 defected graphene sheets are identical in the zigzag and armchair directions, respectively, at low temperatures. It was also observed that the fracture strengths of graphene sheets with STW-1 defects in the armchair direction and STW-2 defects in the zigzag direction decrease drastically at higher temperatures and also at lower strain rates. On the other hand, it was noticed that the fracture strengths of graphene sheets with STW-1 defects in the zigzag direction and STW-2 defects in the armchair direction decrease gradually with an increase in the temperature and a decrease in the strain rate. It was also predicted that the failure morphology of graphene sheets with STW-1 defects in the zigzag direction and STW-2 defects in the armchair direction depends on the defect concentration and the strain rate.

Interband transitions in closed-shell vacancy containing graphene quantum dots complexed with heavy metals

High-performance optical detection of toxic heavy metals by using graphene quantum dots (GQDs) requires a strong interaction between the metals and GQDs, which can be reached through artificial creation of vacancy-type defects in GQDs.

Atomic structure of defects and dopants in 2D layered transition metal dichalcogenides

Transmission electron microscopy can directly image the detailed atomic structure of layered transition metal dichalcogenides, revealing defects and dopants.

Understanding the graphitization and growth of free-standing nanocrystalline graphene using in situ transmission electron microscopy

Graphitization of polymers is an effective way to synthesize nanocrystalline graphene on different substrates with tunable shape, thickness and properties. The catalyst free synthesis results in crystallite sizes on the order of a few nanometers, significantly smaller than commonly prepared polycrystalline graphene. Even though this method provides the flexibility of graphitizing polymer films on different substrates, substrate free graphitization of freestanding polymer layers has not been studied yet. We report for the first time the thermally induced graphitization and domain growth of free-standing nanocrystalline graphene thin films using in situ TEM techniques. High resolution transmission electron microscopy (HRTEM), selected area electron diffraction (SAED) and electron energy loss spectroscopy (EELS) techniques were used to analyze the graphitization and the evolution of nanocrystalline domains at different temperatures by characterizing the crystallinity and domain size, further supported by ex situ Raman spectroscopy. The graphitization was comparable to the substrate supported heating and the temperature dependence of graphitization was analyzed. In addition, the in situ analysis of the graphitization enabled direct imaging of some of the growth processes taking place at different temperatures.

Atomically Thin Interfacial Suboxide Key to Hydrogen Storage Performance Enhancements of Magnesium Nanoparticles Encapsulated in Reduced Graphene Oxide

As a model system for hydrogen storage, magnesium hydride exhibits high hydrogen storage density, yet its practical usage is hindered by necessarily high temperatures and slow kinetics for hydrogenation-dehydrogenation cycling. Decreasing particle size has been proposed to simultaneously improve the kinetics and decrease the sorption enthalpies. However, the associated increase in surface reactivity due to increased active surface area makes the material more susceptible to surface oxidation or other side reactions, which would hinder the overall hydrogenation-dehydrogenation process and diminish the capacity. Previous work has shown that the chemical stability of Mg nanoparticles can be greatly enhanced by using reduced graphene oxide as a protecting agent. Although no bulklike crystalline MgO layer has been clearly identified in this graphene-encapsulated/Mg nanocomposite, we propose that an atomically thin layer of honeycomb suboxide exists, based on first-principles interpretation of Mg K-edge X-ray absorption spectra. Density functional theory calculations reveal that in contrast to conventional expectations for thick oxides this interfacial oxidation layer permits H₂ dissociation to the same degree as pristine Mg metal with the added benefit of enhancing the binding between reduced graphene oxide and the Mg nanoparticle, contributing to improved mechanical and chemical stability of the functioning nanocomposite.

Direct observation of multiple rotational stacking faults coexisting in freestanding bilayer MoS2

Electronic properties of two-dimensional (2D) MoS₂ semiconductors can be modulated by introducing specific defects. One important type of defect in 2D layered materials is known as rotational stacking fault (RSF), but the coexistence of multiple RSFs with different rotational angles was not directly observed in freestanding 2D MoS₂ before. In this report, we demonstrate the coexistence of three RSFs with three different rotational angles in a freestanding bilayer MoS₂ sheet as directly observed using an aberration-corrected transmission electron microscope (TEM). Our analyses show that these RSFs originate from cracks and dislocations within the bilayer MoS₂. First-principles calculations indicate that RSFs with different rotational angles change the electronic structures of bilayer MoS₂ and produce two new symmetries in their bandgaps and offset crystal momentums. Therefore, employing RSFs and their coexistence is a promising route in defect engineering of MoS₂ to fabricate suitable devices for electronics, optoelectronics, and energy conversion.

Graphene Strained by Defects

Using graphene nanomechanical resonators we demonstrate the extent to which the mechanical properties of multilayer graphene films are controllable, in real time, through introduction and rearrangement of defects. We show both static and re-entrant (cyclical) changes in the tensile stress using a combination of ion implantation, chemical functionalization, and thermal treatment. While the dramatic increase in static tensile stress achievable through laser annealing can be of importance for various MEMS applications, we view the direct observation of a time-variable stress as even more significant. We find that defect-rich films exhibit a slow relaxation component of the tensile stress that remains in the resonator long after the laser exposure is finished (t_relax ≈ 100 s ≫ t_cooling), analogous to a wind-up toy. We attribute this persistent component of the time-variable stress to a set of metastable, multivacancy structures formed during the laser anneal. Our results indicate that significant stress fields generated by multivacancies, in combination with their finite lifetime, could make them a powerful and flexible tool in nanomechanics.

From Permeation to Cluster Arrays: Graphene on Ir(111) Exposed to Carbon Vapor

Our scanning tunneling microscopy and X-ray photoelectron spectroscopy experiments along with first-principles calculations uncover the rich phenomenology and enable a coherent understanding of carbon vapor interaction with graphene on Ir(111). At high temperatures, carbon vapor not only permeates to the metal surface but also densifies the graphene cover. Thereby, in addition to underlayer graphene growth, upon cool down also severe wrinkling of the densified graphene cover is observed. In contrast, at low temperatures the adsorbed carbon largely remains on top and self-organizes into a regular array of fullerene-like, thermally highly stable clusters that are covalently bonded to the underlying graphene sheet. Thus, a new type of predominantly sp²-hybridized nanostructured and ultrathin carbon material emerges, which may be useful to encage or stably bind metal in finely dispersed form.

Stop-Frame Filming and Discovery of Reactions at the Single-Molecule Level by Transmission Electron Microscopy

We report an approach, named chemTEM, to follow chemical transformations at the single-molecule level with the electron beam of a transmission electron microscope (TEM) applied as both a tunable source of energy and a sub-angstrom imaging probe. Deposited on graphene, disk-shaped perchlorocoronene molecules are precluded from intermolecular interactions. This allows monomolecular transformations to be studied at the single-molecule level in real time and reveals chlorine elimination and reactive aryne formation as a key initial stage of multistep reactions initiated by the 80 keV e-beam. Under the same conditions, perchlorocoronene confined within a nanotube cavity, where the molecules are situated in very close proximity to each other, enables imaging of intermolecular reactions, starting with the Diels-Alder cycloaddition of a generated aryne, followed by rearrangement of the angular adduct to a planar polyaromatic structure and the formation of a perchlorinated zigzag nanoribbon of graphene as the final product. ChemTEM enables the entire process of polycondensation, including the formation of metastable intermediates, to be captured in a one-shot "movie". A molecule with a similar size and shape but with a different chemical composition, octathio[8]circulene, under the same conditions undergoes another type of polycondensation via thiyl biradical generation and subsequent reaction leading to polythiophene nanoribbons with irregular edges incorporating bridging sulfur atoms. Graphene or carbon nanotubes supporting the individual molecules during chemTEM studies ensure that the elastic interactions of the molecules with the e-beam are the dominant forces that initiate and drive the reactions we image. Our ab initio DFT calculations explicitly incorporating the e-beam in the theoretical model correlate with the chemTEM observations and give a mechanism for direct control not only of the type of the reaction but also of the reaction rate. Selection of the appropriate e-beam energy and control of the dose rate in chemTEM enabled imaging of reactions on a time frame commensurate with TEM image capture rates, revealing atomistic mechanisms of previously unknown processes.

Direct imaging of rotating molecules anchored on graphene

There has been significant research interest in controlling and imaging molecular dynamics, such as translational and rotational motions, especially at a single molecular level. Here we applied aberration-corrected transmission electron microscopy (ACTEM) to actuate and directly image the rotational motions of molecules anchored on a single-layer-graphene sheet. Nanometer-sized carbonaceous molecules anchored on graphene provide ideal systems for monitoring rotational motions via ACTEM. We observed the preferential registry of longer molecular axis along graphene zigzag or armchair lattice directions due to the stacking-dependent molecule-graphene energy landscape. The calculated cross section from elastic scattering theory was used to experimentally estimate the rotational energy barriers of molecules on graphene. The observed energy barrier was within the range of 1.5-12 meV per atom, which is in good agreement with previous calculation results. We also performed molecular dynamics simulations, which revealed that the edge atoms of the molecule form stably bonds to graphene defects and can serve as a pivot point for rotational dynamics. Our study demonstrates the versatility of ACTEM for the investigation of molecular dynamics and configuration-dependent energetics at a single molecular level.

Phosphorene under electron beam: from monolayer to one-dimensional chains

Phosphorene, a single sheet of black phosphorus, is an elemental two-dimensional material with unique properties and potential applications in semiconductor technology. While few-layer flakes of the material have been characterized using transmission electron microscopy, very little is known about its response to electron irradiation, which may be particularly important in the context of top-down engineering of phosphorus nanostructures using a focused electron beam. Here, using first-principles simulations, we study the production of defects in a single phosphorene sheet under impacts of energetic electrons. By employing the McKinley-Feshbach formalism and accounting for the thermal motion of atoms, we assess the cross section for atom displacement as a function of electron energy. We further investigate the energetics and dynamics of point defects and the stability of ribbons and edges under an electron beam. Finally, we show that P atomic chains should be surprisingly stable, and their atomic structure is not linear giving rise to the absence of a gap in the electronic spectrum.

Molecular dynamics study on the mechanical response and failure behaviour of graphene: performance enhancement via 5–7–7–5 defects

A one atom-thick sheet of carbon exhibits outstanding elastic moduli and tensile strength in its pristine form but structural defects which are inevitable in graphene due to its production techniques can alter its structural properties.

Atomic Structure of Graphene Subnanometer Pores

The atomic structure of subnanometer pores in graphene, of interest due to graphene's potential as a desalination and gas filtration membrane, is demonstrated by atomic resolution aberration corrected transmission electron microscopy. High temperatures of 500 °C and over are used to prevent self-healing of the pores, permitting the successful imaging of open pore geometries consisting of between -4 to -13 atoms, all exhibiting subnanometer diameters. Picometer resolution bond length measurements are used to confirm reconstruction of five-membered ring projections that often decorate the pore perimeter, knowledge which is used to explore the viability of completely self-passivated subnanometer pore structures; bonding configurations where the pore would not require external passivation by, for example, hydrogen to be chemically inert.

Thermally Induced Dynamics of Dislocations in Graphene at Atomic Resolution

Thermally induced dislocation movements are important in understanding the effects of high temperature annealing on modifying the crystal structure. We use an in situ heating holder in an aberration corrected transmission electron microscopy to study the movement of dislocations in suspended monolayer graphene up to 800 °C. Control of temperature enables the differentiation of electron beam induced effects and thermally driven processes. At room temperature, the dynamics of dislocation behavior is driven by the electron beam irradiation at 80 kV; however at higher temperatures, increased movement of the dislocation is observed and provides evidence for the influence of thermal energy to the system. An analysis of the dislocation movement shows both climb and glide processes, including new complex pathways for migration and large nanoscale rapid jumps between fixed positions in the lattice. The improved understanding of the high temperature dislocation movement provides insights into annealing processes in graphene and the behavior of defects with increased heat.

Large-Scale Molecular Simulations on the Mechanical Response and Failure Behavior of a defective Graphene: Cases of 5-8-5 Defects

Understanding the effect of defects on mechanical responses and failure behaviors of a graphene membrane is important for its applications. As examples, in this paper, a family of graphene with various 5-8-5 defects are designed and their mechanical responses are investigated by employing molecular dynamics simulations. The dependence of fracture strength and strain as well as Young's moduli on the nearest neighbor distance and defect types is examined. By introducing the 5-8-5 defects into graphene, the fracture strength and strain become smaller. However, the Young's moduli of DL (Linear arrangement of repeat unit 5-8-5 defect along zigzag-direction of graphene), DS (a Slope angle between repeat unit 5-8-5 defect and zigzag direction of graphene) and DZ (Zigzag-like 5-8-5 defects) defects in the zigzag direction become larger than those in the pristine graphene in the same direction. A maximum increase of 11.8% of Young's modulus is obtained. Furthermore, the brittle cracking mechanism is proposed for the graphene with 5-8-5 defects. The present work may provide insights in controlling the mechanical properties by preparing defects in the graphene, and give a full picture for the applications of graphene with defects in flexible electronics and nanodevices.

The formation mechanism of multiple vacancies and amorphous graphene under electron irradiation

The evolution of multiple vacancies (Vns) in graphene under electron irradiation (EI) was explored systematically by long time non-equilibrium molecular dynamics simulations, with n varying from 4 to 40. The simulations showed that the Vns form haeckelites in the case with small n, while forming holes as n increases. The scale of the haeckelites, characterized by the number of pentagon-heptagon pairs, grows linearly with n. Such a linear relationship can be interpreted as a consequence of compensating the missing area, caused by the Vns, in order to maintain the area of the perfect sp(2) network by self-healing. Beyond that, the scale of the haeckelite vs. the density of missing atoms is predicted to be Sh ∼ 6Dn, where Sh and Dn are the percentage of non-hexagonal rings and missing atoms, respectively. This study provides an intuitive picture of the formation of amorphous graphene under EI and the quantitative understanding of the mechanism.

Three-fold rotational defects in two-dimensional transition metal dichalcogenides

As defects frequently govern the properties of crystalline solids, the precise microscopic knowledge of defect atomic structure is of fundamental importance. We report a new class of point defects in single-layer transition metal dichalcogenides that can be created through 60° rotations of metal-chalcogen bonds in the trigonal prismatic lattice, with the simplest among them being a three-fold symmetric trefoil-like defect. The defects, which are inherently related to the crystal symmetry of transition metal dichalcogenides, can expand through sequential bond rotations, as evident from in situ scanning transmission electron microscopy experiments, and eventually form larger linear defects consisting of aligned 8-5-5-8 membered rings. First-principles calculations provide insights into the evolution of rotational defects and show that they give rise to p-type doping and local magnetic moments, but weakly affect mechanical characteristics of transition metal dichalcogenides. Thus, controllable introduction of rotational defects can be used to engineer the properties of these materials.

Discriminative modulation of the highest occupied molecular orbital energies of graphene and carbon nanotubes induced by charging

The highest occupied molecular orbital (HOMO) energies of carbon nanotubes (CNTs) and graphene are crucial in fundamental and applied research of carbon nanomaterials, and so their modulation is desired. Our first-principles calculations reveal that the HOMO energies of CNTs and graphene can both be raised by negatively charging, and that the rate of increase of the HOMO energy of a CNT is much greater and faster than that of graphene with the same number of C atoms. This discriminative modulation holds true regardless of the number of C atoms and the CNT type, and so is universal. This work provides a new opportunity to develop all-carbon devices with CNTs and graphene as different functional elements.

Energetics of atomic scale structure changes in graphene

An overview of theoretical and experimental studies concerned with energetics of atomic scale structure changes in graphene, including thermally activated and electron irradiation-induced processes.

Repeated growth-etching-regrowth for large-area defect-free single-crystal graphene by chemical vapor deposition

Reducing nucleation density and healing structural defects are two challenges for fabricating large-area high-quality single-crystal graphene, which is essential for its electronic and optoelectronic applications. We have developed a method involving chemical vapor deposition (CVD) growth followed by repeated etching-regrowth, to solve both problems at once. Using this method, we can obtain single-crystal graphene domains with a size much larger than that allowed by the nucleation density in the initial growth and efficiently heal structural defects similar to graphitization but at a much lower temperature, both of which are impossible to realize by conventional CVD. Using this method with Pt as a growth substrate, we have grown ∼3 mm defect-free single-crystal graphene domains with a carrier mobility up to 13,000 cm2 V(-1) s(-1) under ambient conditions.

Detailed formation processes of stable dislocations in graphene

We use time-dependent HRTEM to reveal that stable dislocation pairs in graphene are formed from an initial complex multi-vacancy cluster that undergoes multiple bond rotations and adatom incorporation. In the process, it is found that the transformation from the formed complex multi-vacancy cluster can proceed without the increase of vacancy because many atoms and dimers are not only evaporated but also actively adsorbed. In tight-binding molecular dynamics simulations, it is confirmed that adatoms play an important role in the reconstruction of non-hexagonal rings into hexagonal rings. From density functional theory calculations, it is also found from simulations that there is a favorable distance between two dislocations pointing away from each other (i.e. formed from atom loss). For dislocation pairs pointing away from each other, the hillock-basin structure is more stable than the hillock-hillock structure for dislocation pairs pointing away from each other (i.e. formed from atom loss).

The role of the bridging atom in stabilizing odd numbered graphene vacancies

Vacancy defects in graphene with an odd number of missing atoms, such as the trivacancy, have been imaged at atomic resolution using aberration corrected transmission electron microscopy. These defects are not just stabilized by simple bond reconstructions between under-coordinated carbon atoms, as exhibited by even vacancies such as the divacancy. Instead we have observed reconstructions consisting of under-coordinated bridging carbon atoms spanning the vacancy to saturate edge atoms. We report detailed studies of the effect of this bridging atom on the configuration of the trivacancy and higher order odd number vacancies, as well as its role in defect stabilization in amorphous systems. Theoretical analysis using density functional theory and tight-binding molecular dynamics calculations demonstrate that the bridging atom enables the low energy reconfiguration of these defect structures.