Conserved atomic bonding sequences and strain organization of graphene grain boundaries

Grain Size Engineering of CVD-Grown Large-Area Graphene Films

Graphene, a single atomic layer of graphitic carbon, has attracted much attention because of its outstanding properties hold great promise for a wide range of technological applications. Large-area graphene films (GFs) grown by chemical vapor deposition (CVD) are highly desirable for both investigating their intrinsic properties and realizing their practical applications. However, the presence of grain boundaries (GBs) has significant impacts on their properties and related applications. According to the different grain sizes, GFs can be divided into polycrystalline, single-crystal, and nanocrystalline films. In the past decade, considerable progress has been made in engineering the grain sizes of GFs by modifying the CVD processes or developing some new growth approaches. The key strategies involve controlling the nucleation density, growth rate, and grain orientation. This review aims to provide a comprehensive description of grain size engineering research of GFs. The main strategies and underlying growth mechanisms of CVD-grown large-area GFs with nanocrystalline, polycrystalline, and single-crystal structures are summarized, in which the advantages and limitations are highlighted. In addition, the scaling law of physical properties in electricity, mechanics, and thermology as a function of grain sizes are briefly discussed. Finally, the perspectives for challenges and future development in this area are also presented.

Structural dynamics of polycrystalline graphene

The exceptional properties of the two-dimensional material graphene make it attractive for multiple functional applications, whose large-area samples are typically polycrystalline. Here, we study the mechanical properties of graphene in computer simulations and connect these to the experimentally relevant mechanical properties. In particular, we study the fluctuations in the lateral dimensions of the periodic simulation cell. We show that over short timescales, both the area A and the aspect ratio B of the rectangular periodic box show diffusive behavior under zero external field during dynamical evolution, with diffusion coefficients D_{A} and D_{B} that are related to each other. At longer times, fluctuations in A are bounded, while those in B are not. This makes the direct determination of D_{B} much more accurate, from which D_{A} can then be derived indirectly. We then show that the dynamic behavior of polycrystalline graphene under external forces can also be derived from D_{A} and D_{B} via the Nernst-Einstein relation. Additionally, we study how the diffusion coefficients depend on structural properties of the polycrystalline graphene, in particular, the density of defects.

Defects in graphene-based heterostructures: topological and geometrical effects

The combination of graphene (Gr) and graphene-like materials provides the possibility of using two-dimensional (2D) atomic layer building blocks to create unprecedented architectures. The most attractive characteristics are strongly dependent on the various spatial structures, mainly including in-plane heterostructures butt-joined at the side of an atomic monolayer through covalent bonds, van der Waals (vdW) heterostructures involving a vertically stacked hybrid structure, and their combinations. Heterostructures can not only overcome the limitations inherent to each material but may also obtain new features by appropriate material combination. However, heterostructures made of vdW force superposition or covalent bond splicing are prone to defects. The introduction of external and internal defects causes local deformation and stress in the material, thereby affecting the physical properties of the material, such as its transport properties and mechanical properties. Therefore, research, utilization and control of these defects are highly critical. This paper reviews the vacancy, topological and geometrical effects of defects in modulating the structures and mechanical responses of Gr-based heterostructures. Moreover, the coupling effects of various defects on the Gr-based heterostructures in multi-physics fields are also discussed. This work aims to improve the understanding of the physical mechanism of defective configurations and their association in low dimensions, so as to realize various configurations and to aid the search for new usages.

The combination of graphene (Gr) and graphene-like materials provides the possibility of using two-dimensional (2D) atomic layer building blocks to create unprecedented architectures.

Deep Learning Segmentation of Complex Features in Atomic-Resolution Phase-Contrast Transmission Electron Microscopy Images

Phase-contrast transmission electron microscopy (TEM) is a powerful tool for imaging the local atomic structure of materials. TEM has been used heavily in studies of defect structures of two-dimensional materials such as monolayer graphene due to its high dose efficiency. However, phase-contrast imaging can produce complex nonlinear contrast, even for weakly scattering samples. It is, therefore, difficult to develop fully automated analysis routines for phase-contrast TEM studies using conventional image processing tools. For automated analysis of large sample regions of graphene, one of the key problems is segmentation between the structure of interest and unwanted structures such as surface contaminant layers. In this study, we compare the performance of a conventional Bragg filtering method with a deep learning routine based on the U-Net architecture. We show that the deep learning method is more general, simpler to apply in practice, and produces more accurate and robust results than the conventional algorithm. We provide easily adaptable source code for all results in this paper and discuss potential applications for deep learning in fully automated TEM image analysis.

Traction-separation laws of graphene grain boundaries

Molecular dynamics simulations are used to extract the traction-separation laws (TSLs) of symmetric grain boundaries of graphene. Grain boundaries with realistic atomic structures are constructed using different types of dislocations. The TSLs of grain boundaries are extracted by using cohesive zone volume elements (CZVEs) ahead of the crack tip. The traction and separation of each cohesive zone volume element are calculated during the crack growth. The traction and separation values obtained for the cohesive elements predict that the TSLs of grain boundaries have a bilinear form. The areas under the traction-separation curves are used to calculate the separation energy of the grain boundaries. The results show that as the grain boundary misorientation angle increases the separation energy of the grain boundaries decreases. The impact of temperature on the traction separation laws is studied. The results show that, with an increase of the temperature from 0.1 K to 300 K, the separation energy first increases to reach its peak at around 25 K and then slightly decreases.

Efficient Structural Relaxation of Polycrystalline Graphene Models

Large samples of experimentally produced graphene are polycrystalline. For the study of this material, it helps to have realistic computer samples that are also polycrystalline. A common approach to produce such samples in computer simulations is based on the method of Wooten, Winer, and Weaire, originally introduced for the simulation of amorphous silicon. We introduce an early rejection variation of their method, applied to graphene, which exploits the local nature of the structural changes to achieve a significant speed-up in the relaxation of the material, without compromising the dynamics. We test it on a 3200 atoms sample, obtaining a speed-up between one and two orders of magnitude. We also introduce a further variation called early decision specifically for relaxing large samples even faster, and we test it on two samples of 10,024 and 20,000 atoms, obtaining a further speed-up of an order of magnitude. Furthermore, we provide a graphical manipulation tool to remove unwanted artifacts in a sample, such as bond crossings.

Large Suspended Monolayer and Bilayer Graphene Membranes with Diameter up to 750 µm

In this paper ultra clean monolayer and bilayer Chemical Vapor Deposited (CVD) graphene membranes with diameters up to 500 µm and 750 µm, respectively have been fabricated using Inverted Floating Method (IFM) followed by thermal annealing in vacuum. The yield decreases with size but we show the importance of choosing a good graphene raw material. Dynamic mechanical properties of the membranes at room temperature in different diameters are measured before and after annealing. The quality factor ranges from 200 to 2000 and shows no clear dependence on the size. The resonance frequency is inversely proportional to the diameter of the membranes. We observe a reduction of the effective intrinsic stress in the graphene, as well as of the relative error in the determination of said stress after thermal annealing. These measurements show that it is possible to produce graphene membranes with reproducible and excellent mechanical properties.

Atomic-Precision Fabrication of Quasi-Full-Space Grain Boundaries in Two-Dimensional Hexagonal Boron Nitride

Precise control and in-depth understanding of the interfaces are crucial for the functionality-oriented material design with desired properties. Herein, via modifying the long-standing bicrystal strategy, we proposed a novel nanowelding approach to build up interfaces between two-dimensional (2D) materials with atomic precision. This method enabled us, for the first time, to experimentally achieve the quasi-full-parameter-space grain boundaries (GBs) in 2D hexagonal boron nitride (h-BN). It further helps us unravel the long-term controversy and confusion on the registry of GBs in h-BN, including (i) discriminate the relative contribution of the strain and chemical energy on the registry of GBs; (ii) identify a new dislocation core-Frank partial dislocation and four new antiphase boundaries; and (iii) confirm the universal GB faceting. Our work provides a new paradigm to the exploitation of structural-property correlation of interfaces in 2D materials.

Molecular Dynamics of Chirality Definable Growth of Single-Walled Carbon Nanotubes

In order to achieve the chirality-specific growth of single-walled carbon nanotubes (SWCNTs), it is crucial to understand the growth mechanism. Even though many molecular dynamics (MD) simulations have been employed to analyze the SWCNT growth mechanism, it has been difficult to discuss the chirality determining kinetics because of the defects remaining on the SWCNTs grown in simulations. In this study, we demonstrate MD simulations of defect-free SWCNTs, that is, chirality definable SWCNTs, under the optimized carbon supply rate and temperature. The chiralities of the SWCNTs were assigned as (14,1), (15,2), and (9,0), indicating the preference of near-zigzag and pure-zigzag SWCNTs. The SWCNTs contained at least one complete row of defect-free walls consisting of only hexagons. The near-zigzag SWCNTs grew via a kink-running process, in which bond formation between a carbon atom at a kink and a neighboring carbon chain led to formation of a hexagon with a new kink at the SWCNT edge. Defects including pentagons and heptagons were sometimes formed but effectively healed into hexagons on metal surfaces. The pure-zigzag SWCNTs grew by the kink-running and the hexagon nucleation processes. In addition, chirality change events along SWCNTs with incorporation of pentagon-heptagon pair defects were observed in the MD simulations. Here, pentagons and heptagons were frequently observed as adjacent pairs, resulting in ( n, m) chirality changes by (±1,0), (0,±1), (1,-1), or (-1,1).

Grain Boundaries and Tilt-Angle-Dependent Transport Properties of a 2D Mo2C Superconductor

The grain boundaries (GBs) of graphene and molybdenum disulfide have been extensively demonstrated to have a strong influence on electronic, thermal, optical, and mechanical properties. 2D transition-metal carbides (TMCs), known as MXenes, are a rapidly growing new family of 2D materials with many fascinating properties and promising applications. However, the GB structure of 2D TMCs and the influence of GB on their properties remain unknown. Here, we used aberration-corrected scanning transmission electron microscopy combined with electrical measurements to study the GB characteristic of highly crystalline 2D Mo₂C superconductor, a newly emerging member of the 2D TMC family. The 2D Mo₂C superconductor shows a unique tilt-angle-dependent GB structure and electronic transport properties. Different from the reported 2D materials, the GB of 2D Mo₂C shows a peculiar dislocation configuration or sawtooth pattern depending on the tilt angle. More importantly, we found two new periodic GBs with different periodic structures and crystallographic orientations. Electrical measurements on individual GBs show that GB structure strongly affects the transport properties. In the normal state, an increasingly stronger electron localization behavior is observed at the GB region with increasing tilt angle. In the superconducting state, the magnitude of the critical current across the GBs is dramatically reduced, associated with local suppression of superconductivity at GBs. These findings provide new understandings on the GB structure of 2D TMCs and the influence of GB on 2D superconductivity, which would be helpful for tailoring the properties of 2D TMCs through GB engineering.

Conjugated π electron engineering of generalized stacking fault in graphene and h-BN

Generalized-stacking-fault energy (GSFE) serves as an important metric that prescribes dislocation behaviors in materials. In this paper, utilizing first-principle calculations and chemical bonding analysis, we studied the behaviors of generalized stacking fault in graphene and h-BN. It has been shown that the π bond formation plays a critical role in the existence of metastable stacking fault (MSF) in graphene and h-BN lattice along certain slip directions. Chemical functionalization was then proposed as an effective means to engineer the π bond, and subsequently MSF along dislocation slips within graphene and h-BN. Taking hydrogenation as a representative functionalization method, we demonstrated that, with the preferential adsorption of hydrogen along the slip line, π electrons along the slip would be saturated by adsorbed hydrogen atoms, leading to the moderation or elimination of MSF. Our study elucidates the atomic mechanism of MSF formation in graphene-like materials, and more generally, provides important insights towards predictive tuning of mechanic properties in two-dimensional nanomaterials.

Atomistic dynamics of sulfur-deficient high-symmetry grain boundaries in molybdenum disulfide

As a common type of structural defect, grain boundaries (GBs) play an important role in tailoring the physical and chemical properties of bulk crystals and their two-dimensional (2D) counterparts such as graphene and molybdenum disulfide (MoS₂). In this study, we explore the atomic structures and dynamics of three kinds of high-symmetry GBs (α, β and γ) in monolayer MoS₂. Atomic-resolution transmission electron microscopy (TEM) is used to characterize their formation and evolutionary dynamics, and atomistic simulation based analysis explains the size distribution of α-type GBs observed under TEM and the inter-GB interaction, revealing the stabilization mechanism of GBs by pre-existing sulfur vacancies. The results elucidate the correlation between the observed GB dynamics and the migration of sulfur atoms across GBs via a vacancy-mediated mechanism, offering a new perspective for GB engineering in monolayer MoS₂, which may be generalized to other transition metal dichalcogenides.

Epitaxial Templating of Two-Dimensional Metal Chloride Nanocrystals on Monolayer Molybdenum Disulfide

We demonstrate the formation of ionic metal chloride (CuCl) two-dimensional (2D) nanocrystals epitaxially templated on the surface of monolayer molybdenum disulfide (MoS₂). These 2D CuCl nanocrystals are single atomic planes from a nonlayered bulk CuCl structure. They are stabilized as a 2D monolayer on the surface of the MoS₂ through interactions with the uniform periodic surface of the MoS₂. The heterostructure 2D system is studied at the atomic level using aberration-corrected transmission electron microscopy at 80 kV. Dynamics of discrete rotations of the CuCl nanocrystals are observed, maintaining two types of preferential alignments to the MoS₂ lattice, confirming that the strong interlayer interactions drive the stable CuCl structure. Strain maps are produced from displacement maps and used to track real-time variations of local atomic bonding and defect production. Density functional theory calculations interpret the formation of two types of energetically advantageous commensurate superlattices via strong chemical bonds at interfaces and predict their corresponding electronic structures. These results show how vertical heterostructured 2D nanoscale systems can be formed beyond the simple assembly of preformed layered materials and provide indications about how different 2D components and their interfacial coupling mode could influence the overall property of the heterostructures.

Mechanical properties and failure behavior of phosphorene with grain boundaries

Using the density-functional tight-binding method, we studied the effect of grain boundaries on the mechanical properties and failure behavior of phosphorene. We found that the high-angle tilt boundaries with a higher density of (5∣7) defect pairs (oriented along the armchair direction) are stronger than the low-angle tilt boundaries with a lower defect density, and similarly the high-angle boundaries with a higher density of (4∣8) defect pairs (oriented along the zigzag direction) are stronger than the low-angle boundaries with a lower defect density. The failure is due to the rupture of the most pre-strained bonds in the heptagons of the (5∣7) defect pair or octagons of the (4∣8) pairs. The high-angle grain boundaries are better at accommodating the pre-strained bonds in heptagon and octagon defects, leading to a higher failure stress and strain. The results cannot be described by a Griffith-type fracture mechanics criterion, since this does not take into account the bond pre-stretching. Interestingly, these anomalous mechanical and failure characteristics of tilt grain boundaries in phosphorene are also shared by graphene and hexagonal boron nitride, signifying that they may be universal for 2D materials. The findings revealed here may be useful in tuning the mechanical properties of phosphorene via defect engineering for specific applications.

Automatic software correction of residual aberrations in reconstructed HRTEM exit waves of crystalline samples

We develop an automatic and objective method to measure and correct residual aberrations in atomic-resolution HRTEM complex exit waves for crystalline samples aligned along a low-index zone axis. Our method uses the approximate rotational point symmetry of a column of atoms or single atom to iteratively calculate a best-fit numerical phase plate for this symmetry condition, and does not require information about the sample thickness or precise structure. We apply our method to two experimental focal series reconstructions, imaging a β-Si₃N₄ wedge with O and N doping, and a single-layer graphene grain boundary. We use peak and lattice fitting to evaluate the precision of the corrected exit waves. We also apply our method to the exit wave of a Si wedge retrieved by off-axis electron holography. In all cases, the software correction of the residual aberration function improves the accuracy of the measured exit waves.

In Situ Atomic Level Dynamics of Heterogeneous Nucleation and Growth of Graphene from Inorganic Nanoparticle Seeds

An in situ heating holder inside an aberration-corrected transmission electron microscope (AC-TEM) is used to investigate the real-time atomic level dynamics associated with heterogeneous nucleation and growth of graphene from Au nanoparticle seeds. Heating monolayer graphene to an elevated temperature of 800 °C removes the majority of amorphous carbon adsorbates and leaves a clean surface. The aggregation of Au impurity atoms into nanoparticle clusters that are bound to the surface of monolayer graphene causes nucleation of secondary graphene layers from carbon feedstock present within the microscope chamber. This enables the in situ study of heterogeneous nucleation and growth of graphene at the atomic level. We show that the growth mechanism consists of alternating C cluster attachment and indentation filling to maintain a uniform growth front of lowest energy. Back-folding of the graphene growth front is observed, followed by a process that involves flipping back and attaching to the surrounding region. We show how the highly polycrystalline graphene seed evolves with time into a higher order crystalline structure using a combination of AC-TEM and tight-binding molecular dynamics (TBMD) simulations. This helps understand the detailed lowest-energy step-by-step pathways associated with grain boundaries (GB) migration and crystallization processes. We find the motion of the GB is discontinuous and mediated by both bond rotation and atom evaporation, supported by density functional theory calculations and TBMD. These results provide insights into the formation of crystalline seed domains that are generated during bottom-up graphene synthesis.

Evolution of domains and grain boundaries in graphene: a kinetic Monte Carlo simulation

To understand the mystery of preferential mismatching angle of grain boundaries (GB) in multi-crystalline graphene observed experimentally, a systematic kinetic Monte Carlo simulation is designed to explore how a two-dimensional amorphous carbon system evolves into graphene domains and GBs. The details of the evolution, including the graphene domain nucleation, growth, rotation, coalescence, the corresponding GB motion, rotation and elimination, are observed. One hundred individual simulations with different initial configurations are performed and our simulation confirms that it is the Stone-Wales (SW) transformation that dominates the GB fast annealing process, and the results show that graphene domains with small angle GBs (<10°) tend to be annihilated but those with medium angles (>15°) tend to become large angle (≈30°), which is a consequence of the fact that the formation energies of GBs have two minima at 0° and 30°. The behavior of the formation energies is also responsible for the distribution of GBs' mismatch angles obtained by our simulations, which is very similar to those broadly observed experimentally.

Detailed Atomic Reconstruction of Extended Line Defects in Monolayer MoS2

We study the detailed bond reconstructions that occur in S vacancies within monolayer MoS2 using a combination of aberration-corrected transmission electron microscopy, density functional theory (DFT), and multislice image simulations. Removal of a single S atom causes little perturbation to the surrounding MoS2 lattice, whereas the loss of two S atoms from the same atomic column causes a measurable local contraction. Aggregation of S vacancies into linear line defects along the zigzag direction results in larger lattice compression that is more pronounced as the length of the line defect increases. For the case of two rows of S line vacancies, we find two different types of S atom reconstructions with different amounts of lattice compression. Increasing the width of line defects leads to nanoscale regions of reconstructed MoS2 that are shown by DFT to behave as metallic channels. These results provide important insights into how defect structures could be used for creating metallic tracks within semiconducting monolayer MoS2 films for future applications in electronics and optoelectronics.

A generalized Read–Shockley model and large scale simulations for the energy and structure of graphene grain boundaries

The grain boundary (GB) energy is a quantity of fundamental importance for understanding several key properties of graphene.

Mechanism of strength reduction along the graphenization pathway

Even though polycrystalline graphene has shown a surprisingly high tensile strength, the influence of inherent grain boundaries on such property remains unclear. We study the fracture properties of a series of polycrystalline graphene models of increasing thermodynamic stability, as obtained from a long molecular dynamics simulation at an elevated temperature. All of the models show the typical and well-documented brittle fracture behavior of polycrystalline graphene; however, a clear decrease in all fracture properties is observed with increasing annealing time. The remarkably high fracture properties obtained for the most disordered (less annealed) structures arise from the formation of many nonpropagating prefracture cracks, significantly retarding failure. The stability of these reversible cracks is due to the nonlocal character of load transfer after a bond rupture in very disordered systems. It results in an insufficient strain level on neighboring bonds to promote fracture propagation. Although polycrystallinity seems to be an unavoidable feature of chemically synthesized graphenes, these results suggest that targeting highly disordered states might be a convenient way to obtain improved mechanical properties.

Atomic Defects in Two Dimensional Materials

Atomic defects in crystalline structures have pronounced affects on their bulk properties. Aberration-corrected transmission electron microscopy has proved to be a powerful characterization tool for understanding the bonding structure of defects in materials. In this article, recent results on the characterization of defect structures in two dimensional materials are discussed. The dynamic behavior of defects in graphene shows the stability of zigzag edges of the material and gives insights into the dislocation motion. Polycrystalline graphene is characterized using advanced electron microscopy techniques, revealing the global crystal structure of the material, as well as atomic-resolution observation of the carbon atom positions between neighboring crystal grains. Studies of hexagonal boron nitride (hBN) are also visited, highlighting the interlayer bonding, which occurs upon defect formation, and characterization of grain boundary structures. Lastly, defect structures in monolayer polycrystalline transition metal dichalcogenides grown by CVD are discussed.

Probing Crystallinity of Graphene Samples via the Vibrational Density of States

The purity of graphene samples is of crucial importance for their experimental and practical use. In this regard, the detection of the defects is of direct relevance. Here, we show that structural defects in graphene samples give rise to clear signals in the vibrational density of states (VDOS) at specific peaks at high and low frequencies. These can be used as an independent probe of the defect density. In particular, we consider grain boundaries made of pentagon-heptagon pairs, and show that they lead to a shift of the characteristic vibrational D mode toward higher frequency; this distinguishes these line defects from Stone-Wales point defects, which do not lead to such a shift. Our findings may be instrumental for the detection of structural lattice defects using experimental techniques that can directly measure VDOS, such as inelastic electron tunneling and inelastic neutron spectroscopy.