Graphene Grain Boundaries Research Articles

Effect of grain boundaries on thermal transport in bi-layer graphene nano-ribbons

Defects and grain boundaries (GBs) in graphene often form during its growth and have been extensively characterized experimentally. Moreover, in graphene with two or more layers, distinct defect profiles have been identified in different layers. Although these defects and GBs are known to reduce the thermal transport in monolayer graphene, their impact on the overall thermal transport in graphene with two or more layers remains obscure, especially when unique defect profiles exist in different layers. In this study, we employ molecular dynamics simulations to investigate the role of GBs in one of the bi-layer graphene nanoribbons (GNRs), which results in a moiré-like pattern on one side of the GB. We discovered that while the GBs in one of the bi-layer GNR sheets reduce the overall in-plane thermal conductivity, κ, the reduction is mitigated by the pristine layer due to the interlayer van der Waals interaction. By closely examining different phonon modes in individual layers, we elucidate the κ reduction mechanisms in each layer. Our findings offer valuable insights into thermal engineering in graphene-based heterostructures as well as into exotic graphene bi-layer structures, such as those with moiré patterns.

Non-Amontons frictional behaviors of grain boundaries at layered material interfaces

Against conventional wisdom, corrugated grain boundaries in polycrystalline graphene, grown on Pt(111) surfaces, are shown to exhibit negative friction coefficients and non-monotonic velocity dependence. Using combined experimental, simulation, and modeling efforts, the underlying energy dissipation mechanism is found to be dominated by dynamic buckling of grain boundary dislocation protrusions. The revealed mechanism is expected to appear in a wide range of polycrystalline two-dimensional material interfaces, thus supporting the design of large-scale dry superlubric contacts.

Fracture behaviour of bicrystalline graphene characterized via freestanding indentation

Using molecular mechanics (MM) simulations, the failure stress of bicrystalline graphene with different tilt angles is investigated using their free-standing indentation behaviour, in which two types of grain boundaries, including armchair (ac) and zigzag (zz) grain boundaries, and two types of indenter tip, including cylindrical and spherical tips are considered. For reference purposes, the corresponding results under inplane stretching are also examined. It is found that the failure stress of grain boundary (GB) in bicrystalline graphene decreases with the decrease of the GB tilt angle [Formula: see text], which is similar to that determined in inplane stretching. In indentation, the stress concentration under the indenter tip will decrease the failure stress of graphene; in addition, the out-of-plane deformation of graphene in indentation can partially release the pretension induced by the GB in bicrystalline graphene. For the GB with a small prestress, the effect of the former is larger than that of the latter; but for the GB with a larger prestress, the effect of the latter is larger than that of the former. Consequently, the effect of tilt angle [Formula: see text] on the GB strength of bicrystalline graphene is lower in indentation than that given by inplane stretching.

First principles study of electronic structure and transport in graphene grain boundaries

Grain boundaries play a major role for electron transport in graphene sheets grown by chemical vapor deposition. Here we investigate the electronic structure and transport properties of idealized graphene grain boundaries (GBs) in bi-crystals using first principles density functional theory (DFT) and non-equilibrium Greens functions. We generated 150 different grain boundaries using an automated workflow where their geometry is relaxed with DFT. We find that the GBs generally show a quasi-1D bandstructure along the GB. We group the GBs in four classes based on their conductive properties: transparent, opaque, insulating, and spin-polarizing and show how this is related to angular mismatch, quantum mechanical interference, and out-of-plane buckling. Especially, we find that spin-polarization in the GB correlates with out-of-plane buckling. We further investigate the characteristics of these classes in simulated scanning tunnelling spectroscopy and diffusive transport along the GB which demonstrate how current can be guided along the GB.

Analytical energy formalism and kinetic effects of grain boundaries: A case study of graphene

Grain boundaries (GBs), inherent in polycrystalline materials, manifest a diverse array of features that substantially affect material properties. However, the incomplete knowledge of the relevance between structures and energetics of GBs impedes the understanding of their effects. Here, taking graphene as an example, we propose an analytical energy formula for GBs in grain-boundary angle space. Our study reveals that any given GB can be characterized by a geometric combination of symmetric GBs, adhering to the principle of uniformly distributing their dislocation cores along straight trajectories. The formation probability of GBs, as predicted by our theoretical derivation, aligns well with both high-throughput calculations and experimental statistics. Furthermore, we unveil the elusive kinetic effects on GBs by contrasting experimental statistics with energy-dependent thermodynamic effects. This study not only presents a robust model to describe energetically favorable GBs in graphene, offering insight into the formation of GBs in two-dimensional materials, but also reveals the kinetic effects of GBs in material synthesizing process.

The Evolution of Grain Boundary Dislocations in Graphene Induced by Strain: Three-Mode Phase-Field Crystal Method

The evolution and role mechanisms of grain boundary structures during the deformation process of graphene are of great significance for understanding the deformation behavior of graphene and optimizing its mechanical properties. This article takes single-layer graphene as the research object and establishes a double crystal graphene model using the three-mode phase-field crystal method, deeply exploring the evolution mechanisms of dislocations at small-angle symmetrical tilt grain boundaries in graphene under strain. In view of the relaxation and deformation process, the relationship between the number of multiple dislocations and the grain boundary angle of graphene was studied at atomic scale, and the deformation and failure mechanism of double crystal graphene under tensile load was revealed, and it is also discussed from the aspect of the free energy.<br>It is found that, after relaxation, with the increase of grain boundary angle, the density of dislocations at the grain boundary decreases, and the number of specific types of dislocations (5|8|7 and 5|7 dislocations) increases. Under stress loading parallel to the grain boundary, the changes of free energy of the systems containing grain boundaries with different angles show the same trend: At first, they descend to the inflection point and then rise abnormally, and the dislocation behavior can not effectively alleviate the stress concentration caused by continuous loading in the system, leading to failure.<br>Under tensile load, the free energy’s change of the systems is divided into four stages, of which the stage (I): the dislocations at grain boundaries are slightly deformed but does not change its structure. The stage (Ⅱ): dislocations at the grain boundaries are transformed into 5|7 or 5|9 dislocation due to C-C bond fracture or rotation. Dislocations that are "incompatible" have higher energy, making them more conducive to improving the tensile properties of graphene. The stage (Ⅲ): the 5|7 and 5|9 dislocations, begin to fail, and the free energy shows a tendency to decrease significantly. The stage (Ⅳ): the double crystal graphene systems have completely failed. The system with a grain boundary angle of 10° exhibits the most substantial free energy decrease in Stages (Ⅰ), (Ⅱ), and (Ⅲ), and possesses the highest overall tensile strength.<br>This work contributes to understanding the micromechanical behavior of graphene at the atomic scale.

Grain boundary-free graphene sheets for better electrical transport properties prepared by an electrochemical method

Abstract Though good qualities of graphene have been prepared by the electrochemical method, the quality in terms of grain boundaries which has a consequential impact on its electrical properties has not yet been investigated in detail. In this work, grain boundaries and their electrical properties in graphene prepared by the electrochemical method have been investigated. The grain boundary in graphene has been examined from images obtained by a high-resolution transmission electron microscope. The finding reveals no grain boundaries in the graphene sheet prepared by the electrochemical method. As a result, a high current value has been obtained which may be attributed to the smooth passage of charge careers due to the absence of grain boundaries in graphene. The finding suggests that the prepared graphene sheets using the above-mentioned method are excellent in qualities that can be potentially used in various electronic devices, such as field-effect transistors, solar cells, transparent electrodes, interconnects, etc.

Anisotropic bending of graphene with grain boundaries: Insights from tight-binding simulations

Graphene grain boundaries (GBs) are associated with distinct mechanical and physical properties. To utilize these properties requires comprehensive investigation of the GB-controlled nanomechanics. Currently, there is short of fundamental understanding of the out-of-plane bending of graphene in the presence of GBs and the mechanical properties of related curved structures. Here with density functional theory-based tight-binding objective molecular simulations, we revealed anisotropic nonlinear bending of graphene with tilt GBs. The anisotropy and nonlinearity are caused by the dislocation cores which display out-of-plane protrusions. In addition, we investigated the GB-controlled elastic responses of curved graphene configurations, and established the coupling between the elastic modulus and local curvature near the GBs. Our findings serve as useful references for 3D graphene structure design utilizing GBs and can be generalized to other 2D materials.

Grain-Boundary-Induced Ultrasensitive Molecular Detection of Graphene Film.

Graphene has been considered a promising platform for molecular detection due to the graphene-enhanced Raman scattering (GERS) effect. However, the GERS performance of pristine graphene is limited by a low chemically active surface and insufficient density of states (DOS). Although diverse defects have been introduced, it remains a great challenge to improve the enhancement performance. Here, we show that graphene grain boundaries (GBs) possess stronger adsorption capacity and more abundant DOS. Thus, GERS performance increases with the atomic percentage of GBs, which makes nanocrystalline graphene (NG) film a superior GERS substrate. For R6G as a probe molecule, a low detection limit of 3 × 10-10 M was achieved. Utilizing the high chemical activity of GBs, we also fabricated NG film decorated with Au particles using a one-step quenching strategy, and this hybrid film exhibits an extremely low limit of detection down to 5 × 10-11 M, outperforming all the reported graphene-based systems.

Strength criterion of graphene GBs combining discrete bond strength and varied bond stretch

The strength criterion of graphene grain boundaries (GBs) under complex stress states plays an important role in guiding the design of high-performance graphene-related materials and devices under severe mechanical environments like ultrastrong structural materials or flexible electronics. However, finding a unified strength criterion that can adapt to different GB angles and loading states is still a challenge. In this work, we proposed a general method to construct the strength criterion of graphene GBs that includes the atomic details of defect. Firstly, systematic molecular dynamics (MD) simulations were carried out to explore the fracture behaviors of graphene GBs with different GB angles and loading states. Then, bond strength of heptagon ring σ t h R was obtained by projecting the applied stress field to the fractured bond direction, which gives the same value for the same type of C-C bond of same GB angle under different loading states. Besides, to further unify the bond strength of different GB angles, the residual stress caused by other pentagon–heptagon defects was considered by using the disclination dipole theory, in which the intrinsic bond strength σ t h 0 for different GB angles collapses to the same value. With this scenario, the strength criterion of graphene GBs is presented as the bond stretch stress generated by external load exceeds any bond strength of the hexagon–heptagon defect. Furthermore, a unified bond strength is found, linearly decreasing with the equilibrium bond length, which can further be applied to the strength criterion of other defective structures like two types of SW defects (without analytical solution of residual stress) and even pristine graphene. The present results provide a comprehensive understanding of the failure of graphene by considering the balance of bond strength of defective structure and bond stretch stress generated by external load, which may pave the way to construct the atomic structure based strength criterion of other two-dimensional materials.

Structural properties of grain boundary in graphene grown on germanium substrates with different orientations

The direct synthesis of graphene with high-quality on semiconducting germanium (Ge) substrates has been developed recently, which has provided a promising way to integrate graphene with semiconductors for the application of electronic devices. However, the defects such as grain boundaries (GBs) introduced during the growth process have a significant influence on the crystalline quality of graphene and the performance of related electronic devices. Therefore, the investigation of the formation of GBs in graphene grown on a Ge substrate is essential for optimizing the crystalline quality of graphene. Herein, the formation mechanism and microstructure of GBs in graphene grown on Ge (110), Ge (001), and Ge (111) substrates via a chemical vapor deposition method are revealed. Ex situ atomic force microscopy is utilized to monitor the evolution of graphene domains. It is found that a single crystalline graphene film without GBs is formed on Ge (110), while polycrystalline graphene films with GBs are grown on Ge (001) and Ge (111) substrates, as suggested by transmission electron microscopy and x-ray photoelectron spectroscopy measurements. Our work may motivate the future exploration in improving the crystalline quality of graphene grown on a semiconducting substrate and the performance of associated electronic devices.

Tunable ion transport across graphene through tailoring grain boundaries

Grain boundaries (GBs) are common features in materials and can tune their physical and/or chemical properties. GBs in graphene could degrade electrical or thermal properties and, thus, are widely supposed to be avoided in related applications. However, the potential to utilize GBs in graphene remains to be explored. Here we reveal that, contrary to traditional negative effects, GBs can efficiently tune ion transport properties, but this remains poorly understood. By controlling the GB density in graphene, we achieve precise tuning of proton permeance with a range of 2 orders of magnitude. We study the reactivity of GBs and attain 3–6 times higher permeance of ions for GB-rich samples than for GB-poor samples. We obtain a proton conductivity 3–4 orders of magnitude higher than commercial Nafion membranes with higher selectivity. Our work discloses the crucial roles of GBs to tailor ion transport and shows the potential of designing GBs in 2D material for membrane applications. • Tuning proton permeance by controlling grain boundary in graphene • Grain boundary sites are preferentially etched under mild etching conditions • Ultrafast proton permeance is achieved by preferential etching of grain boundary Grain boundaries exist widely in graphene. To better understand their role in ionic transport, Zhang et al. experimentally study the role and potential of grain boundaries in graphene to tailor ion transport and achieve enhanced proton permeance by preferential etching of grain boundary sites.

Ab initio phonon transport across grain boundaries in graphene using machine learning based on small dataset

Establishing the structure-property relationship for grain boundaries (GBs) is critical for developing next-generation functional materials but has been severely hampered due to its extremely large configurational space. Atomistic simulations with low computational cost and high predictive power are strongly desirable, but the conventional simulations using empirical interatomic potentials and density functional theory suffer from the lack of predictive power and high computational cost, respectively. A machine learning interatomic potential (MLIP) recently emerged but often requires extensive size of the training dataset, making it a less feasible approach. Here, we demonstrate that an MLIP trained with a rationally designed small training dataset can predict thermal transport across GBs in graphene with ab initio accuracy at an affordable computational cost. We employed a rational approach based on the structural unit model to find a small set of GBs that can represent the entire configurational space and thus can serve as a cost-effective training dataset for the MLIP. Only 5 GBs were found to be enough to represent the entire configurational space of graphene GBs. Using the atomistic Green's function approach and the MLIP, we revealed that the structure-thermal resistance relation in graphene does not follow the common understanding that large dislocation density causes larger thermal resistance. In fact, thermal resistance is nearly independent of dislocation density at room temperature and is higher when the dislocation density is small at sub-room temperature. We explain this intriguing behavior with the buckling near a GB causing a strong scattering of flexural phonon modes. In this paper, we show that a machine learning technique combined with conventional wisdom (e.g., structural unit model) can extend the recent success of ab initio thermal transport simulation, which has been mostly limited to single crystals, to complex yet practically important polycrystals with GBs.

Simultaneous Extraction of the Grain Size, Single-Crystalline Grain Sheet Resistance, and Grain Boundary Resistivity of Polycrystalline Monolayer Graphene.

The electrical properties of polycrystalline graphene grown by chemical vapor deposition (CVD) are determined by grain-related parameters—average grain size, single-crystalline grain sheet resistance, and grain boundary (GB) resistivity. However, extracting these parameters still remains challenging because of the difficulty in observing graphene GBs and decoupling the grain sheet resistance and GB resistivity. In this work, we developed an electrical characterization method that can extract the average grain size, single-crystalline grain sheet resistance, and GB resistivity simultaneously. We observed that the material property, graphene sheet resistance, could depend on the device dimension and developed an analytical resistance model based on the cumulative distribution function of the gamma distribution, explaining the effect of the GB density and distribution in the graphene channel. We applied this model to CVD-grown monolayer graphene by characterizing transmission-line model patterns and simultaneously extracted the average grain size (~5.95 μm), single-crystalline grain sheet resistance (~321 Ω/sq), and GB resistivity (~18.16 kΩ-μm) of the CVD-graphene layer. The extracted values agreed well with those obtained from scanning electron microscopy images of ultraviolet/ozone-treated GBs and the electrical characterization of graphene devices with sub-micrometer channel lengths.

Growth and Etching of the Grain Boundaries in Polygonal Graphene Islands.

The grain boundary is an intrinsic defect within mono- and multi-layer polygonal graphene islands during the chemical vapor deposition growth process. It greatly influences their mechanical and electronic properties. However, the precise characterization and formation mechanism of grain boundaries still remain unclear. In this work, H2 etching experiments show that a polygonal etched hole originates from the natural location of a grain boundary beyond the nucleation site in polygonal monolayer graphene. Furthermore, colorful Raman mapping provides a visualized method to explore the distribution of grain boundaries in polygonal bilayer graphene. Therefore, a deep understanding of the growth kinetics of mono- and bi-layer polygonal graphene was obtained through etching engineering combined with Raman spectroscopy.

Electronic transport across extended grain boundaries in graphene

Owing to its superlative carrier mobility and atomic thinness, graphene exhibits great promise for interconnects in future nanoelectronic integrated circuits. Chemical vapor deposition (CVD), the most popular method for wafer-scale growth of graphene, produces monolayers that are polycrystalline, where misoriented grains are separated by extended grain boundaries (GBs). Theoretical models of GB resistivity focused on small sections of an extended GB, assuming it to be a straight line, and predicted a strong dependence of resistivity on misorientation angle. In contrast, measurements produced values in a much narrower range and without a pronounced angle dependence. Here we study electron transport across rough GBs, which are composed of short straight segments connected together into an extended GB. We found that, due to the zig-zag nature of rough GBs, there always exist a few segments that divide the crystallographic angle between two grains symmetrically and provide a highly conductive path for the current to flow across the GBs. The presence of highly conductive segments produces resistivity between 102 to 104 Ω μm regardless of misorientation angle. An extended GB with large roughness and small correlation length has small resistivity on the order of 103 Ω μm, even for highly mismatched asymmetric GBs. The effective slope of the GB, given by the ratio of roughness and lateral correlation length, is an effective universal quantifier for GB resistivity. Our results demonstrate that the probability of finding conductive segments diminishes in short GBs, which could cause a large variation in the resistivity of narrow ribbons etched from polycrystalline graphene. We also uncover spreading resistance due to the current bending in the grains to flow through the conductive segments of the GB and show that it scales linearly with the grain resistance. Our results will be crucial for designing graphene-based interconnects for future integrated circuits.

Phononic Thermal Transport along Graphene Grain Boundaries: A Hidden Vulnerability.

While graphene grain boundaries (GBs) are well characterized experimentally, their influence on transport properties is less understood. As revealed here, phononic thermal transport is vulnerable to GBs even when they are ultra‐narrow and aligned along the temperature gradient direction. Non‐equilibrium molecular dynamics simulations uncover large reductions in the phononic thermal conductivity (κ p) along linear GBs comprising periodically repeating pentagon‐heptagon dislocations. Green's function calculations and spectral energy density analysis indicate that the origin of the κ p reduction is hidden in the periodic GB strain field, which behaves as a reflective diffraction grating with either diffuse or specular phonon reflections, and represents a source of anharmonic phonon–phonon scattering. The non‐monotonic dependence with dislocation density of κ p uncovered here is unaccounted for by the classical Klemens theory. It can help identify GB structures that can best preserve the integrity of the phononic transport.

Improved contact properties of graphene-metal hybrid interfaces by grain boundaries

Graphene-metal (MGr) hybrid contacts have been broadly used to improve the contact properties of two-dimensional (2D) electric devices. Since grain boundaries of graphene are inevitable, it is quite necessary to investigate how the grain boundaries affect the contact properties of graphene-metal interfaces. Herein, based on first-principles calculations, we comprehensively studied the contact properties of graphene with grain boundaries deposited on different transition metals substrates including Ni, Pd and Cu(111) slabs. Our calculations show that the grain boundaries always narrow and lower the tunneling barrier of the contacts, which will significantly increase the tunneling possibility of the carriers at the contacts. These results suggest a very convenient method to improve the performance of the graphene-based devices.

Spontaneous Time-Reversal Symmetry Breaking at Individual Grain Boundaries in Graphene.

Graphene grain boundaries (GBs) have attracted interest for their ability to host nearly dispersionless electronic bands and magnetic instabilities. Here, we employ quantum transport and universal conductance fluctuation measurements to experimentally demonstrate a spontaneous breaking of time-reversal symmetry across individual GBs of chemical vapor deposited graphene. While quantum transport across the GBs indicate spin-scattering-induced dephasing and hence formation of local magnetic moments, below T≲4 K we observe complete lifting of time-reversal symmetry at high carrier densities (n≳5×10^{12} cm^{-2}) and low temperature (T≲2 K). An unprecedented thirtyfold reduction in the universal conductance fluctuation magnitude with increasing doping density further supports the possibility of an emergent frozen magnetic state at the GBs. Our experimental results suggest that realistic GBs of graphene can be a promising resource for new electronic phases and spin-based applications.

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.