Measurement of the intrinsic strength of crystalline and polycrystalline graphene

Comprehensive Review of RF MEMS Switches in Satellite Communications

The miniaturization and low power consumption characteristics of RF MEMS (Radio Frequency Microelectromechanical System) switches provide new possibilities for the development of microsatellites and nanosatellites, which will play an increasingly important role in future space missions. This paper provides a comprehensive review of RF MEMS switches in satellite communication, detailing their working mechanisms, performance optimization strategies, and applications in reconfigurable antennas. It explores various driving mechanisms (electrostatic, piezoelectric, electromagnetic, thermoelectric) and contact mechanisms (capacitive, ohmic), highlighting their advantages, challenges, and advancements. The paper emphasizes strategies to enhance switch reliability and RF performance, including minimizing the impact of shocks, reducing driving voltage, improving contacts, and appropriate packaging. Finally, it discusses the enormous potential of RF MEMS switches in future satellite communications, addressing their technical advantages, challenges, and the necessity for further research to optimize design and manufacturing for broader applications and increased efficiency in space missions. The research findings of this review can serve as a reference for further design and improvement of RF MEMS switches, which are expected to play a more important role in future aerospace communication systems.

Button shear testing for adhesion measurements of 2D materials

Two-dimensional (2D) materials are considered for numerous applications in microelectronics, although several challenges remain when integrating them into functional devices. Weak adhesion is one of them, caused by their chemical inertness. Quantifying the adhesion of 2D materials on three-dimensional surfaces is, therefore, an essential step toward reliable 2D device integration. To this end, button shear testing is proposed and demonstrated as a method for evaluating the adhesion of 2D materials with the examples of graphene, hexagonal boron nitride (hBN), molybdenum disulfide, and tungsten diselenide on silicon dioxide and silicon nitride substrates. We propose a fabrication process flow for polymer buttons on the 2D materials and establish suitable button dimensions and testing shear speeds. We show with our quantitative data that low substrate roughness and oxygen plasma treatments on the substrates before 2D material transfer result in higher shear strengths. Thermal annealing increases the adhesion of hBN on silicon dioxide and correlates with the thermal interface resistance between these materials. This establishes button shear testing as a reliable and repeatable method for quantifying the adhesion of 2D materials.

Ultrahigh Critical Current Density across Sliding Electrical Contacts in Structural Superlubric State

In conventional sliding electrical contacts (SECs), large critical current density (CCD) requires a high ratio between actual and apparent contact area, while low friction and wear require the opposites. Structural superlubricity (SSL) has the characteristics of zero wear, near zero friction, and all-atoms in real contact between the contacting surfaces. Here, we show a measured current density up to 17.5  GA/m^{2} between microscale graphite contact surfaces while sliding under ambient conditions. This value is nearly 146 times higher than the maximum CCD of other SECs reported in literatures (0.12  GA/m^{2}). Meanwhile, the coefficient of friction for the graphite contact is less than 0.01 and the sliding interface is wear-free according to the Raman characterization, indicating the presence of the SSL state. Furthermore, we estimate the intrinsic CCD of single crystalline graphite to be 6.69  GA/m^{2} by measuring the scaling relation of CCD. Theoretical analysis reveals that the CCD is limited by thermal effect due to the Joule heat. Our results show the great potential of the SSL contacts to be used as SECs, such as micro- or nanocontact switches, conductive slip rings, or pantographs.

Anisotropic mechanical properties of α-MoO3 nanosheets

The mechanical behaviors of 2D materials are fundamentally important for their potential applications in various fields. α-Molybdenum trioxide (α-MoO3) crystals with unique electronic, optical, and electrochemical properties, have attracted extensive attention for their use in optoelectronic and energy conversion devices. From a mechanical viewpoint, however, there is limited information available on the mechanical properties of α-MoO3. Here, we developed a capillary force-assisted peeling method to directly transfer α-MoO3 nanosheets onto arbitrary substrates. Comparatively, we could effectively avoid surface contamination arising from the polymer-assisted transfer method. Furthermore, with the help of an in situ push-to-pull (PTP) device during SEM, we systematically investigated the tensile properties of α-MoO3. The measured Young's modulus and fracture strengths along the c-axis (91.7 ± 13.7 GPa and 2.1 ± 0.9 GPa, respectively) are much higher than those along the a-axis (55.9 ± 8.6 GPa and 0.8 ± 0.3 GPa, respectively). The in-plane mechanical anisotropy ratio can reach ∼1.64. Both Young's modulus and the fracture strength of MoO3 show apparent size dependence. Additionally, the multilayer α-MoO3 nanosheets exhibited brittle fracture with interplanar sliding due to poor van der Waals interaction. Our study provides some key points regarding the mechanical properties and fracture behavior of layered α-MoO3 nanosheets.

High-Strength Amorphous Silicon Carbide for Nanomechanics

For decades, mechanical resonators with high sensitivity have been realized using thin-film materials under high tensile loads. Although there are remarkable strides in achieving low-dissipation mechanical sensors by utilizing high tensile stress, the performance of even the best strategy is limited by the tensile fracture strength of the resonator materials. In this study, a wafer-scale amorphous thin film is uncovered, which has the highest ultimate tensile strength ever measured for a nanostructured amorphous material. This silicon carbide (SiC) material exhibits an ultimate tensile strength of over 10 GPa, reaching the regime reserved for strong crystalline materials and approaching levels experimentally shown in graphene nanoribbons. Amorphous SiC strings with high aspect ratios are fabricated, with mechanical modes exceeding quality factors 108 at room temperature, the highest value achieves among SiC resonators. These performances are demonstrated faithfully after characterizing the mechanical properties of the thin film using the resonance behaviors of free-standing resonators. This robust thin-film material has significant potential for applications in nanomechanical sensors, solar cells, biological applications, space exploration, and other areas requiring strength and stability in dynamic environments. The findings of this study open up new possibilities for the use of amorphous thin-film materials in high-performance applications.

Determining local modulus and strength of heterogeneous films by force-deflection mapping of microcantilevers

Estimating the elastic modulus and strength of heterogeneous films requires local measurement techniques. For local mechanical film testing, microcantilevers were cut into suspended many-layer graphene using a focused ion beam. An optical transmittance technique was used to map thickness near the cantilevers, and multipoint force-deflection mapping with an atomic force microscope was used to record the compliance of the cantilevers. These data were used to estimate the elastic modulus of the film by fitting the compliance at multiple locations along the cantilever to a fixed-free Euler-Bernoulli beam model. This method resulted in a lower uncertainty than is possible from analyzing only a single force-deflection. The breaking strength of the film was also found by deflecting cantilevers until fracture. The average modulus and strength of the many-layer graphene films are 300 and 12 GPa, respectively. The multipoint force-deflection method is well suited to analyze films that are heterogeneous in thickness or wrinkled.

Retrieving Grain Boundaries in 2D Materials

The coalescence of randomly distributed grains with different crystallographic orientations can result in pervasive grain boundaries (GBs) in 2D materials during their chemical synthesis. GBs not only are the inherent structural imperfection that causes influential impacts on structures and properties of 2D materials, but also have emerged as a platform for exploring unusual physics and functionalities stemming from dramatic changes in local atomic organization and even chemical makeup. Here, recent advances in studying the formation mechanism, atomic structures, and functional properties of GBs in a range of 2D materials are reviewed. By analyzing the growth mechanism and the competition between far-field strain and local chemical energies of dislocation cores, a complete understanding of the rich GB morphologies as well as their dependence on lattice misorientations and chemical compositions is presented. Mechanical, electronic, and chemical properties tied to GBs in different materials are then discussed, towards raising the concept of using GBs as a robust atomic-scale scaffold for realizing tailored functionalities, such as magnetism, luminescence, and catalysis. Finally, the future opportunities in retrieving GBs for making functional devices and the major challenges in the controlled formation of GB structures for designed applications are commented.

Topological Stone-Wales Defects Enhance Bonding and Electronic Coupling at the Graphene/Metal Interface

Defects play a critical role for the functionality and performance of materials, but the understanding of the related effects is often lacking, because the typically low concentrations of defects make them difficult to study. A prominent case is the topological defects in two-dimensional materials such as graphene. The performance of graphene-based (opto-)electronic devices depends critically on the properties of the graphene/metal interfaces at the contacting electrodes. The question of how these interface properties depend on the ubiquitous topological defects in graphene is of high practical relevance, but could not be answered so far. Here, we focus on the prototypical Stone-Wales (S-W) topological defect and combine theoretical analysis with experimental investigations of molecular model systems. We show that the embedded defects undergo enhanced bonding and electron transfer with a copper surface, compared to regular graphene. These findings are experimentally corroborated using molecular models, where azupyrene mimics the S-W defect, while its isomer pyrene represents the ideal graphene structure. Experimental interaction energies, electronic-structure analysis, and adsorption distance differences confirm the defect-controlled bonding quantitatively. Our study reveals the important role of defects for the electronic coupling at graphene/metal interfaces and suggests that topological defect engineering can be used for performance control.

Established Model on Polycrystalline Graphene Oxide and Analysis of Mechanical Characteristic

It may cause more novel physical effects that the combination with in-plane defects induced by grain boundaries (GBs) and quasi three-dimensional system induced by oxidation functional group. Different from those in blocks, these new physical effects play a significant role in the mechanical properties and transport behavior. Based on the configuration design, we investigate the in-plane and out-plane geometric deformation caused by the coupling of GBs and oxygen-containing functional groups and establish a mechanical model for the optimal design of the target spatial structure. The results show that the strain rate remarkably affect the tensile properties of polycrystalline graphene oxide (PGO). Under high oxygen content (R = 50%), with the increasing strain rate, the PGO is much closer to ductile fracture, and the ultimate strain and stress will correspondingly grow. The growth of temperature reduces the ultimate stress of PGO, but the ultimate strain remains constant. When the functional groups are distributed at the edge of the GBs, the overall strength decreases the most, followed by the distribution on the GBs. Meanwhile, the strength of PGO reaches the greatest value when the functional groups are distributed away from the GBs.

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.

Towards Repeatable, Scalable Graphene Integrated Micro-Nano Electromechanical Systems (MEMS/NEMS)

The demand for graphene-based devices is rapidly growing but there are significant challenges for developing scalable and repeatable processes for the manufacturing of graphene devices. Basic research on understanding and controlling growth mechanisms have recently enabled various mass production approaches over the past decade. However, the integration of graphene with Micro-Nano Electromechanical Systems (MEMS/NEMS) has been especially challenging due to performance sensitivities of these systems to the production process. Therefore, ability to produce graphene-based devices on a large scale with high repeatability is still a major barrier to the commercialization of graphene. In this review article, we discuss the merits of integrating graphene into Micro-Nano Electromechanical Systems, current approaches for the mass production of graphene integrated devices, and propose solutions to overcome current manufacturing limits for the scalable and repeatable production of integrated graphene-based devices.

Functional Grain Boundaries in Two-Dimensional Transition-Metal Dichalcogenides

ConspectusTwo-dimensional (2D) transition-metal dichalcogenides (TMDs) are a class of promising low-dimensional materials with a variety of emergent properties which are attractive for next-generation electronic and optical devices; such properties include tunable band gaps, high electron mobilities, high exciton binding energies, excellent thermal stability and flexibility. During the synthesis process of these materials, especially chemical vapor deposition, defects such as grain boundaries (GBs) inevitably exist. GBs are the interfaces between differently oriented grains and are line defects in 2D crystals. While GBs can degrade the overall quality of 2D materials and adversely affect some of their electrical and mechanical properties, recent results show that GBs give rise to or enhance a wide range of unique electrical, mechanical, and chemical properties of the GBs in 2D TMDs. The effects of GBs on 2D material properties are complex and diverse, providing exciting opportunities to realize new functionalities by manipulating the local structure and properties. Notably, these effects are strongly related to atom types, dislocation cores, crystal misorientation at GBs, and both in- and out-of-plane deformation. The exploitation of GBs for novel applications requires a deepened understanding of synthesis, postprocessing, defect structures, GB properties, and GB structure-property relationships in 2D materials.In this Account, we first introduce a detailed classification of GBs in 2D TMDs based on atomic structure, symmetry, and the local coordination of both transition metals and chalcogenide atoms. The GB types in typical MoS₂ (high-symmetry hexagonal structure) and ReS₂ (low-symmetry monoclinic structure) are taken as examples. Next, we describe the properties of GBs in 2D TMDs, including thermodynamic and kinetic, mechanical, thermal, electrical, magnetic, chemical, and electrocatalysis properties as well as several application areas where these may be exploited. Here we provide systematic atomic-level and electronic level explanations of these properties to clarify their dependences on GB structures. Applications that extend from these properties, including functional electronics, chemical sensors, and electrocatalysts, are also described. Finally, we provide several perspectives and suggest promising opportunities for exploiting the novel properties of GBs in 2D TMDs. We expect that this Account will further stimulate the fundamental research of GBs and boost the wide application of multifunctional devices.

Micromechanical Landscape of Three-Dimensional Disordered Graphene Networks

Disordered carbons can be considered under the modeling framework of disordered graphene networks (DGNs) due to the continuous three-dimensional connectivity and high graphitization. Correlating microstructures and mechanical behaviors of DGNs to their topology is pivotal to revealing more intrinsic features hidden by disorder. Herein, starting from basic deformations and topology, we investigate DGNs with various densities to explore their micromechanical landscape. Both the tension and shear of DGNs exhibit prolonged plastic platforms through local tearing of microstructures. However, compression displays special plastic damages of forming kinklike puckers and sp³-bonded carbon, resulting in a tension-compression asymmetry of DGNs. Out-of-plane topological defects contribute to the main negative-curvature topology in deformed DGNs. Moreover, there are novel scaling laws where both the Young's modulus and strength (logarithms) follow an inversely proportional scaling with respect to average angular defects. Ashby charts demonstrate that the mechanical properties of DGNs can reach the theoretical limit region, surpassing those of most conventional materials.

Growth and Selective Etching of Twinned Graphene on Liquid Copper Surface

Although grain boundaries (GBs) in two-dimensional (2D) materials have been extensively observed and characterized, their formation mechanism still remains unexplained. Here a general model has reported to elucidate the mechanism of formation of GBs during 2D materials growth. Based on our model, a general method is put forward to synthesize twinned 2D materials on a liquid substrate. Using graphene growth on liquid Cu surface as an example, the growth of twinned graphene has been demonstrated successfully, in which all the GBs are ultra-long straight twin boundaries. Furthermore, well-defined twin boundaries (TBs) are found in graphene that can be selectively etched by hydrogen gas due to the preferential adsorption of hydrogen atoms at high-energy twins. This study thus reveals the formation mechanism of GBs in 2D materials during growth and paves the way to grow various 2D nanostructures with controlled GBs.

Improvement of alkali metal ion batteries via interlayer engineering of anodes: from graphite to graphene

Interlayer engineering of graphite anodes in alkali metal ion (M = Li, Na, and K) batteries is carried out based on the first-principles calculations. By increasing the interlayer spacing of graphite, the specific capacity of Li or Na does not increase while that of K increases continuously (from 279 mA h g^-1 at the equilibrium interlayer spacing to 1396 mA h g^-1 at the interlayer spacing of 20.0 Å). As the interlayer spacing increases, the electrostatic potential of graphite becomes smoother, and the ability to buffer the electrostatic potential fluctuation becomes poorer in M ions. These two effects jointly lead to minima of the diffusion barrier of M ions on graphite (0.01-0.05 eV), instead of strictly monotonous declines with the increasing interlayer spacing. To perform the interlayer engineering of anode candidates more efficiently, a set of high-throughput programs has been developed and can be easily applied to other systems. Our research has guiding significance for achieving the optimal effect in interlayer engineering experimentally.

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.

Roughening for Strengthening and Toughening in Monolayer Carbon Based Composites

Three-dimensional (3D) aggregation of graphene is dramatically weak and brittle due primarily to the prevailing interlayer van der Waals interaction. In this report, motivated by the recent success in synthesis of monolayer amorphous carbon (MAC) sheets, we demonstrate that outstanding strength and large plastic-like strain can be achieved in layered 3D MAC composites. Both surface roughening and the ultracompliant nature of MACs count for the high strength and gradual failure in 3D MAC. Such properties are not seen when intact graphene or multiple stacked MACs are used as building blocks for 3D composites. This work demonstrates a counterintuitive mechanism that surface roughening due to initial defects and low rigidity may help to realize superb mechanical properties in 3D aggregation of monolayer carbon.

Machine Learning Pipeline for Segmentation and Defect Identification from High-Resolution Transmission Electron Microscopy Data

In the field of transmission electron microscopy, data interpretation often lags behind acquisition methods, as image processing methods often have to be manually tailored to individual datasets. Machine learning offers a promising approach for fast, accurate analysis of electron microscopy data. Here, we demonstrate a flexible two-step pipeline for the analysis of high-resolution transmission electron microscopy data, which uses a U-Net for segmentation followed by a random forest for the detection of stacking faults. Our trained U-Net is able to segment nanoparticle regions from the amorphous background with a Dice coefficient of 0.8 and significantly outperforms traditional image segmentation methods. Using these segmented regions, we are then able to classify whether nanoparticles contain a visible stacking fault with 86% accuracy. We provide this adaptable pipeline as an open-source tool for the community. The combined output of the segmentation network and classifier offer a way to determine statistical distributions of features of interest, such as size, shape, and defect presence, enabling the detection of correlations between these features.

Structural Defects, Mechanical Behaviors, and Properties of Two-Dimensional Materials

Since the success of monolayer graphene exfoliation, two-dimensional (2D) materials have been extensively studied due to their unique structures and unprecedented properties. Among these fascinating studies, the most predominant focus has been on their atomic structures, defects, and mechanical behaviors and properties, which serve as the basis for the practical applications of 2D materials. In this review, we first highlight the atomic structures of various 2D materials and the structural and energy features of some common defects. We then summarize the recent advances made in experimental, computational, and theoretical studies on the mechanical properties and behaviors of 2D materials. We mainly emphasized the underlying deformation and fracture mechanisms and the influences of various defects on mechanical behaviors and properties, which boost the emergence and development of topological design and defect engineering. We also further introduce the piezoelectric and flexoelectric behaviors of specific 2D materials to address the coupling between mechanical and electronic properties in 2D materials and the interactions between 2D crystals and substrates or between different 2D monolayers in heterostructures. Finally, we provide a perspective and outlook for future studies on the mechanical behaviors and properties of 2D materials.

Mechanical Properties of Graphene Oxide Coupled by Multi-Physical Field: Grain Boundaries and Functional Groups

Graphene and graphene oxide (GO) usually have grain boundaries (GBs) in the process of synthesis and preparation. Here, we “attach” GBs into GO, a new molecular configuration i.e., polycrystalline graphene oxide (PGO) is proposed. This paper aims to provide an insight into the stability and mechanical properties of PGO by using the molecular dynamics method. For this purpose, the “bottom-up” multi-structure-spatial design performance of PGO and the physical mechanism associated with the spatial structure in mixed dimensions (combination of sp2 and sp3) were studied. Also, the effect of defect coupling (GBs and functional groups) on the mechanical properties was revealed. Our results demonstrate that the existence of the GBs reduces the mechanical properties of PGO and show an “induction” role during the tensile fracture process. The presence of functional groups converts in-plane sp2 carbon atoms into out-of-plane sp3 hybrid carbons, causing uneven stress distribution. Moreover, the mechanical characteristics of PGO are very sensitive to the oxygen content of functional groups, which decrease with the increase of oxygen content. The weakening degree of epoxy groups is slightly greater than that of hydroxyl groups. Finally, we find that the mechanical properties of PGO will fall to the lowest values due to the defect coupling amplification mechanism when the functional groups are distributed at GBs.

Self-Assembly-Driven Nanomechanics in Porous Covalent Organic Framework Thin Films

Nanomechanics signifies a key tool to interpret the macroscopic mechanical properties of a porous solid in the context of molecular-level structure. However, establishing such a correlation has proved to be significantly challenging in porous covalent organic frameworks (COFs). Structural defects or packing faults within the porous matrix, poor understanding of the crystalline assembly, and surface roughness are critical factors that contribute to this difficulty. In this regard, we have fabricated two distinct types of COF thin films by controlling the internal order and self-assembly of the same building blocks. Interestingly, the defect density and the nature of supramolecular interactions played a significant role in determining the corresponding thin films' stress-strain behavior. Thin films assembled from nanofibers (∼1-2 μm) underwent large deformation on the application of small external stress (Tp-Azo_fiber film: E ≈ 1.46 GPa; H ≈ 23 MPa) due to weak internal forces. On the other hand, thin films threaded with nanospheres (∼600 nm) exhibit a much stiffer and harder mechanical response (Tp-Azo_sphere film: E ≈ 15.3 GPa; H ≈ 66 MPa) due to strong covalent interactions and higher crystallinity. These porous COF films further exhibited a significant elastic recovery (∼80%), ideal for applications dealing with shock-resistant materials. This work provides in-depth insight into the fabrication of industrially relevant crystalline porous thin films and membranes by addressing the previously unanswered questions about the mechanical constraints in COFs.

Anomalous fracture in two-dimensional rhenium disulfide

Low-dimensional materials usually exhibit mechanical properties from those of their bulk counterparts. Here, we show in two-dimensional (2D) rhenium disulfide (ReS2) that the fracture processes are dominated by a variety of previously unidentified phenomena, which are not present in bulk materials. Through direct transmission electron microscopy observations at the atomic scale, the structures close to the brittle crack tip zones are clearly revealed. Notably, the lattice reconstructions initiated at the postcrack edges can impose additional strain on the crack tips, modifying the fracture toughness of this material. Moreover, the monatomic thickness allows the restacking of postcrack edges in the shear strain-dominated cracks, which is potentially useful for the rational design of 2D stacking contacts in atomic width. Our studies provide critical insights into the atomistic processes of fracture and unveil the origin of the brittleness in the 2D materials.

Ultra-strong stability of double-sided fluorinated monolayer graphene and its electrical property characterization

Fluorinated graphene has a tunable band gap that is useful in making flexible graphene electronics. But the carbon-fluorine (C-F) bonds in fluorinated graphene can be easily broken by increased temperature or electron beam irradiation. Here, we demonstrate that the stability of fluorinated graphene is mainly determined by its C-F configuration. The double-sided fluorinated graphene has a much stronger stability than the single-sided fluorinated graphene under the same irradiation dose. Density functional theory calculations show that the configuration of double-sided fluorinated graphene has a negative and low formation energy, indicating to be an energetically stable structure. On the contrary, the formation energy of single-sided fluorinated graphene is positive, leading to an unstable C-F bonding that is easily broken by the irradiation. Our findings make a new step towards a more stable and efficient design of graphene electronic devices.

Growth and Grain Boundaries in 2D Materials

Grain boundaries (GBs) are a kind of lattice imperfection widely existing in two-dimensional materials, playing a critical role in materials' properties and device performance. Related key issues in this area have drawn much attention and are still under intense investigation. These issues include the characterization of GBs at different length scales, the dynamic formation of GBs during the synthesis, the manipulation of the configuration and density of GBs for specific material functionality, and the understanding of structure-property relationships and device applications. This review will provide a general introduction of progress in this field. Several techniques for characterizing GBs, such as direct imaging by high-resolution transmission electron microscopy, visualization techniques of GBs by optical microscopy, plasmon propagation, or second harmonic generation, are presented. To understand the dynamic formation process of GBs during the growth, a general geometric approach and theoretical consideration are reviewed. Moreover, strategies controlling the density of GBs for GB-free materials or materials with tunable GB patterns are summarized, and the effects of GBs on materials' properties are discussed. Finally, challenges and outlook are provided.

On-Surface Synthesis of Unsaturated Carbon Nanostructures with Regularly Fused Pentagon-Heptagon Pairs

Multiple fused pentagon–heptagon pairs are frequently found as defects at the grain boundaries of the hexagonal graphene lattice and are suggested to have a fundamental influence on graphene-related materials. However, the construction of sp²-carbon skeletons with multiple regularly fused pentagon–heptagon pairs is challenging. In this work, we found that the pentagon–heptagon skeleton of azulene was rearranged during the thermal reaction of an azulene-incorporated organometallic polymer on Au(111). The resulting sp²-carbon frameworks were characterized by high-resolution scanning probe microscopy techniques and feature novel polycyclic architectures composed of multiple regularly fused pentagon–heptagon pairs. Moreover, the calculated analysis of its aromaticity revealed a peculiar polar electronic structure.

Intrinsic and Extrinsic Effects of Microstructure on Properties in Cast Al Alloys

The metallurgy of cast aluminum alloys has always been considered to be different from that of wrought alloys. Metallurgists have been taught that pores are intrinsic in cast aluminum alloys and that mechanical properties in cast aluminum alloys are controlled by dendrite arm spacing, the presence of Fe-bearing particles, and the size of Si particles in Al–Si alloys, which fracture and debond during deformation, leading to premature failure. Whether these effects are intrinsic or extrinsic, i.e., mere correlations due to the structural quality of castings, is discussed in detail. Ideal properties are discussed, based on findings presented mostly in physics literature. Pores and hot tears in aluminum castings are extrinsic. Moreover, the effect of dendrite arm spacing on elongation, precipitation, and subsequent fracture of β–Al₅FeSi platelets, and finally Si particle fracture and debonding are all extrinsic. A fundamental change in how we approach the metallurgy of cast aluminum alloys is necessary.

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.

Borophene Concentric Superlattices via Self-Assembly of Twin Boundaries

Due to its in-plane structural anisotropy and highly polymorphic nature, borophene has been shown to form a diverse set of linear superlattice structures that are not observed in other two-dimensional materials. Here, we show both theoretically and experimentally that concentric superlattice structures can also be realized in borophene via the energetically preferred self-assembly of coherent twin boundaries. Since borophene twin boundaries do not require the creation of additional lattice defects, they are exceptionally low in energy and thus easier to nucleate and even migrate than grain boundaries in other two-dimensional materials. Due to their high mobility, borophene twin boundaries naturally self-assemble to form novel phases consisting of periodic concentric loops of filled boron hexagons that are further preferred energetically by the rotational registry of borophene on the Ag(111) surface. Compared to defect-free borophene, concentric superlattice borophene phases are predicted to possess enhanced mechanical strength and localized electronic states. Overall, these results establish defect-mediated self-assembly as a pathway to unique borophene structures and properties.

Controlled Growth of Single-Crystal Graphene Films

Grain boundaries produced during material synthesis affect both the intrinsic properties of materials and their potential for high-end applications. This effect is commonly observed in graphene film grown using chemical vapor deposition and therefore caused intense interest in controlled growth of grain-boundary-free graphene single crystals in the past ten years. The main methods for enlarging graphene domain size and reducing graphene grain boundary density are classified into single-seed and multiseed approaches, wherein reduction of nucleation density and alignment of nucleation orientation are respectively realized in the nucleation stage. On this basis, detailed synthesis strategies, corresponding mechanisms, and key parameters in the representative methods of these two approaches are separately reviewed, with the aim of providing comprehensive knowledge and a snapshot of the latest status of controlled growth of single-crystal graphene films. Finally, perspectives on opportunities and challenges in synthesizing large-area single-crystal graphene films are discussed.

Defect-enriched tunability of electronic and charge-carrier transport characteristics of 2D borocarbonitride (BCN) monolayers from ab initio calculations

Development of inexpensive and efficient photo- and electro-catalysts is vital for clean energy applications. Electronic and structural properties can be tuned by the introduction of defects to achieve the desirable electrocatalytic activity. Using first-principles molecular dynamics simulations, the structural, dynamical, and electronic properties of 2D borocarbonitride (h-BCN) sheets have been investigated, highlighting how anti-site defects in B and N doped graphene significantly influence the bandgap, and thereby open up new avenues to tune the chemical behavior of the 2D sheets. In the present work, all of the monolayers investigated display direct bandgaps, which reduce from 0.99 eV to 0.24 eV with increasing number of anti-site defects. The present results for the electronic structure and findings for bandgap engineering open up applications of BCN monolayers in optoelectronic devices and solar cells. The influence of the anti-site distribution of B and N atoms on the ultra-high hole/electron mobility and conductivity is discussed based on density functional theory coupled with the Boltzmann transport equation. The BCN defect monolayer is predicted to have carrier mobilities three times higher than that of the pristine sheet. The present results demonstrate that BN doped graphene monolayers are likely to be useful in the next-generation 2D field-effect transistors.

Theoretical strength and rubber-like behaviour in micro-sized pyrolytic carbon

The creation of materials with a combination of high strength, substantial deformability and ductility, large elastic limit and low density represents a long-standing challenge, because these properties are, in general, mutually exclusive. Using a combination of two-photon lithography and high-temperature pyrolysis, we have created micro-sized pyrolytic carbon with a tensile strength of 1.60 ± 0.55 GPa, a compressive strength approaching the theoretical limit of ~13.7 GPa, a substantial elastic limit of 20-30% and a low density of ~1.4 g cm^-3. This corresponds to a specific compressive strength of 9.79 GPa cm³ g^-1, a value that surpasses that of nearly all existing structural materials. Pillars with diameters below 2.3 μm exhibit rubber-like behaviour and sustain a compressive strain of ~50% without catastrophic failure; larger ones exhibit brittle fracture at a strain of ~20%. Large-scale atomistic simulations reveal that this combination of beneficial mechanical properties is enabled by the local deformation of 1 nm curled graphene fragments within the pyrolytic carbon microstructure, the interactions among neighbouring fragments and the presence of covalent carbon-carbon bonds.

Hysteresis and its impact on characterization of mechanical properties of suspended monolayer molybdenum-disulfide sheets

The hysteresis phenomenon frequently arises in two-dimensional (2D) material nanoindentation, which is generally expected to be excluded from characterizing the elastic properties due to the imperfect elastic behaviour. However, the underlying mechanism of hysteresis and its effect on the characterization of the mechanical properties of 2D materials remain unclear. Cyclic loadings are exerted on the suspended monolayer molybdenum-disulfide (MoS2) films in atomic force microscopy (AFM) nanoindentation experiments. The elastic hysteresis loops are observed for most of the force-displacement curves. The friction/wear between the AFM silicon tip and the MoS2 monolayer is deemed to be dominant compared to the friction between the monolayer and the silicon dioxide substrate after the analysis, as determined using the finite element method (FEM) simulation. The loading force-displacement curves instead of the unloading curves have been used to deduce the elastic mechanical properties using a modified regression equation. The mean value of the obtained Young's modulus of monolayer MoS2, E, is equal to 209 ± 18 GPa, which is close to the inherent stiffness value, predicted by first principles calculation. Our results have confirmed that it is not obligatory to exclude the sample data with hysteresis behaviour for characterizing the elastic properties of 2D materials. In addition, all sample sheets have finally been penetrated and the mean breaking stress value, σmax, is 36.6 ± 0.9 GPa, determined using the radius value of the worn tip. Furthermore, the effect of the loading force and the shape/size of the suspended monolayer MoS2 sheets on the hysteresis behaviour in the 2D nanoindentation have also been analyzed and discussed, exhibiting interesting trends. Our findings provide guidance for the characterization of the mechanical properties of 2D materials using the AFM nanoindentation and the experimental samples with elastic hysteresis behaviour.

Nanomechanics of graphene

The super-high strength of single-layer graphene has attracted great interest. In practice, defects resulting from thermodynamics or introduced by fabrication, naturally or artificially, play a pivotal role in the mechanical behaviors of graphene. More importantly, high strength is just one aspect of the magnificent mechanical properties of graphene: its atomic-thin geometry not only leads to ultra-low bending rigidity, but also brings in many other unique properties of graphene in terms of mechanics in contrast to other carbon allotropes, including fullerenes and carbon nanotubes. The out-of-plane deformation is of a 'soft' nature, which gives rise to rich morphology and is crucial for morphology control. In this review article, we aim to summarize current theoretical advances in describing the mechanics of defects in graphene and the theory to capture the out-of-plane deformation. The structure-mechanical property relationship in graphene, in terms of its elasticity, strength, bending and wrinkling, with or without the influence of imperfections, is presented.

Elastic Properties and Fracture Behaviors of Biaxially Deformed, Polymorphic MoTe2

Biaxial deformation of suspended membranes widely exists and is used in nanoindentation to probe elastic properties of structurally isotropic two-dimensional (2D) materials. However, the elastic properties and, in particular, the fracture behaviors of anisotropic 2D materials remain largely unclarified in the case of biaxial deformation. MoTe₂ is a polymorphic 2D material with both isotropic (2H) and anisotropic (1T' and T_d) phases and, therefore, an ideal system of single-stoichiometric materials with which to study these critical issues. Here, we report the elastic properties and fracture behaviors of biaxially deformed, polymorphic MoTe₂ by combining temperature-variant nanoindentation and first-principles calculations. It is found that due to similar atomic bonding, the effective moduli of the three phases deviate by less than 15%. However, the breaking strengths of distorted 1T' and T_d phases are only half the value of 2H phase due to their uneven distribution of bonding strengths. Fractures of both isotropic 2H and anisotropic 1T' phases obey the theorem of minimum energy, forming triangular and linear fracture patterns, respectively, along the orientations parallel to Mo-Mo zigzag chains. Our findings not only provide a reference database for the elastic behaviors of versatile MoTe₂ phases but also illuminate a general strategy for the mechanical investigation of any isotropic and anisotropic 2D materials.

Grain-Boundary-Induced Drastic Sensing Performance Enhancement of Polycrystalline-Microwire Printed Gas Sensors

The development of materials with high efficiency and stable signal output in a bent state is important for flexible electronics. Grain boundaries provide lasting inspiration and a promising avenue for designing advanced functionalities using nanomaterials. Combining bulk defects in polycrystalline materials is shown to result in rich new electronic structures, catalytic activities, and mechanical properties for many applications. However, direct evidence that grain boundaries can create new physicochemical properties in flexible electronics is lacking. Here, a combination of bulk electrosensitive measurements, density functional theory calculations, and atomic force microscopy technology with quantitative nanomechanical mapping is used to show that grain boundaries in polycrystalline wires are more active and mechanically stable than single-crystalline wires for real-time detection of chemical analytes. The existence of a grain boundary improves the electronic and mechanical properties, which activate and stabilize materials, and allow new opportunities to design highly sensitive, flexible chemical sensors.

Bridging the Gap between Reality and Ideal in Chemical Vapor Deposition Growth of Graphene

Graphene, in its ideal form, is a two-dimensional (2D) material consisting of a single layer of carbon atoms arranged in a hexagonal lattice. The richness in morphological, physical, mechanical, and optical properties of ideal graphene has stimulated enormous scientific and industrial interest, since its first exfoliation in 2004. In turn, the production of graphene in a reliable, controllable, and scalable manner has become significantly important to bring us closer to practical applications of graphene. To this end, chemical vapor deposition (CVD) offers tantalizing opportunities for the synthesis of large-area, uniform, and high-quality graphene films. However, quite different from the ideal 2D structure of graphene, in reality, the currently available CVD-grown graphene films are still suffering from intrinsic defective grain boundaries, surface contaminations, and wrinkles, together with low growth rate and the requirement of inevitable transfer. Clearly, a gap still exits between the reality of CVD-derived graphene, especially in industrial production, and ideal graphene with outstanding properties. This Review will emphasize the recent advances and strategies in CVD production of graphene for settling these issues to bridge the giant gap. We begin with brief background information about the synthesis of nanoscale carbon allotropes, followed by the discussion of fundamental growth mechanism and kinetics of CVD growth of graphene. We then discuss the strategies for perfecting the quality of CVD-derived graphene with regard to domain size, cleanness, flatness, growth rate, scalability, and direct growth of graphene on functional substrate. Finally, a perspective on future development in the research relevant to scalable growth of high-quality graphene is presented.

A Review of Current Development of Graphene Mechanics

Graphene, a two-dimensional carbon in honeycomb crystal with single-atom thickness, possesses extraordinary properties and fascinating applications. Graphene mechanics is very important, as it relates to the integrity and various nanomechanical behaviors including flexing, moving, rotating, vibrating, and even twisting of graphene. The relationship between the strain and stress plays an essential role in graphene mechanics. Strain can dramatically influence the electronic and optical properties, and could be utilized to engineering those properties. Furthermore, graphene with specific kinds of defects exhibit mechanical enhancements and thus the electronic enhancements. In this short review, we focus on the current development of graphene mechanics, including tension and compression, fracture, shearing, bending, friction, and dynamics properties of graphene from both experiments and numerical simulations. We also touch graphene derivatives, including graphane, graphone, graphyne, fluorographene, and graphene oxide, which carve some fancy mechanical properties out from graphene. Our review summarizes the current achievements of graphene mechanics, and then shows the future prospects.

Structure of graphene and its disorders: a review

Monolayer graphene exhibits extraordinary properties owing to the unique, regular arrangement of atoms in it. However, graphene is usually modified for specific applications, which introduces disorder. This article presents details of graphene structure, including sp2 hybridization, critical parameters of the unit cell, formation of σ and π bonds, electronic band structure, edge orientations, and the number and stacking order of graphene layers. We also discuss topics related to the creation and configuration of disorders in graphene, such as corrugations, topological defects, vacancies, adatoms and sp3-defects. The effects of these disorders on the electrical, thermal, chemical and mechanical properties of graphene are analyzed subsequently. Finally, we review previous work on the modulation of structural defects in graphene for specific applications.

Nanopatched Graphene with Molecular Self-Assembly Toward Graphene-Organic Hybrid Soft Electronics

Increasing the mechanical durability of large-area polycrystalline single-atom-thick materials is a necessary step toward the development of practical and reliable soft electronics based on these materials. Here, it is shown that the surface assembly of organosilane by weak epitaxy forms nanometer-thick organic patches on a monolayer graphene surface and dramatically increases the material's resistance to harsh postprocessing environments, thereby increasing the number of ways in which graphene can be processed. The nanopatched graphene with the improved mechanical durability enables stable operation when used as transparent electrodes of wearable strain sensors. Also, the nanopatched graphene applied as an electrode modulates the molecular orientation of deposited organic semiconductor layers, and yields favorable nominal charge injection for organic transistors. These results demonstrate the potential for use of self-assembled organic nanopatches in graphene-based soft electronics.

Enhancing the Strength of Graphene by a Denser Grain Boundary

From a device application point of view, the extreme mechanical strength of graphene is highly desirable. However, the unavoidable polycrystalline nature of graphene films produced by chemical vapor deposition (CVD) leads to significant fluctuations in mechanical properties. Although the effects of atomic defects or grain boundaries (GBs) on mechanical strength have been widely studied and some modifications have been applied to enhance the stiffness of graphene, the problems of fragility as well as significantly reduced breaking strength arise. Here we report a systematic study on the effect of elastic modulus and breaking strength of CVD-derived graphene films with a controlled density and distribution of GBs. We find that graphene films become much stronger by hugely increasing the density of GBs without triple junctions (TJs) formed inside, in analogy to the two-dimensional (2D) plum pudding structures. The comprehensive performance with a 2D Young's modulus of 436 N/m (∼1.3 TPa) and 2D breaking strength of 43 N/m (∼128 GPa) can be achieved with the average grain size of 20 nm. Moreover, the existence of TJs will slightly reduce the strength in these GB structures. Due to defect types, the graphene films will show various tearing behaviors after indentation. All these mechanical studies of GBs provide a guideline to obtain the optimal performance of 2D materials through GB structure engineering.

Mechanical and thermal properties of grain boundary in a planar heterostructure of graphene and hexagonal boron nitride

In this study, the mechanical properties of grain boundaries (GBs) in planar heterostructures of graphene and hexagonal boron nitride (h-BN) were studied using the molecular dynamics method in combination with the density functional theory and classical disclination theory. The hybrid interface between graphene and h-BN grains was optimally matched by a non-bisector GB composed of pentagon-heptagon defects arranged in a periodic manner. GB was found to be a vulnerable spot to initiate failure under uniaxial tension; moreover, the tensile strength was found to anomalously increase with an increase in the mismatch angle between graphene and h-BN grains, i.e., the density of pentagon-heptagon defects along the GBs. The disclination theory was successfully adopted to predict the stress field caused by lattice mismatch at the GB. Comparison between stress contours of GBs with different mismatch angles demonstrates that the arrangement of 5-7 disclinations along the GB is crucial to the strength, and the stress concentration at the GB decreases with an increase in disclination density; this results in an anomalous increase of strength with an increase in the mismatch angle of grains. Moreover, the thermal transfer efficiency of the hybrid GB was revealed to be dependent not only on the mismatch angle of grains but also on the direction of the thermal flux. Thermal transfer efficiency from graphene to h-BN is higher than that from h-BN to graphene. Detailed analyses for the phonon density of states (PDOS) of GB atoms were carried out for the mismatch angle-dependence of interfacial conductance. Our results provide useful insights for the application of two-dimensional polycrystalline heterostructures in next-generation electronic nanodevices.

Stillinger-Weber potential for elastic and fracture properties in graphene and carbon nanotubes

This paper presents a new framework for determining the Stillinger-Weber (SW) potential parameters for modeling fracture in graphene and carbon nanotubes. In addition to fitting the equilibrium material properties, the approach allows fitting the potential to the forcing behavior as well as the mechanical strength of the solid, without requiring ad hoc modification of the nearest-neighbor interactions for avoiding artificial stiffening of the lattice at larger deformation. Consistent with the first-principles results, the potential shows the Young's modulus of graphene to be isotropic under symmetry-preserving and symmetry-breaking deformation conditions. It also shows the Young's modulus of carbon nanotubes to be diameter-dependent under symmetry-breaking loading conditions. The potential addresses the key deficiency of existing empirical potentials in reproducing experimentally observed glass-like brittle fracture in graphene and carbon nanotubes. In simulating the entire deformation process leading to fracture, the SW-potential costs several factors less computational time compared to the state-of-the-art interatomic potentials that enables exploration of the fracture processes in large atomistic systems which are inaccessible otherwise.

Optical Forging of Graphene into Three-Dimensional Shapes

Atomically thin materials, such as graphene, are the ultimate building blocks for nanoscale devices. But although their synthesis and handling today are routine, all efforts thus far have been restricted to flat natural geometries, since the means to control their three-dimensional (3D) morphology has remained elusive. Here we show that, just as a blacksmith uses a hammer to forge a metal sheet into 3D shapes, a pulsed laser beam can forge a graphene sheet into controlled 3D shapes in the nanoscale. The forging mechanism is based on laser-induced local expansion of graphene, as confirmed by computer simulations using thin sheet elasticity theory.

Theory of Finite-Length Grain Boundaries of Controlled Misfit Angle in Two-Dimensional Materials

Grain boundaries in two-dimensional crystals are usually thought to separate distinct crystallites and as such they must either form closed loops or terminate at the boundary of a sample. However, when an atomically thin two-dimensional crystal grows on a substrate of nonzero Gaussian curvature, it can develop finite-length grain boundaries that terminate abruptly within a monocrystalline domain. We show that by properly designing the substrate topography, these grain boundaries can be placed at desired locations and at specified misfit angles, as the thermodynamic ground state of a two-dimensional (2D) system bound to a substrate. Compared against the hypothetical competition of growing defectless 2D materials on a Gaussian-curved substrate with consequential fold development or detachment from the substrate, the nucleation and formation of finite-length grain boundaries can be made energetically favorably given sufficient substrate adhesion on the order of tens of meV/Ų for typical 2D materials. New properties specific to certain grain boundary geometries, including magnetism and metallicity, can thus be engineered into 2D crystals through topographic design of their substrates.

Large-Scale Suspended Graphene Used as a Transparent Substrate for Infrared Spectroscopy

Due to weak interactions between micrometer-wavelength infrared (IR) light and nanosized samples, a high signal to noise ratio is a prerequisite in order to precisely characterize nanosized samples using IR spectroscopy. Traditional micrometer-thick window substrates, however, have considerable IR absorption which may introduce unavoidable deformations and interruptions to IR spectra of nanoscale samples. A promising alternative is the use of a suspended graphene substrate which has ultrahigh IR transmittance (>97.5%) as well as unique mechanical properties. Here, an effective method is presented for fabrication of suspended graphene over circular holes up to 150 µm in diameter to be utilized as a transparent substrate for IR spectroscopy. It is demonstrated that the suspended graphene has little impact on the measured IR spectra, an advantage which has led to the discovery of several missing vibrational modes of a 20 nm thick PEO film measured on a traditional CaF₂ substrate. This can provide a better understanding of molecules' fine structures and status of hanging bands. The unique optical properties of suspended graphene are determined to be superior to those of conventional IR window materials, giving this new substrate great potential as part of a new generation of IR transparent substrates, especially for use in examining nanoscale samples.

Mechanical properties of atomically thin boron nitride and the role of interlayer interactions

Atomically thin boron nitride (BN) nanosheets are important two-dimensional nanomaterials with many unique properties distinct from those of graphene, but investigation into their mechanical properties remains incomplete. Here we report that high-quality single-crystalline mono- and few-layer BN nanosheets are one of the strongest electrically insulating materials. More intriguingly, few-layer BN shows mechanical behaviours quite different from those of few-layer graphene under indentation. In striking contrast to graphene, whose strength decreases by more than 30% when the number of layers increases from 1 to 8, the mechanical strength of BN nanosheets is not sensitive to increasing thickness. We attribute this difference to the distinct interlayer interactions and hence sliding tendencies in these two materials under indentation. The significantly better interlayer integrity of BN nanosheets makes them a more attractive candidate than graphene for several applications, for example, as mechanical reinforcements.

Bottom-up Design of Three-Dimensional Carbon-Honeycomb with Superb Specific Strength and High Thermal Conductivity

Low-dimensional carbon allotropes, from fullerenes, carbon nanotubes, to graphene, have been broadly explored due to their outstanding and special properties. However, there exist significant challenges in retaining such properties of basic building blocks when scaling them up to three-dimensional materials and structures for many technological applications. Here we show theoretically the atomistic structure of a stable three-dimensional carbon honeycomb (C-honeycomb) structure with superb mechanical and thermal properties. A combination of sp² bonding in the wall and sp³ bonding in the triple junction of C-honeycomb is the key to retain the stability of C-honeycomb. The specific strength could be the best in structural carbon materials, and this strength remains at a high level but tunable with different cell sizes. C-honeycomb is also found to have a very high thermal conductivity, for example, >100 W/mK along the axis of the hexagonal cell with a density only ∼0.4 g/cm³. Because of the low density and high thermal conductivity, the specific thermal conductivity of C-honeycombs is larger than most engineering materials, including metals and high thermal conductivity semiconductors, as well as lightweight CNT arrays and graphene-based nanocomposites. Such high specific strength, high thermal conductivity, and anomalous Poisson's effect in C-honeycomb render it appealing for the use in various engineering practices.