Negative Poisson's ratio in rippled graphene

Definitive engineering strength and fracture toughness of graphene through on-chip nanomechanics

Fail-safe design of devices requires robust integrity assessment procedures which are still absent for 2D materials, hence affecting transfer to applications. Here, a combined on-chip tension and cracking method, and associated data reduction scheme have been developed to determine the fracture toughness and strength of monolayer-monodomain-freestanding graphene. Myriads of specimens are generated providing statistical data. The crack arrest tests provide a definitive fracture toughness of 4.4 MPam . Tension on-chip provides Young's modulus of 950 GPa, fracture strain of 11%, and tensile strength up to 110 GPa, reaching a record of stored elastic energy ~6 GJ m-3 as confirmed by thermodynamics and quantized fracture mechanics. A ~ 1.4 nm crack size is often found responsible for graphene failure, connected to 5-7 pair defects. Micron-sized graphene membranes and smaller can be produced defect-free, and design rules can be based on 110 GPa strength. For larger areas, a fail-safe design should be based on a maximum 57 GPa strength.

Theoretical insights into the structural, mechanical, and electronic properties of bcc-C40 carbon

Novel materials displaying multiple exceptional properties are the backbone of the advancement of various industries. In the field of carbon materials, the combination of different properties has been extensively developed to satisfy diverse application scenarios, for instance, conductivity paired with exceptional hardness, outstanding toughness coupled with super-hardness, or heat resistance combined with super-hardness. In this work, a new carbon allotrope, bcc-C40 carbon, was predicted and investigated using first-principles calculations based on density functional theory. The allotrope exhibits unique structural features, including a combination of sp3 hybridized diatomic carbon and four-fold carbon chains. The mechanical and dynamic stability of bcc-C40 carbon has been demonstrated by its elastic constants and phonon spectra. Additionally, bcc-C40 carbon exhibits remarkable mechanical properties, such as zero homogeneous Poisson's ratio, superhardness with a value of 58 GPa, and stress-adaptive toughening. The analysis of the electronic properties demonstrates that bcc-C40 carbon is a semiconductor with an indirect band gap of 3.255 eV within the HSE06 functional, which increases with the increase in pressure. At a pressure of 150 GPa, bcc-C40 carbon transforms into a direct band gap material. These findings suggest the prospective use of bcc-C40 carbon as a superhard material and a novel semiconductor.

Nonlinearity induced negative Poisson's ratio of two-dimensional nanomaterials

Materials exhibiting a negative Poisson's ratio have garnered considerable attention due to the improved toughness, shear resistance, and vibration absorption properties commonly found in auxetic materials. In this work, the nonlinear effect on the Poisson's ratio was derived theoretically and verified by first-principle calculations and molecular dynamics simulations of two-dimensional nanomaterials including graphene and hexagonal boron nitride. The analytic formula explicitly shows that the Poisson's ratio depends on the applied strain and can be negative for large applied strains, owing to the nonlinear interaction. Both first-principle calculations and molecular dynamics simulations show that the nonlinear effect is highly anisotropic for graphene, where the nonlinearity-induced negative Poisson's ratio is much stronger for the strain applied along the armchair direction. These findings provide valuable insights into the behavior of materials with negative Poisson's ratios and emphasize the importance of considering nonlinear effects in the study of the Poisson's ratio of two-dimensional materials.

Theoretical Evaluation of Impact Characteristics of Wavy Graphene Sheets with Disclinations Formed by Origami and Kirigami

Evaluation of impact characteristics of carbon nanomaterials is very important and helpful for their application in nanoelectromechanical systems (NEMS). Furthermore, disclination lattice defects can generate out-of-plane deformation to control the mechanical behavior of carbon nanomaterials. In this study, we design novel stable wavy graphene sheets (GSs) using a technique based on origami and kirigami to control the exchange of carbon atoms and generate appropriate disclinations. The impact characteristics of these GSs are evaluated using molecular dynamics (MD) simulation, and the accuracy of the simulation results is verified via a theoretical analysis based on continuum mechanics. In the impact tests, the C₆₀ fullerene is employed as an impactor, and the effects of the different shapes of wavy GSs with different disclinations, different impact sites on the curved surface, and different impact velocities are examined to investigate the impact characteristics of the wavy GSs. We find that the newly designed wavy GSs increasingly resist the kinetic energy (KE) of the impactor as the disclination density is increased, and the estimated KE propagation patterns are significantly different from those of the ideal GS. Based on their enhanced performance in the impact tests, the wavy GSs possess excellent impact behavior, which should facilitate their potential application as high-impact-resistant components in advanced NEMS.

Vibration Control of Diamond Nanothreads by Lattice Defect Introduction for Application in Nanomechanical Sensors

Carbon nanomaterials, such as carbon nanotubes (CNTs) and graphene sheets (GSs), have been adopted as resonators in vibration-based nanomechanical sensors because of their extremely high stiffness and small size. Diamond nanothreads (DNTs) are a new class of one-dimensional carbon nanomaterials with extraordinary physical and chemical properties. Their structures are similar to that of diamond in that they possess sp3-bonds formed by a covalent interaction between multiple benzene molecules. In this study, we focus on investigating the mechanical properties and vibration behaviors of DNTs with and without lattice defects and examine the influence of density and configuration of lattice defects on the two them in detail, using the molecular dynamics method and a continuum mechanics approach. We find that Young’s modulus and the natural frequency can be controlled by alternating the density of the lattice defects. Furthermore, we investigate and explore the use of DNTs as resonators in nanosensors. It is shown that applying an additional extremely small mass or strain to all types of DNTs significantly changes their resonance frequencies. The results show that, similar to CNTs and GSs, DNTs have potential application as resonators in nano-mass and nano-strain sensors. In particular, the vibration behaviors of DNT resonators can be controlled by alternating the density of the lattice defects to achieve the best sensitivities.

Consistent evaluation of continuum scale properties of two-dimensional materials: a case study on graphene

We handshake statistical mechanics with continuum mechanics to develop a methodology for consistent evaluation of the continuum scale properties of two-dimensional materials. The methodology is tested on pristine graphene. Our scope is kept limited to elastic modulus, E, which has been reported to vary between 0.912 TPa and 7 TPa, Poisson's ratio, ν, which has been reported to vary from being negative to a value as large as 0.46, and effective thickness, q, whose value varies between 0.75 Å and 3.41 Å. Such a large scatter arises due to inconsistent evaluation of these properties and making assumptions that may not be valid at atomistic scales. Our methodology combines three separate methods: uniaxial tension, equibiaxial tension, and flexural out-of-plane free vibrations of simply supported sheets, which, when used in tandem in molecular dynamics, can provide consistent values of E, ν and q. The only assumption made in the present study is the validity of the continuum scale thin plate vibration equation to represent the free vibrations of a graphene sheet. Our results suggest that-(i) graphene is auxetic in nature, (ii) E decreases with increasing size and temperature, and (iii) the effective thickness q increases with increasing size and temperature. Further, a robustness study of the computed mechanical properties shows consistent results, with differences varying between 1.4% and 6%.

A novel SiO monolayer with a negative Poisson's ratio and Dirac semimetal properties

Although a number of interesting physical properties such as a negative Poisson's ratio (NPR) and Dirac semimetal (DS) properties have been recently predicted in two-dimensional (2D) materials, the realization of a 2D material that exhibits both of these DS and NPR features has rarely been reported. Here by adopting particle swarm optimization (PSO) algorithms combined with first-principles methods, we successfully construct a novel SiO monolayer (Pmna), the dynamic and thermal stability of which was characterized using phonon spectrum calculations and molecular dynamics simulations. In particular, Young's modulus and Poisson's ratio calculations showed that the Pmna monolayer exhibits high mechanical anisotropy with an in-plane NPR originating from its puckered atomic arrangement. More notably, the band structure of the Pmna monolayer possesses zero bandgap with four Dirac cones in its first Brillouin zone, exhibiting a DS feature. From the calculations of orbital-resolved band structures, the Dirac cone was revealed to originate from the orbital hybridization of Si and O atoms. The Pmna monolayer is the first 2D structure in the Si-O system that has both an NPR and Dirac semi-metal properties, providing a new model for exploring 2D multifunctional materials.

Gallium Thiophosphate: An Emerging Bidirectional Auxetic Two-Dimensional Crystal with Wide Direct Band Gap

Two-dimensional (2D) materials with negative Poisson's ratio (NPR) attract considerable attention because of their exotic mechanical properties. We propose a new 2D material, monolayer GaPS₄, which shows NPR for both in-plane (-0.033) and out-of-plane (-0.62) directions. Such coexistence of NPR in two distinct directions could be explained by its corner- and edge-shared tetrahedra pucker structure. GaPS₄ has an ultralow cleavage energy of 0.23 J m^-2 according to our calculation, such that exfoliation of the bulk material is feasible for the preparation of mono- and few-layer GaPS₄. Direct wide band gap of 3.55 eV and moderate electron mobility have been revealed in monolayer GaPS₄, while the direct gap feature is robust within a strain range of -6% to 6%. These findings render 2D GaPS₄ a promising candidate for applications in nanoelectronics and low-dimensional electromechanical devices.

A Review on Brittle Fracture Nanomechanics by All-Atom Simulations

Despite a wide range of current and potential applications, one primary concern of brittle materials is their sudden and swift collapse. This failure phenomenon exhibits an inability of the materials to sustain tension stresses in a predictable and reliable manner. However, advances in the field of fracture mechanics, especially at the nanoscale, have contributed to the understanding of the material response and failure nature to predict most of the potential dangers. In the following contribution, a comprehensive review is carried out on molecular dynamics (MD) simulations of brittle fracture, wherein the method provides new data and exciting insights into fracture mechanism that cannot be obtained easily from theories or experiments on other scales. In the present review, an abstract introduction to MD simulations, advantages, current limitations and their applications to a range of brittle fracture problems are presented. Additionally, a brief discussion highlights the theoretical background of the macroscopic techniques, such as Griffith's criterion, crack tip opening displacement, J-integral and other criteria that can be linked to the fracture mechanical properties at the nanoscale. The main focus of the review is on the recent advances in fracture analysis of highly brittle materials, such as carbon nanotubes, graphene, silicon carbide, amorphous silica, calcium carbonate and silica aerogel at the nanoscale. These materials are presented here due to their extraordinary mechanical properties and a wide scope of applications. The underlying review grants a more extensive unravelling of the fracture behaviour and mechanical properties at the nanoscale of brittle materials.

Chemically modified graphene films with tunable negative Poisson's ratios

Graphene-derived macroscopic assemblies feature hierarchical nano- and microstructures that provide numerous routes for surface and interfacial functionalization achieving unconventional material properties. We report that the microstructural hierarchy of pristine chemically modified graphene films, featuring wrinkles, delamination of close-packed laminates, their ordered and disordered stacks, renders remarkable negative Poisson’s ratios ranging from −0.25 to −0.55. The mechanism proposed is validated by the experimental characterization and theoretical analysis. Based on the understanding of microstructural origins, pre-strech is applied to endow chemically modified graphene films with controlled negative Poisson’s ratios. Modulating the wavy textures of the inter-connected network of close-packed laminates in the chemically modified graphene films also yields finely-tuned negative Poisson’s ratios. These findings offer the key insights into rational design of films constructed from two-dimensional materials with negative Poisson’s ratios and mechanomutable performance.

Negative Poisson’s ratio, offering unusual properties, is displayed by several materials and predicted for graphene. This work demonstrates such behaviors in monolithic films with interconnected networks of close-packed graphene laminates, and tunability through the chemistry and microstructures.

Predicting Novel 2D MB2 (M = Ti, Hf, V, Nb, Ta) Monolayers with Ultrafast Dirac Transport Channel and Electron-Orbital Controlled Negative Poisson's Ratio

Three-dimensional diborides MB₂, featured in stacking the M layer above the middle of the honeycomb boron layer, have been extensively studied. However, little information on the two-dimensional counterparts of MB₂ is available. Here, by means of evolutionary algorithm and first-principles calculations, we extensively studied the monolayer MB₂ crystal with M elements ranging from group IIA to IVA covering 34 candidates. Our computations screened out eight stable monolayers MB₂ (M = Be, Mg, Fe, Ti, Hf, V, Nb, Ta), and they exhibit Dirac-like band structures. Dramatically, among them, groups IVB-VB transition-metal diboride MB₂ (M = Ti, Hf, V, Nb, Ta) are predicted to be a new class of auxetic materials. They harbor in-plane negative Poisson's ratio (NPR) arising mainly from the orbital hybridization between M d and Boron p orbitals, which is distinct from previously reported auxetic materials. The unusual NPR and the Dirac transport channel of these materials are applicable to nanoelectronics and nanomechanics.

Bubble-wrap carbon: an integration of graphene and fullerenes

Graphene and fullerene, two types of C allotropes with very different structures and properties, have attracted considerable attention from the scientific community as new forms of carbon for several decades. It will be a great advantage to combine the geometrical features of the two. Herein, we report a series of novel two-dimensional carbon allotropes that possess fullerene-like hollow structures (bubbles) embedded in a graphene sheet. These carbon allotropes are both thermally and dynamically stable. Calculations using hybrid functionals show that these two-dimensional carbon allotropes could be metals or semiconductors depending on the size and the pattern of the bubbles. The band gap can be as large as 1.66 eV. Due to the unique atomic configuration, some bubble-wrap carbons have unusual negative Poisson's ratios. The combination of graphene and fullerenes provides an appealing approach to design carbon-based materials with dexterous properties. For example, the insertion of the metal atoms inside the bubbles may greatly enhance the functions of such materials in photovoltaics and catalysis.

Filtration Properties of Auxetics with Rotating Rigid Units

Auxetic structures and materials expand laterally when stretched. It has been argued that this property could be applied in the design of smart filters with tunable sieving properties. This work analyses the filtration properties of a class of auxetic structures which achieve their auxeticity through a rotating rigid unit mechanism, an archetypal mechanism known to be responsible for this behavior in a number of crystalline materials. In particular, mathematical expressions are derived for the space coverage of networks constructed from a variety of quadrilaterals, as well as the pore radius. The latter is indicative of the particle size that can pass through when the particle dimension is comparable to the pore size, whereas the space coverage is indicative of the rate of flow when the particles are of a much smaller dimension than the pore size. The expressions suggest that these systems offer a wide range of pore sizes and space coverages, both of which can be controlled through the way that the units are connected to each other, their shape and the angle between them.

The negative Poisson's ratio in graphene-based carbon foams

Using molecular dynamics simulations, we find an in-plane negative Poisson's ratio intrinsically existing in the graphene-based three-dimensional (3D) carbon foams (CFs) when they are compressed uniaxially. Our study shows that the negative Poisson's ratio in the present CFs is attributed to their unique molecular structures and triggered by the buckling of the CF structures. This mechanism makes the negative Poisson's ratio of CFs strongly depend on their cell length, which offers us an efficient means to tune the negative Poisson's ratio in nanomaterials. Moreover, as the buckling modes of CFs are topographically different when they are compressed in different directions, their negative Poisson's ratio is found to be strongly anisotropic, which is in contrast to the isotropic positive Poisson's ratio observed in CFs prior to buckling. The discovery of the intrinsic negative Poisson's ratio in 3D CFs will significantly expand the family of auxetic nanomaterials. Meanwhile, the mechanism of nano-auxetics proposed here may open up a door to manufacture new auxetic materials on the nanoscale.

Theoretical discovery of novel two-dimensional VA-N binary compounds with auxiticity

Novel two-dimensional V^A-nitride binary compounds with a large negative Poisson's ratio and a suitable band-gap are predicted based on first-principles calculations.