Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene
18 Jul 2008-Science (American Association for the Advancement of Science)-Vol. 321, Iss: 5887, pp 385-388
TL;DR: Graphene is established as the strongest material ever measured, and atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.
Abstract: We measured the elastic properties and intrinsic breaking strength of free-standing monolayer graphene membranes by nanoindentation in an atomic force microscope. The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 newtons per meter (N m(-1)) and -690 Nm(-1), respectively. The breaking strength is 42 N m(-1) and represents the intrinsic strength of a defect-free sheet. These quantities correspond to a Young's modulus of E = 1.0 terapascals, third-order elastic stiffness of D = -2.0 terapascals, and intrinsic strength of sigma(int) = 130 gigapascals for bulk graphite. These experiments establish graphene as the strongest material ever measured, and show that atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.
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TL;DR: Although challenges related to quality control in graphene materials remain to be addressed, the advancement in the understandings of graphene will propel the commercial success of graphene as a compelling technology.
Abstract: The ground-breaking demonstration of the electric field effect in graphene reported more than a decade ago prompted the strong push towards the commercialization of graphene as evidenced by a wealth of graphene research, patents and applications. Graphene flake production capability has reached thousands of tonnes per year, while continuous graphene sheets of tens of metres in length have become available. Various graphene technologies developed in laboratories have now transformed into commercial products, with the very first demonstrations in sports goods, automotive coatings, conductive inks and touch screens, to name a few. Although challenges related to quality control in graphene materials remain to be addressed, the advancement in the understandings of graphene will propel the commercial success of graphene as a compelling technology. This Review discusses the progress towards commercialization of graphene for the past decade and future perspectives. This Review reflects on the 15 years of advances in the field of 2D materials towards commercialization of graphene and its future perspectives.
214 citations
TL;DR: This study provides significant insights into breakdown mechanisms of graphene in the presence of defective structures such as cracks and grain boundaries, and investigates the crystallographic orientations of tears.
Abstract: The understanding of crack formation due to applied stress is key to predicting the ultimate mechanical behavior of many solids. Here we present experimental and theoretical studies on cracks or tears in suspended monolayer graphene membranes. Using transmission electron microscopy, we investigate the crystallographic orientations of tears. Edges from mechanically induced ripping exhibit straight lines and are predominantly aligned in the armchair or zigzag directions of the graphene lattice. Electron-beam induced propagation of tears is also observed. Theoretical simulations account for the observed preferred tear directions, attributing the observed effect to an unusual nonmonotonic dependence of graphene edge energy on edge orientation with respect to the lattice. Furthermore, we study the behavior of tears in the vicinity of graphene grain boundaries, where tears surprisingly do not follow but cross grain boundaries. Our study provides significant insights into breakdown mechanisms of graphene in the ...
213 citations
TL;DR: The mechanical properties of 20 representative graphene grain boundaries were studied using density functional theory and molecular dynamics to form a useful picture of the grain boundary effect on the mechanical propertiesof polycrystalline graphene.
Abstract: As one-dimension line defects, grain boundaries (GBs) can affect many intrinsic properties of graphene. In this paper, the mechanical properties of 20 representative graphene grain boundaries were studied using density functional theory and molecular dynamics. With different arrangements of the pentagonal and heptagonal rings, the grain boundary may remain flat or become inflected up to 72°. For the flat GBs, the intrinsic tensile strength decreases linearly with the formation energy with a maximum value of 93 GPa, close to that of a perfect graphene. The intrinsic tensile strength of the inflected GBs is found to generally decrease with increasing inflection angle. Stone–Wales transformation is identified as the major failure mechanism of graphene GBs at high temperatures, whereas the initial fracture site can be either on the boundary line or inside the domain. These theoretical results constitute a useful picture of the grain boundary effect on the mechanical properties of polycrystalline graphene.
213 citations
TL;DR: In situ optical transmittance spectra and electrical transport properties of ultrathin graphite (3-60 graphene layers) simultaneously during electrochemical lithiation/delithiation and on intercalation are measured, observing an increase of both opticalTransmission and electrical conductivity, strikingly different from other materials.
Abstract: Graphene-based materials have potential as transparent electrodes, but still fall short of desired performance goals. Here, Bao et al. report that upon intercalation of lithium into few-layer graphene, desired sheet resistance and optical transmittance may be achieved.
213 citations
TL;DR: In this article, the effect of atomic scale defects and disorder on the low-energy electronic structure of graphene was investigated by scanning tunneling microscopy and spectroscopy measurements, which reveal that defect sites, besides acting as scattering centers for electrons through local modification of the on-site potential, also induce disorder in the hopping amplitudes.
Abstract: Mechanically exfoliated graphene layers deposited on ${\text{SiO}}_{2}$ substrate were irradiated with ${\text{Ar}}^{+}$ ions in order to experimentally study the effect of atomic scale defects and disorder on the low-energy electronic structure of graphene. The irradiated samples were investigated by scanning tunneling microscopy and spectroscopy measurements, which reveal that defect sites, besides acting as scattering centers for electrons through local modification of the on-site potential, also induce disorder in the hopping amplitudes. The most important consequence of the induced disorder is the substantial reduction in the Fermi velocity, revealed by bias-dependent imaging of electron-density oscillations observed near defect sites.
212 citations
References
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TL;DR: This work shows that graphene's electronic structure is captured in its Raman spectrum that clearly evolves with the number of layers, and allows unambiguous, high-throughput, nondestructive identification of graphene layers, which is critically lacking in this emerging research area.
Abstract: Graphene is the two-dimensional building block for carbon allotropes of every other dimensionality We show that its electronic structure is captured in its Raman spectrum that clearly evolves with the number of layers The D peak second order changes in shape, width, and position for an increasing number of layers, reflecting the change in the electron bands via a double resonant Raman process The G peak slightly down-shifts This allows unambiguous, high-throughput, nondestructive identification of graphene layers, which is critically lacking in this emerging research area
13,474 citations
TL;DR: By using micromechanical cleavage, a variety of 2D crystals including single layers of boron nitride, graphite, several dichalcogenides, and complex oxides are prepared and studied.
Abstract: We report free-standing atomic crystals that are strictly 2D and can be viewed as individual atomic planes pulled out of bulk crystals or as unrolled single-wall nanotubes. By using micromechanical cleavage, we have prepared and studied a variety of 2D crystals including single layers of boron nitride, graphite, several dichalcogenides, and complex oxides. These atomically thin sheets (essentially gigantic 2D molecules unprotected from the immediate environment) are stable under ambient conditions, exhibit high crystal quality, and are continuous on a macroscopic scale.
10,586 citations
TL;DR: In this article, the authors investigated the effect of surface scratches on the mechanical strength of solids, and some general conclusions were reached which appear to have a direct bearing on the problem of rupture, from an engineering standpoint, and also on the larger question of the nature of intermolecular cohesion.
Abstract: In the course of an investigation of the effect of surface scratches on the mechanical strength of solids, some general conclusions were reached which appear to have a direct bearing on the problem of rupture, from an engineering standpoint, and also on the larger question of the nature of intermolecular cohesion. The original object of the work, which was carried out at the Royal Aircraft Establishment, was the discovery of the effect of surface treatment—such as, for instance, filing, grinding or polishing—on the strength of metallic machine parts subjected to alternating or repeated loads. In the case of steel, and some other metals in common use, the results of fatigue tests indicated that the range of alternating stress which could be permanently sustained by the material was smaller than the range within which it was sensibly elastic, after being subjected to a great number of reversals. Hence it was inferred that the safe range of loading of a part, having a scratched or grooved surface of a given type, should be capable of estimation with the help of one of the two hypotheses of rupture commonly used for solids which are elastic to fracture. According to these hypotheses rupture may be expected if (a) the maximum tensile stress, ( b ) the maximum extension, exceeds a certain critical value. Moreover, as the behaviour of the materials under consideration, within the safe range of alternating stress, shows very little departure from Hooke’s law, it was thought that the necessary stress and strain calculations could be performed by means of the mathematical theory of elasticity.
10,162 citations
Book•
01 Jan 1985
TL;DR: In this paper, the physical properties of crystals systematically in tensor notation are presented, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them.
Abstract: First published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects.
8,520 citations
TL;DR: The tensile strengths of individual multiwalled carbon nanotubes (MWCNTs) were measured with a "nanostressing stage" located within a scanning electron microscope and a variety of structures were revealed, such as a nanotube ribbon, a wave pattern, and partial radial collapse.
Abstract: The tensile strengths of individual multiwalled carbon nanotubes (MWCNTs) were measured with a “nanostressing stage” located within a scanning electron microscope. The tensile-loading experiment was prepared and observed entirely within the microscope and was recorded on video. The MWCNTs broke in the outermost layer (“sword-in-sheath” failure), and the tensile strength of this layer ranged from 11 to 63 gigapascals for the set of 19 MWCNTs that were loaded. Analysis of the stress-strain curves for individual MWCNTs indicated that the Young's modulus E of the outermost layer varied from 270 to 950 gigapascals. Transmission electron microscopic examination of the broken nanotube fragments revealed a variety of structures, such as a nanotube ribbon, a wave pattern, and partial radial collapse.
5,011 citations