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: In this paper, the authors give an overview of the developing field of spintronics and outline the experimental and theoretical state-of-the-art of the art. But their focus is on van der Waals heterostructures, which consist of stacks of two-dimensional materials in precisely controlled order.
Abstract: Controlled spin transport in graphene and other two-dimensional materials has become increasingly promising for applications in devices. Of particular interest are custom-tailored heterostructures, known as van der Waals heterostructures, that consist of stacks of two-dimensional materials in a precisely controlled order. This Colloquium gives an overview of this developing field of spintronics and outlines the experimental and theoretical state of the art.
243 citations
Cites background from "Measurement of the Elastic Properti..."
...Lee, Changgu, Xiaoding Wei, Jeffrey W. Kysar, and James Hone (2008), “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321, 385....
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...Singh, Simranjeet, Jyoti Katoch, Jinsong Xu, Cheng Tan, Tiancong Zhu, Walid Amamou, James Hone, and Roland Kawakami (2016), “Nanosecond spin relaxation times in single layer graphene spin valves with hexagonal boron nitride tunnel barriers,” Appl....
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...Mak, Kin Fai, Changgu Lee, James Hone, Jie Shan, and Tony F. Heinz (2010), “Atomically thin mos2: A new direct-gap semiconductor,” Phys....
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TL;DR: 4D imaging, with in situ spatiotemporal resolutions, in ultrafast electron microscopy (UEM), demonstrates the promise of UEM in real-space imaging of dynamics.
Abstract: With advances in spatial resolution reaching the atomic scale, two-dimensional (2D) and 3D imaging in electron microscopy has become an essential methodology in various fields of study. Here, we report 4D imaging, with in situ spatiotemporal resolutions, in ultrafast electron microscopy (UEM). The ability to capture selected-area-image dynamics with pixel resolution and to control the time separation between pulses for temporal cooling of the specimen made possible studies of fleeting structures and morphologies. We demonstrate the potential for applications with two examples, gold and graphite. For gold, after thermally induced stress, we determined the atomic structural expansion, the nonthermal lattice temperature, and the ultrafast transients of warping/bulging. In contrast, in graphite, striking coherent transients of the structure were observed in both image and diffraction, directly measuring, on the nanoscale, the longitudinal resonance period governed by Young's elastic modulus. The success of these studies demonstrates the promise of UEM in real-space imaging of dynamics.
243 citations
TL;DR: In this article, a new strategy for providing ZRC with enhanced cathodic and barrier protection mechanisms simultaneously was reported, where the graphene oxide (GO) nanosheets were modified by highly crystalline and conductive polyaniline (PANI) nanofibers in the form of Emeraldine salt (ES) through an in situ polymerization of aniline in the presence of GO as an oxidant.
243 citations
TL;DR: In this article, the buckling strain of single flakes of different geometries was measured by simultaneous Raman measurements through the shift of either the G or 2D phonons of graphene.
Abstract: Central to most applications involving monolayer graphene is its mechanical response under various stress states. To date most of the work reported is of theoretical nature and refers to tension and compression loading of model graphene. Most of the experimental work is indeed limited to bending of single flakes in air and the stretching of flakes up to typically ~1% using plastic substrates. Recently we have shown that by employing a cantilever beam we can subject single graphene into various degrees of axial compression. Here we extend this work much further by measuring in detail both stress uptake and compression buckling strain in single flakes of different geometries. In all cases the mechanical response is monitored by simultaneous Raman measurements through the shift of either the G or 2D phonons of graphene. In spite of the infinitely small thickness of the monolayers, the results show that graphene embedded in plastic beams exhibit remarkable compression buckling strains. For large length (l)-to-width (w) ratios (> 0.2) the buckling strain is of the order of -0.5% to -0.6%. However, for l/w <0.2 no failure is observed for strains even higher than -1%. Calculations based on classical Euler analysis show that the buckling strain enhancement provided by the polymer lateral support is more than six orders of magnitude compared to suspended graphene in air.
243 citations
TL;DR: In this article, the authors describe both computational and experimental investigations of the mechanisms and implementations of 2D nanomaterials in the lubrication of interfaces, and present a review focusing on recent developments in the use of two-dimensional materials for controlling the frictional properties of surfaces and interfaces.
243 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