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: It is shown that irradiation with an 80 kV electron beam can selectively remove monolayers in few-layer graphene sheets by means of electron-beam-induced sputtering, and how energy transfer from the electron beam to few- layer graphene sheets leads to unique structural transformations is revealed.
Abstract: Graphene has remarkable electronic properties, such as ballistic transport and quantum Hall effects1,2,3, and has also been used as a support for samples in high-resolution transmission electron microscopy4,5 and as a transparent electrode in photovoltaic devices6. There is now a demand for techniques that can manipulate the structural and physical properties of graphene, in conjunction with the facility to monitor the changes in situ with atomic precision. Here, we show that irradiation with an 80 kV electron beam can selectively remove monolayers in few-layer graphene sheets by means of electron-beam-induced sputtering. Aberration-corrected, low-voltage, high-resolution transmission electron microscopy with sub-angstrom resolution is used to examine the structural reconstruction occurring at the single atomic level. We find preferential termination for graphene layers along the zigzag orientation for large hole sizes. The temporal resolution can also be reduced to 80 ms, enabling real-time observation of the reconstruction of carbon atoms during the sputtering process. We also report electron-beam-induced rapid displacement of monolayers, fast elastic distortions and flexible bending at the edges of graphene sheets. These results reveal how energy transfer from the electron beam to few-layer graphene sheets leads to unique structural transformations. A variety of structural changes in few-layer graphene samples can be followed with atomic resolution in real time by using high-resolution transmission electron microscopy.
212 citations
Cites background from "Measurement of the Elastic Properti..."
...Although graphene is reported to be the strongest material ever measure...
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TL;DR: In this paper, the intensity of the G band increases with increased graphene layers, and the shape of 2D band evolves into four peaks of bilayer graphene from a single peak of monolayer graphene.
Abstract: The recent progress using Raman spectroscopy and imaging of graphene is reviewed. The intensity of the G band increases with increased graphene layers, and the shape of 2D band evolves into four peaks of bilayer graphene from a single peak of monolayer graphene. The G band will blue shift and become narrow with both electron and hole doping, whereas the 2D band will blue shift with hole doping and red shift with electron doping. Frequencies of the G and 2D band will downshift with increasing temperature. Under compressed strain, the upshift of the G and 2D bands can be found. Moreover, the strong Raman signal of monolayer graphene is explained by interference enhancement effect. As for epitaxial graphene, Raman spectroscopy can be used to identify the superior and inferior carrier mobility. The edge chirality of graphene can be determined by using polarized Raman spectroscopy. All results mentioned here are closely relevant to the basic theory of graphene and application in nanodevices.
211 citations
Cites background from "Measurement of the Elastic Properti..."
...In the last 5 years, some novel properties of graphene were discovered, such as the quantum spin hall effect (4, 5), electron mobility as high as 120,000 cm2/Vs (the charge carriers mobility of graphene is higher than any other semiconductor at room temperature) (1, 6, 7), ballistic transport at room temperature (8–12), enhanced coulomb interaction (13–17), high mechanical strength (18), high thermal conduction (19–22), and suppression of weak localization (23, 24)....
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TL;DR: The present review will provide the guidance for the future research and development of membrane materials and membranes for hydrogen purification, and hence promote the development of sustainable and clean hydrogen energy.
211 citations
TL;DR: In this article, the use of Raman scattering techniques to study the mechanical properties of graphene films is reviewed, and the determination of Gruneisen parameters of suspended graphene sheets under uni-and bi-axial strain is discussed.
Abstract: The use of Raman scattering techniques to study the mechanical properties of graphene films is reviewed here. The determination of Gruneisen parameters of suspended graphene sheets under uni- and bi-axial strain is discussed, and the values are compared to theoretical predictions. The effects of the graphene−substrate interaction on strain and to the temperature evolution of the graphene Raman spectra are discussed. Finally, the relation between mechanical and thermal properties is presented along with the characterization of thermal properties of graphene with Raman spectroscopy.
211 citations
TL;DR: The developed photoreduction process based on a photoreaction will extend the applications of GO to many fields because it can be performed in mild conditions without a photocatalyst.
Abstract: Graphene oxide (GO) nanosheets were reduced by UV irradiation in H2 or N2 under mild conditions (at room temperature) without a photocatalyst. Photoreduction proceeded even in an aqueous suspension of nanosheets. The GO nanosheets reduced by this method were analyzed by X-ray photoelectron spectroscopy and Raman spectroscopy. It was found that epoxy groups attached to the interiors of aromatic domains of the GO nanosheet were destroyed during UV irradiation to form relatively large sp2 islands resulting in a high conductivity. I−V curves were measured by conductive atomic force microscopy (AFM; perpendicular to a single nanosheet) and a two-electrode system (parallel to the nanosheet). They revealed that photoreduced GO nanosheets have high conductivities, whereas nonreduced GO nanosheets are nearly insulating. Ag+ adsorbed on GO nanosheets promoted the photoreduction. This photoreduction method was very useful for photopatterning a conducting section of micrometer size on insulating GO. The developed pho...
211 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