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 reported that boron atoms can be efficiently substituted for carbon in graphene and Boron-doped graphene appears to be a useful tool for engineering the physical and chemical properties of graphene.
Abstract: The introduction of foreign atoms, such as nitrogen, into the hexagonal network of an sp2-hybridized carbon atom monolayer has been demonstrated and constitutes an effective tool for tailoring the intrinsic properties of graphene. Here, we report that boron atoms can be efficiently substituted for carbon in graphene. Single-layer graphene substitutionally doped with boron was prepared by the mechanical exfoliation of boron-doped graphite. X-ray photoelectron spectroscopy demonstrated that the amount of substitutional boron in graphite was ∼0.22 atom %. Raman spectroscopy demonstrated that the boron atoms were spaced 4.76 nm apart in single-layer graphene. The 7-fold higher intensity of the D-band when compared to the G-band was explained by the elastically scattered photoexcited electrons by boron atoms before emitting a phonon. The frequency of the G-band in single-layer substitutionally boron-doped graphene was unchanged, which could be explained by the p-type boron doping (stiffening) counteracting the...
233 citations
TL;DR: As a result of thermal annealing in air, the thinning of MoS2 nanosheet is possible due to its oxidation to form MoO3 .
Abstract: A simple thermal annealing method for layer thinning and etching of mechanically exfoliated MoS2 nanosheets in air is reported. Using this method, single-layer (1L) MoS2 nanosheets are achieved after the thinning of MoS2 nanosheets from double-layer (2L) to quadri-layer (4L) at 330 °C. The as-prepared 1L MoS2 nanosheet shows comparable optical and electrical properties with the mechanically exfoliated, pristine one. In addition, for the first time, the MoS2 mesh with high-density of triangular pits is also fabricated at 330 °C, which might arise from the anisotropic etching of the active MoS2 edge sites. As a result of thermal annealing in air, the thinning of MoS2 nanosheet is possible due to its oxidation to form MoO3 . Importantly, the MoO3 fragments on the top of thinned MoS2 layer induces the hole injection, resulting in the p-type channel in fabricated field-effect transistors.
232 citations
02 Apr 2014-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this article, the authors reported the mechanical improvement in Cu matrix composites reinforced with graphene nanosheets decorated with Ni nanoparticles (GNS-Ni) hybrids, leading to a 61% increase in Young γs modulus (132 GPa) and a 94% improvement in yield strength (268 MPa) by adding only 1.0% GNSs.
Abstract: The present work reports the mechanical improvement in Cu matrix composites reinforced with graphene nanosheets decorated with Ni nanoparticles (GNS–Ni) hybrids. The GNS–Ni hybrids were firstly synthesized by an in situ chemical reduction method and then incorporated into the Cu matrix to fabricate bulk GNS–Ni/Cu composites by spark plasma sintering. Benefiting from the unique characteristic of GNS–Ni hybrids, the GNS–Ni/Cu composites exhibited homogeneously dispersed GNSs and a strong GNS–Cu interface interaction, therefore leading to a 61% increase in Young׳s modulus (132 GPa) and a 94% improvement in yield strength (268 MPa) by addition of only 1.0 vol% GNSs. The GNS–Ni/Cu composites exhibited a load transfer mechanism as verified by a modified shear-lag model. Our study thus shows the potential for GNS–Ni hybrids to be successfully used as a reinforcing phase in metal matrix composites.
232 citations
TL;DR: Comparative studies showed that graphene is superior to other adsorbents including C18 silica, graphitic carbon, and single- and multi-walled carbon nanotubes for the extraction of Pb and reveals the great potential of graphene as an excellent sorbent material in analytical processes.
232 citations
TL;DR: In this paper, the mechanical properties of single-layer black phosphorus under uniaxial deformation were investigated using first-principles calculations, and both the Young's modulus and ultimate strain were found to be highly anisotropic and nonlinear as a result of its quasi-two-dimensional puckered structure.
Abstract: The mechanical properties of single-layer black phosphorus under uniaxial deformation are investigated using first-principles calculations. Both the Young's modulus and ultimate strain are found to be highly anisotropic and nonlinear as a result of its quasi-two-dimensional puckered structure. Specifically, the in-plane Young's modulus is 41.3?GPa in the direction perpendicular to the pucker and 106.4?GPa in the parallel direction. The ideal strain is 0.48 and 0.11 in the perpendicular and parallel directions, respectively.
232 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