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Journal ArticleDOI

Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene

Changgu Lee1, Xiaoding Wei1, Jeffrey W. Kysar1, James Hone1, James Hone2 
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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Citations
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Journal ArticleDOI
TL;DR: The electronic properties of ultrathin crystals of molybdenum disulfide consisting of N=1,2,…,6 S-Mo-S monolayers have been investigated by optical spectroscopy and the effect of quantum confinement on the material's electronic structure is traced.
Abstract: The electronic properties of ultrathin crystals of molybdenum disulfide consisting of N=1,2,…,6 S-Mo-S monolayers have been investigated by optical spectroscopy Through characterization by absorption, photoluminescence, and photoconductivity spectroscopy, we trace the effect of quantum confinement on the material's electronic structure With decreasing thickness, the indirect band gap, which lies below the direct gap in the bulk material, shifts upwards in energy by more than 06 eV This leads to a crossover to a direct-gap material in the limit of the single monolayer Unlike the bulk material, the MoS₂ monolayer emits light strongly The freestanding monolayer exhibits an increase in luminescence quantum efficiency by more than a factor of 10⁴ compared with the bulk material

12,822 citations

Journal ArticleDOI
19 Jun 2009-Science
TL;DR: This review analyzes recent trends in graphene research and applications, and attempts to identify future directions in which the field is likely to develop.
Abstract: Graphene is a wonder material with many superlatives to its name. It is the thinnest known material in the universe and the strongest ever measured. Its charge carriers exhibit giant intrinsic mobility, have zero effective mass, and can travel for micrometers without scattering at room temperature. Graphene can sustain current densities six orders of magnitude higher than that of copper, shows record thermal conductivity and stiffness, is impermeable to gases, and reconciles such conflicting qualities as brittleness and ductility. Electron transport in graphene is described by a Dirac-like equation, which allows the investigation of relativistic quantum phenomena in a benchtop experiment. This review analyzes recent trends in graphene research and applications, and attempts to identify future directions in which the field is likely to develop.

12,117 citations

Journal ArticleDOI
05 Feb 2009-Nature
TL;DR: The direct synthesis of large-scale graphene films using chemical vapour deposition on thin nickel layers is reported, and two different methods of patterning the films and transferring them to arbitrary substrates are presented, implying that the quality of graphene grown by chemical vapours is as high as mechanically cleaved graphene.
Abstract: Problems associated with large-scale pattern growth of graphene constitute one of the main obstacles to using this material in device applications. Recently, macroscopic-scale graphene films were prepared by two-dimensional assembly of graphene sheets chemically derived from graphite crystals and graphene oxides. However, the sheet resistance of these films was found to be much larger than theoretically expected values. Here we report the direct synthesis of large-scale graphene films using chemical vapour deposition on thin nickel layers, and present two different methods of patterning the films and transferring them to arbitrary substrates. The transferred graphene films show very low sheet resistance of approximately 280 Omega per square, with approximately 80 per cent optical transparency. At low temperatures, the monolayers transferred to silicon dioxide substrates show electron mobility greater than 3,700 cm(2) V(-1) s(-1) and exhibit the half-integer quantum Hall effect, implying that the quality of graphene grown by chemical vapour deposition is as high as mechanically cleaved graphene. Employing the outstanding mechanical properties of graphene, we also demonstrate the macroscopic use of these highly conducting and transparent electrodes in flexible, stretchable, foldable electronics.

10,033 citations

Journal ArticleDOI
TL;DR: An overview of the synthesis, properties, and applications of graphene and related materials (primarily, graphite oxide and its colloidal suspensions and materials made from them), from a materials science perspective.
Abstract: There is intense interest in graphene in fields such as physics, chemistry, and materials science, among others. Interest in graphene's exceptional physical properties, chemical tunability, and potential for applications has generated thousands of publications and an accelerating pace of research, making review of such research timely. Here is an overview of the synthesis, properties, and applications of graphene and related materials (primarily, graphite oxide and its colloidal suspensions and materials made from them), from a materials science perspective.

8,919 citations

Journal ArticleDOI
11 Oct 2012-Nature
TL;DR: This work reviews recent progress in graphene research and in the development of production methods, and critically analyse the feasibility of various graphene applications.
Abstract: Recent years have witnessed many breakthroughs in research on graphene (the first two-dimensional atomic crystal) as well as a significant advance in the mass production of this material. This one-atom-thick fabric of carbon uniquely combines extreme mechanical strength, exceptionally high electronic and thermal conductivities, impermeability to gases, as well as many other supreme properties, all of which make it highly attractive for numerous applications. Here we review recent progress in graphene research and in the development of production methods, and critically analyse the feasibility of various graphene applications.

7,987 citations

References
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Journal ArticleDOI
TL;DR: In this article, the authors presented a method to construct an LNNME-ARTICLE-1999-004, which is used in PhysRevLett.82.944.
Abstract: Reference LNNME-ARTICLE-1999-004doi:10.1103/PhysRevLett.82.944View record in Web of Science Record created on 2007-04-23, modified on 2016-08-08

1,447 citations

Journal ArticleDOI
TL;DR: In this paper, the phonon spectra of graphene were calculated as a function of uniaxial tension by density functional perturbation theory to assess the first occurrence of phonon instability on the strain path.
Abstract: Graphene-based $s{p}^{2}$-carbon nanostructures such as carbon nanotubes and nanofibers can fail near their ideal strengths due to their exceedingly small dimensions. We have calculated the phonon spectra of graphene as a function of uniaxial tension by density functional perturbation theory to assess the first occurrence of phonon instability on the strain path, which controls the strength of a defect-free crystal at $0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Uniaxial tensile strain is applied in the $x$ (nearest-neighbor) and $y$ (second nearest-neighbor) directions, related to tensile deformation of zigzag and armchair nanotubes, respectively. The Young's modulus $E=1050\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ and Poisson's ratio $\ensuremath{ u}=0.186$ from our small-strain results are in good agreement with previous calculations. We find that in both $x$ and $y$ uniaxial tensions, phonon instabilities occur near the center of the Brillouin zone, at (${\ensuremath{\epsilon}}_{xx}=0.194$, ${\ensuremath{\sigma}}_{xx}=110\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, ${\ensuremath{\epsilon}}_{yy}=\ensuremath{-}0.016$) and (${\ensuremath{\epsilon}}_{yy}=0.266$, ${\ensuremath{\sigma}}_{yy}=121\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, ${\ensuremath{\epsilon}}_{xx}=\ensuremath{-}0.027$), respectively. Both soft phonons are longitudinal elastic waves in the pulling direction, suggesting that brittle cleavage fracture may be an inherent behavior of graphene and carbon nanotubes at low temperatures. We also predict that a phonon band gap will appear in highly stretched graphene, which could be a useful spectroscopic signature for highly stressed carbon nanotubes.

1,370 citations

Journal ArticleDOI
15 Jun 2000-Nature
TL;DR: Experimental and theoretical elucidation of the electromechanical characteristics of individual single-walled carbonnanotubes (SWNTs) under local-probe manipulation are reported and it is revealed that the conductance of an SWNT sample can be reduced by two orders of magnitude when deformed by an AFM tip.
Abstract: The effects of mechanical deformation on the electrical properties of carbonnanotubes are of interest given the practical potential of nanotubes in electromechanicaldevices, and they have been studied using both theoretical1,2,3,4and experimental5,6 approaches. One recent experiment6 used the tip of an atomic force microscope (AFM) to manipulate multi-wallednanotubes, revealing that changes in the sample resistance were small unlessthe nanotubes fractured or the metal–tube contacts were perturbed. Butit remains unclear how mechanical deformation affects the intrinsic electricalproperties of nanotubes. Here we report an experimental and theoretical elucidationof the electromechanical characteristics of individual single-walled carbonnanotubes (SWNTs) under local-probe manipulation. We use AFM tips to deflectsuspended SWNTs reversibly, without changing the contact resistance; insitu electrical measurements reveal that the conductance of an SWNT samplecan be reduced by two orders of magnitude when deformed by an AFM tip. Ourtight-binding simulations indicate that this effect is owing to the formationof local sp3 bonds caused by the mechanical pushingaction of the tip.

1,172 citations

Journal ArticleDOI
TL;DR: In this article, the Young's modulus of stacks of graphene sheets suspended over photolithographically defined trenches in silicon dioxide was measured using an atomic force microscope, with measured spring constants scaling as expected with the dimensions of the suspended section, ranging from 1to5N∕m.
Abstract: Using an atomic force microscope, we measured effective spring constants of stacks of graphene sheets (less than 5) suspended over photolithographically defined trenches in silicon dioxide. Measurements were made on layered graphene sheets of thicknesses between 2 and 8nm, with measured spring constants scaling as expected with the dimensions of the suspended section, ranging from 1to5N∕m. When our data are fitted to a model for doubly clamped beams under tension, we extract a Young’s modulus of 0.5TPa, compared to 1TPa for bulk graphite along the basal plane, and tensions on the order of 10−7N.

1,146 citations

Journal ArticleDOI
TL;DR: In this article, a tensile strength of 0.15 TPa was computed for individual carbon nanotubes in-situ in a transition electron microscope, based on the force required to break the tube.
Abstract: We have conducted pulling and bending tests on individual carbon nanotubes in-situ in a transition electron microscope. Based on our observation of the force required to break the tube, a tensile strength of 0.15 TPa was computed. From corresponding bending studies on such nanotubes, the Young's modulus was estimated to be 0.9 TPa (0.8 TPa after ‘sub continuum’ corrections). These results suggest a strength that is a large fraction of the elastic modulus, although previous measurements of their elastic stiffness have yielded higher modulus values, by as much as a factor of 2. The result does indicate that individual nanotubes can fail as essentially defect-free materials. Furthermore, we observed no obvious reduction in cross-sectional area prior to the failure. In addition, the bending experiments revealed a remarkable flexibility in these tubes. These unique properties support the potential of nanotubes as reinforcement fibers in structural materials.

1,069 citations