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60-451: Graphene is known for its exceptionally high tensile strength , electrical conductivity , transparency , and being the thinnest two-dimensional material in the world. Despite the nearly transparent nature of a single graphene sheet, graphite (formed from stacked layers of graphene) appears black because it absorbs all visible light wavelengths. On a microscopic scale, graphene is the strongest material ever measured. The existence of graphene

120-495: A ribosome is about 20 nm. The nanometre is also commonly used to specify the wavelength of electromagnetic radiation near the visible part of the spectrum : visible light ranges from around 400 to 700 nm. The ångström , which is equal to 0.1 nm, was formerly used for these purposes. Since the late 1980s, in usages such as the 32 nm and the 22 nm semiconductor node , it has also been used to describe typical feature sizes in successive generations of

180-512: A tensometer at a constant strain (change in gauge length divided by initial gauge length) rate until the sample breaks. When testing some metals, indentation hardness correlates linearly with tensile strength. This important relation permits economically important nondestructive testing of bulk metal deliveries with lightweight, even portable equipment, such as hand-held Rockwell hardness testers. This practical correlation helps quality assurance in metalworking industries to extend well beyond

240-403: A valley degeneracy of g v = 2 {\displaystyle g_{v}=2} . In contrast, for traditional semiconductors, the primary point of interest is generally Γ, where momentum is zero. If the in-plane direction is confined rather than infinite, its electronic structure changes. These confined structures are referred to as graphene nanoribbons . If the nanoribbon has

300-452: A "zig-zag" edge, the bandgap remains zero. If it has an "armchair" edge, the bandgap is non-zero. Graphene's honeycomb structure can be viewed as two interleaving triangular lattices. This perspective has been used to calculate the band structure for a single graphite layer using a tight-binding approximation. Electrons propagating through the graphene honeycomb lattice effectively lose their mass, producing quasi-particles described by

360-533: A 2D analogue of the Dirac equation rather than the Schrödinger equation for spin- ⁠ 1 / 2 ⁠ particles. The cleavage technique led directly to the first observation of the anomalous quantum Hall effect in graphene in 2005 by Geim's group and by Philip Kim and Yuanbo Zhang . This effect provided direct evidence of graphene's theoretically predicted Berry's phase of massless Dirac fermions and proof of

420-437: A conventional tight-binding model, the dispersion relation (restricted to first-nearest-neighbor interactions only) that produces the energy of the electrons with wave vector k is: with the nearest-neighbor (π orbitals) hopping energy γ 0 ≈ 2.8 eV and the lattice constant a ≈ 2.46 Å . The conduction and valence bands correspond to the different signs. With one p z electron per atom in this model,

480-563: A delocalized π-bond , which contributes to a valence band that extends over the whole sheet. This type of bonding is also seen in polycyclic aromatic hydrocarbons . The valence band is touched by a conduction band , making graphene a semimetal with unusual electronic properties that are best described by theories for massless relativistic particles. Charge carriers in graphene show linear, rather than quadratic, dependence of energy on momentum, and field-effect transistors with graphene can be made that show bipolar conduction. Charge transport

540-483: A factor of 10. The ribbons can function more like optical waveguides or quantum dots , allowing electrons to flow smoothly along the ribbon edges. In copper, resistance increases proportionally with length as electrons encounter impurities. Transport is dominated by two modes: one ballistic and temperature-independent, and the other thermally activated. Ballistic electrons resemble those in cylindrical carbon nanotubes. At room temperature, resistance increases abruptly at

600-443: A few graphene layers were published by G. Ruess and F. Vogt in 1948. Eventually, single layers were also observed directly. Single layers of graphite were also observed by transmission electron microscopy within bulk materials, particularly inside soot obtained by chemical exfoliation . From 1961 to 1962, Hanns-Peter Boehm published a study of extremely thin flakes of graphite. The study measured flakes as small as ~0.4 nm , which

660-415: A graphite flake adhered to a substrate, achieving a graphite thickness of 0.00001 inches (0.00025 millimetres ). The key to success was the ability to quickly and efficiently identify graphene flakes on the substrate using optical microscopy, which provided a small but visible contrast between the graphene and the substrate. Another U.S. patent was filed in the same year by Bor Z. Jang and Wen C. Huang for

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720-680: A linear stress–strain relationship , as shown in figure 1 up to point 3. The elastic behavior of materials often extends into a non-linear region, represented in figure 1 by point 2 (the "yield strength"), up to which deformations are completely recoverable upon removal of the load; that is, a specimen loaded elastically in tension will elongate, but will return to its original shape and size when unloaded. Beyond this elastic region, for ductile materials, such as steel, deformations are plastic . A plastically deformed specimen does not completely return to its original size and shape when unloaded. For many applications, plastic deformation

780-403: A material is an intensive property ; therefore its value does not depend on the size of the test specimen. However, depending on the material, it may be dependent on other factors, such as the preparation of the specimen, the presence or otherwise of surface defects, and the temperature of the test environment and material. Some materials break very sharply, without plastic deformation , in what

840-496: A metallic grid. Some of these images showed a "rippling" of the flat sheet, with an amplitude of about one nanometer. These ripples may be intrinsic to the material as a result of the instability of two-dimensional crystals, or may originate from the ubiquitous dirt seen in all TEM images of graphene. Photoresist residue, which must be removed to obtain atomic-resolution images, may be the " adsorbates " observed in TEM images, and may explain

900-561: A method to produce graphene-based on exfoliation followed by attrition. In 2014, inventor Larry Fullerton patented a process for producing single-layer graphene sheets. Graphene was properly isolated and characterized in 2004 by Andre Geim and Konstantin Novoselov at the University of Manchester . They pulled graphene layers from graphite with a common adhesive tape in a process called micro-mechanical cleavage, colloquially referred to as

960-625: A p z orbital that is oriented perpendicularly to the plane. These orbitals hybridize together to form two half-filled bands of free-moving electrons, π, and π∗, which are responsible for most of graphene's notable electronic properties. Recent quantitative estimates of aromatic stabilization and limiting size derived from the enthalpies of hydrogenation (ΔH hydro ) agree well with the literature reports. Graphene sheets stack to form graphite with an interplanar spacing of 0.335  nm (3.35  Å ). Graphene sheets in solid form usually show evidence in diffraction for graphite's (002) layering. This

1020-456: A single layer of graphite on top of silicon carbide. Others grew single layers of carbon atoms on other materials. This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of sp-bonded carbon atoms, as in free-standing graphene. However, there is significant charge transfer between the two materials and, in some cases, hybridization between the d-orbitals of the substrate atoms and π orbitals of graphene, which significantly alter

1080-518: A specific length—the ballistic mode at 16 micrometers and the thermally activated mode at 160 nanometers (1% of the former length). Graphene electrons can traverse micrometer distances without scattering, even at room temperature. Despite zero carrier density near the Dirac points, graphene exhibits a minimum conductivity on the order of 4 e 2 / h {\displaystyle 4e^{2}/h} . The origin of this minimum conductivity

1140-524: A vacuum. Coating the graphene surface with materials such as SiN, PMMA or h-BN has been proposed for protection. In January 2015, the first stable graphene device operation in the air over several weeks was reported for graphene whose surface was protected by aluminum oxide . In 2015, lithium -coated graphene exhibited superconductivity , a first for graphene. Electrical resistance in 40-nanometer-wide nanoribbons of epitaxial graphene changes in discrete steps. The ribbons' conductance exceeds predictions by

1200-544: Is 10 Ω⋅m , lower than the resistivity of silver , which is the lowest known at room temperature. However, on SiO 2 substrates, electron scattering by optical phonons of the substrate has a more significant effect than scattering by graphene's phonons, limiting mobility to 40 000  cm⋅V⋅s . Charge transport can be affected by the adsorption of contaminants such as water and oxygen molecules, leading to non-repetitive and large hysteresis I-V characteristics. Researchers need to conduct electrical measurements in

1260-451: Is ballistic over long distances; the material exhibits large quantum oscillations and large nonlinear diamagnetism . Three of the four outer- shell electrons of each atom in a graphene sheet occupy three sp hybrid orbitals – a combination of orbitals s, p x and p y — that are shared with the three nearest atoms, forming σ-bonds. The length of these bonds is about 0.142 nanometers. The remaining outer-shell electron occupies

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1320-452: Is a large-scale graphene powder production facility in East Anglia . Graphene is a single layer of carbon atoms tightly bound in a hexagonal honeycomb lattice. It is an allotrope of carbon in the form of a plane of sp-bonded atoms with a molecular bond length of 0.142  nm (1.42  Å ). In a graphene sheet, each atom is connected to its three nearest carbon neighbors by σ-bonds , and

1380-495: Is around 3 atomic layers of amorphous carbon. This was the best possible resolution for TEMs in the 1960s. However, it is impossible to distinguish between suspended monolayer and multilayer graphene by their TEM contrasts, and the only known method is to analyze the relative intensities of various diffraction spots. The first reliable TEM observations of monolayers are likely given in references 24 and 26 of Geim and Novoselov's 2007 review. In 1975, van Bommel et al. epitaxially grew

1440-408: Is because the engineering stress is calculated assuming the original cross-sectional area before necking. The reversal point is the maximum stress on the engineering stress–strain curve, and the engineering stress coordinate of this point is the ultimate tensile strength, given by point 1. Ultimate tensile strength is not used in the design of ductile static members because design practices dictate

1500-484: Is called a brittle failure. Others, which are more ductile, including most metals, experience some plastic deformation and possibly necking before fracture. Tensile strength is defined as a stress, which is measured as force per unit area. For some non-homogeneous materials (or for assembled components) it can be reported just as a force or as a force per unit width. In the International System of Units (SI),

1560-431: Is independent of temperature between 10 K and 100 K , showing minimal change even at room temperature (300 K), suggesting that the dominant scattering mechanism is defect scattering . Scattering by graphene's acoustic phonons intrinsically limits room temperature mobility in freestanding graphene to 200 000  cm⋅V⋅s at a carrier density of 10 cm . The corresponding resistivity of graphene sheets

1620-425: Is reversible on heating the graphene to remove the potassium. Due to graphene's two dimensions, charge fractionalization (where the apparent charge of individual pseudoparticles in low-dimensional systems is less than a single quantum) is thought to occur. It may therefore be a suitable material for constructing quantum computers using anyonic circuits. The quantum Hall effect is a quantum mechanical version of

1680-726: Is still unclear. However, rippling of the graphene sheet or ionized impurities in the SiO 2 substrate may lead to local puddles of carriers that allow conduction. Several theories suggest that the minimum conductivity should be 4 e 2 / ( π h ) {\displaystyle 4e^{2}/{(\pi }h)} ; however, most measurements are of the order of 4 e 2 / h {\displaystyle 4e^{2}/h} or greater and depend on impurity concentration. Near zero carrier density, graphene exhibits positive photoconductivity and negative photoconductivity at high carrier density, governed by

1740-504: Is the Landau level and the double valley and double spin degeneracies give the factor of 4. These anomalies are present not only at extremely low temperatures but also at room temperature, i.e. at roughly 20 °C (293 K). Ultimate tensile strength Ultimate tensile strength (also called UTS , tensile strength , TS , ultimate strength or F tu {\displaystyle F_{\text{tu}}} in notation)

1800-421: Is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials, the ultimate tensile strength is close to the yield point , whereas in ductile materials, the ultimate tensile strength can be higher. The ultimate tensile strength is usually found by performing a tensile test and recording the engineering stress versus strain . The highest point of

1860-597: Is the vector of the Pauli matrices , ψ ( r ) {\displaystyle \psi (\mathbf {r} )} is the two-component wave function of the electrons, and E is their energy. The equation describing the electrons' linear dispersion relation is: where the wavevector q is measured from the Brillouin zone vertex K, q = | k − K | {\displaystyle q=\left|\mathbf {k} -\mathrm {K} \right|} , and

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1920-476: Is true of some single-walled nanostructures. However, unlayered graphene displaying only (hk0) rings have been observed in the core of presolar graphite onions. TEM studies show faceting at defects in flat graphene sheets and suggest a role for two-dimensional crystallization from a melt. The hexagonal lattice structure of isolated, single-layer graphene can be directly seen with transmission electron microscopy (TEM) of sheets of graphene suspended between bars of

1980-459: Is unacceptable, and is used as the design limitation. After the yield point, ductile metals undergo a period of strain hardening, in which the stress increases again with increasing strain, and they begin to neck , as the cross-sectional area of the specimen decreases due to plastic flow. In a sufficiently ductile material, when necking becomes substantial, it causes a reversal of the engineering stress–strain curve (curve A, figure 2); this

2040-682: The Hall effect , which is the production of transverse (perpendicular to the main current) conductivity in the presence of a magnetic field . The quantization of the Hall effect σ x y {\displaystyle \sigma _{xy}} at integer multiples (the " Landau level ") of the basic quantity e / h (where e is the elementary electric charge and h is the Planck constant ). It can usually be observed only in very clean silicon or gallium arsenide solids at temperatures around 3  K and very high magnetic fields. Graphene shows

2100-472: The stress–strain curve is the ultimate tensile strength and has units of stress. The equivalent point for the case of compression, instead of tension, is called the compressive strength . Tensile strengths are rarely of any consequence in the design of ductile members, but they are important with brittle members. They are tabulated for common materials such as alloys , composite materials , ceramics , plastics, and wood. The ultimate tensile strength of

2160-471: The Dirac fermion nature of electrons. These effects were previously observed in bulk graphite by Yakov Kopelevich, Igor A. Luk'yanchuk, and others, in 2003–2004. When atoms are placed onto the graphene hexagonal lattice, the overlap between the p z (π) orbitals and the s or the p x and p y orbitals is zero by symmetry. Therefore, p z electrons forming the π bands in graphene can be treated independently. Within this π-band approximation, using

2220-477: The Scotch tape technique. The graphene flakes were then transferred onto a thin silicon dioxide layer on a silicon plate ("wafer"). The silica electrically isolated the graphene and weakly interacted with it, providing nearly charge-neutral graphene layers. The silicon beneath the SiO 2 could be used as a "back gate" electrode to vary the charge density in the graphene over a wide range. This work resulted in

2280-509: The description of polycyclic aromatic hydrocarbons in 2000 by S. Wang and others. Efforts to make thin films of graphite by mechanical exfoliation started in 1990. Initial attempts employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained. In 2002, Robert B. Rutherford and Richard L. Dudman filed for a patent in the US on a method to produce graphene by repeatedly peeling off layers from

2340-484: The early 2000s, several companies and research laboratories have been working to develop commercial applications of graphene. In 2014, a National Graphene Institute was established with that purpose at the University of Manchester, with a £60 million initial funding. In North East England two commercial manufacturers, Applied Graphene Materials and Thomas Swan Limited have begun manufacturing. Cambridge Nanosystems

2400-474: The electronic properties of 3D graphite. The emergent massless Dirac equation was separately pointed out in 1984 by Gordon Walter Semenoff , and by David P. Vincenzo and Eugene J. Mele. Semenoff emphasized the occurrence in a magnetic field of an electronic Landau level precisely at the Dirac point . This level is responsible for the anomalous integer quantum Hall effect . Transmission electron microscopy (TEM) images of thin graphite samples consisting of

2460-485: The electronic structure compared to that of free-standing graphene. Boehm et al. coined the term "graphene" for the hypothetical single-layer structure in 1986. The term was used again in 1987 to describe single sheets of graphite as a constituent of graphite intercalation compounds , which can be seen as crystalline salts of the intercalant and graphene. It was also used in the descriptions of carbon nanotubes by R. Saito and Mildred and Gene Dresselhaus in 1992, and in

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2520-478: The electrons and holes are called Dirac fermions . This pseudo-relativistic description is restricted to the chiral limit , i.e., to vanishing rest mass M 0 , leading to interesting additional features: Here v F ~ 10 m/s (.003 c) is the Fermi velocity in graphene, which replaces the velocity of light in the Dirac theory; σ → {\displaystyle {\vec {\sigma }}}

2580-449: The highly lamellar structure of thermally reduced graphite oxide . Pioneers in X-ray crystallography attempted to determine the structure of graphite. The lack of large single crystal graphite specimens contributed to the independent development of X-ray powder diffraction by Peter Debye and Paul Scherrer in 1915, and Albert Hull in 1916. However, neither of their proposed structures

2640-516: The interplay between photoinduced changes of both the Drude weight and the carrier scattering rate. Graphene doped with various gaseous species (both acceptors and donors) can be returned to an undoped state by gentle heating in a vacuum. Even for dopant concentrations in excess of 10 cm, carrier mobility exhibits no observable change. Graphene doped with potassium in ultra-high vacuum at low temperature can reduce mobility 20-fold. The mobility reduction

2700-680: The laboratory and universal testing machines . Nanometre The nanometre (international spelling as used by the International Bureau of Weights and Measures ; SI symbol: nm ), or nanometer ( American spelling ), is a unit of length in the International System of Units (SI), equal to one billionth ( short scale ) of a meter (0.000000001 m) and to 1000  picometres . One nanometre can be expressed in scientific notation as 1 × 10  m and as ⁠ 1 / 1 000 000 000 ⁠  m. The nanometre

2760-460: The most stable fullerene (as within graphite) only for molecules larger than 24,000 atoms. Graphene is a zero-gap semiconductor because its conduction and valence bands meet at the Dirac points . The Dirac points are six locations in momentum space on the edge of the Brillouin zone , divided into two non-equivalent sets of three points. These sets are labeled K and K'. These sets give graphene

2820-424: The observed rippling. The hexagonal structure is also seen in scanning tunneling microscope (STM) images of graphene supported on silicon dioxide substrates The rippling seen in these images is caused by the conformation of graphene to the substrates' lattice and is not intrinsic. Ab initio calculations show that a graphene sheet is thermodynamically unstable if its size is less than about 20 nm and becomes

2880-427: The parent unit name metre (from Greek μέτρον , [metrοn] Error: {{Lang}}: Non-latn text/Latn script subtag mismatch ( help ) , "unit of measurement"). Nanotechnologies are based on physical processes which occur on a scale of nanometres (see nanoscopic scale ). The nanometre is often used to express dimensions on an atomic scale: the diameter of a helium atom, for example, is about 0.06 nm, and that of

2940-470: The quantum Hall effect: the conductivity quantization is unusual in that the sequence of steps is shifted by 1/2 with respect to the standard sequence and with an additional factor of 4. Graphene's Hall conductivity is σ x y = ± 4 ⋅ ( N + 1 / 2 ) e 2 / h {\displaystyle \sigma _{xy}=\pm {4\cdot \left(N+1/2\right)e^{2}}/h} , where N

3000-434: The rest are equivalent by symmetry. Near the K -points, the energy depends linearly on the wave vector, similar to a relativistic particle. Since an elementary cell of the lattice has a basis of two atoms, the wave function has an effective 2-spinor structure . Consequently, at low energies even neglecting the true spin, electrons can be described by an equation formally equivalent to the massless Dirac equation . Hence,

3060-464: The term "graphite" for the three-dimensional material and reserving "graphene" for discussions about the properties or reactions of single-atom layers. A narrower definition, of "isolated or free-standing graphene", requires that the layer be sufficiently isolated from its environment, but would include layers suspended or transferred to silicon dioxide or silicon carbide . In 1859, Benjamin Brodie noted

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3120-530: The two winning the Nobel Prize in Physics in 2010 for their groundbreaking experiments with graphene. Their publication and the surprisingly easy preparation method that they described, sparked a "graphene gold rush". Research expanded and split off into many different subfields, exploring different exceptional properties of the material—quantum mechanical, electrical, chemical, mechanical, optical, magnetic, etc. Since

3180-563: The two-dimensional material graphene". While small amounts of graphene are easy to produce using the method by which it was originally isolated, attempts to scale and automate the manufacturing process for mass production have had limited success due to cost-effectiveness and quality control concerns. The global graphene market was $ 9 million in 2012, with most of the demand from research and development in semiconductors , electronics, electric batteries , and composites . The IUPAC (International Union of Pure and Applied Chemistry) advises using

3240-574: The unit is the pascal (Pa) (or a multiple thereof, often megapascals (MPa), using the SI prefix mega ); or, equivalently to pascals, newtons per square metre (N/m ). A United States customary unit is pounds per square inch (lb/in or psi). Kilopounds per square inch (ksi, or sometimes kpsi) is equal to 1000 psi, and is commonly used in the United States, when measuring tensile strengths. Many materials can display linear elastic behavior , defined by

3300-450: The use of the yield stress . It is, however, used for quality control, because of the ease of testing. It is also used to roughly determine material types for unknown samples. The ultimate tensile strength is a common engineering parameter to design members made of brittle material because such materials have no yield point . Typically, the testing involves taking a small sample with a fixed cross-sectional area, and then pulling it with

3360-439: The valence band is fully occupied, while the conduction band is vacant. The two bands touch at the zone corners (the K point in the Brillouin zone), where there is a zero density of states but no band gap. Thus, graphene exhibits a semi-metallic (or zero-gap semiconductor) character, although this is not true for a graphene sheet rolled into a carbon nanotube due to its curvature. Two of the six Dirac points are independent, while

3420-544: The zero of energy is set to coincide with the Dirac point. The equation uses a pseudospin matrix formula that describes two sublattices of the honeycomb lattice. Electron waves in graphene propagate within a single-atom layer, making them sensitive to the proximity of other materials such as high-κ dielectrics , superconductors , and ferromagnetic . Graphene exhibits high electron mobility at room temperature, with values reported in excess of 15 000  cm⋅V⋅s . Hole and electron mobilities are nearly identical. The mobility

3480-425: Was correct. In 1918, Volkmar Kohlschütter and P. Haenni described the properties of graphite oxide paper . The structure of graphite was successfully determined from single-crystal X-ray diffraction by J. D. Bernal in 1924, although subsequent research has made small modifications to the unit cell parameters. The theory of graphene was first explored by P. R. Wallace in 1947 as a starting point for understanding

3540-455: Was first theorized in 1947 by Philip R. Wallace during his research on graphite's electronic properties. In 2004, the material was isolated and characterized by Andre Geim and Konstantin Novoselov at the University of Manchester using a piece of graphite and adhesive tape . In 2010, Geim and Novoselov were awarded the Nobel Prize in Physics for their "groundbreaking experiments regarding

3600-463: Was formerly known as the " millimicrometre " – or, more commonly, the " millimicron " for short – since it is ⁠ 1 / 1000 ⁠ of a micrometer . It was often denoted by the symbol mμ or, more rarely, as μμ (however, μμ should refer to a millionth of a micron). The name combines the SI prefix nano- (from the Ancient Greek νάνος , nanos , "dwarf") with

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