Bewise Inc. www.tool-tool.com Reference
source from the internet.Graphene is a
one-atom-thick planar sheet of
sp2-bonded carbon atoms that are
densely packed in a honeycomb crystal lattice. It can be visualized as
an
atomic-scale
chicken wire made of carbon atoms and their bonds. The name comes
from
graphite +
-ene; graphite itself
consists of many graphene sheets stacked together.
The
carbon-carbon bond length in graphene is about 0.142
nm. Graphene is the
basic structural element of some carbon
allotropes including
graphite,
carbon nanotubesand
fullerenes.
It can also be considered as an infinitely large
aromatic molecule,
the limiting case of the family of flat
polycyclic
aromatic hydrocarbons called graphenes.
Image of graphene in a
transmission
electron microscope.
Description
A simple,
non-technical definition has been given in a recent review on graphene:
Graphene
is a flat monolayer of carbon atoms tightly packed into a
two-dimensional (2D) honeycomb lattice, and is a basic building block
for graphitic materials of all other dimensionalities. It can be wrapped
up into 0D fullerenes, rolled into 1D nanotubes or stacked into 3D
graphite.
[1]Previously, graphene was also defined in the chemical literature
as follows:
A single carbon layer of the graphitic structure can
be considered as the final member of the series naphthalene,
anthracene, coronene, etc. and the term graphene should therefore be
used to designate the individual carbon layers in graphite intercalation
compounds. Use of the term "graphene layer" is also considered for the
general terminology of carbons.
[2] The
IUPAC compendium of
technology states: "previously, descriptions such as
graphite layers, carbon
layers, or carbon sheets have been used for the term graphene...it is
not correct to use for a single layer a term which includes the term
graphite, which would imply a three-dimensional structure. The term
graphene should be used only when the reactions, structural relations or
other properties of individual layers are discussed." In this regard,
graphene has been referred to as an infinite alternant (only six-member
carbon ring)
polycyclic
aromatic hydrocarbon (PAH). The largest molecule of this type
consists of 222 atoms and is 10 benzene rings across.
[3] It has proven difficult to synthesize even slightly bigger molecules,
and they still remain "a dream of many organic and polymer chemists".
[4]Furthermore,
ab initio calculations show that a graphene sheet
is thermodynamically unstable with respect to other
fullerene structures
if its size is less than about 10 nm (“graphene is the least stable
structure until about 6000 atoms”
[5]).
[improper
synthesis?] Also, a definition of "isolated or
free standing graphene" has recently been proposed: "graphene is a
single atomic plane of graphite, which—and this is essential—is
sufficiently isolated from its environment to be considered
free-standing."
[6]This definition is narrower than the definitions given above and refers
to cleaved, transferred and suspended graphene monolayers. Other forms
of graphene, such as graphene grown on various metals, can also become
free-standing if transferred to, e.g., SiO
2 or suspended. A
new example of isolated graphene is graphene on SiC after its
passivation with hydrogen.
[7]Occurrence and production
Graphene is essentially an
isolated atomic plane of graphite. Therefore, from this perspective,
graphene has been known since the invention of X-ray crystallography.
Graphene planes become even better separated in intercalated graphite
compounds. In 2004 physicists from
University
of Manchester and Institute for Microelectronics Technology,
Chernogolovka,
Russia, found a way to isolate individual graphene planes by using
Scotch tape and they also measured electronic properties of the obtained
flakes and showed their fantastic quality.
[8]In 2005 the same Manchester group together with researchers from the
Columbia University (see the History chapter below) demonstrated that
quasiparticles in graphene were massless
Dirac fermions.
These discoveries led to the explosion of interest in graphene.
Since
then, hundreds of researchers have entered the area and, naturally,
they carried out the extensive search for relevant earlier papers. The
first literature review was given by the Manchester pioneers themselves
[1].
They cite several papers in which graphene or ultra-thin graphitic
layers were
epitaxiallygrown on various substrates. Also, they point out at a number of
pre-2004 reports in which intercalated graphite compounds were studied
in a transmission electron microscope. In the latter case, researchers
occasionally observed extremely thin graphitic flakes ("few-layer
graphene" and possibly even individual layers). The oldest such
observation was recently discovered by Rodney Ruoff in a 1962
German-language magazine
[9].
It is now well known that tiny fragments of graphene sheets are
produced (along with quantities of other debris) whenever graphite is
abraded, such as when drawing a line with a pencil.
[10]There was little interest in this graphitic residue before 2004/05 and,
therefore, the discovery of graphene is often attributed to
Andre Geim and
colleagues
[11]who introduced graphene in its modern incarnation, although it may be
argued that this is as accurate as attributing the discovery of America
to Columbus.
A couple of years ago, graphene produced by
exfoliation was one of the most expensive materials on Earth, with a
sample that can be placed at the cross section of a human hair costing
more than $1,000 as of April 2008 (about $100,000,000/cm
2).
[10]Since then, exfoliation procedures were scaled up, and now companies
sell graphene by ton.
[12]On the other hand, the price of epitaxial graphene on
silicon carbide is dominated by the substrate price, which is approximately $100/cm
2as of 2009. Even cheaper graphene has been produced by transfer from
nickel by Korean researchers,
[13]with wafer sizes up to 30" reported.
[citation
needed] In the literature, specifically that of
surface science community, graphene has also been commonly referred to
as monolayer graphite. This community has intensely studied epitaxial
graphene on various surfaces (over 300 articles prior to 2004). In some
cases, these graphene layers are coupled to the surfaces weakly enough
(by
Van der
Waals forces) to retain the two dimensional
electronic
band structure of isolated graphene,
[14][15]as also happens
[8]with exfoliated graphene flakes with regard to silicon dioxide. An
example of weakly coupled epitaxial graphene is the one grown on
silicon carbide (see below).
Drawing method
In 2004, the British
researchers obtained graphene by mechanical
exfoliationof graphite. They used Scotch tape to repeatedly split graphite
crystals into increasingly thinner pieces. The tape with attached
optically transparent flakes was dissolved in acetone and, after a few
further steps, the flakes including monolayers were sedimented on a Si
wafer. Individual atomic planes were then hunted in an optical
microscope. A year later, the researchers simplified the technique and
started using dry deposition, avoiding the stage when graphene floated
in a liquid. Relatively large crystallites (first, only a few microns in
size but, eventually, larger than 1 mm and visible by a naked eye) were
obtained by the technique. It is often referred to as a scotch tape or
drawing method. The latter name appeared because the dry deposition
resembles drawing with a piece of graphite.
[16]The key for the success probably was the use of high throughput visual
recognition of graphene on a proper chosen substrate, which provides a
small but noticeable optical contrast. For an example of what graphene
looks like, see its photograph below.
The isolation of graphene
led to the current research boom. Previously, free-standing atomic
planes were often "presumed not to exist"
[8]because they are thermodynamically unstable on a nm scale
[5]and, if unsupported, have a tendency to scroll and buckle
[4].
It is currently believed that intrinsic microscopic roughening on the
scale of 1 nm could be important for the stability of purely 2D
crystals.
[17].
It is interesting to note (see
Talk:Graphene)
that there were a number of previous attempts to make atomically thin
graphitic films by using exfoliation techniques similar to the drawing
method. Multilayer samples down to 10 nm in thickness were obtained.
These efforts were reviewed in
[1].
Furthermore, a couple of very old papers was recently unearthed,
[9]in which researchers tried to isolate graphene, starting with
intercalated compounds (see
History and experimental discovery).
These papers reported the observation of very thin graphitic fragments
(possibly, monolayers) by transmission electron microscopy. Neither of
the earlier observations was sufficient to "spark the graphene gold
rush", until the Science paper did so by reporting not only macroscopic
samples of extracted atomic planes but, importantly, their unusual
properties such as the bipolar transistor effect, ballistic transport of
charges, large quantum oscillations, etc. The discovery of such
interesting qualities intrinsic to graphene gave an immediate boost to
further research, and several groups quickly repeated the initial result
and moved further. These breakthroughs also helped to attract attention
to other production techniques such as epitaxial growth of ultra-thin
graphitic films. In particular, it has later been found that graphene
monolayers grown on SiC and Ir are weakly coupled to these substrates
(how weakly remains debated) and the graphene-substrate interaction can
be passivated further.
Not only graphene but also free-standing
atomic planes of boron nitride, mica, dichalcogenides and complex oxides
were obtained by using the drawing method Unlike graphene, the other 2D
materials have so far attracted surprisingly little attention.
Epitaxial growthon silicon carbide
Yet another method is to heat
silicon carbide to high temperatures (>1100 °C) to reduce it to graphene.
[19]This process produces a sample size that is dependent upon the size of
the SiC substrate used. The face of the silicon carbide used for
graphene creation, the silicon-terminated or carbon-terminated, highly
influences the thickness, mobility and carrier density of the graphene.
Many
important graphene properties have been identified in graphene produced
by this method. For example, the electronic band-structure (so-called
Dirac cone structure) has been first visualized in this material. Weak
anti-localization is observed in this material and not in exfoliated
graphene produced by the pencil trace method. Extremely large,
temperature independent mobilities have been observed in SiC epitaxial
graphene. They approach those in exfoliated graphene placed on silicon
oxide but still much lower than mobilities in suspended graphene
produced by the drawing method. It was recently shown that even without
being transferred graphene on SiC exhibits the properties of massless
Dirac fermions such as the anomalous quantum Hall effect
[24][25][26][27][28].
The weak van der Waals forces that provide the cohesion of
multilayer graphene stacks do not always affect the electronic
properties of the individual graphene layers in the stack. That is,
while the electronic properties of certain multilayered epitaxial
graphenes are identical to that of a single graphene layer,
[29]in other cases the properties are affected
[20][21]as they are for graphene layers in bulk graphite. This effect is
theoretically well understood and is related to the symmetry of the
interlayer interactions.
[29]Epitaxial graphene on silicon carbide can be patterned using
standard microelectronics methods. The possibility of large integrated
electronics on SiC epitaxial graphene was first proposed in 2004
[30]by researchers at the
Georgia
Institute of Technology, only a couple of months after the
discovery of isolated graphene made the drawing method. (A patent for
graphene based electronics was applied for in 2003 and issued in 2006).
Since then, important advances have been made. In 2008, researchers at
MIT Lincoln Labhave produced hundreds of transistors on a single chip and in 2009,
very high frequency transistors have been produced at the Hughes
Research Laboratories on monolayer graphene on silicon carbide.
Epitaxial
growth on metal substrates
This method uses the atomic
structure of a metal substrate to seed the growth of the graphene
(epitaxial growth). Graphene grown on
ruthenium doesn't
typically yield a sample with a uniform thickness of graphene layers,
and bonding between the bottom graphene layer and the substrate may
affect the properties of the carbon layers. Graphene grown on
iridium on the other
hand is very weakly bonded, uniform in thickness, and can be made highly
ordered. Like on many other substrates, graphene on iridium is slightly
rippled. Due to the long-range order of these ripples generation of
minigaps in the electronic band-structure (Dirac cone) becomes visible.
[34]High-quality sheets of few layer graphene exceeding 1 cm
2 (0.2 sq in) in area have been synthesized via chemical vapor deposition
on thin
nickel films.
These sheets have been successfully transferred to various substrates,
demonstrating viability for numerous electronic applications. An
improvement of this technique has been found in
copper foil where the
growth automatically stops after a
single graphene layer, and
arbitrarily large graphene films can be created.
[35]Hydrazine reduction
Researchers have developed a method
of placing
graphene
oxide paper in a solution of pure
hydrazine (a chemical
compound of nitrogen and hydrogen), which reduces the graphene oxide
paper into single-layer graphene.
[36]Sodium reduction of ethanol
A recent publication has
described a process for producing gram-quantities of graphene, by the
reduction of ethanol by sodium metal, followed by
pyrolysis of the
ethoxide product, and washing with water to remove sodium salts.
[37]From nanotubes
Experimental methods for the production
of graphene ribbons are reported consisting of cutting open
nanotubes.
[38]In one such method
multi
walled carbon nanotubes are cut open in solution by action of
potassium
permanganate and
sulfuric acid.
[39]In another method graphene nanoribbons are produced by
plasma etching of
nanotubes partly embedded in a
polymer film
[40]Atomic structure
The atomic structure of isolated,
single-layer graphene was studied by
transmission
electron microscopy (TEM) on sheets of graphene suspended between
bars of a metallic grid.
[17]Electron diffraction patterns showed the expected hexagonal lattice of
graphene. Suspended graphene also showed "rippling" of the flat sheet,
with amplitude of about one nanometer. These ripples may be intrinsic to
graphene as a result of the instability of two-dimensional crystals,
[1][41][42]or may be extrinsic, originating from the ubiquitous dirt seen in all
TEM images of graphene. Atomic resolution real-space images of isolated,
single-layer graphene on silicon dioxide substrates were obtained
[43][44]by
scanning
tunneling microscopy. Graphene processed using lithographic
techniques is covered by
photoresist residue,
which must be cleaned to obtain atomic-resolution images.
[43]Such residue may be the "
adsorbates" observed
in TEM images, and may explain the rippling of suspended graphene.
Rippling of graphene on the silicon dioxide surface was determined by
conformation of graphene to the underlying silicon dioxide, and not an
intrinsic effect.
[43]Graphene sheets in solid form (density > 1 g/cm
3)
usually show evidence in diffraction for
graphite's 0.34 nm
(002) layering. This is true even of some single-walled carbon
nanostructures.
[45]However, unlayered graphene with only (hk0) rings has been found in the
core of
presolargraphite onions.
[46]Transmission
electron microscope studies show faceting at defects in flat
graphene sheets,
[47]and suggest a possible role in this unlayered-graphene for
two-dimensional
dendriticcrystallization from a melt.
Electronic properties
GNR band structure for
zig-zag type. Tightbinding calculations show that zigzag type is always
metallic.
GNR band structure for arm-chair
type. Tightbinding calculations show that armchair type can be
semiconducting or metallic depending on width (chirality).
Graphene
is quite different from most conventional three-dimensional materials.
Intrinsic graphene is a
semi-metal or
zero-gap
semiconductor.
Understanding the electronic structure of graphene is the starting
point for finding the band structure of graphite. It was realized early
on that the E-k relation is linear for low energies near the six corners
of the two-dimensional hexagonal
Brillouin zone,
leading to zero
effective
mass for electrons and holes.
[48][49]Due to this linear (or “
conical")
dispersion relation at low energies, electrons and holes near these six
points, two of which are inequivalent, behave like
relativisticparticles described by the
Dirac equation for spin 1/2 particles.
[50][51]Hence, the electrons and holes are called Dirac
fermions, and the six
corners of the Brillouin zone are called the Dirac points.
[50]The equation describing the E-k relation is
; where the
Fermi velocity vF~ 10
6 m/s.
[51]Electronic transport
Experimental results from
transport measurements show that graphene has a remarkably high
electron mobilityat room temperature, with reported values in excess of 15,000 cm
2V
−1s
−1.
[1]Additionally, the symmetry of the experimentally measured conductance
indicates that the mobilities for holes and electrons should be nearly
the same.
[49]The mobility is nearly independent of temperature between 10 K and 100
K,
[52][53][54]which implies that the dominant scattering mechanism is defect
scattering. Scattering by the acoustic
phonons of graphene
places intrinsic limits on the room temperature mobility to 200,000 cm
2V
−1s
−1at a carrier density of 10
12 cm
−2.
[54][55]The corresponding
resistivityof the graphene sheet would be 10
−6 Ω·cm, less than the
resistivity of
silver,
the lowest resistivity substance known at room temperature.
[56]However, for graphene on silicon dioxide substrates, scattering of
electrons by optical phonons of the substrate is a larger effect at room
temperature than scattering by graphene’s own phonons, and limits the
mobility to 40,000 cm
2 V
−1s
−1.
[54]Despite the zero carrier density near the Dirac points, graphene
exhibits a minimum
conductivityon the order of 4e
2/h. The origin of this minimum
conductivity 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.
[49]Several theories suggest that the minimum conductivity should be 4e
2/πh;
however, most measurements are of order 4e
2/h or greater
[1]and depend on impurity concentration.
[57]Recent experiments have probed the influence of chemical dopants
on the carrier mobility in graphene.
[57][58]Schedin
et al. doped graphene with various gaseous species (some
acceptors, some donors), and found the initial undoped state of a
graphene structure can be recovered by gently heating the graphene in
vacuum. They reported that even for chemical dopant concentrations in
excess of 10
12 cm
−2 there is no observable change
in the carrier mobility.
[58]Chen, et al. doped graphene with
potassium in
ultra high vacuumat low temperature. They found that potassium ions act as expected for
charged impurities in graphene,
[59]and can reduce the mobility 20-fold.
[57]The mobility reduction is reversible on heating the graphene to remove
the potassium.
Due to its two-
dimensional property,
charge fractionalization (where the apparent charge of individual
psuedoparticles in low-dimensional systems is less than a single quantum
[60])
is thought to occur in graphene. It may therefore be a suitable
material for the construction of
quantum computersusing
anyonic circuits.
[61][62]Optical properties
Photograph of graphene
in transmitted light. This one atom thick crystal can be seen with the
naked eye because it absorbs approximately 2.3% of white light, which is
π times
fine-structure
constant.
Graphene's unique electronic properties produce an
unexpectedly high opacity for an atomic monolayer, with a startlingly
simple value: it absorbs
πα ≈ 2.3% of white
light, where
α is
the
fine-structure
constant.
[63]This is "a consequence of the unusual low-energy electronic structure
of monolayer graphene that features electron and hole
conical bandsmeeting each other at the
Dirac
point ... [which] is qualitatively different from more common
quadratic
massive bands".
[64]Based on the Slonczewski-Weiss-McClure (SWMcC) band model of graphite,
the interatomic distance, hopping value and frequency cancel when the
optical conductance is calculated using the
Fresnel equationsin the thin-film limit.
This has been confirmed experimentally,
but the measurement is not precise enough to improve on other techniques
for determining the fine-structure constant.
[65]Recently it has been demonstrated that the
bandgap of graphene can
be tuned from 0 to 0.25 eV (about 5 micron wavelength) by applying
voltage to a dual-gate bilayer graphene
field-effect
transistor (FET) at room temperature.
[66].
The optical response of
graphene
nanoribbons has also been shown to be tunable into the
terahertz regime by an
applied magnetic field
[67]Saturable absorption
It is further confirmed that such
unique absorption could become saturated when the input optical
intensity is above a threshold value. This nonlinear optical behavior is
termed
saturable
absorption and the threshold value is called the saturation
fluency. Graphene can be saturated readily under strong excitation over
the visible to near-infrared region, due to the universal optical
absorption and zero band gap. This has relevance for the mode locking of
fiber lasers, where fullband mode locking has been achieved by graphene
based saturable absorber. Due to this special property, graphene has
wide application in ultrafast photonics.
[68][69]Spin transport
Graphene is thought to be an ideal
material for
spintronicsdue to small
spin-orbit
interaction and near absence of nuclear magnetic moments in carbon.
Electrical spin-current injection and detection in graphene was recently
demonstrated up to room temperature.
[70][71][72]Spin coherence length above 1 micron at room temperature was observed,
[70]and control of the spin current polarity with an electrical gate was
observed at low temperature.
[71]Anomalous quantum Hall effect
The
quantum Hall
effect is relevant for accurate measuring standards of electrical
quantities, and in 1985
Klaus von
Klitzing received the
Nobel prize for its
discovery. The effect concerns the dependence of a transverse
conductivity on a magnetic field, which is perpendicular to a
current-carrying stripe. Usually the phenomenon, the quantization of the
so-called
Hall
conductivity σ
xy at integer multiples of the basic
quantity
e2/h (where
e is the elementary
electric charge and
h is
Planck's
constant) can be observed only in very clean Si or GaAs solids, and
at very low temperatures around 3
K, and at very
high magnetic fields.
Graphene in contrast, besides its high
mobility and minimum conductivity, and because of certain
pseudo-relativistic peculiarities to be mentioned below, shows
particularly interesting behavior just in the presence of a magnetic
field and just with respect to the conductivity-quantization: it
displays an
anomalous quantum Hall effect with the sequence of
steps
shifted by 1/2 with respect to the standard sequence, and
with an additional factor of 4. Thus, in graphene the Hall conductivity
is
, where
n is the
above-mentioned integer "Landau level" index, and the double valley and
double spin degeneracies give the factor of 4.
[1]Moreover, in graphene these remarkable anomalies can even be measured
at room temperature, i.e. at roughly 20 °C.
[52]This anomalous behavior is a direct result of the emergent massless
Dirac electrons in graphene. In a magnetic field, their spectrum has a
Landau level with energy precisely at the Dirac point. This level is a
consequence of the
Atiyah-Singer
index theorem. and is half-filled in neutral graphene,
[50]leading to the "+1/2" in the Hall conductivity.
[73]Bilayer graphene also shows the quantum Hall effect, but with the
standard
sequence, i.e. with
i.e. with only one of the two
anomalies. Interestingly, concerning the second anomaly, the first
plateau at
N = 0 is absent, indicating that bilayer graphene
stays metallic at the neutrality point.
[1]Unlike normal metals, the longitudinal resistance of graphene
shows maxima rather than minima for integral values of the Landau
filling factor in measurements of the
Shubnikov-de
Haas oscillations, which show a phase shift of π, known as
Berry’s phase.
[49][52]The Berry’s phase arises due to the zero effective carrier mass near
the Dirac points.
[74]Study of the temperature dependence of the Shubnikov-de Haas
oscillations in graphene reveals that the carriers have a non-zero
cyclotron mass, despite their zero effective mass from the E-k relation.
[52]Nanostripes: Spin-polarized edge currents
Nanostripes
of graphene (in the "zig-zag" orientation), at low temperatures, show
spin-polarized metallic edge currents, which also suggests applications
in the new field of
spintronics.
(In the "armchair" orientation, the edges behave like semiconductors.
[75])
Graphene oxide
Further information:
Graphite
Oxide By disbursing oxidized and chemically processed
graphite in water, and using paper-making techniques, the monolayer
flakes form a single sheet and bond very powerfully. These sheets,
called
graphene
oxide paper have a measured
tensile modulus of 32
GPa.
[76]The peculiar chemical property of graphite oxide is related to the
functional groups attached to graphene sheets. They even can
significantly change the pathway of polymerization and similar chemical
processes.
[77]Chemical modification
Soluble fragments of graphene can
be prepared in the laboratory
[78]through chemical modification of graphite. First, microcrystalline
graphite is treated with a strongly acidic mixture of
sulfuric acid and
nitric acid. A
series of steps involving oxidation and exfoliation result in small
graphene plates with
carboxylgroups at their edges. These are converted to
acid chloride groups by treatment with
thionyl chloride;
next, they are converted to the corresponding graphene
amide via treatment with
octadecylamine. The resulting material (circular graphene layers of 5.3
angstrom thickness) is
soluble in
tetrahydrofuran,
tetrachloromethane,
and
dichloroethane.
Full
hydrogenationfrom both sides of graphene sheet results in
graphane, but partial
hydrogenation leads to hydrogenated graphene
[79]Thermal properties
The near-room temperature
thermal
conductivity of graphene was recently measured to be between
(4.84±0.44) ×10
3 to (5.30±0.48) ×10
3 Wm
−1K
−1.
These measurements, made by a non-contact optical technique, are in
excess of those measured for carbon nanotubes or diamond. It can be
shown by using the
Wiedemann-Franz
law, that the thermal conduction is
phonon-dominated.
[80]However, for a gated graphene strip, an applied gate bias causing a
Fermi energy shift
much larger than k
BT can cause the electronic contribution to
increase and dominate over the
phonon contribution at
low temperatures. The ballistic thermal conductance of graphene is
isotropic.
[81]Potential for this high conductivity can be seen by considering
graphite, a 3D version
of graphene that has basal plane thermal conductivity of over a 1000
W/mK (comparable to
diamond).
In graphite, the c-axis (out of plane) thermal conductivity is over a
factor of ~100 smaller due to the weak binding forces between basal
planes as well as the larger
lattice spacing.
[82]In addition, the ballistic thermal conductance of a graphene is shown
to give the lower limit of the ballistic thermal conductances, per unit
circumference, length of
carbon nanotubes.
[83]Despite its 2-D nature, graphene has 3
acoustic phonon modes. The two in-plane modes (LA, TA) have a linear
dispersion
relation, whereas the out of plane mode (ZA) has a quadratic
dispersion relation. Due to this, the T
2 dependent thermal
conductivity contribution of the linear modes is dominated at low
temperatures by the T
1.5 contribution of the out of plane
mode.
[83]Some graphene phonon bands display negative
Grüneisen
parameters.
[84]At low temperatures (where most optical modes with positive Grüneisen
parameters are still not excited) the contribution from the negative
Grüneisen parameters will be dominant and
thermal
expansion coefficient (which is directly proportional to Grüneisen
parameters) negative. The lowest negative Grüneisen parameters
correspond to the lowest transversal acoustic ZA modes. Phonon
frequencies for such modes increase with the in-plane
lattice parametersince atoms in the layer upon stretching will be less free to move in
the z direction. This is similar to the behavior of a string which is
being stretched will have vibrations of smaller amplitude and higher
frequency. This phenomenon, named "membrane effect", was predicted by
Lifshitzin 1952.
[85]Mechanical properties
As of 2009, graphene appears to
be one of the strongest materials ever tested. Measurements have shown
that graphene has a breaking strength 200 times greater than
steel.
[86]However, the process of separating it from
graphite, where it
occurs naturally, will require some technological development before it
is economical enough to be used in industrial processes,
[87]though this may be changing soon.
[88]Using an
atomic force
microscope (AFM), the
spring constant of suspended graphene sheets has been measured. Graphene sheets, held
together by
van
der Waals forces, were suspended over
silicon dioxide cavities where an AFM tip was probed to test its mechanical properties.
Its spring constant was in the range 1-5 N/m and the
Young's moduluswas 0.5 TPa, which differs from that of the bulk graphite. These high
values make graphene very strong and rigid. These intrinsic properties
could lead to using graphene for
NEMSapplications such as pressure sensors and resonators.
[89]As is true of all materials, regions of graphene are subject to
thermal and quantum fluctuations in relative displacement. Although the
amplitude of these fluctuations is bounded in 3D structures (even in the
limit of infinite size), the
Mermin-Wagner
theorem shows that the amplitude of long-wavelength fluctuations
will grow logarithmically with the scale of a 2D structure, and would
therefore be unbounded in structures of infinite size. Local deformation
and elastic strain are negligibly affected by this long-range
divergence in relative displacement. It is believed that a sufficiently
large 2D structure, in the absence of applied lateral tension, will bend
and crumple to form a fluctuating 3D structure. Researchers have
observed ripples in suspended layers of graphene,
[17]and it has been proposed that the ripples are caused by thermal
fluctuations in the material. As a consequence of these dynamical
deformations, it is debatable whether graphene is truly a 2D structure.
[1][41][42]Single molecule gas detection
Graphene makes an
excellent sensor due to its 2D structure. The fact that its entire
volume is exposed to its surrounding makes it very efficient to detect
adsorbed molecules.
Molecule detection is indirect: as a gas molecule adsorbs to the surface
of graphene, the location of adsorption experiences a local change in
electrical
resistance. While this effect occurs in other materials, graphene is
superior due to its high electrical conductivity (even when few
carriers are present) and low noise which makes this change in
resistance detectable.
[58]Graphene nanoribbons
Graphene
nanoribbons (GNRs) are essentially single layers of graphene that
are cut in a particular pattern to give it certain electrical
properties. Depending on how the un-bonded edges are configured, they
can either be in a zigzag or armchair configuration. Calculations based
on tight binding predict that zigzag GNRs are always metallic while
armchairs can be either metallic or semiconducting, depending on their
width. However, recent
density
functional theory calculations show that armchair nanoribbons are
semiconducting with an energy gap scaling with the inverse of the GNR
width.
[90]Indeed, experimental results show that the energy gaps do increase with
decreasing GNR width.
[91]However, as of February 2008, no experimental results have measured the
energy gap of a GNR and identified the exact edge structure. Zigzag
nanoribbons are also semiconducting and present spin polarized edges.
Their 2D structure, high electrical and thermal conductivity, and low
noise also make GNRs a possible alternative to copper for integrated
circuit interconnects. Some research is also being done to create
quantum dots by changing the width of GNRs at select points along the
ribbon, creating
quantum
confinement.
[92]willy@tool-tool.com
bw@tool-tool.com www.tool-tool.com
skype:willy_chen_bw mobile:0937-618-190 Head &Administration Office
No.13,Shiang Shang 2nd St., West Chiu Taichung,Taiwan 40356 http://www.tool-tool.com /
FAX:+886 4 2471 4839 N.Branch 5F,No.460,Fu Shin North Rd.,Taipei,Taiwan
S.Branch No.24,Sec.1,Chia Pu East Rd.,Taipao City,Chiayi Hsien,TaiwanWelcome to BW
tool world! We are an experienced tool maker specialized in cutting
tools. We focus on what you need and endeavor to research the best
cutter to satisfy users’ demand. Our customers involve
wide range of industries, like mold & die, aerospace, electronic,
machinery, etc. We are professional expert in cutting field. We would
like to solve every problem from you. Please feel free to contact us,
its our pleasure to serve for you. BW product including: cutting tool、aerospace tool .HSS DIN Cutting tool、Carbide end mills、Carbide cutting tool、NAS Cutting tool、NAS986 NAS965 NAS897 NAS937orNAS907 Cutting Tools,Carbide end mill、disc milling cutter,Aerospace
cutting tool、hss
drill’Фрезеры’Carbide drill、High speed steel、Compound Sharpener’Milling cutter、INDUCTORS FOR PCD’
CVDD(Chemical Vapor Deposition
Diamond )’PCBN
(Polycrystalline Cubic Boron Nitride) ’Core drill、Tapered end
mills、CVD Diamond
Tools Inserts’PCD
Edge-Beveling Cutter(Golden Finger’PCD V-Cutter’PCD Wood tools’PCD Cutting tools’PCD Circular Saw Blade’PVDD End Mills’diamond tool. INDUCTORS FOR PCD .POWDER FORMING MACHINE
‘Single Crystal
Diamond ‘Metric
end mills、Miniature
end mills、Специальные
режущие инструменты ‘Пустотелое сверло
‘Pilot reamer、Fraises’Fresas con mango’
PCD (Polycrystalline
diamond) ‘Frese’POWDER
FORMING MACHINE’Electronics cutter、Step drill、Metal cutting saw、Double margin drill、Gun barrel、Angle milling cutter、Carbide burrs、Carbide tipped cutter、Chamfering tool、IC card engraving cutter、Side cutter、Staple Cutter’PCD diamond cutter specialized in
grooving floors’V-Cut
PCD Circular Diamond Tipped Saw Blade with Indexable Insert’PCD Diamond Tool’Saw Blade with Indexable Insert’NAS tool、DIN or JIS tool、Special tool、Metal slitting saws、Shell end mills、Side and face milling cutters、Side chip clearance saws、Long end mills’
end mill grinder’drill grinder’sharpener、Stub roughing end mills、Dovetail milling cutters、Carbide slot drills、Carbide torus cutters、Angel carbide end mills、Carbide torus cutters、Carbide ball-nosed slot drills、Mould
cutter、Tool manufacturer. Bewise Inc. www.tool-tool.com
Bewise Inc. 
Bewise Inc. 
Bewise Inc. 
![clip_image006[1]](https://h59kma.bay.livefilestore.com/y1mYgBD9Zw4Stlb6nwoxupNZC7u8N-pzFSF7es1d1X2-xPhk-UI93cfKOSL1GPbuiMdN2OoEd06w8u0TocL9gdHTrVpm3JXjqiISW9FUMD-loRz3KFA2ICnL0PCJozULbZOPk_LwuoYw2ibGpR3kGoLYQ/clip_image006%5B1%5D%5B2%5D%203B8516BF.gif?download&psid=1 "clip_image006[1]"){kind=small}
![clip_image006[2]](https://h59kma.bay.livefilestore.com/y1mx6l2aKNhM84ztYTBU4y6D1eW_I2c0rWd2IvwtkeEy11j9CJikwhANmKsRCJ8mDQrePhdxupXRXYBM8ItFjqAaJVouxaW3I26lUhh-T-EJ-SsZvOdMV4Q2Ky0SoU0ZQtxDjm4aqsr56cQ4YeoQwfOQg/clip_image006%5B2%5D%5B2%5D%207FAFC0F1.gif?download&psid=1 "clip_image006[2]"){kind=small}
![clip_image004[1]](https://h59kma.bay.livefilestore.com/y1mYLTytVuvJwwPynVGf-2IrA82ZwDH5e_iudBNxxOjv8J3NcWK0S9nXNg91XtSLpPxQR40ZmSrekoYwwpdkceqG8KVDdtm6RjI94wdu-iCD9Tfdt7fytkgJMN3Q68oVUKbhqfGnLRVEJb3esahStGOWA/clip_image004%5B1%5D%5B2%5D%20678CC3DF.gif?download&psid=1 "clip_image004[1]"){kind=small}
![clip_image017[1]](https://h59kma.bay.livefilestore.com/y1mD-a0lYJvfEgD4rKJ2QaOk8g0L0FPNQhZ8LlMLIlz8dyLIe-_3kJlO0X_6o7r4hR5tTUu_g__wnoDVTXzQpBbVbrAt2WNZXv6oqJqDiyIUoZjydRxL9o_R7L7kQM8cJmLlPqX6MjeMzShhQtA7RZZ9A/clip_image017%5B1%5D%5B2%5D%205C24DEB4.gif?download&psid=1 "clip_image017[1]"){kind=small}
![clip_image017[2]](https://h59kma.bay.livefilestore.com/y1m9Egr5hfblyf6RlRHLNa4agX6qY6W28Bx4O15dkfzBgF12FWxfFzOJ8jGXpDu44akCbIVfjR_pik4zHRzLjAxsijpH3AOlglrcwUnAi7wXsXZ7C7K-4eVomIf3_NkZkodHx4uilRUNSE4G5_moYRBJA/clip_image017%5B2%5D%5B2%5D%2044B61222.gif?download&psid=1 "clip_image017[2]"){kind=small}
![clip_image017[3]](https://h59kma.bay.livefilestore.com/y1mwb5W1FY3J8uuqceiiRPNHxDtoB6OLr5MxO5A_FQbpnGoznRIm7CPAYmPGmanZXWABPmN0MTIyvRwqKfbPlVzO_r2YDy4jExQFWWEMhQUJk5kVjOM89XThrisE2RwvXpW5uc5O2lKNhmEGaurth7FAA/clip_image017%5B3%5D%5B2%5D.gif?download&psid=1 "clip_image017[3]"){kind=small}
![clip_image017[4]](https://h59kma.bay.livefilestore.com/y1mIO1h6hS-xXGD_nDkwmxgHZyUnKrM70wwCyLLPC90DzI6bXQXy8DXZN_7LUhhC3GcF1yKMUf0pN4UBzUoA9p6h0Ot76aXWDN-307K7p0uneVNDQntYMArPJmP7JApAUC4CiYvTxwjnuHZHqb3Xwmf6w/clip_image017%5B4%5D%5B2%5D.gif?download&psid=1 "clip_image017[4]"){kind=small}
Bewise Inc. 
![clip_image010[1]](https://h59kma.bay.livefilestore.com/y1mK9cZtJW6Mtg4hjCjwjNxWD4XqMLW-PV7L54u_gyFRFhSS73Z5g64SNgt-6Z9adv0tZtLNN0Lsx28uZmS3H6DJHal88AU3WOTNL1o9GqxIP7byk4nGqORg4500ftVBPKHjYUUq4hI6rXWGOe4hfk6mg/clip_image010%5B1%5D%5B2%5D%2049831261.gif?download&psid=1 "clip_image010[1]"){kind=small}
![clip_image016[1]](https://h59kma.bay.livefilestore.com/y1mImC_MCnUrhDRdk-CdAz77HfxQdlAwJizy3141dxVkZGl7TWzlLL753__FiviHBOvmTXOiLz_W7yO1zsKQL-kyMyA7f6Ee9jlJsxULu3gtcrZ9688JSS6KIS0FUydVY6rOQAGDH9HbdiIHA8Of9N1PQ/clip_image016%5B1%5D%5B2%5D%201DE4D4B4.gif?download&psid=1 "clip_image016[1]"){kind=small}
![clip_image016[2]](https://h59kma.bay.livefilestore.com/y1m7TojlufTnos28rM4RhP86qP88F5aiG1icWYIqRKLkC5IYyf6PqgADnBuY6ZvE-MrK3diNfO0G-RGaYNPiuYJwr5C0bp-pXlVqMWgL2iGpjROZkKePMMU58ndCkWDkNUGc840rUjD8IR55oG649_x3g/clip_image016%5B2%5D%5B2%5D.gif?download&psid=1 "clip_image016[2]"){kind=small}
Bewise Inc. 
![clip_image006[1]](https://h59kma.bay.livefilestore.com/y1mdMXIa37OojbHtPqHpUdUzW-wiFg5_A6hg8wcaMpZCDjVVzjuOj3lE18DygLHhGNhkU0dDmdWcJlGX3mKTTOOYnrW3EdDfN8Ujoh5ltSpO1M-mNdCKjT1YghcASAhJkipNRN50BAoDx7MrBu5vW3HRw/clip_image006%5B1%5D%5B2%5D%20085AA152.gif?download&psid=1 "clip_image006[1]"){kind=small}
![clip_image009[1]](https://h59kma.bay.livefilestore.com/y1mRsMwalf1cVMZyiYaj7uCPbq20mFPq0qPZtCfwekYqGqcRaK9SYmex4X2rPHwx-UE4zwrOd5CPLyxM42zjmrNYymJGE6AbRaNhgI2vT6QtkbYZUp5jNMya47QFAVh2-8R8BJnPQtjXuNHLKHOaK18DA/clip_image009%5B1%5D%5B2%5D%2076FDDA2B.gif?download&psid=1 "clip_image009[1]"){kind=small}
![clip_image009[2]](https://h59kma.bay.livefilestore.com/y1mqNVWlmf7L8zg1er7YQwVlBOLazlDqCMa0svCUor0PAkze7h6T3EHT8GzeEZC3rse4YQGWZhn77oK8eAU9S3fOpveN9IXMfsyVqETvC__rnnETTZfyvHiyusOHYmmLnYfDu38hEQJGLSMdR-Vo9eQow/clip_image009%5B2%5D%5B2%5D%200A6F99AA.gif?download&psid=1 "clip_image009[2]"){kind=small}
