Graphene 2D

Raman spectra of various carbon nanostructures, which include fuUerenes (OD), nanotubes (ID), and graphene (2D), have been a subject of intensive studies over the last two decades [1-8]. The Raman spectra of these carbon nanostructures have... 

Carbon exists in different allotropic forms, viz. Fullerene (OD, a zerodimensional carbon), carbon nanotube (ID, a one-dimensional carbon), graphene (2D, a two-dimensional carbon), graphite (3D, a three-dimensional carbon) and diamond (3D, a three-dimensional carbon). All the above forms except diamond (which bears sp hybridized carbons) have a structural similarity having sp hybridized carbon. 

Tang Z-R, Yu Q, Xu Y-J (2014) Toward improving the photocatalytic activity of BiV04-graphene 2D-2D composites under visible light by the addition of mediator. RSC Adv... 

The circumference of any carbon nanotube is expressed in terms of the chiral vector = nai ma2 which connects two crystallographically equivalent sites on a 2D graphene sheet [see Fig. 16(a)] [162]. The construction in... 

The ID electronic energy bands for carbon nanotubes [170, 171, 172, 173, 174] are related to bands calculated for the 2D graphene honeycomb sheet used to form the nanotube. These calculations show that about 1/3 of the nanotubes are metallic and 2/3 are semiconducting, depending on the nanotube diameter di and chiral angle 6. It can be shown that metallic conduction in a (n, m) carbon nanotube is achieved when... 

These surprising results can be understood on the basis of the electronic structure of a graphene sheet which is found to be a zero gap semiconductor [177] with bonding and antibonding tt bands that are degenerate at the TsT-point (zone corner) of the hexagonal 2D Brillouin zone. The periodic boundary... 

Closely related to the ID dispersion relations for the carbon nanotubes is the ID density of states shown in Fig. 20 for (a) a semiconducting (10,0) zigzag carbon nanotube, and (b) a metallic (9,0) zigzag carbon nanotube. The results show that the metallic nanotubes have a small, but non-vanishing 1D density of states, whereas for a 2D graphene sheet (dashed curve) the density of states... 

Fig. 20. Electronic 1D density of states per unit cell of a 2D graphene sheet for two (n, 0) zigzag nanotubes (a) the (10,0) nanotube which has semiconducting behavior, (b) the (9, 0) nanotube which has metallic behavior. Also shown in the figure is the density of states for the 2D graphene sheet (dotted line) [178].

Fig. 1. The 2D graphene sheet is shown along with the vector which specifies the chiral nanotube. The chiral vector OA or Cf, = nOf + tnoi defined on the honeycomb lattice by unit vectors a, and 02 and the chiral angle 6 is defined with respect to the zigzag axis. Along the zigzag axis 6 = 0°. Also shown are the lattice vector OB = T of the ID tubule unit cell, and the rotation angle 4/ and the translation r which constitute the basic symmetry operation R = (i/ r). The diagram is constructed for n,m) = (4,2).

Fig. 3. The 2D graphene sheet is shown along with the vector which specifies the chiral nanotube. The pairs of integers ( , ) in the figure specify chiral vectors Cy, (see Table I) for carbon nanotubes, including zigzag, armchair, and chiral tubules. Below each pair of integers (n,m) is listed the number of distinct caps that can be joined continuously to the cylindrical carbon tubule denoted by (n,wi)[6]. The circled dots denote metallic tubules and the small dots are for semiconducting tubules.

Abstract—Experimental and theoretical studies of the vibrational modes of carbon nanotubes are reviewed. The closing of a 2D graphene sheet into a tubule is found to lead to several new infrared (IR)- and Raman-active modes. The number of these modes is found to depend on the tubule symmetry and not on the diameter. Their diameter-dependent frequencies are calculated using a zone-folding model. Results of Raman scattering studies on arc-derived carbons containing nested or single-wall nanotubes are discussed. They are compared to theory and to that observed for other sp carbons also present in the sample. 

A single-w all carbon nanotube can be visualized by referring to Fig. 3, which shows a 2D graphene sheet with lattice vectors a and U2, and a vector C given by... 

In the above eqn, ID refers to the nanotubes whereas 2D refers to the graphene sheet, k is the ID wave vector, and t and Care unit vectors along the tubule axis and vector C, respectively, and p labels the tubule phonon branch. 

Next, we consider the F-point nanotube modes obtained by setting k = Q and /j. = N/2 in eqn (17). The modes correspond to 2D graphene sheet modes at the point k = (A 7r/C)Cin the hexagonal BZ. We consider how such modes transform under the symmetry operations of the groups Qj and Under the ac-... 

Typical X-ray diffraction patterns of three different carbon powder samples are shown in Fig. 3. Two 00/ and two hkO diffraction peaks can be distinguished in the patterns of samples produced at 800°C and 1000°C. The 002 (26 26.9°) and 004 (26 54.9°) peaks correspond to the parallel graphene layers. The 100 (26 43°) and 110 (26 77.8°) diffraction peaks are characteristics of the 2D in-plane symmetry along the graphene layers. Based on its XRD pattern, the powder synthesized at 500°C is not graphitized, which is in agreement with Raman analysis. This low temperature sample also contains traces of iron chlorides. 

Fig. 2.4 Typical Raman spectra of (a) graphite, with peaks labeled as discussed in the text (b) graphene (liquid-phase exfoliated). Inset Evolution of 2D-band with increasing layer numbers [120],...

---