Raman Spectroscopy of Graphene, Graphite and Graphene Nanoplatelets

*Daniel Casimir, Hawazin Alghamdi, Iman Y. Ahmed, Raul Garcia-Sanchez and Prabhakar Misra*

### **Abstract**

The theoretical simplicity of sp2 carbons, owing to their having a single atomic type per unit cell, makes these materials excellent candidates in quantum chemical descriptions of vibrational and electronic energy levels. Theoretical discoveries, associated with sp2 carbons, such as the Kohn anomaly, electron-phonon interactions, and other exciton-related effects, may be transferred to other potential 2D materials. The information derived from the unique Raman bands from a single layer of carbon atoms also helps in understanding the new physics associated with this material, as well as other two-dimensional materials. The following chapter describes our studies of the G, D, and G′ bands of graphene and graphite, and the characteristic information provided by each material. The G-band peak located at ~1586 cm<sup>−</sup><sup>1</sup> , common to all sp2 carbons, has been used extensively by us in the estimation of thermal conductivity and thermal expansion characteristics of the sp2 nanocarbon associated with single walled carbon nanotubes (SWCNT). Scanning electron microscope (SEM) images of functionalized graphene nanoplatelet aggregates doped with argon (A), carboxyl (B), oxygen (C), ammonia (D), fluorocarbon (E), and nitrogen (F), have also been recorded and analyzed using the Gwyddion software.

**Keywords:** Raman spectroscopy, 2-D materials, graphene, graphite, functionalized graphene nanoplatelets

### **1. Introduction**

The elucidation of novel physics related to 2D electronic systems (2DES) has received wide recognition in the form of three Nobel Prizes in Physics in 1985 [1] (Klaus von Klitzing, Max Planck Institute, for the discovery of the integer Quantum Hall Effect), in 1998 [2] (Robert Laughlin, Stanford University, Horst Stormer, Columbia University, and Daniel Tsui, Princeton University, for the discovery of the fractional Quantum Hall Effect), and in 2010 [3] (Andre Geim and Konstantin Novoselov, University of Manchester, for ground-breaking experiments relating to the 2D material graphene).

Since graphene can be considered as the conceptual parent material for all other sp2 nanocarbons, it is the first in our discussion of the two-dimensional characteristics obtainable via Raman spectroscopy. Graphene is a two-dimensional carbon

**6**

*2D Materials*

wearable electronics applications. 2D

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nanomaterial with a single layer of sp2 -hybridized carbon atoms arranged in a crystalline structure of six-membered rings [4, 5]. **Figure 1** illustrates the hexagonal lattice of a perfectly flat graphene sheet and the resulting nanotube after it is rolled along the vector labeled **Ch**. The shaded portion of the nanotube in **Figure 1(b)** represents one unit cell of the resulting armchair nanotube in this case, and it results from rolling the initial planar sheet in **Figure 1(a)**, so that points **A** and **C** coincide with points **B** and **D**, respectively. **Ch** is known as the chiral vector and is constructed from the vector addition of the graphene basis vectors **a1** and **a2**. The integer number of each of the basic lattice vectors used in the construction, n and m, designated for **a1** and **a2** respectively, is arbitrary with the only provision that (0 ≤ |m| ≤ n). The Cartesian components of the lattice vectors **a1** and **a2** are (a√3/2, a/2) and (a√3/2, −a/2), respectively, where the quantity a = aC-C√3 = 2.46 Å. The quantity aC-C is the bond length between two neighboring carbon atoms in the hexagonal lattice equal to 1.42 Å. The chiral vector **Ch** is usually written in terms of the two integers n and m as

$$\mathbf{C\_h = \,n\, \mathbf{a\_1} + \,m\, \mathbf{a\_2}}\tag{1}$$

and has a magnitude of

$$|\mathbf{C\_h}| = a\sqrt{n^2 + m^2 + nm} \tag{2}$$

which equals the carbon nanotube's circumference. In a fashion similar to applying the above rolling operation on the graphene unit cell in **Figure 1** for the construction of single walled carbon nanotubes, graphite can be described in terms of stacking multiple graphene layers one atop the other.

We have also investigated functionalized graphene nanoplatelets, which are comprised of platelet-shaped graphene sheets, identical to those found in SWCNT, but in planar form. Among the samples we used (functionalized oxygen, nitrogen, argon, ammonia, carboxyl and fluorocarbon) all have similar shape. Graphene nanoplatelet aggregates (aggregates of sub-micron platelets with a diameter of <2 μm and a thickness of a few nanometers) were identified, rather than individual nanoplatelets (STREM Data Sheets [6]). According to the manufacturer's (Graphene Supermarket™), structural analysis for fluorinated graphene nanoplatelets (GNP), the lateral dimensions of the wrinkled sheet-like outer surface of the GNP's is ~1–5 μm [6]. The quoted number of graphene layers was also around 37

#### **Figure 1.**

*(a) Construction of a carbon nanotube based on the lattice vectors of a planar hexagonal graphene sheet. (b) The resulting armchair (3, 3) carbon nanotube.*

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*Raman Spectroscopy of Graphene, Graphite and Graphene Nanoplatelets*

layers, based on SEM and TEM analysis [7]. This average number of layers is more than sufficient to consider these sub-micron sized stacked graphene nanoparticles as being in the multi-layer graphene category, and not in the few layer category. This latter property of GNP's is also mentioned in the concluding remarks, in connection

*The linear E vs. k dispersion of graphene near the Brillouin zone K-point (Dirac cone).*

Arguably one of the most striking displays of the two-dimensional nature of graphene is related to its electronic structure; specifically, the behavior of its electron/hole carriers [4]. The resulting dispersion (E vs. **k**) relation of the graphene band structure forces us to rely on Dirac's relativistic wave equation, instead of Schrodinger's equation, to describe the particle dynamics [4]. Therefore, the charge carriers are treated as relativistic massless quantities moving essentially at

**Figure 2** shows one of the six "Dirac cones," which are one of the highly symmetrized K point locations in graphene's Brillouin zone, as shown in **Figure 3**, where the valence and conduction bands touch one another [4]. The experimental verification of this linear dispersion for energies centered at and near the Dirac cone as expressed

> = ±ℏ*vF* |*k*

(**ℏ***vF*)**<sup>2</sup>**

<sup>→</sup>| (3)


in Eq. (3) has also been accomplished by various spectroscopic methods [8].

→) ±

Another significant electronic structural quantity that expresses the twodimensional nature of graphene is the density of states (DOS), g**(E)**, which as its name suggests, gives the density of mobile charge carriers that are available at some temperature T [4]. Unsurprisingly, this quantity also varies linearly, only this time

*DOI: http://dx.doi.org/10.5772/intechopen.84527*

with their two-dimensional classification.

*E*(*k*

with the energy E, as expressed in Eq. (4) [4].

*g*(*E*) = \_\_\_\_\_\_\_ **<sup>2</sup>**

the speed of light [4].

**Figure 2.**

*Raman Spectroscopy of Graphene, Graphite and Graphene Nanoplatelets DOI: http://dx.doi.org/10.5772/intechopen.84527*

*2D Materials*

nanomaterial with a single layer of sp2

written in terms of the two integers n and m as


of stacking multiple graphene layers one atop the other.

and has a magnitude of


in a crystalline structure of six-membered rings [4, 5]. **Figure 1** illustrates the hexagonal lattice of a perfectly flat graphene sheet and the resulting nanotube after it is rolled along the vector labeled **Ch**. The shaded portion of the nanotube in **Figure 1(b)** represents one unit cell of the resulting armchair nanotube in this case, and it results from rolling the initial planar sheet in **Figure 1(a)**, so that points **A** and **C** coincide with points **B** and **D**, respectively. **Ch** is known as the chiral vector and is constructed from the vector addition of the graphene basis vectors **a1** and **a2**. The integer number of each of the basic lattice vectors used in the construction, n and m, designated for **a1** and **a2** respectively, is arbitrary with the only provision that (0 ≤ |m| ≤ n). The Cartesian components of the lattice vectors **a1** and **a2** are (a√3/2, a/2) and (a√3/2, −a/2), respectively, where the quantity a = aC-C√3 = 2.46 Å. The quantity aC-C is the bond length between two neighboring carbon atoms in the hexagonal lattice equal to 1.42 Å. The chiral vector **Ch** is usually

**Ch** = *n***a1** + *m***a2** (1)

which equals the carbon nanotube's circumference. In a fashion similar to applying the above rolling operation on the graphene unit cell in **Figure 1** for the construction of single walled carbon nanotubes, graphite can be described in terms

We have also investigated functionalized graphene nanoplatelets, which are comprised of platelet-shaped graphene sheets, identical to those found in SWCNT, but in planar form. Among the samples we used (functionalized oxygen, nitrogen, argon, ammonia, carboxyl and fluorocarbon) all have similar shape. Graphene nanoplatelet aggregates (aggregates of sub-micron platelets with a diameter of <2 μm and a thickness of a few nanometers) were identified, rather than individual nanoplatelets (STREM Data Sheets [6]). According to the manufacturer's (Graphene Supermarket™), structural analysis for fluorinated graphene nanoplatelets (GNP), the lateral dimensions of the wrinkled sheet-like outer surface of the GNP's is ~1–5 μm [6]. The quoted number of graphene layers was also around 37

*(a) Construction of a carbon nanotube based on the lattice vectors of a planar hexagonal graphene sheet.* 

\_\_\_\_\_\_\_\_\_\_\_

*n*<sup>2</sup> + *m*<sup>2</sup> + *nm* (2)

**8**

**Figure 1.**

*(b) The resulting armchair (3, 3) carbon nanotube.*

layers, based on SEM and TEM analysis [7]. This average number of layers is more than sufficient to consider these sub-micron sized stacked graphene nanoparticles as being in the multi-layer graphene category, and not in the few layer category. This latter property of GNP's is also mentioned in the concluding remarks, in connection with their two-dimensional classification.

Arguably one of the most striking displays of the two-dimensional nature of graphene is related to its electronic structure; specifically, the behavior of its electron/hole carriers [4]. The resulting dispersion (E vs. **k**) relation of the graphene band structure forces us to rely on Dirac's relativistic wave equation, instead of Schrodinger's equation, to describe the particle dynamics [4]. Therefore, the charge carriers are treated as relativistic massless quantities moving essentially at the speed of light [4].

**Figure 2** shows one of the six "Dirac cones," which are one of the highly symmetrized K point locations in graphene's Brillouin zone, as shown in **Figure 3**, where the valence and conduction bands touch one another [4]. The experimental verification of this linear dispersion for energies centered at and near the Dirac cone as expressed in Eq. (3) has also been accomplished by various spectroscopic methods [8].

$$E\left(\vec{k}\right)^{\pm} = \pm \hbar \,\nu\_F \left|\vec{k}\right|\tag{3}$$

Another significant electronic structural quantity that expresses the twodimensional nature of graphene is the density of states (DOS), g**(E)**, which as its name suggests, gives the density of mobile charge carriers that are available at some temperature T [4]. Unsurprisingly, this quantity also varies linearly, only this time with the energy E, as expressed in Eq. (4) [4].

$$\mathbf{g}^{\prime}(\mathbf{E}) = \frac{2}{\pi \left(\hbar \nu\_{F}\right)^{2}} |\mathbf{E}| \tag{4}$$

#### **Figure 3.**

*Graphene's reciprocal space lattice shown with reciprocal lattice vectors b1, and b2. The first Brillouin zone is the region labeled by Γ. Also shown are the six high symmetry regions, Γ, K, M, and K′.*

The 2D nature of graphene plays a direct role in this result, sine g(E), which gives the number of available states within the energy interval E and E + dE, is defined in two-dimensions in terms of the ratio of an element of area dA in k-space per unit wave-vector k.
