Explorando los posibles mecanismos de producción de las

23 valence electrons exist as a free gas surrounding a lattice of metal cations – means that the material is infinitely polarisable.

Following equation 3.1, it is conventional that Raman spectra are displayed in units of wavenumbers relative to the excitation energy, allowing for a direct measurement of the energy of the phonons or molecular vibrations which give rise to features in the spectrum.

3.2.

Raman spectrum of graphene

Raman spectroscopy has a long history in structural analysis of carbon materials, with different allotropes of carbon displaying the same sets of features between 1000 and 3000 cm-1_{, but their shapes, positions and relative intensities giving}

great insight into the material’s structure on the atomic level – Figure 3.2 gives a range of examples of Raman spectra of bulk carbon and carbon nanomaterials.

The Raman spectrum of monolayer graphene was first measured by Ferrari et al. and its most prominent features are the sharp peak at ~1580 cm-1_{, termed the G}

peak, and the more intense peak at ~2700 cm-1_{, the 2D peak (Ferrari 2006), similar to}

the Raman spectrum of bulk graphite (Figure 3.2), which has been measured since the 1970s (Tuinstra 1970, Tsu 1978).

3.2 Raman spectrum of graphene

24

Figure 3.2: Raman spectra of various macroscopic and nano-scale carbon materials, each exhibiting some combination of “D” and “G” peaks (Ferralis 2010).

The G peak can be explained by standard group theory derivations of the normal modes for a single layer of graphene, which gives four normal modes (Tuinstra 1970, Reich 2004), of which the E2g mode is the only Raman active mode. It is important

to point out that the motion of the carbon atoms in the E2g vibrational mode (see Figure

3.3) is a stretching motion between pairs of sp2_{-bonded carbon atoms and does not}

require presence of aromatic rings for its activation, explaining its presence in amorphous carbon and linear chain molecules (Ferrari 2000).

3.2 Raman spectrum of graphene

25

Figure 3.3: Visual representations of the motion of sp2 _{bonded carbon atoms due to}

the A1g and E2g phonon modes, responsible for the D and G bands respectively in

carbon Raman spectra.

The D peak in graphite was measured alongside the G peak in various graphitic materials by Tuinstra & Koenig, and the similarities between the D peak in defective graphite and the peak seen in diamond were immediately dispelled by noting discrepancies in the relative intensity and position of the peak (Tuinstra 1970). This is supported by the observation that the Raman scattering efficiency of sp3 _{carbon in}

diamond is some 55 times smaller than that of planar sp2 _{carbon, thus the small}

volumes of sp3 _{carbon to be expected in high-quality graphite would not lead to a}

sizeable Raman peak (Wada 1980).

Instead, the D peak in pure graphite is explained by the finite particle size of graphite crystals caused by defects or edges. By considering the graphite crystallites as large but finite molecules, a new normal mode of vibration can be deduced, the A1g

phonon (Figure 3.3) which is not Raman active in an infinite crystal (Tuinstra 1970). Further confirmation that the D band in graphitic carbon is due to non-sp2 _{defects can}

be sought by chemical modification of graphite, where reactants add defect sites to the lattice and the distance between defects becomes an effective crystallite size, Wang et al. showed that reactions with boron and oxygen produce a D peak identical to that observed near crystal edges (Wang 1990).

A_{1g E2g}

3.2 Raman spectrum of graphene

26

Figure 3.4: Intra-valley double resonance Raman scattering processes in sp2 _carbon

which lead to (a) the D peak through defect scattering (Ferrari 2007) and (b) the 2D peak in pristine graphene and graphite (Ferrari 2006).

Unusually, the D peak in carbon exhibits a dispersion with excitation energy which Thomsen & Reich explain to be a result of a double resonance process shown in Figure 3.4a, whereby electrons are scattered between the bands of the linear phonon dispersion near the K and Kʹ points of graphite and then elastically scattered by defects or edges (Thomsen 2000, Ferrari 2007). A similar, but intra-valley, scattering process can occur between the branches near the Γ point, giving rise to the Dʹ peak around 1620 cm-1 _{in defective sp}2 _{carbon (Ferrari 2007). By showing, alongside data from}

Vidano et al., that the 2D peak at ~2700 cm-1 _{– then often termed Gʹ – has a dispersion}

which is double that for the D peak, Wang et al. deduced that the 2D peak is the second overtone of the D peak (Vidano 1981, Wang 1990).

It is interesting, then, that we are able to see a 2D peak in pristine graphene and graphite, without the defects which activate the D peak. Ferrari et al. attribute the 2D peak to a double resonance process comprising two phonons at the K and Kʹ points with equal and opposite momentum – arrow q in Figure 3.4b (Ferrari 2006). This two-

a

3.2 Raman spectrum of graphene

27 phonon process does not require defects, and thus the 2D peak is observed in pristine graphene and graphite (Ferrari 2013).

Ferrari et al. describe the same double resonance process for bilayer graphene, where the electronic properties are changed due to interactions between the two layers, causing the π and π* branches of the electronic dispersion to split (Ferrari 2006, Piscanec 2007). This leads to a 2D peak in bilayer graphene comprising four components, visible in the fitting of the 2D peak in Figure 3.5b (Graf 2007). The evolution of the 2D peak with number of atomic layers of graphene (Figure 3.5) clearly distinguishes monolayer and bilayer graphene samples from thicker nanographites and bulk graphite.

Figure 3.5: Change in the shape of the 2D peak of sp2 _{carbon with the number of}

layers, from a single sharp peak in monolayer graphene to a broad doublet in bulk graphite. (a) Note the shift in position and difference in shape of the 2D band with changing excitation frequency (Ferrari 2006), (b) Note the increased splitting of the

components (numbers left) of the 2D peak with increasing layers (Graf 2007).

a