coatings

Review
A Guide to and Review of the Use of
Multiwavelength Raman Spectroscopy for
Characterizing Defective Aromatic Carbon Solids:
from Graphene to Amorphous Carbons
Alexandre Merlen 1 , Josephus Gerardus Buijnsters 2 and Cedric Pardanaud 3, *
1 Institut Matériaux Microélectronique Nanoscience de Provence, IM2NP, UMR CNRS 7334,
Universités d’Aix Marseille et de Toulon, site de l’Université de Toulon, Toulon CS 60584, France;
merlen@univ-tln.fr
2 Department of Precision and Microsystems Engineering, Research Group of Micro and Nano Engineering,
Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands; J.G.Buijnsters@tudelft.nl
3 Laboratoire PIIM, Aix-Marseille Université, CNRS, UMR 7345, Marseille 13397, France
* Correspondence: cedric.pardanaud@univ-amu.fr; Tel.: +33-4-91-28-27-07

Academic Editor: Alessandro Lavacchi

Received: 27 July 2017; Accepted: 11 September 2017; Published: 25 September 2017

Abstract: sp2 hybridized carbons constitute a broad class of solid phases composed primarily of
elemental carbon and can be either synthetic or naturally occurring. Some examples are graphite,
chars, soot, graphene, carbon nanotubes, pyrolytic carbon, and diamond-like carbon. They vary from
highly ordered to completely disordered solids and detailed knowledge of their internal structure
and composition is of utmost importance for the scientific and engineering communities working
with these materials. Multiwavelength Raman spectroscopy has proven to be a very powerful
and non-destructive tool for the characterization of carbons containing both aromatic domains and
defects and has been widely used since the 1980s. Depending on the material studied, some specific
spectroscopic parameters (e.g., band position, full width at half maximum, relative intensity ratio
between two bands) are used to characterize defects. This paper is addressed first to (but not limited
to) the newcomer in the field, who needs to be guided due to the vast literature on the subject, in
order to understand the physics at play when dealing with Raman spectroscopy of graphene-based
solids. We also give historical aspects on the development of the Raman spectroscopy technique
and on its application to sp2 hybridized carbons, which are generally not presented in the literature.
We review the way Raman spectroscopy is used for sp2 based carbon samples containing defects.
As graphene is the building block for all these materials, we try to bridge these two worlds by also
reviewing the use of Raman spectroscopy in the characterization of graphene and nanographenes
(e.g., nanotubes, nanoribbons, nanocones, bombarded graphene). Counterintuitively, because of the
Dirac cones in the electronic structure of graphene, Raman spectra are driven by electronic properties:
Phonons and electrons being coupled by the double resonance mechanism. This justifies the use of
multiwavelength Raman spectroscopy to better characterize these materials. We conclude with the
possible influence of both phonon confinement and curvature of aromatic planes on the shape of
Raman spectra, and discuss samples to be studied in the future with some complementary technique
(e.g., high resolution transmission electron microscopy) in order to disentangle the influence of
structure and defects.

Keywords: multiwavelength Raman spectroscopy; carbon solids; graphene; disordered carbon;

amorphous carbon; nanocarbons

Coatings 2017, 7, 153; doi:10.3390/coatings7100153 www.mdpi.com/journal/coatings

Coatings 2017, 7, 153 2 of 55

1. Introduction
Raman spectroscopy is an inelastic light scattering process that allows to identify and characterize
the structure of molecules from gas to solid phase, from amorphous to crystals. It is created by a
fluctuating electric dipole caused by both the incident light beam and by the elementary excitations
of the scattered media: E.g., ro-vibrations of free molecules, phonons in crystals, impurities, and
local vibrational modes. In material sciences, it is used routinely, since the 1970s, to characterize
carbon-based materials, ranging from very well organized carbons such as four coordinated diamond;
to three coordinated aromatic carbons such as graphene [1,2], nanotubes [3], and nanoribbons, down
to amorphous carbons [4]. The latter materials are disordered carbon solids containing a mixture of
tri- and tetravalent bonds [5], with or without hetero atoms [6]. In between the two extremities of
highly ordered and the very disordered three coordinated aromatic carbons, nanographites which
display a local order at the nanometric scale (nanographites can refer here to soots, coals, pyrolitic
graphite, implanted graphene/graphite, etc.), are also covered by this spectroscopic technique.
Researchers new to the field are in general astonished by the huge amount of papers found in
a first raw bibliographic search. The main aim of this review paper is to help them in identifying
how Raman spectroscopy aids in studying different forms of aromatic carbons containing defects.
To emphasize the role of Raman spectroscopy played in this aromatic carbon community, a quick
bibliographic search on Web of Science returns more than 1700 publications having the keyword
“graphite” in the title and the keyword “Raman” in the topic. This number increases up to 9000 items
when replacing “graphite” with “graphene” in the title, which makes a huge number of publications.
The number of publications remains high (close to 900) if both “graphene” and “Raman” are considered
as keywords in the title, implying that they are intrinsically correlated. This strong correlation is still
significant for amorphous carbons as the amount of publications reaches 220 with the keywords
“Raman + amorphous carbon” or “diamond like carbon” both in the title. We will detail the origin of
this correlation below.
At this stage the most relevant questions are: How is Raman spectroscopy generally used
(or how can it be used) for characterizing carbon-based materials, and what can we learn from
the Raman spectra? The answer to these questions is not easy to give as it depends on the goal
of the study: Basic characterization, or deeper fundamental study, or both. What is sure is that in
all cases Raman spectroscopy gives information on defects. Most often in the scientific literature
it is used to confirm that the good allotrope has been obtained after a given preparatory process
(e.g., ion implantation, deposition varying relevant parameters like pressure or substrate temperature,
mechanical modification by milling) or to quantify the amount of defects or structure deformation
introduced after a given transformation of the pristine sample. It can also be used to give a
rough estimation of the stored hydrogen content [6,7], to monitor chemical changes under some
physicochemical process, to determine mechanical stress or stress release, to characterize the electronic
properties, diameter of carbon nanotubes, coupling between a carbon phase and another environment,
and so forth. Occasionally, Raman spectroscopy is employed to obtain more fundamental information
on the material properties, such as the Grüneisen parameter [8]. In this paper, we review the most
important uses of multiwavelength Raman spectroscopy of sp2 based carbon samples containing
defects to answer the questions detailed above for these peculiar materials. We emphasize the role
played by the laser wavelength used because of resonance effects that can be positive (i.e., allow to
obtain additional information) or negative (i.e., introduction of unwanted experimental biases due to
the wavelength dependency of the Raman cross sections for sp2 or sp3 carbons [9], merging of bands
due to dispersion behavior caused by resonance effects, etc.).
In Section 2, we give an introductive and historical background of Raman spectroscopy in general
and then applied to carbons. As the history of Raman spectroscopy starts at the same time as the
beginnings of quantum mechanics, we have decided to give some details on the latter as well since
generally it is skipped from specialized text books and review papers. Section 2 is split into three
subparts, one giving the historical context, another giving some basics on the Raman effect, and the
Coatings 2017, 7, 153 3 of 55

last one is more focused on Raman spectroscopy applied in the study of carbon solids. In Section 3, we
give results (basically correlation between Raman spectroscopic parameters such as band intensity
Coatings 2017, 7, 153    3 of 54 
ratios, band position and band width, for different laser wavelength) related to different kinds of
aromatic containing
Section 3,  we  give  carbons
results that rangecorrelation 
(basically  from disordered
between graphene to amorphous
Raman  spectroscopic  carbons.such 
parameters  Theas  aim of
band 
Section 3 isintensity 
to give aratios,  band 
concrete position 
and and view
practical band onwidth, 
how for  different 
Raman laser  wavelength) 
spectroscopy related 
can be used to 
to classify
different kinds of aromatic containing carbons that range from disordered graphene to amorphous 
the nanostructure under investigation and its defectiveness. The guiding principle of this review
carbons. The aim of Section 3 is to give a concrete and practical view on how Raman spectroscopy 
section is the increase of complexity of the samples through the pages. In Section 4, we highlight the
can  be  used  to  classify  the  nanostructure  under  investigation  and  its  defectiveness.  The  guiding 
role of phonon confinement for a variety of nanocarbons and conclude our review.
principle of this review section is the increase of complexity of the samples through the pages. In 
Section 4, we highlight the role of phonon confinement for a variety of nanocarbons and conclude 
2. Raman Spectroscopy of Carbon Solids: Basics
our review. 
2.1. A Brief History of Raman Spectroscopy
2. Raman Spectroscopy of Carbon Solids: Basics 
The historical milestones (experimental, theoretical, and instrumental) on the Raman effect
2.1. A Brief History of Raman Spectroscopy 
applied to carbon have been summarized in Figure 1. Below, we give more details. First light scattering
experiments The were performed
historical  in 1922
milestones  by Brillouin
(experimental,  [10] and in
theoretical,  1923
and  by Compton,
instrumental)  on  who used X-rays
the  Raman  effect  [11].
During the six
applied  to  following
carbon  have  years,
been Raman was involved
summarized  in Below, 
in  Figure  1.  53 communications
we  give  more  focused on scattering
details.  First  light 
processes in liquids [12] that led him and his students to observe a new effect in the optical region.
scattering experiments were performed in 1922 by Brillouin [10] and in 1923 by Compton, who used 
X‐rays [11]. During the six following years, Raman was involved in 53 communications focused on 
In 1928, Raman [13] finally realized he observed the analogue of the Compton effect: An inelastic
light scattering processes in liquids [12] that led him and his students to observe a new effect in the optical 
scattering process, but in the visible range of radiation. Two groups of unresolved bands were
region.  In  1928,  Raman  [13]  finally  realized  he  observed  the  analogue  of  the  Compton  effect:  An 
observed: One at a higher wavelength compared to the wavelength of the incident light (Stokes lines,
inelastic  light  scattering  process,  but  in  the  visible  range  of  radiation.  Two  groups  of  unresolved 
more intense) and one at a lower wavelength (anti-Stokes lines, less intense). The denomination as
bands were observed: One at a higher wavelength compared to the wavelength of the incident light 
Stokes or anti-Stokes lines is due to Woods [12] who noticed that, phenomenologically, this Raman
(Stokes  lines,  more  intense)  and  one  at  a  lower  wavelength  (anti‐Stokes  lines,  less  intense).  The 
effectdenomination as Stokes or anti‐Stokes lines is due to Woods [12] who noticed that, phenomenologically, 
gave a shift in wavelength as does fluorescence, a phenomenon discovered by Stokes in 1852
on fluorite, CaF2effect 
this  Raman  [14]. gave 
Somea  German researchers
shift  in  wavelength  as doubted the discovery
does  fluorescence,  of the Raman
a  phenomenon  effect by 
discovered  as they
failedStokes in 1852 on fluorite, CaF
to reproduce it, but Sommerfeld played a major role in the acceptance of the Raman effect by the
2 [14]. Some German researchers doubted the discovery of the Raman 

effect  as  community

international they  failed  to [15,16].
reproduce 
Theit,  but  Sommerfeld 
history played  a 
of this discovery ismajor  role  in 
discussed inthe  acceptance 
detail in Singhof etthe 
al. [17].
Raman effect by the international community [15,16]. The history of this discovery is discussed in 
The inelastic scattering of light in the visible range was then found very promising for the study
detail in Singh et al. [17]. The inelastic scattering of light in the visible range was then found very 
of molecular structures because the process allows to obtain infrared and far-infrared information
promising for the study of molecular structures because the process allows to obtain infrared and   
(ro-vibrational states) using and detecting light in the visible range. Before the most efficient detector
far‐infrared information (ro‐vibrational states) using and detecting light in the visible range. Before 
at that time (photography) was used, the Raman effect was first observed by coupling a spectroscope
the most efficient detector at that time (photography) was used, the Raman effect was first observed 
with by coupling a spectroscope with the naked eye [15]. 
the naked eye [15].

 
Figure 1. Quick chronology of the Raman effect. 
Figure 1. Quick chronology of the Raman effect.
Coatings 2017, 7, 153 4 of 55

The theoretical background at the basis of the understanding of the Raman effect started to
be established before the experimental discovery of the effect itself: In 1923, Smekal quantized a
two-energy level system [18]. Two years later, Kramers and Heisenberg [19] obtained the expression of
the scattering cross section of an electromagnetic wave by an atom described by quantum mechanics.
In 1927, Dirac derived the same expression by quantizing both the matter and light, creating quantum
electrodynamics [20]. Nowadays, the theory is generally labelled the Kramers–Heisenberg–Dirac
(KHD) theory. In 1932, Breit reviewed this quantum theory of dispersion (Among other points, we
learn in his paper the well-known fact that both the Schrödinger and matrix mechanics from Born,
Heisenberg, and Jordan were tested to obtain the Kramers–Heisenberg formula of dispersion, and
that they both lead to the same result.) [21]. In 1934, Placzek [22] introduced the bond-polarizability
theory of Raman scattering. This approach is still useful nowadays as it allows “easy” manipulation
of Raman intensities. It is based on a time-dependent perturbation theory and on some assumptions,
among others that the nuclei of the molecules are fixed and that the system is in its ground electronic
state, which prevent the theory from being used for resonance effects. The main advantages of this
semi-classical theory is that point group theory can be used for deriving selection rules based on
symmetry considerations. In 1961, Albrecht reported multiple hypothesis, introducing vibronic states
and allowing his theory to be used for normal and resonance Raman scattering [23]. In 1956, Born, who
is well known to first give the interpretation of the wave function squared absolute value, co-wrote a
very detailed book about the dynamics of crystals in which some sections are dedicated to the Raman
effect [24]. In 1964, Loudon reviewed the knowledge acquired on the theory adapted to crystals; the
theory (he contributed to create in 1963) focusing in his paper on cubic, axial, and biaxial crystals, using
the first order perturbation theory applied to a system with three systems interacting: The radiation,
the electron, and the lattice (phonon) [25]. In his paper, he also reviewed crystal excitations involved
in the Raman effect which are not only phonons. In 1967, Ganguly and Birman developed the theory
of lattice Raman scattering in insulators [26]. Reviewing the period from the seventies to the present
days is a complex task due to the increasing number of papers published in this period. This explosion
of works related to Raman spectroscopy can be explained by the invention of the laser, which provides
monochromatic intense photons. A bibliographic search with the key words “Raman + spectroscopy”
in the title returns more than 21,000 papers. This number falls to 3200 if the research is restricted to
the material science field only. In the 1970s, the number of papers published per year was just close
to 5, whereas currently about 140 papers are published each year. The two series Light Scatterings in
Solids [27] and Recent Advances in Linear and Non-Linear Raman Spectroscopy [28] will be helpful to the
readers who want to follow the evolution of this field in more detail. The Journal of Raman Spectroscopy
(published by John Wiley & Sons, Inc.) is a dedicated journal that publishes in the field. Raman
spectroscopy is now routinely used in many labs to characterize many kinds of solids, transparent
or absorbent, thick or monoatomically thin, and so forth. It is coupled with an optical microscope
that focalizes the laser beam to a restricted sampling area/volume and helps in collecting light more
efficiently after it got scattered with matter, at the micrometer lateral resolution. The reader will take
advantage in reading the reference from Gouadec and Colomban [29] which is very well adapted to
efficiently learn both the theoretical and experimental basics and which illustrates these basics on
well-chosen examples.
The evolution of this field of research has been correlated to the evolution of the experimental
techniques. It reached its apogee in the 1940s, studying first molecules in liquids and then in gas
(first measurements where done unsuccessfully in gas phase from 1924 to 1928 by Rocard [30,31]).
Due to both low Raman scattering cross sections (see below) and absorption of light, studying crystals
was not easy until the advent of the laser in the 1960s (see Figure 1). Only transparent samples
like diamond and CdS, with a large volume probed, are reported in the period 1930–1960 [32,33].
In 1928, Mandelstam and Landsberg intended to measure Brillouin spectra of quartz, but instead
they observed faint new lines with an unexpected shift, which were in fact the corresponding Raman
lines of quartz [34]. Lasers, contrary to the mercury lamp previously used, offered many advantages
Coatings 2017, 7, 153 5 of 55

such as: High power, monochromaticity, and coherence, thus opening the era of studying solids.
Coatings 2017, 7, 153    5 of 54 
In parallel, progress had been made in electronics so that photomultipliers were used first before the
CCD (charged coupled device) cameras [35] which were invented in 1970, based on semiconductors
CCD (charged coupled device) cameras [35] which were invented in 1970, based on semiconductors 
technology arranged in arrays. The CCD camera was applied first in the field of Raman spectroscopy
technology arranged in arrays. The CCD camera was applied first in the field of Raman spectroscopy 
forfor solids in 1987 for characterizing ultrathin organized layers of organic films [36] without using 
solids in 1987 for characterizing ultrathin organized layers of organic films [36] without using
specific molecules in which resonance effects enhance the Raman signature, as was done before
specific molecules in which resonance effects enhance the Raman signature, as was done before by 
by Rabolt 
Rabolt et et al. 
al. [37]. 
[37]. More 
Moreinformation 
informationon onthe 
theinstrumental 
instrumental aspect
aspect  can
can  be be found
found  in in the
the  work
work  by by 
Adar et al. [38]. The early history of the Raman effect can also be found in a review by Long [39]. 
Adar et al. [38]. The early history of the Raman effect can also be found in a review by Long [39].
Laser 
Laser coupling 
coupling to  nanometric 
to nanometric metalmetal  nanoparticles 
nanoparticles or  atomic 
or atomic force  microscopy 
force microscopy tips 
tips [40] [40]  reaching
allows allows 
reaching nanometric resolution, but this is another topic and will not be covered in this paper. Before 
nanometric resolution, but this is another topic and will not be covered in this paper. Before discussing
discussing more details on the use of Raman spectroscopy for characterizing carbon allotropes, we 
more details on the use of Raman spectroscopy for characterizing carbon allotropes, we first provide
first provide some basic theoretical knowledge on Raman spectroscopy. 
some basic theoretical knowledge on Raman spectroscopy.

2.2.2.2. Basic Knowledge on Raman and Resonance Raman Spectroscopy 
Basic Knowledge on Raman and Resonance Raman Spectroscopy
TheThe 
aimaim  of  the 
of the following 
following paragraph 
section is  to 
is to give thegive 
mainthe  main  physical 
physical ideas  behind 
ideas behind normalnormal  and 
and resonant
resonant  Raman  scattering,  and  not  to  give  a  complete  lesson  on  Raman  spectroscopy 
Raman scattering, and not to give a complete lesson on Raman spectroscopy theory, including cross theory, 
including  cross  section  calculations/band  intensities  in  the  case  of  normal  and  resonant  Raman 
section calculations/band intensities in the case of normal and resonant Raman scattering. For a
scattering. For a deeper learning, we refer to the works of Rocard and Long [30,41] for the basics and 
deeper learning, we refer to the works of Rocard and Long [30,41] for the basics and applications in
applications in material sciences and [41] for the full quantum theory applied to free molecules. The 
material sciences and [41] for the full quantum theory applied to free molecules. The review by Born
review  by  Born  and  Huang  [24]  displays,  among  other  useful  developments,  a  full  description  of 
and Huang [24] displays, among other useful developments, a full description of calculations leading
calculations leading to the Placzek’s formalism. For solids, the studies by Cardona et al. [42,43] are 
to the Placzek’s formalism. For solids, the studies by Cardona et al. [42,43] are highly recommended.
highly recommended. 
2.2.1. Experimental Set-Up
2.2.1. Experimental Set‐Up 
The typical experimental set-up applied for Raman spectroscopy measurements, with a
The  typical  experimental  set‐up  applied  for  Raman  spectroscopy  measurements,  with  a 
backscattering geometry, is presented in Figure 2a. Briefly, a laser beam is aligned by a set of mirrors
backscattering geometry, is presented in Figure 2a. Briefly, a laser beam is aligned by a set of mirrors 
andand driven to an objective that focalizes it on the sample placed on a motorized XY stage. Depending 
driven to an objective that focalizes it on the sample placed on a motorized XY stage. Depending on
theon 
set-up, differentdifferent 
the  set‐up,  laser sources
laser (laser wavelength
sources  from λ0 = from 
(laser  wavelength  244–1064 nm)
λ0  =  with their
244–1064  nm) corresponding
with  their 
optics can be found. Depending on the community, either the wavelength or the laser energy is used
corresponding optics can be found. Depending on the community, either the wavelength or the laser 
to display spectroscopic data. They are related by the expression (see Equation (1)):
energy is used to display spectroscopic data. They are related by the expression (see Equation (1)): 
514.5
E0 (eV 2.41 514.5  
eV) = 2.41 (1) (1)
λ0λ(nm
nm)

(a) (b) 

Figure 2. Experimental set‐up with a backscattering geometry: (a) Details of the system; (b) Definition 
Figure 2. Experimental set-up with a backscattering geometry: (a) Details of the system; (b) Definition
of the numerical aperture (N.A.), with n the index of refraction of the medium in which the lens is 
of the numerical aperture (N.A.), with n the index of refraction of the medium in which the lens is
working and α the maximal half‐angle of the cone of light that can enter or exit the lens. 
working and α the maximal half-angle of the cone of light that can enter or exit the lens.

 
Coatings 2017, 7, 153 6 of 55

After light and matter have interacted in the sample, the photons (either reflected, elastically
scattered, inelastically scattered, or other photons coming from competing processes such as
fluorescence) are collected by the same objective and driven to a filter that diminishes the intensity
of the elastic photons. Generally, the cut-off frequency of this filter is close to 50–100 cm–1 , meaning
that modes with a lower wavenumber will not be detected. Photons other than the elastic ones are
then driven to a monochromator in which light dispersion occurs. Light is finally spread on a CCD
camera, converted in an electronic signal that is recorded on a computer. The spot radius on the
sample, R, is ≈ 0.6λ 0
N.A. , where λ0 is the laser wavelength and N.A. the numerical aperture as defined in
Figure 2b, n being the refractive index separating the sample and the optics. According to the Rayleigh
criterion, R is also the lateral resolution, as it is the smallest distance between two points that can be
probed. The XY stage is generally motorized in order to work in a mapping mode: The stage moves
to different x,y-positions at which spectra are recorded to check spatial inhomogeneity at the micron
scale. The vertical resolution, labelled ∆z, is generally of the order of the micron, if the material is
transparent. In addition, it can be adjusted using confocal mode. Note that it can be lower if the
material under investigation is absorbing the laser light. More details on the experimental operation of
Raman spectroscopy can be found in the paper by Gouadec and Colomban [29].

2.2.2. Conservation Rules

Raman photons are created by a fluctuating electric-dipole in the scattering medium, by the
simultaneous action of the incident light beam and the elementary excitations of the solid, leading to
→
an induced polarization moment P. To describe this interaction, three ways can be used. The easiest
one describes classically both electromagnetic field and matter. The second one describes, classically,
the electromagnetic field but quantifies matter. The third one quantifies both.
Let us start by introducing the classical monochromatic electric field of the incident laser
→ → → → →
E = E0 cos (ω0 t − k0 × r ), E0 being its amplitude, ω0 its frequency, k0 its plane wave propagation
→
vector (which is k0 = ω0 /c in vacuum, c being the speed of light) and r the 3D position in space.
→
The elementary excitation of the crystal, called the phonon, has a crystal momentum called q , and a
→
corresponding frequency ωq , for each value of q . As the system is isolated, two conservation rules
(on total energy and momentum) occur, leading respectively to Equation (2) and (3):

ω0 = ωS + ωq (2)
→ → →
k0 = kS + q (3)
→
where ωs and kS are the scattered light frequency and wavevector, respectively. Due to these
conservation rules, the geometry of the experiment normally determines orientation and magnitude
of the scattering wave vector. In current experiments, the backscattering geometry (i.e., θ = 180◦ , see
Figure 3 for the definition of this angle) is one of the mostly routinely used in labs. The displacement of
→ → →
a peculiar ion in the unit cell around its rest position is given by u( r , t) ∝ Q(ωq , t)ei(ωq t− q × r ) , where
Q(ωq , t) is the phonon coordinate. The phonon coordinate is a linear combination of bond lengths and
→
bond angles and is associated to the normal modes of vibration. Whatever the crystal symmetry, | q |
→
varies from 0 to a value | q max | which is of the order of 1/a, a being the typical lattice parameter, close to
1 Å. In the visible range of radiation, considering the conservation rule on momentum, and whatever
→ → →
the value of θ, as the ratio between | q max | and |k0 − kS | is close to 100, it means that necessarily the
→
phonon that will satisfy the conservation rule will be close to | q | ≈ 0, i.e., close to the center of the
Brillouin zone. For higher order processes (i.e., involving more than just one phonon), the wave vector
conservation rule becomes Equation (4):
→ → →
k 0 = k S + ∑ qi (4)
i
Coatings 2017, 7, 153 7 of 55

As a consequence,
Coatings 2017, 7, 153    not only phonons at the center of the Brillouin zone can contribute now.7 of 54 

(a)  (b) 

Figure 3. Scattering geometry: (a) Photon/phonon interaction; (b) Corresponding momentum. 
Figure 3. Scattering geometry: (a) Photon/phonon interaction; (b) Corresponding momentum.

2.2.3. Classical Expressions for Molecules 
2.2.3. Classical Expressions for Molecules
Before considering the more complex case of solids, we introduce some basics of Raman theory 
Before considering the more complex case of solids, we introduce some basics of Raman theory
for  molecules.  The  incident  electromagnetic  field  induces  a  dipolar  momentum  in  an  electronic 
for molecules. The incident electromagnetic field induces a dipolar momentum in an electronic system,
system,  the  ρ‐component  (ρ , ,   being  given  by  ∑ α ,  with  the  polarizability  tensor 
the ρ-component (ρ = x, y, z) being given by Pρ ≈ ∑σ αρσ Eσ , with the polarizability tensor αρσ ,
αρσ,  (higher  order  terms,  related  to  hyper‐Raman  spectroscopy,  are  not  mentioned  here).  The 
(higher order terms, related to hyper-Raman spectroscopy, are not mentioned here). The components
components of αρσ can be approximated by a Taylor expansion. For simplicity, let us forget about the 
of αρσ can be approximated by a Taylor expansion. For simplicity, let us forget about the ρ and
ρ and σ indexes coding for directions in space, and let us assume we consider a linear molecule with 
σ indexes coding for directions in space, and let us assume we consider a linear molecule with a
a normal vibrational coordinate Q(t) characterized by an intrinsic vibrational frequency ωvib. Then, 
normal vibrational coordinate Q(t) characterized by an intrinsic vibrational frequency ωvib . Then,
α
α ≈α α(0) + ( ∂Q∂α cos cos
ω (ω .  The  term  ∂α   is  sometimes  noted  R  and  called  the  first 
)
Q = Q0
×Q 0 vib t ). The term ( ∂Q ) Q= Q is sometimes noted R and called the
0
order  Raman 
first order Ramantensor.  It  gives 
tensor. the  coupling 
It gives strength 
the coupling of  the 
strength of nuclear  and and
the nuclear electronic  coordinates. 
electronic By 
coordinates.
including both the expression of the incident electric field and the polarizability elements expansion, 
By including both the expression of the incident electric field and the polarizability elements expansion,
one obtains by using the product of two cosines the following expression (see Equation (5)): 
one obtains by using the product of two cosines the following expression (see Equation (5)):

α cos ω E0 Q0 cos ω ω cos ω ω   (5) 

P ≈ α(0) cos (ω0 t) + 2 R × (cos ([ω0 − ωvib ]t) + cos ([ω0 + ωvib ]t)) (5)
2
in which we have omitted the    term, for simplicity, and the random phase of the nuclear mode 
→ →
of vibration acquired during the scattering process. This expression contains three terms: The first 
in which we have omitted the k0 × r term, for simplicity, and the random phase of the nuclear mode
one  has  the acquired
of vibration same  frequency 
during theas scattering
the  incident  laser 
process. and 
This is  interpreted 
expression as three
contains due  to  elastic 
terms: TheRayleigh 
first one
scattering, the second and third ones having their frequencies lowered or increased by the frequency 
has the same frequency as the incident laser and is interpreted as due to elastic Rayleigh scattering, the
ω vib.  These 
second and latter  terms 
third ones are  respectively 
having their frequenciesinterpreted 
loweredas  ordue  to  the by
increased inelastic  Stokes ωand 
the frequency anti‐Stokes 
vib . These latter
Raman scattering. These processes are represented in an energy diagram in Figure 4a–c, respectively. 
terms are respectively interpreted as due to the inelastic Stokes and anti-Stokes Raman scattering.
For the Stokes photon, and far from the oscillating dipole, the amplitude of the electric field is given 
These processes are represented in an energy diagram in Figure 4a–c, respectively. For the Stokes
by classical electrodynamics as (see Equation (6)): 
photon, and far from the oscillating dipole, the amplitude of the electric field is given by classical
electrodynamics as (see Equation (6)): ω ω e
| | sinφ  (6) 
4πε
(ω0 − ωvib )2 eikS r
EStokes = | PStokes | sin ϕ (6)
φ being the orientation given from the dipole axis and ε
4πε0 c2 0 the permittivity of vacuum. The outgoing 
r
flux  of  energy  is  given  by  the  Poynting  vector:  | | .  Integrating  over  the  unit 
ϕ being the orientation given from the dipole axis and ε0 the permittivity of vacuum. The outgoing
sphere, this flux gives the total energy radiated by the Stokes induced dipole (see Equation (7)): 
flux of energy is given by the Poynting vector: SStokes = ε20 c | EStokes |2 . Integrating over the unit sphere,
this flux gives the total energy radiated by the ω Stokes
ω induced dipole (see Equation (7)):
σ | |   (7) 
12πε
(ω0 − ωvib )4
σStokes = ( Q0 E0 )2 | R|2
The classical theory then predicts the fourth power (sign − is replaced by + if we consider anti‐ (7)
12πε0 c3
Stokes), the incident beam intensity    and the  | |   dependencies. However, it fails to reproduce 
resonance effects, Stokes, and anti‐Stokes intensity ratio behavior with temperature, etc. 
 
Coatings 2017, 7, 153 8 of 55
Coatings 2017, 7, 153    9 of 54 

where 
The α
classical   is composed of k products in the form of 
theory
then predicts the fourth power (sign − is replaced 1  by
for Stokes and 
+ if we consider

anti-Stokes), the incident beam intensity E0 2 and the | R|2 dependencies. However, it fails to reproduce
resonance effects,
Stokes,   for anti‐Stokes processes. 
and anti-Stokes intensity ratio behavior with temperature, etc.

 
Figure  4.  Jablonski  diagram  of  Rayleigh  scattering  (a),  non‐resonant  Stokes  (b)  and  anti‐Stokes  (c) 
Figure 4. Jablonski diagram of Rayleigh scattering (a), non-resonant Stokes (b) and anti-Stokes
Raman scattering, and pre‐resonant (d) and resonant Raman scatterings (e,f). 
(c) Raman scattering, and pre-resonant (d) and resonant Raman scatterings (e,f).
2.2.5. Raman Effect in Crystals 
2.2.4. Semi-Classical Expression for Molecules
For well oriented crystals, the same kind of expressions holds but with some changes. First, the 
vibrational 
When matterquantum  number 
is treated is  replaced 
quantum mechanically, factor of these
by  the  Bose some expbehaviors
ω/ 1 better
are ,  k  being  the 
reproduced.
Boltzmann constant and T the temperature expressed in K. Second, for monocrystals, one must take 
We only consider the first order induced dipole here. During the scattering process, one incident
care of the incident and scattered polarization directions. In general, one has the differential cross 
photon (of energy h̄ω0 , h̄ being the Planck constant divided by 2π) is annihilated, and one photon
section expressed as (Equation (11)): 
and one phonon are created. Below, all the results are obtained in the framework of time-dependent
perturbation theory applied for a moleculedσ(details in Chapter 4 of [41]), limited here to the first order of
∝ e α   (11) 
expansion [22]. Let us define the unperturbed dΩ initial and final states of the molecule considered: |i i and
| f i respectively. The ρ-component (ρ = x, y, z) of the first order induced dipole is ( Pρ )fi = ∑ (αρσ )fi Eσ ,
where dΩ is a solid angle, e0ρ and esσ are the ρth and σth components of respectively the incident 
σ  
whereand  )fi = h f |αρσ
(αρσscattered  |i i is the transition
  elementary  polarizability,
polarization  as given incan 
vectors.  It  sometimes  Equation (8): as:  dσ/dΩ ∝
be  found 
| α | , dσ/dΩ ∝ | | , or  dσ/dΩ ∝ ∑ .  For  single 
 crystals,  by 
1 h f | p̂ρ |r ihr | p̂σ |  iand 
i h , one can deduce the symmetry of 
f | p̂σ |r ihr | p̂ρ |i i
(αρσ )fi = ∑
measuring the dependence of the scattered intensity on 
ωri − ω0 − iΓr
+
ωrf + ω0 + iΓr
the Raman tensor and hence the symmetry of the corresponding Raman‐active phonon [45]. 
}
(8)
r
To determine the cross sections experimentally, one needs first a reference with a known Raman 
r 6 =
cross  section.  In  order  to  deduce  the  i, cross 
f section  relatively  to  the  reference  material,  one  has  to 
correct from electromagnetic biases such as reflection losses which can be different from the reference 
The summation r runs over all the states |r i of the molecule. ωri = ωr − ωi , h̄ωi and h̄ωf being the
material and the sample to analyze (due to specific refractive index) or interference effects [46–48]. 
energies of the initial and final states, respectively. Γr is related to the lifetime of the level r (damping
The reader interested in the method can read the detailed work of Klar et al. that was performed on 
factor).graphene [49]. 
The numerator h f | p̂ρ |r ihr | p̂σ |i i is the product of two transition electric dipole terms: One for a
transition from |i i to |r i (absorption) and one from |r i to | f i (emission). Term one and two under the
sum will not play the same role depending on the comparison between ω0 and ωri,f : The first term
can increase a lot if ω0 ≈ ωri , being predominant in the case of resonance condition, whereas this is
not the case for the second one that is still present even far from resonance conditions. In general, all
the pathways connecting |i i and | f i with non-null transition electric dipole terms must be considered
Coatings 2017, 7, 153 9 of 55

in the summation. Representing this scattering in an energy diagram is simplified by introducing a

virtual state and its corresponding virtual level of energy (i.e., not a stationary state coming from the
resolution of the Schrodinger’s equation), as it is done in Figure 4b,c (the virtual level is marked by a
dashed line). The case where ω0  ωri is represented in Figure 4b (Stokes) and c (anti-Stokes), whereas
the case ω0 ≈ ωri is represented in Figure 4d–f corresponding respectively to pre-resonance, discrete
resonance and continuum resonance Raman scatterings. By considering the Born–Oppenheimer
condition (electron and nucleus motions are not coupled), one has the vibronic wavefunction that
can be written |r i =|er i|vr i with the corresponding quantum number vr for vibration and the energy
}ωr = }ωer + }ωvr . In the ground electronic state, the expression of (αρσ )fi (see Equation (8)) does not
change a lot. It is labelled “the A-term” in the Albrecht denomination [23]. However, if one introduces
a perturbation calculated by considering electron–nucleus interaction (i.e., the electronic Hamiltonian
is expanded in the nuclear displacements around the equilibrium position Q0 ), then other additional
terms (called B, C, and D terms) appear in the previous expression of (αρσ )fi . More information about
the meaning of these terms can be found in the paper by Long [41].
As the electric dipole moments can be expanded in a Taylor series over the normal vibrational
coordinates, one can obtain the following expression (Equation (9)):
 
∂αρσ
hvf |αρσ |vi i ≈ αρσ (0)
h vf | vi i + ∑ × h v f | Qk | vi i + . . . (9)
k
∂Qk Q = Q0

√ √
with hv f | Qk |vi i = vi + 1 if v f = vi + 1, vi if v f = vi − 1, or 0 in the other cases, noting the elements
(k)
∝
∂α
of the Raman tensor as Rρσ ( ∂Qρσ ) . We can notice that the vibrational mode will be Raman
k Q = Q0
active only if this last term is different from zero. This condition defines the so-called “selection rules”.
They are directly related to the symmetry of the system. See [44] for further details. Considering that
the molecule is not oriented preferentially, the total energy radiated by the Raman effect is given by
the expression (Equation (10)):
 2
 
σStokes−fi ∝ (ω0 − ωvib )4 E02  ∑ ( α ) (10)
 
ρσ fi 
 ρσ

 2
where |(αρσ )fi |2 is composed of k products in the form of ( ∂Qρσ )
 ∂α
 × (vi + 1) for Stokes and

k Q = Q0
 2
 ∂αρσ
( ∂Q )  × (vi ) for anti-Stokes processes.

k Q = Q0

2.2.5. Raman Effect in Crystals

For well oriented crystals, the same kind of expressions holds but with some changes. First,
the vibrational quantum number is replaced by the Bose factor n = [exp (}ω/kT ) − 1]−1 , k being the
Boltzmann constant and T the temperature expressed in K. Second, for monocrystals, one must take
care of the incident and scattered polarization directions. In general, one has the differential cross
section expressed as (Equation (11)):
 2
dσ  
∝ ∑ e0ρ αρσ eSσ  (11)
 
dΩ ρσ 

where dΩ is a solid angle, e0ρ and esσ are the ρth and σth components of respectively the
→ →
incident e0 and scattered eS elementary polarization vectors. It sometimes can be found as:
→ → 2 → → 2
dσ/dΩ ∝ |e0 × [α] × eS | , dσ/dΩ ∝ |e0 × R × eS | , or dσ/dΩ ∝ | ∑ e0ρ Rρσ eSσ |2 . For single crystals,
ρσ
→ →
by measuring the dependence of the scattered intensity on and e0
can deduce the symmetry of eS , one
the Raman tensor and hence the symmetry of the corresponding Raman-active phonon [45].
Coatings 2017, 7, 153 10 of 55

To determine the cross sections experimentally, one needs first a reference with a known Raman
cross section. In order to deduce the cross section relatively to the reference material, one has to correct
from electromagnetic biases such as reflection losses which can be different from the reference material
and the sample to analyze (due to specific refractive index) or interference effects [46–48]. The reader
interested in the method can read the detailed work of Klar et al. that was performed on graphene [49].
Coatings 2017, 7, 153    10 of 54 
2.3. Basic Properties of Graphene and Related Materials
2.3. Basic Properties of Graphene and Related Materials 
Due to its valency, carbon exists under several allotropic forms—such as diamond, graphite,
graphene,Due nanotubes, and fullerene—and
to  its  valency,  many several 
carbon  exists  under  other forms will forms—such 
allotropic  likely be discovered in thegraphite, 
as  diamond,  future [50].
graphene, nanotubes, and fullerene—and many other forms will likely be discovered in the future [50]. 
Plasma and nanoscale plasma/surface interactions are processes responsible for a large number of them
Plasma 
(we do and  nanoscale 
not pretend plasma/surface 
to list all interactions 
these interactions; they canare 
beprocesses 
found in responsible 
the review by for Ostrikov
a  large  number   
et al. [51]).
of  them  (we  do  not  pretend  to  list  all  these 
3 interactions;  they  can  be 
Roughly speaking, two families exist: The “sp family” (with the tetra-coordinated diamond), and the found  in  the  review  by   
“sp2 Ostrikov  et  al. 
the[51]).  Roughly  speaking,  two  families  with
exist: many
The  “sp 3  family”  (with  the  tetra‐
family” with graphene as the model of aromatics, possibilities in between the two
coordinated diamond), and the “sp2 family” with the graphene as the model of aromatics, with many 
families [52]. Amorphous carbons can mix aromatic sp2 and sp3 carbons, as well as heteroatoms.
possibilities  in  between  the  two  families  [52].  Amorphous  carbons  can  mix  aromatic  sp2  and  sp3 
Graphene is a monolayer thick crystal organized as displayed in Figure 5a. The hybridization
carbons, as well as heteroatoms. 
between one s-orbital and two p-orbitals leads to a trigonal planar structure with three in-plane sp2
Graphene is a monolayer thick crystal organized as displayed in Figure 5a. The hybridization 
σ bonds and one out-of-plane π bond. The σ bonds are responsible of the robustness of the lattice,
between one s‐orbital and two p‐orbitals leads to a trigonal planar structure with three in‐plane sp 2 σ 

whereas the π bond, by binding covalently with a neighbor π bond, is responsible of

bonds  and  one  out‐of‐plane  π  bond.  The  σ  bonds  are  responsible  of  the  robustness  of  the  lattice,  the electronic
conduction. Two
√ atoms per unit cell are √ necessary to reproduce the crystal, and the two vectors,
whereas the π bond, by binding covalently with a neighbor π bond, is responsible of the electronic 
a1 =conduction. 
(3a/2, a Two  3/2) atoms 
and a2per =unit  cell −
(3a/2, are  3/2), with
a necessary  a = 1.42 Å,
to  reproduce  are
the  displayed
crystal,  in two 
and  the  Figure 5a [53].
vectors,   
3 /2, √3/2  vectors
The reciprocal-lattice and  3b1/2,
are and √3/2
b2 . In, with a = 1.42 
this momentum space, three specific points of the
, are displayed in Figure 5a [53]. The 
reciprocal‐lattice vectors are b
Brillouin zone are the Г, M and K1 and b points. 2. In this momentum space, three specific points of the Brillouin 
The lower part of Figure 5b represents the electronic structure
zone are the Г, M and K points. The lower part of Figure 5b represents the electronic structure in 
in vicinity of the K point, where the π and π* bands meet with a zero-gap energy. The dispersion of
the πvicinity of the K point, where the π and π* bands meet with a zero‐gap energy. The dispersion of the 
and π* bands is E± ≈ ±v F q, where v F is the Fermi velocity, and q the momentum measured
π  and to
relatively π*  bands 
the is  [54]. The, shape
K point where of the   is  electronic
the  Fermi  velocity, 
bands formsand  q 
a the 
conemomentum 
which is calledmeasured 
a Dirac
relatively to the K point [54]. The shape of the electronic bands forms a cone which is called a Dirac 
cone, because of the linear dispersion curve. It is because of this peculiar point that graphene is called
cone, because of the linear dispersion curve. It is because of this peculiar point that graphene is called 
a semi-metal. A review by Neto et al. presents the basic theoretical aspects of graphene’s peculiar
a semi‐metal. A review by Neto et al. presents the basic theoretical aspects of graphene’s peculiar 
electronic properties [53]. Note that the sp2 behavior can be partially modified by some mechanisms,
electronic properties [53]. Note that the sp2 behavior can be partially modified by some mechanisms, 
suchsuch as chemical adsorption of hydrogen on top of C atoms, that modify curvature and then induce 
as chemical adsorption of hydrogen on top of C atoms, that modify curvature and then induce a
mixed sp2 /sp32/sp
a mixed sp state [55].
3 state [55]. 

 
(a)  (b)  (c) 

Figure 5. Honeycomb lattice of graphene. (a) Unit‐cell vectors (a1 and a2). (b) Electronic structure in 
Figure 5. Honeycomb lattice of graphene. (a) Unit-cell vectors (a1 and a2). (b) Electronic structure in the
the reciprocal lattice. Г, K, and M are high symmetry points in this space. (c) Phonon dispersion curve 
reciprocal lattice. Г, K, and M are high symmetry points in this space. (c) Phonon dispersion curve and
and  Raman  spectra  (LO,  LA, iTO,  iTA,  oTO,  and  oTA.  O  and  A  refer  to  optic  and  acoustic  phonon 
Raman spectra (LO, LA, iTO, iTA, oTO, and oTA. O and A refer to optic and acoustic phonon branches,
branches, L and T refer to longitudinal and transversal, and i and o refer to in plane or out of plane, 
L and T refer to longitudinal and transversal, and i and o refer to in plane or out of plane, respectively).
respectively). 

The upper part of Figure 5c displays the phonon dispersion [56] for a Г‐M‐K‐Г trajectory in the 
Brillouin zone (the figure is generally presented with the phonon energy horizontally). As there are 
two  atoms  in  the  unit  cell,  there  are 3  ×  2  phonon  branches.  “O” and  “A”  stand  for  optical (three 
branches) and acoustic (three branches) phonon branches, acoustic branches being close to zero at the 
center of the Brillouin zone. “L” and “T” stand for lateral or transverse vibrations and “i‐” or “o‐” stand 
for in plane or out of plane. The lower part of Figure 5c displays a typical Raman spectrum for defect 
Coatings 2017, 7, 153 11 of 55

The upper part of Figure 5c displays the phonon dispersion [56] for a Г-M-K-Г trajectory in the
Brillouin zone (the figure is generally presented with the phonon energy horizontally). As there are
two atoms in the unit cell, there are 3 × 2 phonon branches. “O” and “A” stand for optical (three
branches) and acoustic (three branches) phonon branches, acoustic branches being close to zero at the
Coatings 2017, 7, 153 
center  
of the Brillouin zone. “L” and “T” stand for lateral or transverse vibrations and “i-” or “o-” 11 of 54 
stand
for in plane or out of plane. The lower part of Figure 5c displays a typical Raman spectrum for defect
free and defective graphene. In this spectral range, one can observe the presence of one band (called 
free and defective graphene. In this spectral range, one can observe the presence of one band (called
the G band) at 1582 cm−1 for the defect free sample, whereas one can see two extra bands (the D and 
the G band) at 1582 cm−1 for the defect free sample, whereas one can see two extra bands (the D and D’
D’ bands) for the defective sample. As it has been discussed in Section 2.2.2, not all the phonons give 
bands) for the defective sample. As it has been discussed in Section 2.2.2, not all the phonons give rise
rise  to  a  band  in  the  Raman  spectrum.  We  give  more  information  about  the  Raman  spectra  of 
to a band in the Raman spectrum. We give more information about the Raman spectra of graphene
graphene related materials in the next section. 
related materials in the next section.

2.4. Raman Spectra of Graphene, Graphite, and Disordered Carbons 
2.4. Raman Spectra of Graphene, Graphite, and Disordered Carbons
This paragraph is separated in two subsections. The first one gives usable information about the 
This section is separated in two subsections. The first one gives usable information about the
origin and behavior of the bands often encountered for aromatic based materials. The second section 
origin and behavior of the bands often encountered for aromatic based materials. The second section
deals with a historical overview of the findings about Raman spectroscopy in the field, in a linear way. 
deals with a historical overview of the findings about Raman spectroscopy in the field, in a linear way.

2.4.1. Basics of Raman Spectroscopy for Graphene and Graphite 
2.4.1. Basics of Raman Spectroscopy for Graphene and Graphite
Raman spectra
Raman spectra of
of aa wide
wide variety
variety of
of disordered
disordered carbons
carbons are
are displayed
displayed in
in Figure
Figure 66 in
in order
order to
to 
overview what varies and how much in terms of band intensities, width, position, etc. The Raman 
overview what varies and how much in terms of band intensities, width, position, etc. The Raman
spectra displayed in Figure 6 are obtained from a highly oriented pyrolytic graphite, nanographites, 
spectra displayed in Figure 6 are obtained from a highly oriented pyrolytic graphite, nanographites,
and amorphous carbon (we do not specify the kind of synthesis here as we consider only the main 
and amorphous carbon (we do not specify the kind of synthesis here as we consider only the main
trends in the Raman spectra). Note that a complete discussion about what is called “intensity” in the 
trends in the Raman spectra). Note that a complete discussion about what is called “intensity” in the
literature when speaking about band fitting procedures, is given in Section 2.6. 
literature when speaking about band fitting procedures, is given in Section 2.6.

 
Figure 6. Raman spectra of graphite and disordered carbons recorded at 514 nm. (a) Attribution of the 
Figure 6. Raman spectra of graphite and disordered carbons recorded at 514 nm. (a) Attribution
main 
of the bands 
main in  the  first, 
bands in the second,  and  third 
first, second, andorder 
thirdregions. 
order (b)  Same  for 
regions. (b) a  variety 
Same for of  more  disordered 
a variety of more
disordered
carbons.  carbons.

Graphite belongs to the P63/mmc ( ) space group. If considering only a graphene plane, at the 
Г  point  of  the  Brillouin  zone,  there  are  six  normal  modes  that  possess  only  one  mode  (doubly 
degenerate in plane) with a E2g representation, which is Raman active (see [57]). Its wavenumber is 
at 1582 cm−1 and it gives rise to the so‐called “G band”. Its width is close to 15 cm−1 and it is mainly 
due  to  an  electron–phonon  coupling  interaction  [58].  By  combining  two  graphene  planes  to  build 
graphite, one can obtain another Raman active mode that gives rise to a band at 42 cm−1, which cannot 
Coatings 2017, 7, 153 12 of 55

Graphite belongs to the P63 /mmc (D6h 4 ) space group. If considering only a graphene plane, at

the Г point of the Brillouin zone, there are six normal modes that possess only one mode (doubly
degenerate in plane) with a E2g representation, which is Raman active (see [57]). Its wavenumber is at
1582 cm−1 and it gives rise to the so-called “G band”. Its width is close to 15 cm−1 and it is mainly due
to an electron–phonon coupling interaction [58]. By combining two graphene planes to build graphite,
one can obtain another Raman active mode that gives rise to a band at 42 cm−1 , which cannot be
measured by standard set-ups as the one presented here. Then for standard set-up operation, only one
band should be detected. However, this is not the case: For pure graphite, for example (see Figure 6a),
one extra band with a high intensity is detected (one-third of the G band intensity, at 2720 cm−1 ). This
band is composed of several bands for graphite and few layers graphene, but has a Lorentzian shape
for monolayer graphene and disordered graphite in which stacking in the c direction is not like in
graphite [1,59]. Its intensity, compared to the G band can vary from 3 to 1/3 from graphene to graphite,
respectively. When disorder increases, this band broadens, overlapping with other bands and nearly
disappears. For amorphous carbon, the intensity compared to that of the G band is lower than 6% (see
Figure 6b). There are also several weaker bands (2–5% of the G band intensity, at 2450, 3240, 4300 cm−1 )
and even weaker bands, marked by stars (≈0.4% of the G band intensity at 1750 cm− 1 ). Most of the
weak bands are listed in the paper by Kawashima and Katagiri [60]. As proposed by the international
consensus, these bands are due to the double resonance mechanism which is described in detail in
Section 2.5. A defective graphite presents other bands that can be as intense as the G band at 1350
and 1615 cm−1 (see Figure 6). These bands are activated by defects due to the breaking of the crystal
symmetry that relax the Raman selection rules. They are called the “D and D’ bands”, respectively.
The “D” stands for “defect” and has nothing to do with the diamond band that lies at 1332 cm−1 .
The intense bands lying below 1640 cm−1 are due to first order phonons (see the phonon relation
dispersion in Figure 5c). In the range ≈2000–3000 cm−1 , they are due to two-phonon processes and
named 2D, D + D’, 2D’, and so forth. For higher wavenumbers, they are due to third order processes,
etc. When increasing the order of the process, the intensity is generally diminished because of the
cross section which becomes less and less probable. Considering the less intense bands, the D” band
is present in the shoulder of the D band of very defective samples. It is always needed when fitting
(see Section 2.6). Other bands are the 2450 cm− 1 band, which has been attributed recently to a D +
D” band by Couzi et al. [61], the D + D’ (in literature, the wrong D + G label is often found [62]), the
2D’ bands and the 2D + G band. Even weaker bands are present and marked by stars in Figure 6a.
The 1750 cm−1 band is called the M band and has been understood in the framework of the double
resonance mechanism [63].
In Figure 6b, one can see that when disorder increases, the bands broaden, and the relative
intensity of the bands changes: The D band increases with disorder and then decreases when being
close to an amorphous carbon. These two behaviors have been related to the coherence length La
(obtained from structural analysis), with the two historical formulae (Equations (12) [64] and (13) [4,5]):

ID c
For La > 2 nm : = (Tuinstra and Koenig relation) (12)
IG La

ID
For La < 2 nm : = c0 L2 (Ferrari’s relation) (13)
IG
c and c’ are parameters that depend on the fourth power of the laser wavelength [4,65,66] and
that can vary from one sample to the other [65,67]. Why ID /IG behaves like 1/L a for La > 2 nm is also
justified in Section 3.1. Since 2010, an upgrade was published that allows a better understanding of
the information retrieved from the intensity ratio. It is presented in Section 3.3. Note that instead
of ID /IG , another spectral parameter that is often used is proportional to ID /IG × E0 (eV)4 , E0 being
the laser energy. This is because the c and c’ parameters evolve as the fourth power of the laser
wavelength [66,68]. It allows to compare results from different wavelength on a same plot.
Coatings 2017, 7, 153 13 of 55

One important fact about band parameters behavior is that some bands disperse, which normally
does not happen according to constant eigenenergy’s values obtained by quantum mechanics. This,
again, is due to the double resonance mechanism, detailed in Section 2.5. Here, we briefly describe
what is observed. The D band disperses linearly with the energy of the laser used, the slope being close
to 50 cm− 1 ·eV− 1 . This is a consequence of the double resonance mechanism. This has been observed
for many aromatic based carbons, with different amounts of disorder (see Figure 7), an offset being
present from one sample to the other (in the range ± 15 cm− 1 ). The D-band dispersion is useful for
differencing an aromatic based sample from a diamond based sample because the 1332 cm− 1 band in
the latter case does not disperse. The D’ band also displays a dispersion (not shown here) but it is less
significant than that  of the D band.
Coatings 2017, 7, 153  13 of 54 

 
Figure 7. Dispersion relations of the (a) G band and (b) D band for many disordered samples (data 
Figure 7. Dispersion relations of the (a) G band and (b) D band for many disordered samples (data
derived from literature as indicated). 
derived from literature as indicated).

The 2D band has twice the slope of the D band (not shown here). Several other weaker bands also 
The 2D band has twice the slope of the D band (not shown here). Several other weaker bands also
display a dispersive behavior, which can be explained by the double resonance mechanism [61,69]. The 
display a dispersive
G  band  behavior,
is  not  due  which
to  the  so  called can be explained
double  bymechanism 
resonance  the doubleand  resonance mechanism
for  perfect  graphite [61,69].
and 
Thegraphene, it does not display dispersion, lying at 1582 cm
G band is not due to the so called double resonance −1 mechanism and for perfect graphite and
. However, its position can change with 
graphene, it does not display dispersion, lying at 1582 cm− 1 . However,
the state of disorder in the material, in the range 1590–1600 cm its position can change with
−1 (for nanocrystalline graphite) down 

to 1520 cm  for amorphous carbons. This band position is sensitive to clustering of the sp2 phase, 
−1

bond  disorder,  presence  of  sp2  rings  and/or  chains,  presence  of  sp3  carbons  and  the  way  they  are 
coupled to aromatic carbons [70]. Due to the electronic resonance Raman process (see Figure 4e and 
f), the G band can display a dispersion behavior, as displayed in Figure 7b, driven by the size of the 
aromatic domains (from roughly 0.5 eV up to few eVs for few aromatic carbon clusters [71]). This is 
Coatings 2017, 7, 153 14 of 55

the state of disorder in the material, in the range 1590–1600 cm− 1 (for nanocrystalline graphite) down
to 1520 cm− 1 for amorphous carbons. This band position is sensitive to clustering of the sp2 phase,
bond disorder, presence of sp2 rings and/or chains, presence of sp3 carbons and the way they are
coupled to aromatic carbons [70]. Due to the electronic resonance Raman process (see Figure 4e,f), the
G band can display a dispersion behavior, as displayed in Figure 7b, driven by the size of the aromatic
domains (from roughly 0.5 eV up to few eVs for few aromatic carbon clusters [71]). This is particularly
true for amorphous carbons. To our knowledge, this dispersion parameter is generally not used to
better characterize amorphous carbons with small aromatic size skeleton, but should be used more
often such as was done in the work by Lajaunie et al. [72].
The width of the G band (ГG ) can be used to have an idea about the amount of defects (even if
depending on the sample there are some differences, as can be seen in Part 3 with doped graphene,
for example). It varies generally from 10 up to 200 cm− 1 from graphene to amorphous carbons, but
can be influenced by doping. It was found to vary roughly as a power law of La [5] for a large variety
of samples, but it was found to vary as 1/La for samples with La in the range 20–65 nm [65]. Using
only ГG is not enough to better characterize the sample analyzed, since the ID /IG parameter can be
different for two kinds of samples whereas ГG is the same.

2.4.2. Historical Aspects

The following section is meant to provide an intermezzo, but detailed description of historical
highlights in Raman spectroscopy of aromatic carbons. This section is less essential to the general
reading of this paper, and therefore we refer to Section 2.5 on the double resonance mechanism for a
continued subject reading.
Figure 8 displays the most important historical breakthroughs in Raman spectroscopy of aromatic
carbons. First Raman spectra from a carbon were obtained on diamond in 1930. A band was observed
at 1332 cm− 1 [73], with a better understanding of the first and second orders reported in 1970 [74].
The phonon spectrum of graphite was modelled and obtained for the first time in 1965 [75,76]. Only
two modes are Raman active according to the point group symmetry analysis. In 1970, Tuinstra
and Koenig [64] detected with Raman spectroscopy only one band at 1575 cm− 1 for graphite and
attributed it to a doubly degenerate deformation vibration of hexagonal rings, corresponding to the
E2g mode (The true frequency admitted today is 1582 cm− 1 [77], but at that time the authors did not
realize they used a high power (300 mW instead of the few mW or even less for absorbent materials)
that can increase the equilibrium temperature of the sample, resulting in a downshift of the bands.)
Moreover, they compared graphite with more disordered carbons (i.e., activated charcoal, lampblack,
and vitreous carbon) and found a new band close to 1355 cm− 1 . They noted that this band is close to
the 1332 cm− 1 band of diamond, but ruled out the fact that the 1355 cm− 1 band is due to sp3 carbons.
They also showed that the relative height ratio between the 1355 cm− 1 band (labelled D band, for
“defect-induced band”) and the 1575 cm− 1 band (labelled G band for “graphite allowed band”) is
correlated to the crystallite size, La , retrieved from X-ray diffraction measurements. This is the so
called Tuinstra–Koenig relation. In 1978, Tsu et al. observed three behaviors that are nowadays used
to characterize defects and electronic structure of aromatic carbons [77]. First, they observed a new
mode at 1627 cm− 1 that they attributed wrongly to a splitting of the E2g mode. Then, they saw a high
shift of the 1575 cm− 1 band (up to 1590 cm− 1 ) and finally they observed the presence of a band at
2742 cm− 1 , twice the frequency of the 1370 cm− 1 band (also high shifted) even if the 1370 cm− 1 band
is not present in the spectrum. Nowadays, we label the 1627 and 2742 cm− 1 bands as the D’ and 2D
band, respectively. Using a different polarization configuration, Vidano et al. [78] related the D, G, D’,
and 2D bands to in-plane vibrations and noticed the composite behavior of the 2D band, prophesying
that once well understood, this behavior could help in better characterizing disorder and structural
imperfection. Indeed, the shape and intensity of this 2D band was found to be very dependent on the
electronic structure and the number of stacked layers in a multilayer graphene sample [1], and to the
quality of the layer stacking in nano graphite by Cançado et al. [59], for example. The spectroscopic
Coatings 2017, 7, 153 15 of 55

parameters of all these bands were noticed to be very dependent on the structure of the samples and
then, to give a quick and good idea of the degree of graphitization, a thermal treatment was performed
on different carbon fibers, coals, and pyro carbons between 450 and 3000 ◦ C [78–80] and later, on
amorphous carbons by Ferrari and Robertson [5].
Coatings 2017, 7, 153    15 of 54 

 
Figure 8. Chronology of the Raman effect applied to aromatic carbon. 
Figure 8. Chronology of the Raman effect applied to aromatic carbon.

D Band and Combination Band Dispersions 
D Band and Combination Band Dispersions
In 1979, Nemanich and Sollins attributed the 2D band plus weaker bands appearing at 2450 and 
In 1979,
3248  Nemanich
cm−1  to  anddensity 
vibrational  Sollinsof 
attributed the 2D using 
states  features,  band plus weaker
calculated  bands dispersion 
phonon  appearing curves 
at 2450 of 
and
3248 − 1
cm to vibrational density of states features, using calculated phonon dispersion curves of
graphite [81]. However, this was not completely satisfactory as the 2D band, even when the graphite 
graphite [81]. However, this was not completely satisfactory as the 2D band, even when the graphite
sample is defect free, is of the same order of magnitude as the G band, whereas it should depend on 
sample is defect free, is of the same order of magnitude as the G band, whereas it should depend on
the defect density according to this hypothesis (Before the physical origin of the 2D band was well 
theunderstood, it was named the G’ band, exactly because it was always observed in the spectra together 
defect density according to this hypothesis (Before the physical origin of the 2D band was well
understood, it was named
with  the  Raman  allowed the G’ band,
G  band.  The exactly because
D*  band  it was
can  also  alwaysin 
be  found  observed in theBe 
the  literature.  spectra together
careful,  the 
with the Raman allowed G band. The D* band can also be found in the literature. Be careful, the
denomination D* is used since 2016 for another band. See in the paragraph text for details.). Part of 
the  problem D*
denomination was  issolved 
used sincewhen 2016Vidano,  in  1981,  band.
for another noticed See
that 
inthe 
theD paragraph
and  2D‐band  textfrequencies  were 
for details.). Part
dependent on the laser wavelength (the D band varying from 1360 down to 1330 cm
of the problem was solved when Vidano, in 1981, noticed that the D and 2D-band frequencies −1 when using 
were
on the laser wavelength (the D band varying from 1360 down to 1330 cm− 1 when using
laser wavelengths from 488 nm up to 647 nm, and a slope which is twice for the 2D band) [82], hiding 
dependent
a vibronic resonance behavior. The same kind of dispersion for the D and 2D bands was observed on 
laser wavelengths from 488 nm up to 647 nm, and a slope which is twice for the 2D band) [82], hiding
other  graphites 
a vibronic resonance [83,84],  carbon 
behavior. Theblacks 
same[68], 
kindhydrogenated 
of dispersionamorphous 
for the D and carbons  [85],  and 
2D bands waslater  on 
observed
carbon nanotubes [86,87] and most recently on graphene [62] (and references therein). The slope is 
on other graphites [83,84], carbon blacks [68], hydrogenated amorphous carbons [85], and later on
close to 50 cm
carbon nanotubes/eV for the D band and close to the double for the 2D band. Dispersion of weaker 
−1
[86,87] and most recently on graphene [62] (and references therein). The slope is
bands, mainly due to combination modes such as 2D + G, 2D + 2G, etc., were also reported in [4,5,60]. 
− 1
close to 50 cm /eV for the D band and close to the double for the 2D band. Dispersion of weaker
In 1984, Mernagh et al. also noticed that the  /   ratio was depending on the laser wavelength 
bands, mainly due to combination modes such as 2D + G, 2D + 2G, etc., were also reported in [4,5,60].
[68], which is another proof that the D band arises from a resonant effect (if not, the ratio should be 
In 1984, Mernagh et al. also noticed that the ID /IG ratio was depending on the laser
constant  because  of  the  ω dependency  in  the  non‐resonant  Raman  cross  section  affecting  all   
wavelength [68], which is another proof that the D band arises from a resonant effect (if not, the
non‐resonant bands). In 1989, Knight and White determined the c value appearing in the Tuinstra 
ratio should be constant because of the ≈ ω0 4 dependency in the non-resonant Raman cross section
and Koenig relation at 4.4 nm and that was done with 514 nm lasers [88] before the work of Cançado 
affecting all non-resonant bands). In 1989, Knight and White determined the c value appearing in
et al. [65]. In 1998, Tan et al. studied thermal effects on graphite and ion implanted graphite [89]. By 
thecomparing Stokes and anti‐Stokes spectra, the D and 2D bands were found shifted differently for a 
Tuinstra and Koenig relation at 4.4 nm and that was done with 514 nm lasers [88] before the
work of Cançado et al. [65]. In 1998, Tan et al. studied thermal effects on graphite and ion implanted
given temperature, without clear explanation [89]. The origin of the dispersive effect of the D and 2D 
graphite [89]. By
band  were  comparing
tentatively  Stokes
given  and anti-Stokes
by  Pócsik  et  al.  [90] spectra, the D and
and  Matthews  et 2Dal. bands were
[91]  in  1998 found shifted
and  1999, 
differently for a given temperature, without clear explanation [89]. The origin of the dispersive effect
respectively. The slopes of the dispersions were reproduced in their work by considering a coupling 
of between 
the D and 2D band
electrons  were
and  tentatively
phonons  given
with  the  same bywave 
Pócsik et al.near 
vector  [90]the 
and K  Matthews
point  of  the etBrillouin 
al. [91] in 1998
zone 
and  (and 
1999,called  the 
respectively. The  quasi 
slopesselection  rule).  However, 
of the dispersions werethis  coupling in
reproduced was  introduced 
their work by ad  hoc  and  a
considering
moreover the authors failed to reproduce the puzzling anti‐Stokes behavior. Thomsen and Reich went 
coupling between electrons and phonons with the same wave vector near the K point of the Brillouin
a step further by calculating the Raman cross section of graphite in a double resonance process [92] 
zone (and called the k ≈ q quasi selection rule). However, this coupling was introduced ad hoc and
(completed 
moreover the authorsby  Saito failed
et  al.  [93]),  and  were 
to reproduce able 
the to  reproduce 
puzzling both  the 
anti-Stokes D  and Thomsen
behavior. 2D  dispersion  relations 
and Reich went
together with the Stokes/anti‐Stokes shifts. This double resonance mechanism is due to a heritage of the 
way  Raman  spectroscopy  is  treated  in  semiconductors  and  in  which  Cardonna  played  a  major   
role  [27,42,45].  Because  of  conservation  rules  of  energy  and  momentum,  the  double  resonance 
process,  involving  photons,  electron‐hole  pairs  and  phonons,  and  described  a  little  bit  more  in 
Section 3, selectively enhances a peculiar phonon wavevector (close to the K‐point in the Brillouin 
Coatings 2017, 7, 153 16 of 55

a step further by calculating the Raman cross section of graphite in a double resonance process [92]
(completed by Saito et al. [93]), and were able to reproduce both the D and 2D dispersion relations
together with the Stokes/anti-Stokes shifts. This double resonance mechanism is due to a heritage
of the way Raman spectroscopy is treated in semiconductors and in which Cardonna played a major
role [27,42,45]. Because of conservation rules of energy and momentum, the double resonance process,
involving photons, electron-hole pairs and phonons, and described a little bit more in Section 3,
selectively enhances a peculiar phonon wavevector (close to the K-point in the Brillouin zone) and
then a phonon frequency [57]. For the D-band, a phonon and a defect are involved. For the 2D-band,
only two phonons (without defect) are necessary. This explains why the 2D-band is always visible,
even for defect free samples. The Stokes/anti-Stokes differences were understood, as the double
resonance mechanism does not involve the same phonons during creation (Stokes) or annihilation
(anti-Stokes) processes. In 2007, Pimenta et al. published a paper prophesying that being able to
reproduce the resonant Raman behaviors will allow to better characterize disorder in nano-graphite
based systems [94].
Graphene was experimentally first obtained in 2004 [95] and most of its fantastic electronic
properties, related to the Dirac cone, were reviewed soon after [53,96]. The ability of Raman
spectroscopy to study these properties is presented in the work by Ferrari and Basko [62]. Jorio,
Cançado, and Lucchese et al., in a series of papers [97–102], were able to characterize and distinguish
the influence of 0D and 1D defects on graphene. Venezuela et al. published a theoretical paper in
2011 [69] in which they calculated the double resonant Raman spectra of defective graphene, and
reproduced the dispersion of D, D’, 2D bands and weaker ones (which are combination bands but
not necessarily, some bands being attributed to acoustic branches). (The names of the bands do
not necessarily respect the names given by other authors in the literature. For example, on the one
hand the D” band in their paper can be labelled D4 in other papers such as [61]. On the other hand,
Venezuela et al. labelled bands D3, D4, D5, etc. Note that we did not use their labelling here. The
supplementary information of [62] gives (among other things) valuable information on the history of
this nomenclature.) Weaker bands, due to two phonon scatterings, were also observed and understood
in the framework of the double resonance mechanism [103,104]. In 2012, Eckmann et al. showed that
the intensity of the D’ band compared to the D band, which is not sensitive to the amount of defects, is
however sensitive to the nature of the defect (sp3 , vacancy, edge) [105]. A bibliometric search with the
key words “double resonance” + “graphite” + “Raman” in the abstract returns at present 122 papers,
concerning not only graphene but also other allotropes like carbon nanotubes, meaning this double
resonance mechanism is well established. In fact, it is so well established that it is now used on other
isoelectronic and structural analogs of graphene such as 2D dichalcogenides (ME2 , M = metal, E = S,
Se or Te) to interpret multiwavelength Raman spectra [106–108].
However, two things have to be noticed at this point about understanding Raman cross sections:
First, we have to mention the existence of an alternative approach and second we need to introduce
a possible recent breakthrough. Thus, first: Another approach was performed to model the Raman
spectrum of graphite based materials. It started in 2002 by Castiglioni et al. [109–116]. This approach
is based on calculating resonant Raman cross sections of disconnected aromatic molecules of different
sizes, governed by interactions between π electrons and the nuclei. This approach is also able
to reproduce the D-band dispersion. Even if the double resonant mechanism is now commonly
used and admitted, it does not mean the molecular approach has ceased today. For example, the
group of Castiglioni recently published a paper on a polycyclic aromatic hydrocarbon resembling a
longitudinally confined graphene ribbon with armchair edge [117]. Their technique could be applied
in the future because it can help in studying confined and nanoshaped graphene. As a proof, the
authors were able to reproduce the intensity of the G + D combination band which could be used as
an experimental measure of confinement in graphitic materials, as they claimed. The second thing
to be noticed, the possible breakthrough mentioned above, is that in 2016 the group of Heller et al.
re-interpreted the theory of graphene Raman scattering using the Kramers–Heisenberg–Dirac theory
Coatings 2017, 7, 153 17 of 55

without needing to introduce the double resonance mechanism [118]. Therefore, the authors were
able to describe with a second order perturbation theory (double resonance mechanism is a fourth
order perturbation theory [45]) the following characteristics: The bands’ dispersive behavior, defect
sensitivity, Stokes/anti-Stokes anomalies, intensities, etc. Many other effects have now to be
reproduced in the framework of this theory, especially concerning recent advances on UV Raman to
probe the dispersion of graphene far away from the K point of the Brillouin zone (see at the end of
Section 3.1), before being able to admit that this theory is better than the double resonance mechanism
theory. We have to mention that Placzeck’s theory also works fine to reproduce coupling effects
between layers in a multi-layer graphene, being able to reproduce the out-of-plane mode variation
with the number of stacked layers, in the range 10–50 cm−1 [119].
For more defective samples (such as carbon blacks, soots, nanographite, and amorphous carbons)
other bands were reported many times in the literature, already since 1985. The D3 and D4 bands are
examples of such bands. (In that nomenclature, the D1 and D2 bands are the D and D’ bands lying at
1350 and 1620 cm−1 . In the literature, the D3 band is sometimes called the A-band and the D4 band
is occasionally referred to as the TPA band (which stands for transpolyacetylene). They are found at
≈1500 and ≈1200 cm− 1 , respectively [66,120–123]. They are generally difficult to observe as they fall
in the D-G region, and for very defective materials, the D and G bands are broad (Γ ≈100 cm−1 or so),
so that only the D4 band can be seen as a shoulder on the overall spectrum. The D4 band has been
recently understood in the framework of the double resonance mechanism too [61]. More precisely,
using a large variety of disordered graphitic carbon materials, Couzi et al. [61] have shown with the
help of multiwavelength spectroscopy that this band is in fact composed of three sub-bands (the D*,
D**, and D”) that disperse differently. However, the authors failed in relating the intensity of these
sub-bands to the La parameter, essentially because the main factors governing the resonant Raman
process (and thus the corresponding band intensities) are related to the nature of defects (point defect,
edge defect, staking fault, curved or twisted planes, etc.). Note that the D” at 1100 cm−1 in the visible
range has been introduced by Venezuela et al. [69] in 2011. We give more information on the D” band
in the last paragraph of Section 3.4. The Raman spectra of amorphous carbons can be seen as simpler,
because only a broad asymmetric band is seen close to 1500 cm−1 . However, this is incorrect, and
for several reasons. First, many different kinds of amorphous carbon exist: sp2 dominated ones (a-C),
sp3 dominated ones (ta-C, t referring to tetrahedral), one containing hetero-atoms such as H (a-C:H,
ta-C:H, . . . ) or N. Their structure and properties are related but widely varying [124–126]. Second,
as there is some aromatic carbon embedded in their structure, some resonance occurs [127]. Ferrari
and Robertson studied and reviewed the Raman behavior of such materials in the 2000s [4,5,128].
Contrary to the Tuinstra and Koenig relation, the Ferrari’s relation says that when the size of the
aromatic domains is large, then the D band is intense. This relation was supposed to be connected to
the Tuinstra and Koenig relation for an L value of 2 nm, imposing a relation between c and c’, but this
connection was found empirically. More than a decade later, the evolution of ID /IG on a large scale of
L was understood, and the change of slope was found close to 1 nm [101]. It was done by bombarding
a graphene layer varying the flux of incident ions creating the surface coverage of “0D” defects in
the honey comb structure. The average distance between these 0D defects, LD , was then introduced
and a relation between ID /IG and LD found. Very recently, the group of Cançado et al. disentangled
the contribution of graphene samples containing 0D (point) and 1D (line) defects, by giving ID /IG in
function of La and LD [97]. More details on the way ion bombardment can help to better understand
Raman spectra are given in Section 3.3. Just note that very recent improvements have been done by
the same group in order to distinguish point defects and line defects using multiwavelength Raman
spectroscopy [97].
The historical approach in this review is mainly focused on Raman spectroscopy of graphene
based samples. However, one should note that other allotropes played an important role in the
historical development of Raman spectroscopy of carbons as well, which we rapidly cite here. C60 has
been discovered by Kroto in 1985 [129]. Vibronic resonance effects in C60 were evidenced 5–6 years
Coatings 2017, 7, 153 18 of 55

later (taking into account only the A term from Albrecht’s theory and reproducing the two orders
of magnitude enhancement) [130–132]. Carbon nanotubes (CNT) were studied intensively since
1991, after their discovery (or rediscovery [133]) by Iijima [134]. Raman spectra of CNT not only
contain G, D, and 2D bands, but also the well-known radial breathing modes (RBM). As Raman
spectroscopy is a resonant process, these RBM frequencies and intensities depend on the nanotube
electronic structure which is itself driven by the way the graphene plates are rolled. The Kataura
plot is a tool that can give the intensity of a given mode in function of the laser used to perform the
Raman spectroscopic measurements [135]. Raman spectroscopy can thus be seen as a power tool to
distinguish between different nanotubes, the symmetry aspects of which are reviewed in the review
paper by Barros et al. [136].

2.5. Brief Introduction to the Double Resonance Mechanism

Below, we give the basics of the double resonance mechanism which is a fourth order perturbation
theory. The reader who also wants to learn about the details of this mechanism is referred to the
following papers [2,137–139].
The Raman cross section contains sums of terms like the following one in Equation (14) (Γ terms,
accounting for relaxations processes, have been omitted in the denominator, for simplicity):

hi | He−Radiation | aih a| He−phonon or defect |bihb| He−phonon or defect |cihc| He−Radiation | f i

(14)
(}ω0 − }ωa←i ))(}ω0 − [}ωb←i − }ωvib ])(}ω0 − [}ωc←i − }ωvib ])

Here, He–Radiation and He–phonon or defect are the Hamiltonians describing the interaction between
electrons and light, and electron and phonons (or defects), respectively. |ii and | f i are the initial and
final electronic states, | ai, |bi, and |ci are intermediate states corresponding to the intermediate steps of
the double resonance mechanism. In the reciprocal space, when the valence and conduction bands cross
→
at the K-point (see Figure 5b), an incoming photon with the energy }ω0 and wave vector k0 can always
excite an electron/hole pair in the vicinity of this crossing point. This is how the double resonance
mechanism starts: An electron-hole pair is excited by the incoming photon that is absorbed. Then,
→
the electron is scattered by a phonon or a defect with a vibrational energy }ωvib and wavevector q .
Many different scatterings can occur (see Figure 9), however only the resonant one will modify
the Raman cross section by minimizing its denominator. Other scatterings are possible (not displayed
on Figure 9, see Figure 2 of [62] for a complete description). After the scattering process between the
→ →
excited electron and the phonon, the electron has a k0 + q wavevector. The electron is then scattered
back by a phonon or a defect, and finally the electron-hole pair recombines, emitting a new photon with
the energy }ω0 − }ωvib , if one considers the Stokes process. The first resonances occur from |i i to | ai,
and the second resonance occurs from | ai to |bi. The third and fourth steps are not resonant. Changing
the energy of the incident photon will select another phonon that will maximize the Raman cross
section, leading to the dispersion of the D and 2D bands. The intravalley process, using a scattering
with a defect and with a phonon, will give rise to the D’ band. The intervalley process between K
and K’ points in the Brillouin zone will give rise to the D band if the excited electron is scattered by a
phonon and a defect, or to the 2D band if the scattering by the defect is replaced by a scattering back
with another phonon.
Then, for the bands appearing because of the intervalley process, we have a set of two coupled
quantities (electron and phonon momentums + dispersion relation) that obey the quasi selection rule
q ≈ 2 k, meaning the phonon with wavevector q will couple preferentially with the electronic state
that has the 2 k wavevector measured from the K point. Using multiwavelength Raman spectroscopy
data allows to follow the iLO and iTO phonon energies along the dispersion relations, exploring the
Brillouin zone, which is strictly forbidden for conventional Raman spectroscopy (see for example
Section 3.1 and Figure 12 in the article by Malard et al. [139]).
Changing the energy of the incident photon will select another phonon that will maximize the Raman 
cross  section,  leading  to  the  dispersion  of  the  D  and  2D  bands.  The  intravalley  process,  using  a 
scattering  with  a  defect  and  with  a  phonon,  will  give  rise  to  the  D’  band.  The  intervalley  process 
between K and K’ points in the Brillouin zone will give rise to the D band if the excited electron is 
scattered by a phonon and a defect, or to the 2D band if the scattering by the defect is replaced by a 
Coatings 2017, 7, 153 19 of 55
scattering back with another phonon. 

 
Figure 
Figure 9. 
9. Double 
Doubleresonant scattering 
resonant scatteringfor 
forthe 
thevalence 
valenceand 
andconduction 
conductionbands,  adapted 
bands, from 
adapted [92]. [92].
from (a) 
Electron‐hole excitation followed by non‐resonant phonon scattering. (b) Intravalley process giving 
(a) Electron-hole excitation followed by non-resonant phonon scattering. (b) Intravalley process
rise to the D’ band: Phonon (resonant) + defect scattering. (c,d) Intervalley processes giving rise to D 
giving rise to the D’ band: Phonon (resonant) + defect scattering. (c,d) Intervalley processes giving rise
and 2D processes with phonon (resonant) + defect and double phonon processes, respectively. 
to D and 2D processes with phonon (resonant) + defect and double phonon processes, respectively.

  above can be very useful for quantum calculations: A procedure

The quasi selection rule cited
for calculations can be to identify first the different scattering configurations between electrons and
phonons by using analytical laws describing the electronic structure and phonon dispersion relation in
order to perform Density Functional calculations in a second step, as they are more time consuming.
2D integration in the Brillouin zone is then necessary to take into account contributions from all the
directions. Quantum interferences can occur, as the cross section is proportional to the square of the
absolute value of a sum of terms integrated on the Brillouin zone (see [140]).

2.6. Intensity, Band Profiles, and Models for Fitting Spectra of Aromatic Carbons
If we do not take into account the instrumental transfer function that can be negligible in
many cases (If the natural width is comparable to the width of the instrumental transfer function,
which is generally a Gaussian function, then the intensity of the band is a convolution between the
natural line shape and the instrumental function. Depending on the grating used, the instrumental
width varies but is in general close to 1 cm−1 .), the total intensity of one phonon mode with a
wavevector q0 and a frequency ω(q0 ), in a perfect crystal, is spread on a symmetric profile which is
Lorentzian, see Equation (15): (If one considers only the dominant term of (αρσ )fi (Equation (8) in
Section 2.2.4) and applies the square of the modulus to calculate the Raman intensity, one will find:
|1/(ωri − ω0 − iΓr )|2 = 1/[(ωri − ω0 )2 + (Γr )2 ])

1
I (ω) ∝ (15)
(ω − ω(q0 ))2 + (Γ0 )2

The full width at half maximum of this band, Γ0 , is the inverse of the phonon lifetime, with
electron–phonon and electron–electron interactions that can contribute. For the G band of graphene
it was shown that the dominant term that determines the width is the electron–phonon coupling
that leads to 11 cm−1 at room temperature [58,141]. At the other extreme, the material is amorphous.
The analysis of the profile of Raman modes of amorphous carbon has led to many studies [142,143]
(and references from Ferrari et al., see Section 3.6). The profile of a Raman mode is related to the
neighboring of the vibrating molecule or atoms. Any variation in this neighboring will affect the width
of the Raman mode. For single crystals, all atoms have equivalent environment and the associated
Raman bands are sharp. This is evidently not the case for an amorphous material where each atom has
a specific environment and the ranges of values of bond angles and bond distances are wider than
Coatings 2017, 7, 153 20 of 55

in a crystalline material. This leads to a broadening of the bands, which is effectively observed for
amorphous carbons. Usually, a Gaussian function is used to fit the Raman bands, even if, as mentioned
by Wang et al. [144], there is no clear justification for using this function.
In between amorphous materials and perfect crystals, defects play a role in the disturbed Raman
scattering process. The double resonance mechanism involving defects is an example, but it is not
the only one. Another mechanism that can influence the inelastic scattered light is confinement at
the nanoscale. Defects can localize the wavefunction of the phonon, leading to a delocalization of
→
its momentum in the Brillouin zone, due to the Heisenberg principle, relaxing the | q | ≈ 0 rule.
→
Then, because of the phonon dispersion relation ω( q ), it allows to explore away from the Г point,
new frequencies appearing in the Raman spectrum. Richter et al. [145] succeeded in understanding
asymmetric profiles observed on the band at 520 cm−1 in silicon by following this approach, the
phonon confinement model. They proposed to multiply the phonon wavefunction by a Gaussian
function that localizes the phonon [145]. It can account for linewidth increase and wavenumber
decrease. The intensity of the band is written as (see Equation (16)):

→ → → 2 2
W ( q )e−( q −q0 ) L /4
Z
→
I (ω ) ∝ 2
d2 q (16)
BZ → 2
(ω − ω ( q )) + (Γ0 /2)

By choosing a good weighting function W, and by describing correctly the phonon branches in
the Brillouin zone (BZ) and integrating the above expression, one can obtain the influence of phonon
confinement on the shape of the spectrum. This was done for graphene by Puech et al. in 2016 [146]. LO
and TO phonons introduced a second G band component at a lower wavelength (close to 1550 cm−1 ),
but also broadened all the bands
Another kind of profile, which is asymmetric, has to be mentioned: The Breit–Wigner–Fano (BWF)
profile (see Equation (17)):
 2
1 + (ω − ω(q0 ))/qΓ0
I (ω) ∝  2 (17)
1 + (ω − ω(q0 ))/Γ0
→
where the q parameter is a real number (here, q has nothing to do with the q momentum, not enough
letters being possible to choose in the many alphabets usable). 1/q accounts for an interaction between
a phonon and a continuum of states. It is generally used to fit the G bands of metallic nanotubes.
Sometimes it can be used just because it is convenient to use it, e.g., to account for confinement effects
or an unresolved band lying in the wing of the G band. Then, the term 1/q has no physical meaning.

2.7. Procedures for Fitting of the First Order Region

To fit what is often called the first order region (1000–1700 cm−1 ), a large variety of procedures
have been reported in the literature. Here, we just mention some of them (more details will be given in
the corresponding sub sections of Section 3):

• One band: The G band is fitted by a Lorentzian if symmetric, and by a BWF if not symmetric.
• Three bands: The G, D, and D’ bands are fitted by Lorentzians. D and D’ bands are sometimes
labelled D1 and D2 , respectively. The D’ band is less intense than the D band by an order of
magnitude and can be forgotten when the D and is much less intense than the G band.
• Four bands: The G, D, and D’ bands are fitted by Lorentzians and a Gaussian band is added in
the redshift wing of the G band (close to 1500 cm−1 ). This band is sometimes called the D3 band,
in other cases it is called the A band.
• Five bands: Same as the four bands model, but adding another band around 1200 cm−1 , which is
sometimes found Lorentzian, otherwise found Gaussian. This band is called the D4 band, or D”
since the theoretical work of Venezuela et al. [69].
Coatings 2017, 7, 153 21 of 55

• Six bands: Same as the five bands model, but with another distinct band close to 1150 cm−1 .
This band is generally more easily seen using red laser (633/785 nm) instead of green/blue lasers.
• Recent developments [61] have revealed that the bands around 1100–1200 cm−1 are in fact three
bands (D”, D*, and D**) with different dispersion behavior (see Figure 6).
• Occasionally, no D’ band is observed (possibly merged with the G band so that authors do not try
to decompose each component).
• Sometimes, the D and G bands which are Lorentzian are accompanied by two other broader
bands (Gaussian or of different line shape) that are red-shifted compared to the D and G bands.
The term amorphous component can often be found as well.

We advise the reader to carefully check for the relative intensity ratio notation used in the
literature. In some papers, for example, the ratios of two band intensities are the area ratios (noted A),
sometimes it is the maximum intensity (noted I) and elsewhere it is reported without fitting (noted H).
Jorio et al. [147] performed a comparison between AD /AG and ID /IG for bombarded graphene and
found that ID /IG should be used instead of AD /AG .

2.8. Examples of How Comparison with First-Principle Calculations Can Help

Systems are sometimes so complex that the use of first-principle calculations are more than needed,
helping in retrieving quantitative data of the structure or kind of defects. Lattice-dynamic behavior of a
crystal affects physical properties such as phonon dispersion, which (as we know) can be compared to
Raman spectra for some points of the Brillouin zone. Our aim in this part is not to detail the theory
from the first-principle, but to illustrate the use of the theory and which information can be retrieved.
The reader who is interested in more details about the basics of the lattice vibration theory is advised
to read the seminal paper by Born and Huang [24], and the reader who would like to know more
about the density functional (perturbation) theory, the methodology, and its approximations could
read the review paper by Baroni et al. [148]. Such theories are implemented in open source codes like
QUANTUM-ESPRESSO [149] or licensed codes like the Vienna Ab Initio Simulation Package (VASP).
As a first example, Mohiuddin et al. applied an external strain on a graphene plane both
experimentally (observing the splitting of the E2G Raman active mode) and theoretically [8]. The good
match between both experiment and theory strengthens the physical description of the graphene on
the basis of the calculation. Going a step further is possible as well: Bonini et al. [141] were able to
determine from first principle the thermal properties of graphene and graphite, enhancing the role
of electron–phonon and phonon–phonon interactions and compared them with the band shift and
band width (σG and ГG ) evolution with temperature. ГG being essentially due to electron-phonon
coupling at room temperature, whereas the band width of the infrared active mode is narrower, only
caused by phonon–phonon interactions. Next example is about identifying defects signature, which
is a holy grail in the field [69], and will be discussed in much more detail in Sections 3.3–3.6 (some
issues can be found in the review article by Ferrari and Basko [62]). Here, we mention the fact that for
carbon nanotubes, the works by Saidi et al. [150] have revealed that di-vacancies and other defects
influence the non-resonant G bands more than the radial breathing modes. These defects can also
affect the intensity of the resonant Raman bands, allowing them to be identified by this way [151,152].
As a final example, we would like to mention graphene oxide, which is a heavily oxidized carbon.
The G band of graphene oxide has been found blue shifted experimentally, compared to graphene.
Its explanation was obtained with the help of first principles [153]: Graphene oxide can be composed
of sp2 areas surrounded by an alternating pattern of single-double carbon bonds.

3. Raman Spectroscopy of Different Aromatic Carbons

In this section, we review the way multiwavelength Raman spectroscopy is used in literature
to better characterize aromatic based carbons, by focusing on more and more disordered aromatic
carbons. The aim is to give a concrete and practical view on how Raman spectroscopy can be used
Coatings 2017, 7, 153 22 of 55

to classify the nanostructure. Figure 10 displays the Raman cross sections of typical graphene based
materials compared  to some other relevant molecules or reference materials.
Coatings 2017, 7, 153  22 of 54 

 
Figure 10. Raman cross section for carbonaceous materials compared to reference materials. Sources: 
Figure 10. Raman cross section for carbonaceous materials compared to reference materials. Sources:
Diamond [154], graphene [49], nanographite [65], benzene [155], silicon [156], SERS [157]. Note that 
Diamond [154], graphene [49], nanographite [65], benzene [155], silicon [156], SERS [157]. Note that
Raman cross section of solids can sometimes be difficult to obtain because of substrate effects that can 
Raman cross section of solids can sometimes be difficult to obtain because of substrate effects that can
give rise to interference effects that depend on the thicknesses and optical indexes, as it was shown 
give rise to interference effects that depend on the thicknesses and optical indexes, as it was shown for
for graphene [48,158] and earlier for amorphous carbon [46]. 
graphene [48,158] and earlier for amorphous carbon [46].
3.1. Graphene 
We start with graphene in Section 3.1, and will continue with what we call nanographenes
Graphene has many astonishing properties (that are reviewed by Peres [159]). One of them is 
in Section 3.2 (nanotubes,
the  existence  nanohorns,
of  Dirac  cones  crossing nanocones,
at  the  Fermi nanofibers),
level  at  the  K followed by Brillouin 
point  of  the  bombarded zone graphene
(see 
Figure 5b), 
in Section and  that 
3.3, very determine 
defective mostly 
carbons the coal,
(e.g., transport 
soot,properties 
black carbons)in  graphene.  As  there 
in Section is  some 
3.4 and graphite
electronic 
intercalated resonance  with 
compounds incoming 
in Section 3.5.photons, 
We will these 
finishcones 
with also  determine 
amorphous the  properties 
carbons of  Raman 
in Section 3.6.
spectra,  which  can  appear  counterintuitively.  The  main  thing  to  keep  in  mind  about  Raman 
spectroscopy  of  graphene  is  that  it  is  then  driven  by  the  electron  properties—how  they  move, 
3.1. Graphene
interfere, and interact—affects the Raman spectra. Disorder can modify the electronic properties, and 
Graphene has many astonishing properties (that are reviewed by Peres [159]). One of them is the
then can find finger prints in the Raman spectra because of the resonance mentioned above. Among 
existence of Dirac cones crossing at the Fermi level at the K point of the Brillouin zone (see Figure 5b),
other defects, one can find: Adsorbed species, folded regions, rippling, vacancies, topological defects 
and that determine mostly the transport properties in graphene. As there is some electronic resonance
(such as Stone–Wales defects), charged impurities on wafer [159], and so forth. 
Graphene is the building block of nanocarbons: Staking individual (graphene) layers will give 
with incoming photons, these cones also determine the properties of Raman spectra, which can appear
rise to multi‐layer graphene and eventually graphite. Rolling it, results in the formation of carbon 
counterintuitively. The main thing to keep in mind about Raman spectroscopy of graphene is that it is
then nanotubes. 
driven by the Creating  point 
electron defects  or  linear they
properties—how defects 
move,(edge  or  grain and
interfere, boundaries)  can  account 
interact—affects the for 
Raman
different processes such as ion implantation or crystal growth under thermal treatment of amorphous 
spectra. Disorder can modify the electronic properties, and then can find finger prints in the Raman
carbons, for example. If one wants to understand the Raman spectrum of aromatic carbon containing 
spectra because of the resonance mentioned above. Among other defects, one can find: Adsorbed
samples, one has to understand first the Raman spectrum of graphene. Many reviews can be found on 
species, folded regions, rippling, vacancies, topological defects (such as Stone–Wales defects), charged
Raman spectroscopy applied to graphene, but we advise the reader to first use the work of Ferrari [62] 
impurities on wafer [159], and so forth.
and its useful 13 pages of supplementary information, or the work of Beams et al. [160]. Below, we 
Graphene is the building block of nanocarbons: Staking individual (graphene) layers will give
give some trends before focusing, in paragraph 3.2, on some specific nanoforms and on few kinds of 
rise to multi-layer graphene and eventually graphite. Rolling it, results in the formation of carbon
defective graphene samples. 
nanotubes. Graphene 
Creatingwithout  defect  gives 
point defects rise defects
or linear to  two  main 
(edgebands: 
or grainThe  symmetry  allowed 
boundaries) G  band 
can account for and 
different
another band, the 2D band. For multilayer graphene, useful information can be found in the work of 
processes such as ion implantation or crystal growth under thermal treatment of amorphous carbons,
Malard et al. [139]. The G band is due to the E
for example. If one wants to understand the Raman 2g phonon at the center of the Brillouin zone (and called 
spectrum of aromatic carbon containing samples,
the Г‐point). The 2D band is due to TO phonons around the K point in the Brillouin zone, and is active 
one has to understand first the Raman spectrum of graphene. Many reviews can be found on Raman
due to the double resonance mechanism [57], as presented briefly in Section 2.5. As an illustration, 
spectroscopy applied to graphene, but we advise the reader to first use the work of Ferrari [62] and
multi‐layer graphene was found to display characteristic Raman spectra, especially in the 2D spectral 
its useful 13[1]. 
region  pages ofhas 
As  it  supplementary information,
different  electronic  structures orclose 
the work
to  the ofK Beams et al.because 
point,  and  [160]. Below, we give
the  double 
someresonance mechanism connects phonons to the electronic structure, the position, shape (composed of 
trends before focusing, in Section 3.2, on some specific nanoforms and on few kinds of defective
graphene samples.
several overlapped bands), and intensity of the 2D band(s) can be used to distinguish from monolayer 
Coatings 2017, 7, 153 23 of 55

Graphene without defect gives rise to two main bands: The symmetry allowed G band and
another band, the 2D band. For multilayer graphene, useful information can be found in the work of
Malard et al. [139]. The G band is due to the E2g phonon at the center of the Brillouin zone (and called
the Г-point). The 2D band is due to TO phonons around the K point in the Brillouin zone, and
is active due to the double resonance mechanism [57], as presented briefly in Section 2.5. As an
illustration, multi-layer graphene was found to display characteristic Raman spectra, especially in
the 2D spectral region [1]. As it has different electronic structures close to the K point, and because
the double resonance mechanism connects phonons to the electronic structure, the position, shape
(composed of several overlapped bands), and intensity of the 2D band(s) can be used to distinguish
from Coatings 2017, 7, 153 
monolayer up  to 5–10 stacked layers. The relative intensity ratio between the 2D and G bands
23 of 54 
was also found to be dependent on the number of layers: I2D /IG is close to 3 for monolayer graphene,
up to 5–10 stacked layers. The relative intensity ratio between the 2D and G bands was also found to 
and falls down to 0.3 for highly oriented pyrolytic graphite (HOPG). Then, the Raman plot σ2D versus
be dependent on the number of layers: I2D/IG is close to 3 for monolayer graphene, and falls down to 
I2D /IG can be used to rapidly have an idea of the quality of the graphene samples handled. Figure 11
0.3 for highly oriented pyrolytic graphite (HOPG). Then, the Raman plot σ2D versus I2D/IG can be used 
gives such an illustration for two wavelengths: 514 and 633 nm. The HOPG samples have been cleaved
to  rapidly  have  an  idea  of  the  quality  of  the  graphene  samples  handled.  Figure  11  gives  such  an 
by the tape method to obtain multilayer graphene flakes that were deposited on a silicon substrate.
illustration for two wavelengths: 514 and 633 nm. The HOPG samples have been cleaved by the tape 
Raman spectra
method  to have
obtain  been obtained
multilayer  from allflakes 
graphene  the flakes. For 514
that  were  nm, HOPG
deposited  is situated
on  a  silicon  at (2725;
substrate.  0.3) and
Raman 
the monolayer is situated at (2686; 3). One can see that, with this method, many intermediates are
spectra have been obtained from all the flakes. For 514 nm, HOPG is situated at (2725; 0.3) and the 
obtained. The broadening
monolayer  is  situated around the
at  (2686;  3). guide for the
One  can  see  eyes
that,  lines
with  can
this be due tomany 
method,  stacking faults thatare 
intermediates  modify
obtained. The broadening around the guide for the eyes lines can be due to stacking faults that modify 
the electronic structure of the multilayers, and thus the 2D shape and intensity [161–163]. One has to
the electronic structure of the multilayers, and thus the 2D shape and intensity [161–163]. One has to 
note that σG slightly depends also on the number of layers but the shift compared to HOPG is no more
note that σ G slightly depends also on the number of layers but the shift compared to HOPG is no 
than 5–6 cm−1 [164]. The width of the G band, due to electron–phonon coupling has been evaluated to
more  −than  5–6  cm−1  [164].  The  width  of  the  G  band,  due  to  electron–phonon  coupling  has  been 
be 11.5 cm 1 [58], phonon–phonon scattering being responsible to 4–5 cm−1 extra broadening found
evaluated  to  be  11.5  cm   [58],  phonon–phonon  scattering  being  responsible  to  4–5  cm−1  extra 
−1
experimentally. For graphite and multilayer graphene, we mention the existence of a C band, which
broadening found experimentally. For graphite and multilayer graphene, we mention the existence 
is sensitive to coupling between layers: It lies at 44 cm−1 for graphite and
of a C band, which is sensitive to coupling between layers: It lies at 44 cm shifts regularly down to
−1 for graphite and shifts 
− 1
31 cmregularly down to 31 cm
for bilayer graphene [165].
−1 for bilayer graphene [165]. 

2740 mech. cliv. graphite

HOPG (514)
(514)

2720 doped graphene

(514)
2D (cm )
-1

2700 HOPG (633)

2680
graphene
514
2660 mech. cliv. graphene
graphite 633
(633)
2640
0.1 1
I2D/IG
 
Figure 11. 2D band position as function of I2D/IG for laser wavelengths of 514 and 633 nm. Graphene 
Figure 11. 2D band position as function of I2D /IG for laser wavelengths of 514 and 633 nm. Graphene
frequencies were obtained from [1]. Empty squares are from mechanically cleaved graphene flakes 
frequencies were obtained from [1]. Empty squares are from mechanically cleaved graphene flakes
(original data). Stars are from [160] (doped with carrier density from −3 × 1013 cm−2 to +4 × 1013 cm−2), 
(original data). Stars are from [160] (doped with carrier density from −3 × 1013 cm−2 to +4 × 1013
the downshift corresponds to positive doping, whereas upshift corresponds to negative doping. 
cm−2 ), the downshift corresponds to positive doping, whereas upshift corresponds to negative doping.
As another example, dopant impurities can modify the Raman spectrum of graphene [166–168]. 
Playing with the electron doping (i.e., changing the position of the Fermi level) modifies the Raman 
As another example, dopant impurities can modify the Raman spectrum of graphene [166–168].
spectrum: The band positions and intensities are modified [169]. In Figure 11, the doping effect on a 
Playing with the electron doping (i.e., changing the position of the Fermi level) modifies the Raman
single layer graphene has been added: Doping with electrons or holes can increase or decrease σ2D, 
spectrum: The band positions and intensities are modified [169]. In Figure 11, the doping effect on a
and both diminish I2D/IG. The effects of doping have been reviewed in 2007 [137] and in 2015 [160]. 
single layer graphene has been added: Doping with electrons or holes can increase or decrease σ2D ,
We report that changing the carrier density also affects the D band spectroscopic parameters [170]. 
and both diminish I2D /IG . The effects of doping have been reviewed in 2007 [137] and in 2015 [160].
Impurities adsorbed on graphene can also modify carrier mobility and thus the Raman spectrum of 
We report that changing the carrier density also affects the D band spectroscopic parameters [170].
graphene [171], changing the D band intensity. 
Substrate effects on the position of the 2D and G bands (downshift, splitting) have been reported 
in the works of Das and Calizo et al. [164,172,173]. Strain can be such effect [174]. If that is the case, 
Frank  et  al.  demonstrated  that  using  different  wavelength  gives  very  different  2D  band  shape. 
Among others, doping can be an important and unintentional effect as it can change the position of 
the 2D band, as shown by Yang et al., [175], for graphene grown on SiC, or by Das et al., [176], for 
Coatings 2017, 7, 153 24 of 55

Impurities adsorbed on graphene can also modify carrier mobility and thus the Raman spectrum of
graphene [171], changing the D band intensity.
Substrate effects on the position of the 2D and G bands (downshift, splitting) have been reported
in the works of Das and Calizo et al. [164,172,173]. Strain can be such effect [174]. If that is the case,
Frank et al. demonstrated that using different wavelength gives very different 2D band shape. Among
others, doping can be an important and unintentional effect as it can change the position of the 2D
band, as shown by Yang et al., [175], for graphene grown on SiC, or by Das et al., [176], for other
substrates. However, as doping also affects the G band position and width, checking G band anomalies
can be used to detect such an unwanted effect. Roughly, for electron or hole concentrations higher
than 1013 cm−2 , the G band width is diminished by a factor of 2 (i.e., close to 7–8 cm–1 ) [176]. G
band splitting and intensity enhancement (i.e., Surface Enhanced Raman Scattering) were observed
for multilayer graphene in contact with Ag and Au [177]. The splitting and intensity enhancement
were found to be higher for single layers. As the 2D band intensity was found diminished by the Ag
deposition, an n-type doping effect was concluded. A p-doping effect was deduced for Au deposition
because of the 2D band shift. If the reader is interested in the detection of graphene combined with the
SERS effect, a further reading of the 2013 review can be found in the work of Xu et al. [178]. A good
way to differentiate between doping effect and subtract effect is to plot σG versus σ2D of the analyzed
samples (this differentiation is possible because strain affects the band position by changing bond
length and angles between bonds, whereas doping affects the electron–phonon coupling [179]).
Depending on the optical constants of the substrate on which the graphene layer is deposited, the
substrate (layer) thickness, the numerical aperture of the objective used or the wavelength of light used
for performing the micro Raman spectroscopy analysis, the absolute intensity of the G and 2D bands
can be altered due to electromagnetic interference effects so that their relative intensity ratio is changed
in appearance [48,158]. For example, for a SiO2 substrate layer thickness in the range of 225–375 nm,
I2D /IG appears to vary from 2 to 8 instead of being constant at ≈3. A refined analysis was performed
by Klar et al. [49] who were interested in the absolute intensities of the G and 2D bands for multilayer
graphene, checking numerical aperture effects, wavevector polarization, substrate effect, etc.
We have to mention a breakthrough due to deep UV Raman spectroscopy that has been used
only since very recently (2015) on graphene [180]. The advantage is that, due to the double resonance
mechanism, one gets far away from the K point in the Brillouin zone, exploring a larger part of the
dispersion relations, for example near the M point of the Brillouin zone. The (}ω0 )4 wavelength
dependency of the G band intensity was confirmed for 266 nm (4.7 eV), but a surprising (}ω0 )−1
relationship was found for the 2D band. It would lead to the conclusion that I2D /IG is proportional to
(}ω0 )5 . On nanographites [65], Cançado et al., who observed a La dependency, did not observe any
(}ω0 ) dependency, but their data were recorded in the visible range, in a small range of wavelength.
Tyborski et al. observed that when the 2D band disappears, the two phonon density of states rises in
the 2600–3300 cm−1 spectral region [181]. Among the many things they deduced from their analysis,
taking into account symmetry arguments, they were able to deduce from this spectral region, the
maximum frequency of the LO phonon at 1626 cm−1 , and its frequency at the M point at 1408 cm−1 .
Saito et al. performed predictive calculations up to 177 nm (7 eV) [182]. They also determined the
asymmetry parameter evolution with }ω0 , appearing in the Breit–Wigner–Fano profile of metallic
nanotubes (see Section 3.2.3 for more details) what has never been down before, to our knowledge.
Finally, Raman spectroscopic measurements from UV up to 325 nm were performed on multilayer
graphene in order to test the model predictions on the number of bands shaping the 2D band of
multilayer graphene (due to the complex electronic structure close to the K point). The 2D band profile
was found to change: For monolayer graphene, three sub bands appear at 325 nm [183]. The one
with the lowest frequency (2800 cm−1 ), supposed to have the same origin as the G* band, has an
intensity enhanced when the number of layer increases, whereas the one with the highest frequency
(2900 cm−1 ) display another behavior. This experimental result is found to be in agreement with
previous calculations announcing three strong bands and a weak band caused by four electron-hole
Coatings 2017, 7, 153 25 of 55

scattering processes involved in the double resonance mechanism [184]. To conclude about UV Raman
spectroscopy, it allows deeper exploration of the Brillouin zone.
Finally, Raman spectroscopy can also be used to determine mechanical properties [185], study
strain effects [186], and characterize grain boundaries [187,188] of graphene grown on a substrate.
In addition, it is used to deduce the thermal conductivity of suspended graphene [189], and to monitor
electrostatic deflection of suspended graphene [190].

3.2. Graphene based Nanoforms

3.2.1. Nomenclature
A huge number of different carbon nanoforms are now produced around the world such as single
and multiwall nanotubes, bamboo nanotubes, nanotube forests, fullerenes, nano-onions, nanocones,
stacked nanocones, scrolled graphene, nanofibers, nanowalls, nanosheets, and nanoplates. Graphene
is definitely their building block, and by applying a transformation, such as stacking, cutting, circularly
wrapping, scrolling, coiling, screwing, etc., all the other forms can be obtained. In 2012, the editors of
the journal Carbon decided to propose a nomenclature to classify all these sp2 carbon nanoforms [191].
To help researchers in their bibliographic studies, they proposed to classify all the known forms in
three families: Molecular forms (0D), cylindrical nanoforms (1D), layered nanoforms (2D). Another
family should be included, to our opinion, and called “graphenic carbon materials”, as was reported
in [192]. This fourth family contains graphite, carbon fibers, and could also include all amorphous
carbons that are based on aromatic rings, but at a local order. If one considers the addition of oxygen
to the carbon nanoforms, an alternative approach to categorize them was proposed in the work of
Wick et al. [193], based on their toxicologic identification.
For some of these families, the state of the art is not yet enough advanced to propose a bijection
between all the members of the above families and their Raman spectra. Below, we present the
understanding and main trends about Raman spectroscopy of some of the nanoforms and, where
possible, the links between different kinds of nanoforms.

3.2.2. Nanodomains, Nanoribbons

Graphene edges, labelled as 1D defects, exist in two configurations which are named zigzag and
armchairs, related to the shape of the terminal carbons of the hexagons (see Figure 12a). Nanoribbons
are delimited by these edges, which give them peculiar electronic properties (See for example Section
7 in the work of Mohr et al. [140].), forming gaps in the electronic dispersion relations due to spatial
confinement of the electron wavefunction. This can affect their Raman spectra, again due to resonance.
The first Raman study on edges was performed by Cançado et al. in 2004 on step-like edges on
graphite [194]. Roughly 2 microns away from a step, no D band was observed whereas a D band
and a D’ band were observed on both zigzag and armchair configurations. The intensity of the D’
band was found non-sensitive to these two configurations, whereas the D band was found to be more
intense for armchair edges than zigzag edges. The explanation of these two behaviors is that as the D’
band is an intravalley process (see Section 2.4), momentum conservation upon the double resonance
mechanism can be satisfied whatever the direction in the Brillouin zone, whereas for the D band,
which is an intervalley process, it cannot be satisfied for zigzag edges (see [139,194] for more details).
You et al. [195] have also investigated this point in 2008. They observed that a piece of graphene with
two edges separated by 90◦ have necessarily different chirality (this is the case if the angles are 30◦ ,
90◦ , or 150◦ , whereas when it is 60◦ or 120◦ the chirality is the same, due to geometry). They also
observed that the D band intensity is weaker for zigzag edges. Note that because graphene edges
are sometimes not perfect at the micrometric scale (the size of the laser beam once focalized on the
surface of a sample), especially when graphene is obtained by mechanical cleavage, it can be difficult
to always conclude on the zigzag or armchair edge origin with Raman spectroscopy [196]. In 2014,
Islam et al. took into account non-ideal edges orientation at a scale smaller than the micrometric size
Coatings 2017, 7, 153 26 of 55

of the spot (see Figure 1 of [197]). Raman spectroscopy is now used to control the properties of edges
of individual grains grown by chemical vapor deposition on large scales (few tens of microns) [187].
Because of a lack of translation symmetry, the edges do not have the same environment as in
between edges of the ribbons, thus their vibrational frequencies should be different. Bands lying
at 1450 and 1530 cm−1 have been observed in 2010 by Ren et al. and attributed to localized edge
phonon modes of zigzag and armchair configurations terminated by H atoms [198]. These bands were
observed only with red laser but not with green laser, meaning a resonance behavior may happen.
Vibrational density of states calculations taking into account different sizes and shapes of nanoribbons
were performed by Mazzamuto et al. in 2011 [199]. Among other features, out of plane edge localized
modes were predicted at 630 cm−1 for armchair nanoribbons, whereas in plane edge localized modes
were found at 480 cm−1 for zigzag nanoribbons [199]. Non-resonant Raman spectra were also studied
in the same period by Saito et al. [200]. They found that, depending on the edge configuration
and polarization directions of the incident and scattered photons relatively to the edge orientation,
a symmetry selection rule for phonons appeared. Very recently, the group of Castiglioni published a
paper on a polycyclic aromatic hydrocarbon resembling a longitudinally confined graphene ribbon with
armchair edge and found the presence of G and D bands, low wavenumber bands, and combination
modes in the 2500–3250 cm−1 spectral region like in graphene, with intensity very sensitive to laser
wavelength due to resonance effect [117]. Radial breathing like modes, looking like the one found
in nanotubes (see Section 3.2.3), have also been predicted and detected [201,202]. Verzhbitskiy et al.
have shown that below 1000 cm−1 , the spectral region is very sensitive to the edge morphology and
functionalization [203], as can be seen in Figure 12b, as is found for the radial breathing modes of
carbon nanotubes (see below) or poly aromatic hydrogenated molecules [117]. Moreover, the D band
dispersion is found to vary from 10 to 30 cm−1 /eV, lower than the classical 50 cm−1 /eV, allowing to
use multiwavelength Raman spectroscopy as a detector of such nanostructures. Very recently, the
Raman spectroscopy
Coatings 2017, 7, 153    of nanoribbons has been reviewed by Casiraghi and Prezzi [204]. 26 of 54 

 
Figure 12. Nanoribbons. (a) Zigzag and armchair nanoribbons; (b) Typical spectra of a real nanoribbon, 
Figure 12. Nanoribbons. (a) Zigzag and armchair nanoribbons; (b) Typical spectra of a real nanoribbon,
as studied by Casiraghi et al. [204]. 
as studied by Casiraghi et al. [204].

Because of a lack of translation symmetry, the edges do not have the same environment as in 
between edges of the ribbons, thus their vibrational frequencies should be different. Bands lying at 
1450 and 1530 cm−1 have been observed in 2010 by Ren et al. and attributed to localized edge phonon 
modes  of  zigzag  and  armchair  configurations  terminated  by  H  atoms  [198].  These  bands  were 
observed only with red laser but not with green laser, meaning a resonance behavior may happen. 
Coatings 2017, 7, 153 27 of 55

Coatings 2017, 7, 153    27 of 54 
3.2.3. Nanotubes
3.2.3. Nanotubes 
Basically, a single wall carbon nanotube (SWNT) can be seen as a rolled piece of graphene (see inset
Basically, a single wall carbon nanotube (SWNT) can be seen as a rolled piece of graphene (see 
of Figure 13). The way this piece is rolled is named the chirality of the tube [205,206]. This chirality
inset  of  Figure  13).  The  of
defines several properties way 
the this 
tube:piece  is  rolled 
Its geometry is  named 
(diameter) butthe  chirality 
also of  the properties
its electronic tube  [205,206]. 
(band  
This chirality defines several properties of the tube: Its geometry (diameter) but also its electronic 
gap). Due to their quasi unidimensional structure (quantum confinement) the electronic density of
properties 
states (band exhibits
of SWNTs gap).  Due 
Vanto  their singularities,
Hove quasi  unidimensional  structure  (quantum 
which are singularities associated confinement) 
to a very high the 
electronic 
density density  of 
of electronic states Therefore,
states. of  SWNTs  theexhibits 
chiralityVan  Hove 
defines the singularities, 
allowed electronicwhich  are  singularities 
transition between
associated  to  a  very  high  density  of  electronic  states.  Therefore,  the 
Van Hove singularities with a photonic excitation. In addition, the chirality also governschirality  defines  the the
allowed 
band
electronic  transition  between  Van  Hove  singularities  with  a  photonic  excitation. 
gap and a tube can be either metallic or semi-conductor. As a result, it is possible to plot all the In  addition,  the 
chirality also governs the band gap and a tube can be either metallic or semi‐conductor. As a result, 
allowed electronic transitions with the diameter of the SWNT. This plot is called the Kataura plot [135].
it is possible to plot all the allowed electronic transitions with the diameter of the SWNT. This plot is 
As Raman scattering for SWNTs obeys a resonant mechanism, the Kataura plot directly indicates
called  kind
which the  Kataura 
of tube plot  [135].  As 
is resonant for Raman 
a given scattering 
excitation for  SWNTs  obeys 
wavelength. a  resonant 
The final recorded mechanism, 
Raman signal the 
Kataura plot directly indicates which kind of tube is resonant for a given excitation wavelength. The 
will come only from the resonating tubes. As a consequence, the Raman cross section of SWNTs is
final recorded Raman signal will come only from the resonating tubes. As a consequence, the Raman 
extremely high (contrary to their IR signal) [207], and since the pioneering work by Rao et al. [87],
cross section of SWNTs is extremely high (contrary to their IR signal) [207], and since the pioneering 
Raman spectroscopy has been extensively used for the study of SWNTs [208]. The typical first order
work by Rao et al. [87], Raman spectroscopy has been extensively used for the study of SWNTs [208]. 
Raman spectrum of SWNTs is divided in three parts:
The typical first order Raman spectrum of SWNTs is divided in three parts: 
• The low frequency region (typically between 100 and 300 cm−1 ), which is associated to radial
 The  low frequency 
breathing modes (RBM), region  (typically 
see Figure 13.between  100 and 300 
The frequency cm−1modes
of these ), which is associated 
is directly related to radial 
to the
breathing modes (RBM), see Figure 13. The frequency of these modes is directly related to the 
diameter of the tubes. One can find a review on RBM not only limited to nanotubes published
diameter of the tubes. One can find a review on RBM not only limited to nanotubes published 
recently by Ghavanloo et al. [209];
recently by Ghavanloo et al. [209]; 
• The D band (around 1300 cm−1 ), related to defects (as for graphite and graphene);
 The D band (around 1300 cm−11), related to defects (as for graphite and graphene); 
• The G band (around 1550 cm− ), also similar to the G band of graphite and graphene.
 The G band (around 1550 cm−1), also similar to the G band of graphite and graphene. 

Radial
breathing
modes

0 250 500 1200 1400 1600 1800

-1
Raman shift (cm )  
Figure 13. Example of carbon nanotube Raman spectrum (λ
Figure 13. Example of carbon nanotube Raman spectrum (λ00 = 514 nm). 
= 514 nm).

Nevertheless,  in  the  case  of  SWNTs  the  profile  is  related  to  their  electronic  properties.  As 
Nevertheless, in the case of SWNTs the profile is related to their electronic properties.
mentioned above, it is possible to determine which kind of tube is resonant for a given excitation 
As mentioned above, it is possible to determine which kind of tube is resonant for a given excitation
wavelength  using  the  Kataura  plot,  and  then  resonance  allows  to  identify  the  kind  of  nanotube 
wavelength using the Kataura plot, and then resonance allows to identify the kind of nanotube
probed [210]. If the resonant tubes are metallic, the G band exhibits an asymmetric profile named 
probed [210]. If the resonant tubes are metallic, the G band exhibits an asymmetric profile named
Breit–Wigner–Fano (BWF). This feature is not present for semi‐conducting tubes and is coming from 
Breit–Wigner–Fano (BWF). This feature is not present for semi-conducting tubes and is coming from a
a specific interaction between the phonons and the electronic continuum [211]. Saito et al. performed 
specific interaction between the phonons and the electronic continuum [211]. Saito et al. performed
calculations on the shape of the Breit–Wigner–Fano profile for different excitation energies, taking 
calculations on the shape of the Breit–Wigner–Fano profile for different excitation energies, taking into
into account the double resonance mechanism and found that the shape is modified [182]. 
account the double resonance mechanism and found that the shape is modified [182].
To conclude this part, rings of single nanotubes with different diameters have been synthetized 
To conclude this part, rings of single nanotubes with different diameters have been synthetized
since 2006 [212]. Ring size‐dependent Raman G‐band splitting in carbon nanotubes has been reported 
since 2006 [212]. Ring size-dependent Raman G-band splitting in carbon nanotubes has been reported
and attributed to the resonance condition changes caused by additional curvatures in rings instead 
of attributed to bond length change induced by curvature/strain (ring diameter ranging from 129 to 
372 nm generates strain in the range 0.3%–1.3%) [213]. When deconvoluted, the sub bands were found 
Coatings 2017, 7, 153 28 of 55

and attributed to the resonance condition changes caused by additional curvatures in rings instead
Coatings 2017, 7, 153 
of attributed to bond   length change induced by curvature/strain (ring diameter ranging from 28 of 54  129 to
372 nm generates strain in the range 0.3–1.3%) [213]. When deconvoluted, the sub bands were found to
to lie at σ = = 1535 cm
lie at σG1 G1 1535 cm−1 , , σ
−1 G2 = 1553 cm−1
= 1553 cm−, σ G3 = 1563 cm−1, σ
1, σ −1G4 = 1575 cm−1, σ−
G51 = 1593 cm−1 and σ
−1G6  = 1603 
σG2 G3 = 1563 cm , σG4 = 1575 cm , σG5 = 1593 cm and σG6
cm −1. This splitting rises for strains up to roughly 1%. Such splitting was found on strained graphene 
= 1603 cm−1 . This splitting rises for strains up to roughly 1%. Such splitting was found on strained
as well [8]. 
graphene as well [8].

3.2.4. Fullerenes 
3.2.4. Fullerenes
Here we briefly review the main papers dealing about the Raman spectroscopy of fullerenes. 
Here we briefly review the main papers dealing about the Raman spectroscopy of fullerenes. First,
First, fullerene are mixture of pentagonal and hexagonal rings which leads to a curved shape, like a 
fullerene are mixture of pentagonal and hexagonal rings which leads to a curved shape, like a soccer
soccer 
ball, theball, 
name the ofname  of  footballene 
footballene being  encountered 
being encountered sometimes, sometimes, 
referring to referring 
C60 . Sinceto  Ctheir
60.  Since  their 
discovery
discovery in 1985, once vaporizing graphite using laser light [129], fullerenes have been extensively 
in 1985, once vaporizing graphite using laser light [129], fullerenes have been extensively studied
studied  using spectroscopy.
using Raman Raman  spectroscopy.  Among 
Among others, others, 
C60 , C70 , CC80
60, 
,C C84
70, have
C80,  C 84  have 
been been  up
detected, detected, 
to C400up  to 
[214].
C 400 [214]. The paper of Dresselhaus in 1996 [215], and then the one of Kuzmany et al. in 2004 [216] 
The paper of Dresselhaus in 1996 [215], and then the one of Kuzmany et al. in 2004 [216] both review
both review the Raman spectroscopy of C
the Raman spectroscopy of C60 and related 60 and related materials, from pristine C
materials, from pristine C60 up to peapods, 60 up to peapods, 
which are
which are single wall nanotubes filled by C
single wall nanotubes filled by C60 molecules 60 molecules [216]. Contrary to the other sp 2
[216]. Contrary to the other sp carbon forms 2 carbon forms 
presented
presented in our review, fullerenes exhibit specific Raman modes that can be easily identified. For 
in our review, fullerenes exhibit specific Raman modes that can be easily identified. For example, as
example, as shown in Figure 14, in the case of C
shown in Figure 14, in the case of C60 , the modes 60, the modes labelled Hg(1) to Hg(8) rise at 272, 433, 
labelled Hg(1) to Hg(8) rise at 272, 433, 709, 772,
−
709, 772, 1099, 1252, 1425, and 1575 cm 1
1099, 1252, 1425, and 1575 cm , respectively, −1 , respectively, and the modes labelled Ag(1) and Ag(2) rise at 
and the modes labelled Ag(1) and Ag(2) rise at 496 and
1470 cm−1 . The intensity
496 and 1470 cm of the Ag(2) mode at 1470 cm−1 is much
−1. The intensity of the Ag(2) mode at 1470 cm −1 is much more intense than the other 
more intense than the other modes
modes 
due to adue  to  a  vibronic 
vibronic couplingcoupling  that  enhances 
that enhances its Raman its intensity
Raman  intensity 
for E0 close for toE02.6
  close  to  2.6 This
eV [130]. eV  [130]. 
band  
This band intensity can be used as a probe of the coupling between C
intensity can be used as a probe of the coupling between C60 and its environment, 60 and its environment, like was 
like was shown by
shown 
Bardelangby  et
Bardelang  et  al.  [217], 
al. [217], where C60 has where  C60  has  been 
been introduced introduced 
in an in  an  open 
open framework. Due framework.  Due  to 
to different selection
different selection rules, the corresponding modes for C
rules, the corresponding modes for C70 are different [218].70 are different [218]. Both C
Both C60 and C70 can be polymerized 60 and C70 can be 
under
polymerized under UV radiation [219], leading to the rise of low vibrational modes at 118 cm
UV radiation [219], leading to the rise of low vibrational modes at 118 cm , which correspond to –1 –1, which 

correspond to bonds between C
bonds between C60 in the solid 60  in the solid phase. Note that heating C
phase. Note that heating C60 thin films can 60 thin films can lead to the 
lead to the formation of
formation of highly disordered nanographites [220]. 
highly disordered nanographites [220].

C70

Ag(2)
C60
*

250 500 750 1000 1250 1500

-1
Raman shift (cm )  
Figure 14. Raman spectra obtained from fullerenes C
Figure 14. Raman spectra obtained from fullerenes C6060 and C 70. The band at 520 cm
and C70 . The band at 520 cm−1 and marked by 
−1
and marked by
a star is due to the underlying silicon wafer. λ  = 514 nm. 
a star is due to the underlying silicon wafer. λ0 = 514 nm.
0

3.2.5. Nanocones 
3.2.5. Nanocones
Nanocones, 
Nanocones, also also called 
called nanohorns, are typically 
nanohorns, are typically 2–5 nm 
2–5 nm in diameter 
in diameter and 40–50 nm 
and 40–50 nm in length, 
in length,
looking like needles, the number of pentagons at their tips piloting their shape, as for fullerenes [221]. 
looking like needles, the number of pentagons at their tips piloting their shape, as for fullerenes [221].
They were first obtained by Iijima et al. in 1999 [222], and Raman spectra performed at that time were 
They were first obtained by Iijima et al. in 1999 [222], and Raman spectra performed at that time were
looking 
looking like 
like Raman 
Raman spectra  in  between
spectra in between  nanographite
nanographite  and
and  amorphous
amorphous  carbons.
carbons.  Depending 
Depending on  on the 
the
synthesis conditions, four different types have been identified, and labelled because of their shape 
synthesis conditions, four different types have been identified, and labelled because of their shape
observed by transmission electron microscopy: Dahlia‐like, bud‐like, seed‐like, and petal‐like [223]. 
observed by transmission electron microscopy: Dahlia-like, bud-like, seed-like, and petal-like [223].
A typical spectrum of a nanocone is displayed in Figure 15. By increasing the pressure up to 8 GPa, 
some  types  debundle  whereas  others  change  from  one  type  to  the  other,  and  new  promising 
configurations,  of  interest  for  future  functionalization,  have  been  found  [223].  Calculations  by 
Sasaki et  al.  [224]  predict  the  existence  of  a  topological  D  band,  shifted  by  50  cm−1  and  being  non 
Coatings 2017, 7, 153    29 of 54 

dispersive with the incoming photon energy. However, to our knowledge, such a shift has not yet 
been observed. 
Coatings 2017, 7, 153 29 of 55
In  situ  Raman  spectroscopy  reported  done  by  Pena‐Alvarez  et  al.  [223],  has  revealed  several 
interesting things: The G band high shifts with stress, a band rises close to 1510 cm−1 (looking like the 
G band of an amorphous carbon), all the bands increase their width, and the most important thing: 
A typical spectrum of a nanocone is displayed in Figure 15. By increasing the pressure up to 8 GPa, some
The width of the D band increases much more than the G band. Exactly all these effects have been 
types debundle whereas others change from one type to the other, and new promising configurations,
found in a large variety of disordered samples that are not nanocones (ranging from nanographite to 
of interest for future functionalization, have been found [223]. Calculations by Sasaki et al. [224]
amorphous carbon) exhibiting very typical, similar, and often encountered Raman spectra, looking 
predict the existence of a topological D band, shifted by 50 cm−1 and being non dispersive with the
like the orange one in Figure 6b [66]. 
incoming photon energy. However, to our knowledge, such a shift has not yet been observed.

500 1000 1500 2000 2500 3000

-1
Raman shift (cm )  
Figure 15. Typical Raman spectrum of a nanocone. The insert is an illustration. 
Figure 15. Typical Raman spectrum of a nanocone. The insert is an illustration.

In  a  previous  study  [66],  we  have  used  a  simple  parametric  model  to  describe  the  relation 
In situ Raman spectroscopy reported done by Pena-Alvarez et al. [223], has revealed several
between the spectroscopic parameters ID/IG, ГG, ГD, and the presence of a band close to 1500 cm−1, for 
interesting things: The G band high shifts with stress, a band rises close to 1510 cm−1 (looking like the
a  huge  variety  of  disordered  carbons and  using  three  wavelengths  from  325  to  633  nm  (based  on 
G band of an amorphous carbon), all the bands increase their width, and the most important thing:
empirical  laws  relating  these  parameters  to  La  plus  the  assumption  that  the  ( ω )4  dependency 
The width of the D band increases much more than the G band. Exactly all these effects have been
affecting ID/IG also prevails for the Ferrari relation). To reproduce the spectra well, an unknown source 
found in a large variety of disordered samples that are not nanocones (ranging from nanographite to
of  broadening  of  the  D  band  was  absolutely  needed  for  514  and  633  nm,  but  not  for  325  nm, 
amorphous carbon) exhibiting very typical, similar, and often encountered Raman spectra, looking
highlighting a resonance effect. Except the resonance effect which was not studied by Pena‐Alvarez 
like the orange one in Figure 6b [66].
et al. [223], exactly all these effects have been observed in stressed nanocones as can be seen in Figure 
In a previous study [66], we have used a simple parametric model to describe the relation between
16. In this figure, we compare the width of the G band (ГG) versus ID/IG scaled by the laser wavelength 
the spectroscopic parameters ID /IG , ГG , ГD , and the presence of a band close to 1500 cm−1 , for a huge
(λ0) for the large variety of samples analyzed by Pardanaud et al. [66], (referred here to “disordered 
variety of disordered carbons and using three wavelengths from 325 to 633 nm (based on empirical
carbons”),  heated  amorphous  carbons  (work  of  Pardanaud  et  al.  [225,226]),  bombarded  graphite 
laws relating these parameters to La plus the assumption that the (}ω0 )4 dependency affecting ID /IG
(work of Niwase et al. [227]) and the nanocones from the work of Pena‐Alvarez et al. [223]. The grey 
also prevails for the Ferrari relation). To reproduce the spectra well, an unknown source of broadening
lines are the models based on the Tuinstra and Ferrari relations (see the work of Pardanaud et al. [66], 
of the D band was absolutely needed for 514 and 633 nm, but not for 325 nm, highlighting a resonance
for more details) and stand for disordered graphite and amorphous carbons, respectively. All these 
effect. Except the resonance effect which was not studied by Pena-Alvarez et al. [223], exactly all these
data  draw  a  common  pattern  that  has  to  do  with  the  so‐called  “amorphization  trajectory”  of 
effects have been observed in stressed nanocones as can be seen in Figure 16. In this figure, we compare
Ferrari [4], presented in more details in Section 3.6. Briefly, starting from a perfect graphite, on the 
the width of the G band (ГG ) versus ID /IG scaled by the laser wavelength (λ0 ) for the large variety of
left corner of the figure, both ГG and ID/IG increase, ГG being linear with ID/IG. At a certain point (in the 
samples analyzed by Pardanaud et al. [66], (referred here to “disordered carbons”), heated amorphous
range ID/IG = 0.6–3), ID/IG starts to decrease whereas ГG continues to increase, changing the trajectory 
carbons (work of Pardanaud et al. [225,226]), bombarded graphite (work of Niwase et al. [227]) and
in this plot. This happens when 
the nanocones from the work of Pena-Alvarez et al. [223]. The grey lines are the models based on the
 both the Ferrari relation and Tuinstra and Koenig’s law meet, and/or 
Tuinstra and Ferrari relations (see the work of Pardanaud et al. [66], for more details) and stand for
disordered
a new set of bands close to 1200 and 1500 cm
graphite and amorphous carbons, respectively. −1 appears, and/or 
All these data draw a common pattern that
 to
has the D bands broaden more than excepted. 
do with the so-called “amorphization trajectory” of Ferrari [4], presented in more details in
Section 3.6.change 
This  Briefly,of 
starting fromis a observed 
trajectory  perfect graphite, ondisordered 
for  both  the left corner of theand 
carbons  figure, and ID /I
both ГG where 
nanocones  G
the 
increase, Г G being linear with I D /I G . At
compressive stress has been increased up to 8 GPa.  a certain point (in the range I D /I G = 0.6–3), I D /I G starts to
decrease whereas ГG continues to increase, changing the trajectory in this plot. This happens when
Widths are generally related to lifetimes, here the decay lifetime of the iTO phonon involved in 
the D band, due to confinement effect induced by external compressive stress, can be the cause of the 
• both the Ferrari relation and Tuinstra and Koenig’s law meet, and/or
band width increase. The rise of the 1510 cm
•
−1 band when increasing the compressive stress, can be 
a new set of bands close to 1200 and 1500 cm −1 appears, and/or
understood qualitatively as a phonon confinement effect too [146]. Note that for L
• the D bands broaden more than excepted. a = 2 nm, Puech et al. 

This change of trajectory is observed for both disordered carbons and nanocones where the
compressive stress has been increased up to 8 GPa.
Coatings 2017, 7, 153 30 of 55

Widths are generally related to lifetimes, here the decay lifetime of the iTO phonon involved
in the D band, due to confinement effect induced by external compressive stress, can be the cause
of the band width increase. The rise of the 1510 cm−1 band when increasing the compressive stress,
Coatings 2017, 7, 153    30 of 54 
can be understood qualitatively as a phonon confinement effect too [146]. Note that for L a = 2 nm,
Puech et al. were able to produce a peak which is close to−1 1550 cm −1 , 40 cm−1 away from the detected
were able to produce a peak which is close to 1550 cm , 40 cm−1 away from the detected position. 
position. However, in their calculations they used flat graphite, whereas nanocones are not flat. Bonds,
However, in their calculations they used flat graphite, whereas nanocones are not flat. Bonds, and 
and then
then of
of course
course  band positions,are 
band  positions,  arehowever 
however affected
affected  by by curvature
curvature  [8] that 
[8]  so  so that a combined
a  combined  effect effect
of  of
phonon confinement plus curvature may explain the existence of this band at 1510 cm − 1 . That band
phonon confinement plus curvature may explain the existence of this band at 1510 cm −1 . That band 
was not observed on disordered samples studied by Pardanaud et al. [66], using UV, due to resonance
was not observed on disordered samples studied by Pardanaud et al. [66], using UV, due to resonance 
effects. We believe that in situ multiwavelength Raman spectroscopy coupled to skeleton analysis of 
effects. We believe that in situ multiwavelength Raman spectroscopy coupled to skeleton analysis of
TEM images (like the one performed by Oschatz et al. [228], or by Da Costa et al. [229]) performed on 
TEM images (like the one performed by Oschatz et al. [228], or by Da Costa et al. [229]) performed on
stressed nanocones could be the next insight to pave the way between 2D ordered and 3D disordered 
stressed nanocones could be the next insight to pave the way between 2D ordered and 3D disordered
aromatic carbons, especially by taking advantage of resonance effects. 
aromatic carbons, especially by taking advantage of resonance effects.

 
Figure 16. Г
Figure ID /IDG
16. ГG vs.G vs. I /IGplot for a large variety of disordered graphitic samples. Grey lines are obtained
 plot for a large variety of disordered graphitic samples. Grey lines are obtained 
from a fit (more explanation in in 
from  a  fit  (more  explanation  thethe  work 
work ofof Pardanaud
Pardanaud  et 
et al. 
al. [66]. 
[66].Data 
Data obtained 
obtainedfrom  disordered 
from disordered
carbons (514 and 325 nm data) were also obtained from this paper. Data of implanted HOPGHOPG 
carbons  (514  and  325  nm  data)  were  also  obtained  from  this  paper.  Data  of  implanted  (triangles)
(triangles) 
were taken fromwere [230]taken 
and from [230]  respectively,
from [231], and  from  [231], 
andrespectively,  and  those 
those of thermally of  thermally 
heated amorphous heated 
carbons
amorphous  carbons  were  taken  from  [225].  Data  belonging  to  nanocones  under  high  pressure  are 
were taken from [225]. Data belonging to nanocones under high pressure are given in green stars, and
given in green stars, and were extracted from [223]. 
were extracted from [223].
3.3. Disordered Graphene as a Reference for More Disordered Carbons 
3.3. Disordered Graphene as a Reference for More Disordered Carbons
Structural defects that may appear during a growth process or some processing can modify local 
Structural defects that may appear during a growth process or some processing can modify local
properties and make new properties varying from one kind of defect to another [232]. As an example, 
properties and make new properties varying from one kind of defect to another [232]. As an example,
defective graphenes composed of randomly oriented domains, called amorphous 2D materials, have 
been graphenes
defective observed  in 2011 
composedunder  ofelectron beams  [233]. Here, 
randomly oriented we  focus 
domains, calledon amorphous
the Raman spectra of  point have
2D materials,
been observed in 2011 under electron beams [233]. Here, we focus on the Raman spectra of pointone 
defects  (0D),  line  defects  (1D),  and  Stone–Wales  defects.  Writing  “disorder”,  or  “defect”,  defects
(0D), immediately thinks about the D and D’ bands, not only the G and 2D bands. Even though the shape 
line defects (1D), and Stone–Wales defects. Writing “disorder”, or “defect”, one immediately
of the G and 2D bands can also be changed by disorder (we will see that in Section 3.4), we will now 
thinks about the D and D’ bands, not only the G and 2D bands. Even though the shape of the G and
focus  on  the  D  and  D’  bands  that  become  activated  by  defects,  whereas  they  are  forbidden  by 
2D bands can also be changed by disorder (we will see that in Section 3.4), we will now focus on the
selection rules for perfect graphene planes. We just mention that the rise of these bands subsequently 
D andto ion irradiation was first studied in the 1980s and 1990s on graphite [227,234–238], giving an insight 
D’ bands that become activated by defects, whereas they are forbidden by selection rules for
perfect graphene planes. We just mention that the rise of these bands subsequently to ion irradiation
to the production and behavior of defects in graphite. 
was first studied in the 1980s and 1990s on graphite [227,234–238], giving an insight to the production
Coming back to graphene, in 2012 Eckmann et al. [105] showed that the intensity of the D’ band 
and behavior of defects in graphite.
compared to the D band (I D/ID’) is very effective to discriminate between different kinds of defects: 

ID/ID’ = 3.5, the minimum value, is found for boundaries, whereas I
Coming back to graphene, in 2012 Eckmann et al. [105] showed D/ID’  is close to 7 for vacancy like 
that the intensity of the D’ band
defects and up to 13 for sp
compared to the D band (ID /I defects. The I
3
) is very D/ID’ ratio is interesting because, according to the resonance 
effective to discriminate between different kinds of defects:
D’
Raman theory, it is not sensitive to the number of defects but only to the type of defects. Until today, 
ID /ID’ = 3.5, the minimum value, is found for boundaries, whereas ID /ID’ is close to 7 for vacancy like
we  do  not  know  if  all  defects  activate  these  D  and  D’  bands.  To  answer  this  question,  one  has  to 
defects and up to 13 for sp3 defects. The ID /ID’ ratio is interesting because, according to the resonance
introduce  in  a  controlled  way  many  kinds  of  defects  in  graphene  and  record  their  corresponding 
Raman theory, it is not sensitive to the number of defects but only to the type of defects. Until today,
Raman spectra. Since 2006, this task has been challenged mainly by the group of Jorio and Cançado 
we doby not know if
studying  0D all[98,99,101] 
defects activate
and  1D these D defects 
[65,67]  and D’of  bands. To answer
graphene  thisand 
separately,  question, one
together  has to
very 
recently [97], and also with 0D defects in multilayer graphene [99,100]. Eckmann et al. also challenged 
 Coatings 2017, 7, 153    31 of 54 

this point, by comparing sp3‐C, vacancies, and substitutional boron atoms, thereby highlighting the 
role played by the D’ band [239]. 
Coatings 2017, 7, 153
In 2006 and 2007, Cançado et al. worked first on nanographites with crystallites delimited by 1D 31 of 55

defects  (and  obtained  by  heating  diamond  like  carbons),  and  clarified  the  Tuinstra  and  Koenig 
relation, highlighting the ( ω )4 dependency of the ID/IG ratio for 1D defects [65,67,240]. Moreover, 
introduce in a controlled way many kinds of defects in graphene and record their corresponding
they have shown that the width of the D, G , D’, and 2D bands verify a relation which is: Г = A + B/La, 
Raman spectra. Since 2006, this task has been challenged mainly by the group of Jorio and Cançado by
A and B being constants (A = 11 cm−1 for the G band, for example, close to the 11.5 cm–1 calculated for 
studying 0D [98,99,101] and 1D [65,67] defects of graphene separately, and together very recently [97],
the perfect graphite crystal [58]). As a direct consequence, ID/IG and Г are linear if plotted one against 
and also with 0D defects in multilayer graphene [99,100]. Eckmann et al. also challenged this point, by
the other for these nanographites, with La in the range 20–65 nm. This is what is evidenced in the 
comparing sp3 -C, vacancies, and substitutional boron atoms,
bottom of Figure 16. Another direct consequence is that Г thereby highlighting the role played by
G and ГD evolve linearly too, with a slope 
theclose to 1. 
D’ band [239].
In In 2010, Lucchese et al. [101] introduced their well‐known “local activation model” in order to 
2006 and 2007, Cançado et al. worked first on nanographites with crystallites delimited by 1D
defects (and obtained by heating diamond like carbons), and clarified the Tuinstra and Koenig relation,
reproduce the spectra obtained on graphene samples bombarded at different fluences by 90 eV Ar + 

highlighting the (}ω0 )4 dependency of the ID /IG ratio for 1D defects [65,67,240]. Moreover, they have
ions. They found the following expression (see Equation (18)) for 0D defects by writing the evolution 
shown that the width of the D, G , D’, and 2D bands verify a relation which is: Г = A + B/La , A and
equation of the S and A regions as shown in Figure 17a,b 
B being constants (A = 11 cm−1 for the G band, for example, close to the 11.5 cm–1 calculated for the
perfect graphite crystal [58]). As a direct consequence, ID /IG and Г 1are linear/ if plotted
  one against
(18)  the
other for these nanographites, with L2a in the range 20–65 nm. This is what is evidenced in the bottom
of Figure 16. Another direct consequence is that ГG and ГD evolve linearly too, with a slope close to 1.
Here, rS (see Figure 17a) is the radius of the structurally disordered area around the defect, and 
In 2010, Lucchese et al. [101] introduced their well-known “local activation model” in order to
rA the radius of the activated region (i.e., the region in which the selection rules are broken leading to  +
reproduce the spectra obtained on graphene samples bombarded at different fluences by 90 eV Ar
the intervalley double resonance mechanism and giving rise to a D band). CA and CS are constants 
ions. They found the following expression (see Equation (18)) for 0D defects by writing the evolution
whose origins are discussed in [101] (CA is related to the Raman cross sections, CS is related to the 
equation of the S and A regions
geometry of the defect), L as shown in Figure 17a,b
D is the average distance between defects. In the regime where the quantity 

of defects is small (i.e., when the mean distance between defects is large compared to r
 2
πrS 2 − r2 )
π(rA
 A − rS), a first 

ID 2 2
r A − r S  L2− − S
order Taylor expansion of the above equation reduces to Equation (19): 
h 2 /L2
i
L2 − πr
= CA 2 e D −e D  + CS 1 − e S D (18)
IG rA − 2rS 2
π
π π   (19) 

 
Figure 17. 0D and 1D local activation models. (a,b) Definition of the structurally damaged regions 
Figure 17. 0D and 1D local activation models. (a,b) Definition of the structurally damaged regions and
and activated regions, with LD, the distance between defects, and La, the size of crystallites surrounded 
activated regions, with LD , the distance between defects, and La , the size of crystallites surrounded by
by edges, for respectively the 0D and 1D defects; (c) ГG as a function of AD/AG. 
edges, for respectively the 0D and 1D defects; (c) ГG as a function of AD /AG .

In their study [101], the defect was a vacancy and the parameters found were: rA = 3 nm, rS = 1 nm, 
CAHere, rS (seeS Figure
 = 4.2, and C 0. For a low number of defects, the I
17a) is the radius of the structurally disordered area around
D/IG ratio behaves like 1/L the defect, and rA
D2, which better fits 

thethe data than the Tuinstra and Koenig 1/L
radius of the activated region (i.e., thearegion in which the selection rules are broken leading to
 relation. In another study [239], no dependency with the 
thetype and number of defects (such as vacancy and sp
intervalley double resonance mechanism and giving rise to a D band). CA and CS are constants
3‐C) was obtained using this ratio (but a difference 

was noticed from 3D materials, see Figure 3 and its discussion in that study). However, comparing 
whose origins are discussed in [101] (CA is related to the Raman cross sections, CS is related to the
D and D’ intensities with the type and number of defects leads to a strong correlation. In the low 
geometry of the defect), LD is the average distance between defects. In the regime where the quantity
of concentration regime, one can find Equation (20): 
defects is small (i.e., when the mean distance between defects is large compared to rA − rS ), a first
order Taylor expansion of the above equation reduces to Equation (19):
, , ,
  (20) 
, , 2 , 2 , 2,
ID r −r πr
≈ C A π A 2 S + CS π 2S (19)
IG LD LD

In their study [101], the defect was a vacancy and the parameters found were: rA = 3 nm, rS = 1 nm,
CA = 4.2, and CS ≈ 0. For a low number of defects, the ID /IG ratio behaves like 1/LD 2 , which better fits
the data than the Tuinstra and Koenig 1/La relation. In another study [239], no dependency with the
Coatings 2017, 7, 153 32 of 55

type and number of defects (such as vacancy and sp3 -C) was obtained using this ratio (but a difference
was noticed from 3D materials, see Figure 3 and its discussion in that study). However, comparing
D and D’ intensities with the type and number of defects leads to a strong correlation. In the low
concentration regime, one can find Equation (20):

ID CA,D (rA,D 2 − rS,D 2 )

≈ (20)
ID0 CA,D0 (rA,D0 2 − rS,D0 2 ) + CS,D0 rS,D0 2

with the subscript D or D’ to refer to the D or D’ bands. One can see that the ID /ID’ ratio strongly
depends on the CS,D’ coefficient, which is found to be equal to 0.1 for sp3 defects whereas it is 1.2 for
vacancy defects.
Ribeiro-Soares et al. studied 1D defects in graphene [102]. They heated a diamond-like carbon
from 1200 to 2800 ◦ C. They obtained an expression for the ID /IG intensity ratio [102], by noting that
two sets of two bands have to be considered: A first set of D and G bands occurring from the activated
region, and one set of D and G bands, downshifted due to softening of the phonon modes, occurring
from highly disordered areas. Let us thus consider a structurally damaged ribbon (width lS ), and
activated region (width lA ) and the mean size of a crystallite La (see Figure 17b). The evaluation of
the intensity coming from the structurally damaged ribbon is purely geometric, whereas that of the
ones from the activated region is geometric plus an exponential function introduced to account for the
localization of the scattering giving rise to the D band. The final expression is then (see Equation (21):
h i
ID CA,D lA ( La − 2lS ) 1 − e−2( LA −2lS )/l A + 4CS,D lS ( La − lS )
= (21)
IG CA,G ( La − 2lS )2 + 4CS,G lS ( La − lS )

The C constants are related to the cross sections and contain the wavelength dependency.
The values of lS and lA were found to be 1.4 nm and 4 nm, respectively, and in very good agreement
with Scanning Tunneling Microscopy (STM) data. When La >> lS (i.e., the size of the structurally
disordered region is negligible compared to the size of the crystallites), one obtains Equation (22):
 
ID C A,D l A + 4CS,D lS 1
≈ (22)
IG C A,G La

which perfectly reproduces the Tuinstra and Koenig expression obtained experimentally in 1970.
The group of Jorio and Cançado produced recently a work that aims to disentangle the contribution of
0D and 1D defects coexisting on graphene related materials [97]. Figure 17c displays for both 0D and
1D defects the plot of ГG as function of the AD /AG ratio scaled with the laser energy, A being the band
area (see comment in Section 2.7).
We now focus on another kind of defects named topological defects. These are non-hexagonal
arrangements of carbon atoms in the graphene lattice. They are reported for most of the graphene
based materials such as SWNTs, graphene [241,242] and graphite [243]. This kind of defect introduces
a curvature in the flat geometry of a graphene layer. Probably one of the most studied topological
defects is displayed in Figure 18: The Stone–Thrower–Wales (STW) defect (44 papers found using a
bibliometric tool focused on abstracts), which corresponds to two pentagon-heptagon pairs. It is not
easy to determine the precise frequency associated to the Raman signature of these defects. Theoretical
calculations with SWNTs reported that the characteristic frequency of the STW defects should lie
between 1820 and 1962 cm−1 , depending on the local curvature of the tube [244]. On the other hand,
SERS measurements performed with SWNTs have shown two modes at 1139 and 1183 cm−1 associated
to STW defects [245]. Theoretical calculations predict, among other things, a softening of the G band by
−26 cm−1 , and a hardening of the D band by +13 cm−1 [246]. A way to detect their Raman signature
would be to use SERS, as suggested in the work of Itoh et al. [247].
Theoretical calculations with SWNTs reported that the characteristic frequency of the STW defects 
should lie between 1820 and 1962 cm−1, depending on the local curvature of the tube [244]. On the 
other hand, SERS measurements performed with SWNTs have shown two modes at 1139 and 1183 cm−1 
associated to STW defects [245]. Theoretical calculations predict, among other things, a softening of 
the G band by −26 cm
Coatings 2017, 7, 153
−1, and a hardening of the D band by +13 cm−1 [246]. A way to detect their Raman 
33 of 55
signature would be to use SERS, as suggested in the work of Itoh et al. [247]. 

 
Figure 18. Stone–Wales defect. 
Figure 18. Stone–Wales defect.

3.4. Very Defective Carbons: Pyrocarbons, Coals, and Soots

The first reported work on very defective carbons is from Tuinstra and Koenig who found the
relation relating the intensities of the D and G bands for activated charcoal, lampblack, and vitreous
carbon, as reported above. In 1984, Lespade et al. [79] reported the Raman spectra of many disordered
carbons such as pyrocarbons and fibers, using heat treatment to change the structure of these materials
that were found to be graphitizable and not graphitizable. Four graphitization indexes were found:
The frequency of the G band, its width, the intensity ratio ID /IG , and the width of the 2D band. Among
others, they introduced a graphitization trajectory in the Г2D vs. ГG plot, distinguishing between 2D
and 3D order [79]. The behavior of the 2D band according to a 3D order (related to the stacking order)
was elucidated in more details 24 years later by Cançado et al. who heated diamond-like carbons in the
range 2200–2700 ◦ C [59]. Among other things, they evidenced a contribution of the band coming from
3D graphite and a contribution from graphene, and were able to relate their relative intensity ratio to
the size of the crystallites in the c direction up to roughly 200 nm. Today, the number and origin of
the 2D sub-bands have been understood for multilayer graphene [1] in the framework of the double
resonance mechanism and more complex things can occur such as folding [248], misorientation [162],
and stacking faults that can modify the intensities and shape. All these processes may also contribute
to the intensity ratio spreading displayed in Figure 11. Table 1 in the paper by Larouche et al. [249]
resumes the main spectral indicators that are used in the literature to deduce information about the
structure of very defective carbons. They presented the influence of curvature by introducing the
distance parameter Leq , which is the average continuous graphene length including tortuosity of
graphenic planes (see Figure 19). They showed that this tortuosity is very well correlated to the 2D
band width. Note that they defined tortuosity as the number of phonons produced at the K point
divided by the number of phonons produced at the Г point of the Brillouin zone. We advise the reader
that tortuosity is generally derived differently, from the analysis of HRTEM images [250,251]. The main
message of this paper though is that the 2D band width is a good parameter to gain an insight into
the tortuosity.

Table 1. Characteristics of ta-C:H and various a-C:H sub-types.

Types sp3 (at.%) H (at.%) Eg (eV) Hardness (GPa) Density (g/cm3 )

ta-C:H 70 25–30 2–2.5 >20 2.4
PLCH 70 40–60 2–4 soft <1.2
DLCH 40–60 20–40 1–2 <20 2.0
GLCH <30 <20 <1 soft 1.6
GLCHH 30 30–40 >1 soft 1.3
 Types  sp3 (at.%)  H (at.%) Eg (eV) Hardness (GPa) Density (g/cm3)
ta‐C:H  70  25–30  2–2.5  >20  2.4 
PLCH  70  40–60  2–4  soft  <1.2 
DLCH  40–60  20–40  1–2  <20  2.0 
GLCH 
Coatings 2017, 7, 153 <30  <20  <1  soft  1.6  34 of 55
GLCHH  30  30–40  >1  soft  1.3 

 
Figure 19. Tortuosity as defined by Larouche et al. [249]. The domains represented by red arrows (L
Figure 19. Tortuosity as defined by Larouche et al. [249]. The domains represented by red arrows (Laa) )
are aromatic domains without defects. The domains represented by purple arrows (L
are aromatic domains without defects. The domains represented by purple arrows (Leq ) are composed 
eq ) are composed
of several aromatic domains, in‐between there are curved graphene sites. 
of several aromatic domains, in-between there are curved graphene sites.

We now focus on soots and pyrocarbons (see a typical Raman spectrum on Figure 20). First of all,
what is the difference between soots and pyrocarbons? When processing hydrocarbons (varying
pressure, P, and temperature, T, in the reactor), gas phase nucleation leads to soots, whereas
heterogeneous nucleation on the substrate leads to the formation of pyrocarbons, which can contain
up to 5 at. % of hydrogen [252]. The Raman spectroscopy of soots (e.g., diesel soots, spark discharge
soots, commercial black carbons) has been investigated in detail in 2005 [122]. To fit all the data in the
1000–1700 cm−1 spectral region, five bands were necessary: D (called D1 ), D’ (called D2 ), and G bands,
Coatings 2017, 7, 153    34 of 54 
plus two less intense bands, the D3 and D4 bands, lying at 1500 and close to 1180 cm−1 (dependent on
the wavelength of the laser), respectively. The best fit found was a four Lorentzian fit plus a Gaussian
Table 1. Characteristics of ta‐C:H and various a‐C:H sub‐types. 
lineshape for the D3 band. The need of such a band was first proposed  by Rouzaud et al. [253]. In 2009,
BrunettoTypes  sp3 (at.%)  H (at.%)and aromatic
Eg (eV)dominated
Hardness (GPa) Density (g/cm
in flames to) mimic
3
et al. bombarded some aliphatic soots produced
Figure  20. 
ta‐C:H  Raman  spectrum 
70  obtained 
25–30 from  a  pyrocarbon. 
2–2.5  The  inset  represents 
>20  a  rough 
the effect of irradiation encountered in the primitive solar nebulae [254]. The authors used a σG vs. ГG laminar 
2.4 
PLCH  70  40–60  3 bonds (blue), sp bonds (red), and hydrogen bonds (green). 
2–4  soft  <1.2 
plot pyrocarbon with defects (black bonds), sp
to compare their Raman spectra to the one collected on meteorites, interplanetary dusts and the
DLCH 
(λ0 = 633 nm).  40–60  20–40  1–2  <20  2.0 
grains collected from the Wild 2 comets. They found them very similar, allowing them to suppose
GLCH  <30  <20  <1  soft  1.6 
that theGLCHH 
irradiation played 30 
a major30–40 
role in the processing
>1 
of the carbon
soft 
materials at1.3  the beginning
Pyrocarbons  are  generally  deposited  on  substrates  by  cracking  hydrocarbons  at  temperatures 
of the solar system. Recently, the multiwavelength analysis is being used more than in the past to
higher than 900 °C, using chemical vapor deposition processes. Using infiltration process, pyrocarbons 
give better refined information on soots. For example, in 2011, combining temperature programmed
are used mainly in carbon/carbon fiber composites, whose aim is to withstand mechanical stress at high 
oxidation and multiwavelength Raman spectroscopy (514–785 nm), Schmidt et al. noticed that a
temperature [252]. A large variety of pyrocarbon textures exist. Among them, we can cite rough laminar 
structure/reactivity relation from different soots can be obtained [255]. In 2015, in the framework of
(columnar structures), smooth laminar, and regenerative laminar [258]. High resolution TEM shows 
soot formation, Russo et al. evidenced that by changing the wavelength of the laser they were able
columnar and wavy structures (produced by pentagons during the deposition process [259]). Their 
to relate the origin of the fuel molecule and the structure of the soot [256]. The G band was found to
TEM fringes length was found to be 1.6, 2.3, and 2.6 nm, respectively. In particular, the Raman D   
display an asymmetric profile, and a D5 band (attributed to the presence of olefinic chains lying in
band width was found to be a good spectroscopic criterion to distinguish them. Bourrat et al. [258] 
grainFigure 19. Tortuosity as defined by Larouche et al. [249]. The domains represented by red arrows (L
boundaries), in the range 1100–1200 cm−1 , was found to be more intense using 633 nm instead a) 
of
found Г D = 80, 85, and 110 cm −1 for rough, smooth, and regenerative laminar pyrocarbon, respectively. 
are aromatic domains without defects. The domains represented by purple arrows (L eq) are composed 
green or blue lasers. Ess et al. were able to −1 relate the structural change of soots−1under heating under
The ranges were refined later: Г ◦DC = 80–90 cm  for rough laminar, ГD = 90–130 cm  for smooth laminar, 
of several aromatic domains, in‐between there are curved graphene sites. 
oxygen atmosphere up to 600 and relate it to the organic carbon content [257].
and ГD = 170–200 cm  for regenerative laminar [123,260]. The interpretation is that ГD is sensitive to 
−1

curvature effects, as is suggested by TEM analysis. ГG is spread on a narrower range, i.e., from 55 to 
70 cm−1. 
We  finish  this  section  by  focusing  on  the  D”  band,  sometimes  called  D4  band  and  lying  in 
between 1100 and 1200 cm−1. It has been used for a long time to fit spectra of disordered samples 
(especially soot materials) and amorphous carbons with some local order (i.e., those containing sp2 
aromatic domains). It is sometimes called the TPA band (for trans‐polyacetylene), as it lies close to 
the mode found in nanodiamonds [261]. It has been recently considered in the fitting procedure of 
nanoporous  carbons  [262].  The  history  of  this  band  and  its  relation  to  the  2450  cm−1  band,  first 
reported in the work of Nemanich, [81], for defectless graphite, is important to mention here because 

 
Figure 20. 
Figure  Raman spectrum 
20. Raman  spectrum obtained 
obtained from 
from a 
a pyrocarbon. 
pyrocarbon. The 
Theinset 
inset represents 
represents a a rough 
rough laminar 
laminar
pyrocarbon with defects (black bonds), sp 3 bonds (blue), sp bonds (red), and hydrogen bonds (green).
pyrocarbon with defects (black bonds), sp  bonds (blue), sp bonds (red), and hydrogen bonds (green). 
3

(λ00 = 633 nm). 
(λ = 633 nm).

Pyrocarbons  are  generally  deposited  on  substrates  by  cracking  hydrocarbons  at  temperatures 
higher than 900 °C, using chemical vapor deposition processes. Using infiltration process, pyrocarbons 
are used mainly in carbon/carbon fiber composites, whose aim is to withstand mechanical stress at high 
temperature [252]. A large variety of pyrocarbon textures exist. Among them, we can cite rough laminar 
(columnar structures), smooth laminar, and regenerative laminar [258]. High resolution TEM shows 
Coatings 2017, 7, 153 35 of 55

Pyrocarbons are generally deposited on substrates by cracking hydrocarbons at temperatures

higher than 900 ◦ C, using chemical vapor deposition processes. Using infiltration process, pyrocarbons
are used mainly in carbon/carbon fiber composites, whose aim is to withstand mechanical stress at
high temperature [252]. A large variety of pyrocarbon textures exist. Among them, we can cite rough
laminar (columnar structures), smooth laminar, and regenerative laminar [258]. High resolution TEM
shows columnar and wavy structures (produced by pentagons during the deposition process [259]).
Their TEM fringes length was found to be 1.6, 2.3, and 2.6 nm, respectively. In particular, the Raman D
band width was found to be a good spectroscopic criterion to distinguish them. Bourrat et al. [258]
found ГD = 80, 85, and 110 cm−1 for rough, smooth, and regenerative laminar pyrocarbon, respectively.
The ranges were refined later: ГD = 80–90 cm−1 for rough laminar, ГD = 90–130 cm−1 for smooth
laminar, and ГD = 170–200 cm−1 for regenerative laminar [123,260]. The interpretation is that ГD is
sensitive to curvature effects, as is suggested by TEM analysis. ГG is spread on a narrower range, i.e.,
from 55 to 70 cm−1 .
We finish this section by focusing on the D” band, sometimes called D4 band and lying in
between 1100 and 1200 cm− 1 . It has been used for a long time to fit spectra of disordered samples
(especially soot materials) and amorphous carbons with some local order (i.e., those containing sp2
aromatic domains). It is sometimes called the TPA band (for trans-polyacetylene), as it lies close to
the mode found in nanodiamonds [261]. It has been recently considered in the fitting procedure
of nanoporous carbons [262]. The history of this band and its relation to the 2450 cm− 1 band,
first reported in the work of Nemanich, [81], for defectless graphite, is important to mention here
because it illustrates the fact that studying disordered materials helps in understanding the spectra
of well-ordered materials. The D” band origin has been understood by Venezuela et al. [69] in 2011
on perfect graphene (it is mainly due to phonons associated to the KГ direction in the Brillouin zone).
In 2013, May et al. [263] were able to calculate the shape of the 2450 cm− 1 band in the framework of the
double resonance mechanism on perfect graphene involving TO and LA phonons close to the K point.
They were able to reproduce its dispersion and change of shape depending on the laser wavelength.
In 2016, Zhou et al. [183] observed on perfect graphene the laser sensitivity of the D” and D + D”
bands in the UV range. In 2014, Herzinger et al. [264] created defective graphene and nanotubes by
bombardment with high energy ions, and characterized the dispersion behavior of this D” band.
Couzi et al. [61] determined on defective aromatic carbons (graphite nanoplatelets, heat-treated glassy
carbons, pyrograph nanofilaments, and multiwall nanotubes) the behavior of the D” band, identifying
two new bands (D* and D**) lying close to the D” band, but with positive dispersion behavior, and
reproduced the dispersion of the D + D” in the near UV. We have to note that the D*, D**, and D” bands
do overlap, creating the well-known D4 band often used to fit Raman spectra of soots. Very recently,
the D4 and D3 bands were observed on nanotubes and partially exfoliated by acid treatment [265].

3.5. Graphite Intercalated Compounds

In this part, we briefly present some results about a kind of material that must be cited because it
displays a large variety of structures and because it has great application potential in different fields
(such as energy storage, superconductivity, nano-medicine, etc. [266] and references therein): Graphite
intercalated compounds (GICs). GICs are multilayered materials sufficiently ordered to exhibit staging
in which the number of graphitic layers in between adjacent intercalants can be varied in a controlled
way. The interlayer spacing can be tuned from 0.34 up to 1 nm [267]. The denomination n-stage
GICs can be found in [268], n defining the constant number of graphene layers between any nearest
pair of intercalant layers. More details about the staging can also be found in [266]. The diminution
of the interlayer spacing distance reduced the van der Waals interaction between planes so that
it can be envisaged as a route to form graphene and nano-ribbons [269]. The list of metals and
small molecules that can be embedded in between graphene planes is huge and not exhaustive here:
Alkali-metals (K, Li, Cs, Rb); alkali-earth-metals (Be, Ca, Ba); halogens; C60 [270]; FeCl3 [271]; H2 SO4
and HSO4 − [272]; AsF5 , HNO3 , and SbCl5 [273]; etc. Intercalants can be electron donors or electron
Coatings 2017, 7, 153 36 of 55

acceptors. Thus, charge transfer and strain are intrinsic effects in GICs, and Raman spectroscopy
is sensitive to both. Raman study of highly staged GICs allowed to disentangle both effects [274].
A seminal work by Solin presenting an overview of the Raman spectroscopy of these compounds was
published in 1980 [275]. A more recent work on a combination of Raman spectroscopy and ab initio
calculations of GICs by Chacon-Torres et al. was reported in 2014 [266]. Inner graphene layers (also
called interior layers) and outer graphene layers (also called graphene layers bounded by intercalants)
can be differentiated by the G line splitting, with σG of the blue component that can reach values as
high as 1636 cm− 1 [266,273]. Superconductivity has been observed in many GICs (with the highest
critical temperature found at a relatively high temperature, 11.5 K, for CaC6 , see references [266]) and
multiwavelength Raman spectroscopy is a central characterization tool because superconductivity
may be due to electron–phonon interaction and mediated by phonons [276]. Multiwavelength Raman
spectroscopy also allows a direct measurement of the Fermi level by observing the Pauli blocking
(which results in the 2D band intensity vanishing by tuning the wavelength of the laser) [271].

3.6. Amorphous and Diamond-Like Carbons

Most of the work cited on Raman spectroscopy of amorphous carbons [277] comes from the
thousands of times cited papers by Ferrari et al. Their four landmark papers were published from
2000 to 2005 and  combine all together a comprehensive view of the understanding about Raman
Coatings 2017, 7, 153  36 of 54 
spectroscopy of amorphous carbons [4–6,70], based on many other papers that we will not cite all
here. The study of Raman spectroscopy of amorphous carbons was completed in 2015 by the work of
here. The study of Raman spectroscopy of amorphous carbons was completed in 2015 by the work of 
Zhang et al. [278], as we will see soon hereafter.
Zhang et al. [278], as we will see soon hereafter. 
To begin with, amorphous carbons are generally containing sp33,, sp
To begin with, amorphous carbons are generally containing sp sp22 carbons, and heteroatoms 
carbons, and heteroatoms
(such 3
as hydrogen). sp3 carbons determine the mechanical properties (hardness, density), whereas the 
carbons determine the mechanical properties (hardness, density), whereas
(such as hydrogen). sp
the sp2 aromatic clusters determine the optical properties (energy gap), mainly due to the π/π* bonds
sp  aromatic clusters determine the optical properties (energy gap), mainly due to the π/π* bonds 
2

with
with thethe energy
energy gapgap in
in the
the IR–visible–UV
IR–visible–UV range,
range, depending
depending on on their
their size.
size. Adding
Adding hydrogen,
hydrogen, and
and 
organizing the structure by heating the sample, can change the optical properties together with
organizing the structure by heating the sample, can change the optical properties together with the 
the structure
structure  [7,124–126,225,279–282]
[7,124–126,225,279–282]  and and Raman
Raman  spectroscopy
spectroscopy  can can
help help in checking
in  checking  the changes.
the  changes.  For 
For example, hydrogen changes the electronic structure, which leads to a Raman resonance mechanism
example, hydrogen changes the electronic structure, which leads to a Raman resonance mechanism 
that can be observed, helping in quantifying the amount of hydrogen in the amorphous carbons [283].
that can be observed, helping in quantifying the amount of hydrogen in the amorphous carbons [283]. 
Depending on the amount of aromatic/aliphatic 2sp 2 3 carbons and hydrogen atoms, several
Depending on the amount of aromatic/aliphatic sp /sp3/sp
 carbons and hydrogen atoms, several kinds 
kinds of amorphous
of  amorphous  carbons
carbons  can  can be distinguished:
be  distinguished:  a‐C, a-C, ta-C,
ta‐C,  a-C:H,
a‐C:H,  andta‐C:H. 
and  Thet t stands 
ta-C:H.The  stands for
for 
tetracoordinated as these carbons contain generally close to 70% of sp 3 carbons. A basic scheme of
tetracoordinated as these carbons contain generally close to 70% of sp  carbons. A basic scheme of the 
3

the ternary phase diagram for amorphous carbons is displayed in Figure 21. More information can
ternary phase diagram for amorphous carbons is displayed in Figure 21. More information can be 
be found in [70,124]. The classification is however more complex, with even more variety of samples.
found in [70,124]. The classification is however more complex, with even more variety of samples. a‐
a-C:H types are themselves split in subgroups with different properties: PLCH (polymer-like a-C:H),
C:H types are themselves split in subgroups with different properties: PLCH (polymer‐like a‐C:H), 
DLCH ( diamond-like a-C:H), GLCH (graphite-like a-C:H) and GLCHH (graphite-like a-C:H with
DLCH ( diamond‐like a‐C:H), GLCH (graphite‐like a‐C:H) and GLCHH (graphite‐like a‐C:H with 
extra hydrogen subtype), as displayed in Table 1, adapted from [278].
extra hydrogen subtype), as displayed in Table 1, adapted from [278]. 

 
Figure 21. Basic ternary phase diagram of amorphous carbons. 
Figure 21. Basic ternary phase diagram of amorphous carbons.

Except  PLCH,  which  only  displays  a  photoluminescence  background,  Raman  spectra  of 
amorphous carbons generally display two broad overlapped G and D bands, the D band being less 
intense, or disappearing when the amount of sp3 carbons is higher. The D band position displays the 
wavelength dispersion as in graphene but shifted depending on the kind of amorphous carbon, as 
shown in Figure 7b. For the G band, it depends on the local degree of order, as already displayed in 
Figure  7a.  Figure  22  displays  the  Raman  spectra  of  one  a‐C:H  film  (H  being  close  to  30  at.%)  but 
Coatings 2017, 7, 153 37 of 55

Except PLCH, which only displays a photoluminescence background, Raman spectra of

amorphous carbons generally display two broad overlapped G and D bands, the D band being
less intense, or disappearing when the amount of sp3 carbons is higher. The D band position displays
the wavelength dispersion as in graphene but shifted depending on the kind of amorphous carbon,
as shown in Figure 7b. For the G band, it depends on the local degree of order, as already displayed
in Figure 7a. Figure 22 displays the Raman spectra of one a-C:H film (H being close to 30 at.%) but
recorded with five different laser wavelengths, ranging from 266 to 633 nm [72]. The dependence of the
shape with the laser wavelength [284] can be explained mainly by the fact that the sample is composed
of a distribution of aromatic domains which display local electronic structures. The wavelength used is
resonant with one kind of environment that appears stronger in the spectrum. Ferrari et al. proposed
a “three stage” model that can explain the ordering of the sp2 phase going from nanocrystalline
graphite (nc-G) to highly disordered amorphous carbon, explaining the changes in the spectroscopic
parameters [4]. The parameters followed are the ID /IG and σG parameters, and their changes with
the laser wavelength. For example, at 514 nm, the G band position is at 1582 cm−1 for graphite, it
upshifts to 1600 cm−1 for nanographite composed of only sp2 aromatic clusters, whereas it can shift
up to 1630 cm−1 for other forms of sp2 carbons (chains), where sp3 carbons are present. Then, when
starting amorphization, σG diminishes down to 1520 cm−1 . In Figure 23, we illustrate that starting
from an amorphous carbon, we obtain a nanographite. We plot σG for an a-C:H (DLCH) film that
has been heated at a 15 K·min−1 rate, under a 1-bar Ar atmosphere, Raman spectra being recorded
in situ, with ramp 1 stopped at 900 ◦ C. A typical evolution is drawn [225] that informs us that the
amorphous carbon
Coatings 2017, 7, 153    is organizing when temperature is increased, by growth of the size of the carbon 37 of 54 
◦
aromatic clusters. A plateau is reached at 600 C. Ramp 2 is made on the same sample after it has first
been cooled down to room temperature. One can see that the G band at room temperature is now 
been cooled down to room temperature. One can see that the G band at room temperature is now
lying at 1592 cm
lying at 1592 cm−−11. The second ramp informs us that now it behaves like graphite and no more like 
. The second ramp informs us that now it behaves like graphite and no more like an
an  amorphous 
amorphous carbon, 
carbon, withwith  an  upshift 
an upshift of  10
of about about 
cm−10  cm−1,  is
1 , which which  is  for
typical typical  for  a  nanocrystalline 
a nanocrystalline graphite.
graphite. The diminution of σ
The diminution of σG with T for G with T for graphite and graphene is reversible and can be used as a 
graphite and graphene is reversible and can be used as a contact less
contact less thermometer [172,173]. 
thermometer [172,173].
 
G band

D band

633 nm
514 nm
407 nm
325 nm
266 nm
800 1000 1200 1400 1600
-1
Raman shift (cm )  
Figure  22. Raman
Figure 22. Raman spectra
spectra 
ofof  amorphous 
amorphous carbon 
carbon (a‐C:H 
(a-C:H withwith 
aboutabout  30 H)
30 at.% at.%  H)  obtained 
obtained with 
with different
different laser wavelengths. 
laser wavelengths.

Next, we ask “what are the other spectroscopic parameters that can be used to characterize
amorphous carbons?” The 2D band cannot be used in general as it is very low in intensity and very
broad, as can be seen in Figure 6b, except when the amorphous carbon is heated. Another spectroscopic
parameter has been found useful to help in determining the amount of hydrogen bonded in a-C:H: the
so-called m/IG parameter, which is the ratio between the slope of the photoluminescence background,
m, in the range 800–1800 cm−1 divided by the G band intensity. This spectroscopic parameter gives
certain qualitative information, as presented in the work of Casiraghi et al. [6], and in the work of

 
Figure 23. Temperature evolution of σG for a DLCH sample (H/H + C = 29%). In situ measurement is 
done in an environmental cell, under argon atmosphere to avoid oxidation. 
Coatings 2017, 7, 153    37 of 54 
Coatings 2017, 7, 153 38 of 55
been cooled down to room temperature. One can see that the G band at room temperature is now 
lying at 1592 cm−1. The second ramp informs us that now it behaves like graphite and no more like 
Buijnsters et al. [285], but is also sensitive to other defects meaning it cannot be used systematically (see
an  amorphous  carbon,  with  an  upshift  of  about  10  cm−1,  which  is  typical  for  a  nanocrystalline 
the analysis on a heated a-C:H performed by comparing Raman spectroscopy with thermal desorption
graphite. The diminution of σG with T for graphite and graphene is reversible and can be used as a 
spectroscopy and ion beam analysis [7], and calculations at the end of the work of Rose et al. [282]).
contact less thermometer [172,173]. 
It has been found that  the G band width, ГG , is correlated to the sp3 content and the linear dispersion
of σG of as deposited samples correlates to the H content [286]. Then, a good way to represent the
data is to plot σG as a function of ГG , as was doneGfor band
several wavelengths in [72,282]. Figure 24
displays such a plot for different kinds of heated amorphous carbons plus nanocrystalline graphite
D band
(for nc-G, ta-C, and ta-C:H data, see [66]). If one uses ГG as an indicator of local disorder close to sp2
bonds in the material (which can be related to the size of the clusters [5,65] and/or to the sp3 content
close to sp2 bonds [286]), one can use this parameter in order to have an idea of where is the sample
situated in Ferrari’s “three stage 633 nm With this in mind, nc-G is more ordered than a-C:H/D
model”.
514 nm
which are themselves more ordered than ta-C:H and ta-C. Each kind of carbon draws its own line
407 nm
when heated, but all these lines tend converge in a region close to 100 cm−1 . a-C, a-C:H, and a-C:D
325tonm
data were recorded in-situ, contrary 266tonm
ta-C, ta-C:H, and nc-G, and thus appear down shifted due to
dilatation and multi-phonon processes [172,173]. The presence of hydrogen systematically diminishes
800 1000 1200 1400 1600
the position of the G band (for ta-C/ta-C:H and a-C/ta-C:H). -1 The systematic frequency shift between
Raman shift (cm )   the material) is partially
a-C:H and a-C:D that tends to diminish when decreasing ГG (i.e., ordering
due Figure  22.  Raman 
to an isotopical spectra 
shift of  amorphous 
of C-H/C-D bonds,carbon 
as the(a‐C:H  with isabout 
difference in the30 same H)  obtained 
at.% order as for C6with 
H6 and
C6 Ddifferent laser wavelengths. 
6 molecules [287].

Coatings 2017, 7, 153    38 of 54 

mind, nc‐G is more ordered than a‐C:H/D which are themselves more ordered than ta‐C:H and ta‐C. 
Each kind of carbon draws its own line when heated, but all these lines tend to converge in a region 
close to 100 cm−1. a‐C, a‐C:H, and a‐C:D data were recorded in‐situ, contrary to ta‐C, ta‐C:H, and nc‐
G,  and  thus  appear  down  shifted  due  to  dilatation  and  multi‐phonon  processes  [172,173].  The 
presence of hydrogen systematically diminishes the position of the G band (for ta‐C/ta‐C:H and a‐
C/ta‐C:H).  The  systematic  frequency  shift  between  a‐C:H  and  a‐C:D  that    tends  to  diminish  when 
Figure 23. Temperature evolution of σ
decreasing Г Temperature evolution of σGG for a DLCH sample (H/H + C = 29%). In situ measurement is 
G (i.e., ordering the material) is partially due to an isotopical shift of C‐H/C‐D bonds, as 
Figure 23. for a DLCH sample (H/H + C = 29%). In situ measurement is
done in an environmental cell, under argon atmosphere to avoid oxidation. 
the difference is in the same order as for C
done in an environmental cell, under argon6H 6 and C6D6to
atmosphere  molecules [287]. 
avoid oxidation.

Next,  we  ask  “what  are  the  other  spectroscopic  parameters  that  can  be  used  to  characterize 
1600 nc-G
amorphous carbons?” The 2D band cannot be used in general as it is very low in intensity and very 
ta-C
broad,  as  can  be  seen  in  Figure  1580 6b,  except  when  the  amorphous  carbon  is  heated.  Another 
spectroscopic  parameter  has  been  found  useful  to  help  in  determining  the  amount  of  hydrogen 
G (cm )

1560m/IG  parameter,  which  is  the  ratio  between  the  slope  of  the 
-1

bonded  in  a‐C:H:  the  so‐called 

photoluminescence  background,  m,  in  the  range  800–1800  cm−1 ta-C:H divided  by  the  G  band  intensity.   
1540
This  spectroscopic  parameter  gives  certain  qualitative  information,  a-C as  presented  in  the  work  of 
work  of  Buijnsters  et  al.  [285],  a-C:H
Casiraghi  et  al.  [6],  and  in  the 1520 but  is  also  sensitive  to  other  defects 
meaning  it  cannot  be  used  systematically  (see  the  analysis a-C:D on  a  heated  a‐C:H  performed  by 
comparing  Raman  spectroscopy  1500with  thermal  desorption  spectroscopy  and  ion  beam  analysis  [7], 
0 50 100 150 200 250
and calculations at the end of the work of Rose et al. [282]). It has been found that the G band width, 
-1
G (cm )  
ГG, is correlated to the sp3 content and the linear dispersion of σG of as deposited samples correlates 
Figure 
Figure 24. 
24. Plots 
Plots of  σG  vs.  ГG  for  nc‐G  and  different  amorphous  carbons.  Data 
to the H content [286]. Then, a good way to represent the data is to plot σ
of σ were recorded
recorded with
G as a function of Г with   
G, as was 
G vs. ГG for nc-G and different amorphous carbons. Data were
λ L = 514 nm. 
done for several wavelengths in [72,282]. Figure 24 displays such a plot for different kinds of heated 
λL = 514 nm.
amorphous carbons plus nanocrystalline graphite (for nc‐G, ta‐C, and ta‐C:H data, see [66]). If one 
In 2015, a phenomenological model based on dispersion was proposed by Zhang et al. [278] in 
uses ГG as an indicator of local disorder close to sp2 bonds in the material (which can be related to the 
order  to  better  characterize  amorphous 3 carbons  by  analyzing  their  Raman  spectra  recorded  with 
size of the clusters [5,65] and/or to the sp  content close to sp2 bonds [286]), one can use this parameter 
several wavelengths. This model starts with the statement that the G band intensity is the sum of 
in order to have an idea of where is the sample situated in Ferrari’s “three stage model”. With this in 
three kinds of sp2 clusters (see Equation (23)): 
ω, λ ω, λ ω, λ ω, λ   (23) 
where ω is the Raman frequency, λL the laser wavelength, and Ig, Ir and Ic are the intensities of the   
Coatings 2017, 7, 153 39 of 55

In 2015, a phenomenological model based on dispersion was proposed by Zhang et al. [278]
in order to better characterize amorphous carbons by analyzing their Raman spectra recorded with
several wavelengths. This model starts with the statement that the G band intensity is the sum of three
kinds of sp2 clusters (see Equation (23)):

IG (ω, λL ) = Ig (ω, λL ) + Ir (ω, λL ) + Ic (ω, λL ) (23)

where ω is the Raman frequency, λL the laser wavelength, and Ig , Ir and Ic are the intensities of the
nc-G, fused aromatic rings and olefinic chain clusters, respectively. Without going into details here
(the model is detailed in Section 2 and in the appendixes of [278]), this shows that σG is a weighted
average of the resonant frequencies for the three types of sp2 carbons (see Equation (24)):

σG = ng ωg + nr ωr + nc ωc (24)

where ng , nr , and nc are the amount of different kind of carbons that satisfy ng + nr + nc = 1. As ωg , ωr ,
and ωc display a linear dispersion with λL [278], and as the parameters for these linear relations have
been tabulated, one can in principle deduce ng , nr , and nc from the G band dispersion.

4. Discussion

4.1. Role of Resonance

The resonance mechanisms at play in the Raman process of aromatic based carbons allow us to
have a better insight in the study of graphenic materials, making multiwavelength Raman spectroscopy
a relevant tool. So far, the well-known double resonance mechanism, based on scattering of an incoming
photon by a phonon followed by a second scattering by a defect or another phonon, is the best option to
explain most of the behaviors reported in the literature since the 1970s (such as the rising of bands like
D*, D**, D”, D, D’, and 2D and combinations thereof), as we mentioned in this review. This mechanism
can probe the phonon dispersion curve of graphene away from the gamma point of the Brillouin
zone. The dispersion and intensity behaviors of these bands (i.e., the dependency of the D/D’ relative
intensity ratio to the kind of defects, the relative D/G intensity ratio sensitivity to the amount of
defects), the Stokes/anti-Stokes anomalies, the zigzag/armchair dependency, the doping effects are all
explained in the framework of this double resonance mechanism. It must be noticed that mechanisms
alternative to double resonance are also under consideration [118] but still need to be confirmed. So far,
the double resonance mechanism remains considered as the most efficient model.

4.2. Role of Defects

Because of defects implied in this model, Raman spectroscopy can be used to characterize how a
graphenic material is far from its crystalline state. As an illustration, Figure 25a displays the width
of the D band (ГD ) in function of the width of the G band (ГG ), which is similar to focusing on the
ГD /ГG that was done in [288]. Data shown are obtained for many graphenic materials (Another way
that has already been used, is to display the ГD /ГG ratio as function of ГG . We then observe that
the ratio evolves from 2 at ГG = 25 cm−1 down to 1 at ГG = 75 cm−1 , and following it increases up
to 2.3 at ГG = 93 cm−1 , and finally stays constant till ГG = 150 cm−1 . Mallet et al. observed such
a variation of ГD /ГG with La , reaching the lowest value at La = 8 nm (see Figure 13 in the work of
Zhao et al. [271]).) (carbon fibers [289], soots [122,290,291], pyrocarbons [123,252,260], nanocones [223],
a large variety of disordered carbons collected from the Tore Supra tokamak [66], nanographites from
Cançado et al. [65], geothermic carbons from [292], and ion implanted graphites taken from [231]).
Depending on the characteristic size of the aromatic domain, the data are grouped in three different
areas: the lowest rectangle with La higher than roughly 10 nm, the intermediate region with La in the
range of few to 10 nm, and the higher one with La close to 1 nm. Below ГG = 50 cm−1 the evolution
is linear, with a slope close to 1 that was found by Cançado et al. for nanographites [65]. When ГG
Coatings 2017, 7, 153 40 of 55

is close to 75 cm−1 , the slope changes drastically: D, with ГD = 50 cm−1 , broadens extremely fast up
to ГD = 120–150 cm−1 , whereas G only evolves from 50 to 75 cm−1 . This behavior was previously
observed in [66,292] and is now also evidenced for pyrocarbons and nanocones. Note that some
materials do not display the drastic change in slope, such as the data of graphite implanted by ions
that are grouped  around the line ГD = 2ГG − 35.
Coatings 2017, 7, 153  40 of 54 

 
Figure 25. Г
Figure 25. ГDD versus Г
versus ГGG plot. (a) For a large variety of disordered aromatic carbons; (b) Zoom with 
plot. (a) For a large variety of disordered aromatic carbons; (b) Zoom with
suggestion of both phonon confinement and curvature effects. 
suggestion of both phonon confinement and curvature effects.

4.3. Other Effects: Our Propositions 
4.3. Other Effects: Our Propositions
The strategy adopted to deals with this apparent complexity, has been to study graphene with 
The strategy adopted to deals with this apparent complexity, has been to study graphene with
controlled  defects.  Creating  point  defects  [101]  and/or  linear  defects  [97,102]  and  controlling  their 
controlled defects. Creating point defects [101] and/or linear defects [97,102] and controlling their
influence on the Raman spectrum of graphene have been the milestones of a bottom‐up approach 
influence on the Raman spectrum of graphene have been the milestones of a bottom-up approach
aiming at understanding the Raman spectra of more complex aromatic carbons. It has been one of 
aiming at understanding the Raman spectra of more complex aromatic carbons. It has been one of
the best progresses made over the last few years in order to overcome the old Tuinstra and Ferrari 
the best progresses made over the last few years in order to overcome the old Tuinstra and Ferrari
relations that were found to give more or less the order of magnitude/trends. Nowadays, other crucial 
steps have to be made in order to be closer to real materials. Among other effects that must be taken 
into account in the understanding of the Raman spectra, there are: 
 curvature effects; 
 phonon confinement effects (due to poor coupling between different aromatic planes, porosities, 
Coatings 2017, 7, 153 41 of 55

relations that were found to give more or less the order of magnitude/trends. Nowadays, other crucial
steps have to be made in order to be closer to real materials. Among other effects that must be taken
into account in the understanding of the Raman spectra, there are:

• curvature effects;
• phonon confinement effects (due to poor coupling between different aromatic planes,
porosities, etc.);
• and combinations thereof.

The influence of these effects on Raman spectra should be studied in detail in the future on
graphene samples containing point defects and/or linear defects with controlled amounts in order
to disentangle the origin of all the effects. Three good material systems for that hypothetical study
could be:

• heated C60 ;
• bombarded nanoribbons of different shapes and sizes deposited on deformable surfaces;
• in situ measurements of nanocones in high pressure/temperature cells.

For the second kind of materials, we believe that in situ multiwavelength Raman spectroscopy
analysis could be coupled to skeleton analysis of high resolution TEM images (like reported in Da Costa,
Pre, and Farbos et al. [229,251,293] respectively) in order to relate the skeleton and the kind of defects
produced under constraint and to check their influence on the Raman spectrum, via resonance effects.
Concerning what already exists in the literature about curvature and/or phonon confinement
fingerprints in the Raman spectra, the analysis of pyrocarbons, which can be composed of tortuous
planes of varying length, has revealed that the width of the D band is sensitive to curvature effects
of the graphene sheets [123,260]. Nanocones submitted to a pressure increase up to 8 GPa display
some morphological changes that are accompanied by a change in the Raman spectrum too [223].
The corresponding data are displayed in Figure 25b. Among other changes, the increase of the D
band width with the pressure increase is more pronounced than for the G band leading to a rapid
evolution of the D band width compared to the G band width. This rapid evolution is not seen for
implanted graphite samples on which two kinds of signatures (amorphous and nanocrystalline) have
been observed together [231]. An explanation may be that a synergetic effect hinders curvature of
graphene planes, preferring the formation of sp3 defects. This could be due to a characteristic of
phonon confinement as evidenced by Puech et al. (data extracted from Figures 6 and 7 of the work
of Puech et al. [146]). However, we know that both nanocones and pyrocarbons can be composed of
curved aromatic planes and the question remains open: How can curvature affect the spectrum too?
Part of the answer was obtained by observing a band shift of the G band [8], but none was obtained
for defective graphene concerning the D band widths. The arrow in Figure 25b starts from the line
of the confinement model and suggests that curvature produces an extra broadening of the G band.
Recently, an additional source of broadening for the G band was revealed by studying pressurized
graphene membranes and it was attributed to strain (if strain is higher than 1%) [294]. This should
be investigated in more detail, and the question of how curvature can lead to phonon confinement
answered too.

5. Conclusions
Based on the observation that many procedures are available to fit the complex Raman spectra
of very defective aromatic carbons (such as soots, pyrocarbons, coals, and amorphous carbons), we
decided to review the Raman spectroscopic characteristics of these materials. Basically, if someone
wants to perform a structural analysis of a carbon-based sample using only Raman spectroscopy
he/she has to focus on, at least:
Coatings 2017, 7, 153 42 of 55

• the ratio intensity between the D and G bands;

• the presence of additional bands (e.g., 2D, D’, etc.);
• the width of all bands.

The combination of all these parameters will give a first basic idea of the structure, namely if the
sample is well-structured or strongly disordered. Nevertheless, with only a basic Raman measurement
(notably if a single excitation wavelength is used) it is clear that at the present moment a more
detailed analysis of the structural defects will require other complementary experimental tools, such as
high-resolution transmission electron microscopy, which is a pity as Raman spectroscopy is probably
the most simple, fast, and non-destructive analysis method. If possible, we therefore suggest the use of
multiwavelength Raman spectroscopy, since it allows for a better characterization of defects, looking
at band position, relative intensities, and width.
We can reasonably assume that each type of defect has a Raman spectral signature. The point up
to now is to identify each spectral signature, which is a real experimental challenge as in most samples
the different structural defects combine, thus giving rise to a complex Raman spectrum. As suggested
in Figure 25 where curvature effects are evidenced in carbon nanocones and pyrocarbons, the solution
is to work with well controlled samples with specific defects. This systematic approach will pave the
way towards a complete guide for a multiwavelength analysis of all aromatic carbon-based species.

Acknowledgments: Cedric Pardanaud wants to thank Gerard Vignoles and Jean-Marc Leyssale for providing
spectra and inset related to pyrocarbons; Miriam Peña Alvarez for the spectra obtained from nanohorns;
Cinzia Casiraghi and Deborah Prezzi for spectra and inset related to nanoribbons; and Gregory Giacometti
for providing Figure 5b. Finally, Cedric Pardanaud wants to acknowledge Pascale Roubin for previous scientific
discussions and for being at the origin of the carbon thematic in the PIIM Lab in 2007.
Author Contributions: Cedric Pardanaud as last and corresponding author conducted the literature search.
Alexandre Merlen and Cedric Pardanaud performed and analyzed own Raman measurements/data and
contributed equally to the figures building. All three authors were involved in the writing and editing of
the manuscript. Josephus Gerardus Buijnsters performed a deep reading at several steps of the writing process.
Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations
σx (expressed in cm−1 ): Band position of the band labelled x (x could be G, D, 2D, D’, . . . ).
Γx (expressed in cm−1 ): Full width at half maximum of the band labelled x.
Ix (expressed in arbitrary units related to the number of counts on the detector): height of the band labelled x.
Ax (expressed in arbitrary units related to the number of counts on the detector): integrated area of the band
labelled x.

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