graphene nanoplatelet/silicon nitride composites with high electrical conductivity
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C A R B O N 5 0 ( 2 0 1 2 ) 3 6 0 7 – 3 6 1 5
.sc ienced i rec t .com
Avai lab le a t wwwjournal homepage: www.elsevier .com/ locate /carbon
Graphene nanoplatelet/silicon nitride composites with highelectrical conductivity
Cristina Ramirez a, Filipe M. Figueiredo b,*, Pilar Miranzo a, P. Poza c, M. Isabel Osendi a,*
a Institute of Ceramics and Glass, CSI C. Campus Cantoblanco, 28049 Madrid, Spainb University of Aveiro, Ceramics & Glass Eng. Dep., CICECO, Campus de Santiago, 3810-193 Aveiro, Portugalc Departamento de Tecnologıa Mecanica, Universidad Rey Juan Carlos, Mostoles, 28933 Madrid, Spain
A R T I C L E I N F O
Article history:
Received 13 December 2011
Accepted 15 March 2012
Available online 23 March 2012
0008-6223/$ - see front matter � 2012 Elsevihttp://dx.doi.org/10.1016/j.carbon.2012.03.031
* Corresponding authors.E-mail addresses: lebre@ua.pt (F.M. Figuei
csic.es (M.I. Osendi).
A B S T R A C T
Silicon nitride (Si3N4) processed with up to 25 vol.% of graphene nanoplatelets (GNPs) gives
conductive composites with the highest electrical conductivity (40 Scm�1) reported for
these ceramics with added conductive particles. During compaction and pressure-assisted
densification of the composites in the spark plasma sintering (SPS), a preferred orientation
of GNPs occurs. Consequently, the electrical conductivity measured along the direction per-
pendicular to the SPS pressing axis is more than one order of magnitude higher than the
one measured along the parallel direction.
Percolation in the composites is observed for 7–9 vol.% of GNPs, depending on the measur-
ing direction, perpendicular or parallel to the pressing axis. Different conduction mecha-
nisms are apparent for the two orthogonal orientations. Charge transport along the
direction defined by the graphene ab-plane (perpendicular direction) may be explained
by a two dimensional variable range hopping mechanism, whereas conduction in the par-
allel direction shows a more complex behavior, with a metallic-type transition (dr/dT < 0)
for high GNP contents. A thin amorphous layer was identified at the Si3N4/GNPs interface
that may affect the conduction for the parallel configuration.
� 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Silicon nitride-based (Si3N4) ceramics have quite notable
mechanical and thermal properties being at the same time
electric insulators. These ceramics are costly to machine into
complex shapes but they can be formed by electrodischarge
machining (EDM) by adding 30 vol.% (or more) of conducting
particles (e.g. TiC or TiN) [1]. Conductive Si3N4 ceramics that
are easily machinable in complex shapes find applications
in micro-electro-mechanical systems (MEMS) for harsh envi-
ronments owing to their mechanical and wear resistances
under severe conditions [2]. Consequently, there is a great
interest in providing electrical conductivity to this material
to augment its functionalities.
er Ltd. All rights reserved
redo), miosendi@icv.
Over the last five years, ceramic composites containing
CNTs have revealed explicit electrical response to very low
nanotubes contents due to the reduced percolation threshold
of the CNT network [3], which bestow them as attractive mul-
tifunctional materials. On the other hand, the toughening and
thermal conduction enhancements associated to the pres-
ence of CNTs seem more subtle, as both appear much influ-
enced by the nature and role of the CNT/matrix interface,
that is, the type of bonding between the ceramic grains and
CNTs.
Maximum electrical conductivities in the range of 0.1–
1 Scm�1 have been reported for Si3N4 composites containing
CNTs, in particular Tatami et al. [4] obtained 0.79 Scm�1 for
a composite with 19.7 vol.% MWCNTs hot pressed at
.
3608 C A R B O N 5 0 ( 2 0 1 2 ) 3 6 0 7 – 3 6 1 5
1800 �C, Fenyi et al. [5] gave 1.3 Scm�1 for a composite with
8.6 vol.% MWCNTs hot pressed at 1700 �C and Gonzalez-Julian
et al. [6] obtained a percolation threshold of 0.64 vol.% for
MWCNT/Si3N4 composites produced by spark plasma sinter-
ing (SPS) at 1580 �C, giving an upper conductivity limit of
0.17 Scm�1 for the 8.6 vol.% MWCNT composite. Conductive
scanning force microscopy (c-SFM) was particularly useful
in visualizing the CNT networks in these composites, and Ra-
man spectroscopy ensured the good condition of the CNTs,
especially after their exposure to the high sintering tempera-
tures. Although these conductivity figures are relatively mod-
est, it was recently evidenced by Malek et al. [7] that they
suffice to enable the EDM of these composites into microme-
chanical components rendering a smooth surface finish
attributable to the CNTs.
Even more appealing is the alternative use of other carbon
nanostructures, such as graphene nanoplatelets (GNP) or
nanosheets, since they represent a cost-effective option when
compared to CNTs, being also less prone to damage after high
temperature exposure. To the best of our knowledge, just a
few works on ceramics containing GNPs have been reported
[8–10], and even fewer on their electrical properties [8,10].
The potential of GNPs as conductive fillers was firstly tested
in alumina matrix, but the possible and likely effect of the
preferential orientation of the platelets was not assessed [8].
In a recent paper by some of the present authors, the con-
ducting networks in GNP/Si3N4 composites were visualized
by c-SFM [10]. This work revealed an important anisotropic ef-
fect due to the preferential orientation of the highly conduct-
ing graphene ab-plane perpendicularly to the pressing axis of
the SPS furnace, during the composite preparation. Orienta-
tion of platelet-like structures during powder compaction is
not unusual and many examples of this effect can be found
in the literature [11,12]. Noticeable differences in the local
conductivity were thus accounted for arrangements parallel
and perpendicular to the SPS pressing axis. Conductive
ceramics are interesting and desirable for using EDM methods
or for avoiding static electricity effects in friction components
[1,8]. Even the electric anisotropy may find innovative applica-
tions such as for optoelectronic devices [13]. Here, we present
electrical conductivity data collected in directions parallel
and perpendicular to the SPS pressing axis of the composites
(Fig. 1) for a wide range of GNP contents and temperatures
(298–573 K), in order to assess the electrical conductivity of
anisotropic GNP/Si3N4 composites and corresponding trans-
port mechanism.
2. Experimental
2.1. Composites fabrication
A similar procedure as described in previous work was fol-
lowed [10]. A dispersion of the GNPs (Angstron Materials) in
isopropyl alcohol with a concentration of 0.4 mg mL�1 was
prepared by sonication (40 kHz during 1 h) to obtain a good
degree of exfoliation. Si3N4 powders (E-10, Ube Corp.) with
2 wt.% Al2O3 (Baikalox-SM8) and 5 wt.% Y2O3 (HC-Stark) as
sintering additives were homogenized by attrition milling in
isopropyl media during 2 h and mixed with the GNP disper-
sion. This mixture was blade mixed and sonicated during
1 h for homogenizing of all the components. Once the solvent
was removed by rotary evaporation, the composite powders
were dried at 393 K, sieved (63 lm) and placed in a graphite
die for sintering under vacuum (5 Pa) by SPS (Dr. Sinter, SPS-
510CE, Japan) at a maximum temperature of 1898 K during
5 min and applying 50 MPa of uniaxial pressure during the
whole cycle. Temperature was controlled by a pyrometer fo-
cused on the side of the graphite die. Composites with
increasing GNPs contents (4, 7, 11, 14, 17, 21 and 24 vol.%)
were thus fabricated. Sintered specimens were disk-shaped
with dimensions of 20 mm diameter by 2.7 mm thickness.
Density of the samples was measured by the Archimedes
method and their theoretical density calculated by the rule
of mixtures assuming densities of 3.23 gcm�3 for Si3N4 and
2.2 gcm�3 for GNPs; accordingly, all samples were within
99% of the theoretical density.
Raman spectra of the original GNPs and the polished com-
posites were collected at room temperature on a confocal Ra-
man-AFM imaging system (Alpha300 WITec GmbH, Germany)
with a laser excitation wavelength of 532 nm. Raman maps of
150 · 150 pixels and 60 ms of acquisition time per spectrum
were imaged for the composites. Microstructure of the speci-
mens was observed in fracture under a field emission scan-
ning electron microscope (FE-SEM, S-4700 Hitachi, Japan).
Samples for transmission electron microscopy (TEM) were
prepared for observation of the microstructure in the direc-
tion parallel to the SPS pressing axis. Discs with a diameter
around 2.7 mm were cut from the dense specimens and
mechanically thinned up to �100 lm followed by dimple
grinding up to �30–40 lm in the middle of the disc. These thin
slices were glued in a 3 mm diameter Cu grid and finally
thinned in an ion milling Fischione Model 1010 using argon
ions with an initial voltage of 7 kV and current of 2 mA. The
milling conditions were reduced down to a voltage of 2 kV
and a 1 mA current for the last thinning steps, to minimize
damage in the foils. These specimens were examined using
a Philips TECNAI 20 TEM and employing a combination of
bright field (BF) and high resolution (HRTEM) imaging with se-
lected area (SAED) and nano-beam electron diffraction (NBED)
pattern analysis. EDX microanalysis (EDAX, Phoenix, USA)
was also performed in the TEM.
2.2. Electrical characterization
The electrical measurements were carried out on samples
placed on an alumina tubular support with all electrical con-
nections ensured by platinum wires. This sample holder was
then placed inside a tubular furnace to collect data under var-
iable temperature from room temperature up to 573 K, in air.
Different electrode configurations were used to measure the
conductivity in directions parallel and perpendicular to the
SPS pressing axis, as shown in Fig. 1. Ac and dc methods were
used for samples with high and low resistance, respectively.
The dc conductivity was measured with four-probe (dc power
supply Agilent E364·A and a Fluke precision multimeter) on
bars of 13 · 2.3 · 2.5 mm3. Ac data were obtained by imped-
ance spectroscopy (impedance spectrometer Agilent E4980A)
in the frequency range of 20 Hz–2 MHz on large area samples
of 13.5 · 10 · 2.6 mm3. Silver electrodes (Agar 6302) were ap-
Fig. 2 – Electrical conductivity as a function of the GNPs
volume fraction for both orientations of the nanoplatelets in
the GNP-Si3N4 composites: rdc? (solid circles) and rac
00
(crosses). Data points were collected at room temperature
except for the rac? of the 0.07 (Vh) composite, which was
obtained at 573 K (empty circle). The lines are the fittings to
the GEM equation (Eq. (1)) for the perpendicular (solid) and
parallel (dashed) configurations obtained with the
parameters in Table 1. The inset shows the best fit to the
simplest percolation model (Eq. (2), Table 1), in this case only
possible for Vh P 0.11.
Fig. 1 – Diagram of experimental set ups for of dc and ac electrical conductivity (rdc, rac) measurements along both directions:
(a) perpendicular (defined by superscript ?) and (b) parallel (superscript 00) to the SPS pressing axis. Image of the graphite die
setting in the SPS furnace with indication of the pressing direction (c).
C A R B O N 5 0 ( 2 0 1 2 ) 3 6 0 7 – 3 6 1 5 3609
plied to the surfaces of interest. The same silver paste was
used to improve the electrical contacts between the platinum
wires and the sample in the four-probe dc measurements. In
the case of the two probe configuration, the resistance of the
platinum wires was measured separately and subtracted to
the measured resistance. A preliminary assessment showed
that the resistance of the blank specimen and of composites
with 4 and 7 vol.% of GNPs was higher than 10 MX and
therefore it could not be measured, except for the 7 vol.%
GNP sample at temperatures above 574 K. The composites
with GNP contents above 7 vol.% were markedly more con-
ductive and the resistance in the direction parallel to the
pressing axis could be estimated by verifying the ohmic
behavior (at least six data points) for dc voltage less than
0.1 V (11, 14 and 17 vol.% GNP), 0.2 V (21%) and 0.5 V (24%).
No changes in the room temperature conductivity were
registered after cooling, which confirmed that no degradation
of the specimens or the contacts occurred during the high
temperature measurements.
3. Results and discussion
3.1. Electrical percolation in GNP/Si3N4 composites
Fig. 2 shows the room temperature electrical conductivity of
GNP/Si3N4 composites as a function of the GNP volume frac-
tion. A sigmoidal trend is apparent for both perpendicular
(r?) and parallel (r00) electrode configurations, typical of the
percolation behavior often found in mixtures of one highly
conducting phase dispersed within an insulating matrix.
The r? values range from 0.12 to 41 Scm�1 for composites
with 11–24 vol.% GNPs. The upper value is about two orders
of magnitude higher than data for conductive Si3N4 compos-
ites with similar fraction of the conductive phase (25 vol.%
TiN) [1], while for the lower GNP contents the conductivity
is comparable to data reported for CNT/Si3N4 composites with
8 vol.% multiwalled CNTs [6]. Higher CNT contents decreased
the densification of these composites and did not increase
their electrical conductivity [4].
The conductivity data collected along the direction parallel
to the SPS axis is one order of magnitude lower than r?, with
a slight tendency to enlarge the differences when increasing
volume fraction of GNPs. This result fully confirms our previ-
ous localized conductance measurements by c-SFM [10] and it
appears associated to a strong orientation of the ab plane of
the graphene platelets perpendicular to the SPS pressing axis,
as shown in Fig. 3. This pronounced anisotropy may be ex-
plained by the high electrical conductivity along the graphene
sheets and the expectedly much lower conductivity across
them. In fact, while, by definition, graphene does not have a
c-axis (perpendicular to the sheet ab-plane), in practice GNPs
are multilayered (from few to tens of nm thick) with a struc-
Fig. 3 – Typical microstructure by SEM of the composite fracture surface, where GNPs protruding from the Si3N4 matrix are
seen. Certain misalignment of the nano-platelets with respect to the plane perpendicular to SPS pressing axis (corresponding
to the 90� axis) is detected as shown in the images. (a) Slightly rotated GNPs, (b) deviation produced by twisting and (c) by GNP
clustering.
3610 C A R B O N 5 0 ( 2 0 1 2 ) 3 6 0 7 – 3 6 1 5
ture approaching that of graphite as the number of layers in-
creases [8–10]. Pure graphite (including single crystals) or
highly oriented pyrolitic graphite (HOPG) have a conductivity
in the basal ab-plane direction much higher than along the c-
axis [14,15]. Actually, conductivity ratios in the range 102–104
have been reported for graphite single crystals and above
103 for highly oriented pyrolytic graphite [14]. Notwithstand-
ing, these GNP/Si3N4 composites do not exhibit the large dif-
ferences (above two orders of magnitude) observed for
graphite. Instead, the r?:r00 ratio is in the range 10–25 (rising
with increasing GNP volume fraction), as it was also reported
by Stankovich et al. [16] for polyestyrene–graphene compos-
ites. This attenuated ratio can be understood by noticing a
certain rotation degree with respect to the alignment plane
as well as nearly vertical positioned platelets, even though
there is a predominant horizontal orientation induced by
the SPS for the full compositional range (Fig. 3(a)), which
should facilitate the conductivity in this direction.
Detailed HREM observations show another important
microstructural feature of these composites, which is the
presence of an amorphous thin film of about 3 nm at the
interfaces between the Si3N4 grains and the GNPs, as shown
in Fig. 4a. This film is enriched in C, Si, Y, Al and, perhaps, also
some N atoms, according to the EDX microanalysis shown in
Fig. 4b. This amorphous intergranular phase could be a Si–O–
C–Y–Al type glass. Typically, the electrical conductivities of
silicon oxycarbide and oxynitride glasses are in the range
10�13–10�11 Scm�1 at temperatures of the order of 500 �C or
lower [17,18]. Therefore, their contribution to the overall
behavior of the composites should not be much different
from that of the Si3N4 matrix, which has a conductivity of
about 10�13 Scm�1. The composition identified by EDX may
also correspond to an yttrium oxycarbide type phase
Y(O,C)x. This kind of compounds may have conductivity levels
high enough to influence the overall properties of the com-
posite [19]. We will later return to the possible role of this
intergranular phase on the conductivity.
The r?:r00 ratio in the composites can be quantitatively
predicted assuming a percolation-type model behavior. The
electrical conductivity of an insulator/conductor binary mix-
ture (rm) can be expressed as a function of the volume frac-
tion of the conducting filler (Vh) by the general effective
media (GEM) equation [20]:
ð1� VhÞðr1=tl � r1=t
m Þr1=t
l þAr1=tm
þ Vhðr1=th � r1=t
m Þr1=t
h þAr1=tm
¼ 0
A ¼ ð1� Vh;cÞV�1h;c
ð1Þ
where rl and rh are the conductivities of the low and high
conductivity phases, respectively, Vh,c is the critical (percola-
tion) volume fraction of the conducting phase. The exponent
t is a parameter that depends on the connectivity mode (and
thus the shape and orientation) of the conducting phase and
on the conduction mechanisms. Therefore, t may be treated
as a phenomenological parameter typical of the conductivity
of a given composite [20]. The GEM equation has the advan-
tage over conventional percolation models that it allows the
analysis of data close to the percolation threshold.
Fig. 2 shows that the compositional dependence of the
conductivity of the composites can indeed be described by
the GEM equation with rl = 10�13 Scm�1 (the conductivity of
Si3N4 [21], and the fitting parameters Vh,c, t and rh shown in
Table 1. The present analysis is restricted to the room temper-
ature data, since very similar values were obtained at higher
temperatures. The estimated r? upper limit (6.25 · 104 Scm�1)
is two orders of magnitude above the conductivity of highly
crystalline graphene sheets (5.65 · 102 Scm�1 [22]), and it is
not far from the value measured along the ab-plane of mono-
crystalline graphite (�1.7 · 104 Scm�1 [14]). Application of
GEM equation for the case of expandable graphite monoliths
with different densities and orientation of the compressed
graphite worms yields rh in the order of 104 Scm�1 [23], and
the same value was calculated for graphene/polyestyrene
composites [16]. The projected r00 value of the pure GNPs
(4.60 · 102 Scm�1) is about two orders of magnitude lower
than r?, but again in good agreement with monocrystalline
graphite (�1.7 · 102 Scm�1 along the and c-axis [14]). Graphite
paper is slightly less conductive than pure graphite (mainly
due to porosity), but it also shows a near 102 factor between
Fig. 4 – (a) HRTEM image showing an amorphous, �3 nm thin film between an a-Si3N4 grain oriented along B� <113>
(corresponding SAED pattern included) and a GNP observed close to the transversal section perpendicular to the ab plane. (b)
EDX microanalysis of the amorphous layer enriched in C, Si, Al and Y. The Cu peaks observed in the figure are due to the Cu
grid used to mount the sample.
C A R B O N 5 0 ( 2 0 1 2 ) 3 6 0 7 – 3 6 1 5 3611
the in-plane conductivity (103 Scm�1) and that along the c-
axis (20 Scm�1) [23].
The critical GNP percolation volume fraction was found at
Vc,h = 0.073 and 0.087 for r? and r00, respectively. It should be
noticed that the fitting of the r00 values is based on less data
points near the percolation threshold. While slightly different
estimates may perhaps be obtained with more data points, it
can be said that the preferred orientation does not seem to
have a major effect on Vc,h. Literature values show a large
scatter, varying from an extremely low Vc,h = 0.001 for a poly-
styrene matrix containing few layer graphene [16] to nearly
0.20 for GNP/silicone composites [24]. Restricting the compar-
ison to ceramic composites, the actual Vc,h values are rela-
tively high when compared to those obtained for the alike
CNT/Si3N4 composites (Vc,h � 0.01), probably owing to the
higher aspect ratio of CNTs [6]. It is perhaps interesting to
note that the geometrical percolation threshold (equivalent
to Vc,h) of randomly distributed overlapping ellipsoids with as-
pect ratio of 1:10 (similar to the GNPs used in this work [10])
was theoretically estimated to be �0.10 [25]. This value is in
very good agreement with our calculated limit, thus suggest-
ing a homogeneous distribution of the GNPs in the Si3N4 ma-
trix. A considerably lower value of Vh,c ffi 0.03 was obtained for
graphene nanosheets/alumina composites [8]. This difference
may be justified by a GNPs aspect ratio lower than 1:10 in the
case of the alumina-based composites, where a lower perco-
lation threshold would thus be expected [25], although the
possible contribution of the conduction through a carbon-
doped alumina matrix cannot be completely ruled out [26].
The images of GNPs mapped by Raman spectroscopy
(Fig. 5) confirm their homogeneous distribution within the
Si3N4 matrix. These maps further reveal the discontinuous
GNPs pattern (red phase in Fig. 5a) for the composite with
4 vol.% GNP and display the connectivity for the higher
volume fractions, in good agreement with the estimated
electrical percolation threshold (Vh,c, Table 1).
The best fit to the GEM equation yielded t exponents of
4.19 for r?, and 2.98 for r00. These values represent one addi-
tional contribution to the significant scatter observed in this
type of parameter for composites with nano-sized carbon
structures, including e.g. carbon/epoxy (Vc,h = 0.074, t = 4.49
[20]), polystyrene–graphene (Vc,h = 0.001, t = 2.74 [16]) or alu-
mina/GNPs (Vc,h ffi 0.03, t = 1.54 [8]). In many of the reported
examples, t is considerably higher than the expected univer-
sal 1.6–2.0 range (see e.g. Ref. [27] for data on 99 examples),
which is determined solely by the connectivity mode and,
therefore, should be independent of the conducting phase
[20].
The scatter in the literature t data may result from the
analysis procedure. For example, t is often obtained by fitting
to the simplest percolation model
rm ¼ rhðVh � Vc;hÞt ð2Þ
as for the Al2O3/GNP composites mentioned above [9]. Eq. (2)
is valid only for Vh > Vc,h near the percolation threshold.
Nonetheless, the data were also fitted to Eq. (2), as shown
by the inset to Fig. 2. As for the GEM equation estimates,
the percolation thresholds obtained with Eq. (2) are very sim-
ilar for both electrode configurations, albeit slightly higher.
On the contrary, the rh is 20–40 times lower than the values
obtained with the GEM model (Table 1) and, thus, much lower
than the conductivity of graphite (see above). The exponents
are also lower than those obtained with the GEM equation.
While r00 is characterized by a surprisingly (and difficult to
interpret) low t = 0.89, the t = 2.05 obtained for r? is in excel-
lent agreement with that expected for a 3D connectivity
(t = 2). This, however, can hardly be explained in light of the
observed platelets orientation and high conductivity anisot-
ropy. While the GEM equation provides more significant
numerical solutions (and it is also applicable to a broader
compositional range), both models agree on that r? and r00
give similar Vc,h and significantly different exponents, sug-
gesting that the two directions are not equivalent in a perco-
lative sense.
The observed non-universality of t (Eq. (2)) may be
understood by, e.g., assuming a mean-field type behavior
(t = 3) [28], or by the tunneling of charge carriers from one
conducting particle to another, which accounts for a broader
t range (up to 9) [22]. Large t values may also result from a
large range of inter-particle conductances [29,30]. Actually,
the topography and current maps obtained by c-SFM suggest
a broader range of inter-particle connectivity (and thus of
Table 1 – Fitting parameters of the conductivity data as a function of the volume fraction of GNP (Fig. 2), according to the GEMequation (Eq. (1) with rl = 10�13 Scm�1) and the simplest percolation model (Eq. (2)).
GEM model Eq. (1)a Simplest percolation model Eq. (2)b
Vh,c t rh/Scm�1 Vh,c t rh/Scm�1
r? 0.07 4.19 6.25 · 104 0.10 2.05 2.45 · 103
r00 0.09 2.98 4.60 · 102 0.11 0.89 9.95a Data fitted for Vh P 0.07.b Data fitted for Vh P 0.11.
3612 C A R B O N 5 0 ( 2 0 1 2 ) 3 6 0 7 – 3 6 1 5
conductance) along the perpendicular direction [10]. This
could be one of the reasons why t is larger for r? than for r00.
It should be noticed that the possible role(s) of the amor-
phous phase at the interface between Si3N4 and GNP is
difficult to ascertain, based on the above geometric consider-
ations, due to their extremely small volume fraction in com-
parison with the two main components of the composite.
3.2. Variation of the electrical conductivity withtemperature
In order to gain further insight on the possible conduction
mechanism of these composites it is useful to analyse the
temperature dependence of the conductivity. Before, a brief
comment on the electrical conduction of graphene. The
charge transport along the ab-plane of high purity, highly
crystallized graphene is quasi-ballistic and can be due to
electrons or electron holes, in both cases with extraordinarily
high carrier mobilities, displaying a negative, metallic-like
dr/dT [31]. However, graphene platelets obtained by the
chemical reduction of graphene oxide behave quite differ-
ently [22,32]. The full reduction of the sheets is difficult to
achieve and the resulting final microstructure consists of
the highly conducting graphene with dispersed, electrically
resistive graphene oxide clusters [32]. The two-dimensional
electrical conduction along the ab-plane of this material is
suggested to occur via the variable range hoping (2D-VRH)
of the carriers between the pristine graphene domains,
which can be approximated, at sufficiently high temperature,
by
r ¼ r0 expð�B � T�1=3Þ ð3Þ
where r0 is a pre-factor and B is the hopping parameter [32].
Fig. 6(a) shows the r? data plotted as a function of tempera-
ture, confirming the 2D-VRH model dependence in the com-
posites. This is a strong indication that the conduction
mechanism along the perpendicular direction is the same of
chemically reduced graphene, although GNPs are commer-
cially processed by dispersing graphite in liquid media and
ultrasonic cleavage [33], which is supposed to produce
pristine graphene [34]. It is simultaneously an indication
that the Si3N4/GNP interfacial phase does not contribute to
the conductivity of the composite for the perpendicular
orientation.
The hopping parameter is independent of composition
and equals 9.5 ± 0.5 K�1/3. This value is slightly higher
than that we can estimate for alumina/GNP composites
(�5.5 K�1/3) [9], but it is clearly lower than that reported by
Kaiser and co-workers for reduced graphene oxide monolay-
ers (�55 K�1/3 for an applied bias of 100 mV) [32].
Since B varies inversely with the density of states near the
Fermi level, in principle not changed, and the electron local-
ization length, it may be suggested that the lower hopping
parameter of these composites results from stronger overlap-
ping of the electron wave functions. Therefore, one possible
reason for the lower B reported here could thus be a compar-
atively lower fraction (or size) of disordered oxidized clusters
in the composite. Raman spectra were collected on both fresh
and the composite GNPs in order to clarify this hypothesis
(Fig. 7). The low ratio between the intensities of the typical
D (1350 cm�1) and G (1580 cm�1) bands indicates a fairly or-
dered material. Moreover, the ratio is increased after the
SPS, suggesting that this step tends to induce some sort of
disorder. This may be either in the graphene lattice or may
account for higher effect of GNPs edges in the composite,
since the average dimension of the platelets is not far from
the optical resolution (�300 nm). The dimension of the or-
dered domains in the sintered sample is of the order of
25 nm (�60 nm for the fresh GNPs), which is about four times
higher than for the reduced graphene oxide monolayers of
Kaiser et al. [32] (6 nm), both values obtained with the Tuin-
stra-Koenig relation [35]. A more precise estimation of the
size of the ordered regions, by using the integrated intensity
of Raman peaks [36], provides even larger values of 88 nm
(GNPs) and 54 nm (composites). This indeed supports the
hypothesis of shorter hopping distances along the ab plane
of the composite GNPs than for the reduced graphene oxide
monolayers.
The conductivity measured along the parallel direction be-
haves differently (Fig. 6(b)). While the 2D-VRH model still
gives an excellent description of the composites with low
GNP content (with B = 9.5), it fails for the more conductive
samples. In this case, dr00/dT is positive up to a certain tem-
perature and then becomes negative. This transition from a
semiconductor- to metallic-type behavior is apparent at an
increasing temperature, with increasing fraction of connect-
ing GNP particles. This again reinforces the percolative differ-
ences between the two axes of the samples and it clearly
demonstrates that the dominating conduction mechanisms
are indeed different for the high GNP fractions (P17%).
It is interesting to recall that the r?:r00 ratio increases with
increasing GNP content, which can now be ascribed to an
increasing contribution of the graphene in-plane conduction
along the perpendicular direction of the sample, and of the
out-of-plane mechanism along the parallel direction. The
latter is a controversial topic, as it may be coherent or
Fig. 5 – Raman maps of the surface perpendicular to SPS pressing axis of three samples with different GNPs content. (a)
4 vol.%, (b) 14 vol.%, (c) 21 vol.%. The peak intensity of the GNPs G band (1580 cm�1) is imaged in red (or light grey), whereas
the 206 cm�1 band of Si3N4 appears in blue (dark grey).
Fig. 7 – Raman spectra of the original GNPs and of the
composite with 4 vol.% GNPs. Quite similar spectra are
obtained with the characteristic peaks of graphitic samples
(D, G, and 2D). The relative intensity and shape of the 2D
peak indicates the presence of multilayered graphene,
whereas the D peak is ascribed to disordered regions.
Fig. 6 – Conductivity of GNPs/Si3N4 composites plotted according to a variable-range hopping temperature dependence for (a)
perpendicular and (b) parallel electrode configurations. The numbers close to the data series are the corresponding GNP
volume fraction. Solid lines are linear fits to the data, whereas dashed lines are simple guides for the eye.
C A R B O N 5 0 ( 2 0 1 2 ) 3 6 0 7 – 3 6 1 5 3613
incoherent, and undergo a crossover with temperature from
metallic to semiconducting-type behavior [37]. In fact, and
contrary to the behavior of the composites, most of the liter-
ature suggests a positive dr/dT slope for the c-axis conductiv-
ity of graphite (there is no conclusive information for GNPs).
The possible contribution of the interfacial amorphous
phase cannot be ruled out assuming that it has sufficiently
high conductivity (such as the yttrium oxycarbide phases
[19]). For a sufficiently high GNPs content in the parallel con-
figuration, a large fraction of the GNPs are aligned and their
surface connectivity necessarily implies transport from one
GNP to another across the interphase. Since this interphase
is much thinner (10�1 or less) than the GNPs, their resistance
may be smaller or comparable to that of the GNPs. This series
model implies a metal-like behavior of this phase so that its
resistive contribution to the overall composite resistance in-
creases with increasing temperature, whereas the GNPs de-
creases due to its semi-conductor nature. The clarification
of the temperature dependence of r00 will in any case imply
the need for the precise knowledge of the composition of this
3614 C A R B O N 5 0 ( 2 0 1 2 ) 3 6 0 7 – 3 6 1 5
grain boundary phase. At low temperature, though, the GNPs
seem to dominate the electrical behavior of the composite
which can indeed be interpreted assuming the 2D-VRH
model.
4. Summary
Silicon nitride ceramics densified by SPS can be made electri-
cally conducting by dispersing up to 25 vol.% of GNPs. While
some kind the lattice disorder seems to be introduced in the
graphene layers during sintering, a maximum conductivity
of 40 Scm�1 is reported as one of highest values for Si3N4–
based composites. The bulk conductivity shows a remarkable
anisotropic effect with conductivity ratios in the order of 10–
25 between the directions perpendicular and parallel to the
SPS pressing axis. The most conductive direction corresponds
to the preferential orientation of the ab-plane of the GNP per-
pendicularly to the SPS pressing axis. The compositional
dependence of the electrical conductivity displays a percola-
tion-type behavior and it can be satisfactorily modeled by
the GEM equation. The percolation GNP volume threshold
(7–9 vol.%) shows little dependence on the sample orienta-
tion, but the different characteristic GEM exponents and the
temperature dependencies of the conductivity suggest that
both directions are of different percolative nature. The con-
duction of the composite along the perpendicular direction
can be explained by the two dimensional variable range hop-
ping model, as found for the in-plane conduction of chemi-
cally reduced graphene monolayers. A thin amorphous layer
was identified around GNPs that may affect the conduction
of the composites with highest GNP content for the parallel
configuration. The microstructural disorder apparently intro-
duced in the GNPs by the SPS conditions will need further
investigations.
Acknowledgements
This work was funded by the Spanish Ministry of Science and
Innovation (MICINN) under Project number MAT2009-09600,
and the Portuguese Foundation for the Science and Technol-
ogy (FCT, projects Pest-C/CTM/LA0011/2011 and PTDC/CTM-
CER/109843/2009). C. Ramirez acknowledges the financial
support of the JAE-CSIC fellowship Program.
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