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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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