Mechanical, electrical, and thermal properties of graphene nanosheet

Available online at www.sciencedirect.com

CERAMICS INTERNATIONAL

Ceramics International 41 (2015) 8643–8649 www.elsevier.com/locate/ceramint

Mechanical, electrical, and thermal properties of graphene nanosheet/aluminum nitride composites Chuang Yuna, Yongbao Fenga,b,n, Tai Qiua, Jian Yanga, Xiaoyun Lia, Lei Yua b

a College of Materials Science and Engineering, Nanjing Tech University, No. 5 Xinmofan Road, Nanjing 210009, China Nanjing Sanle Electronic Information Industry Group Co. Ltd., No. 5 Guangming Road, Pukou Economic Development Zone, Nanjing 211800, China

Received 18 January 2015; received in revised form 13 March 2015; accepted 13 March 2015 Available online 20 March 2015

Abstract Graphene nanosheet (GNS)/aluminum nitride (AlN) composites were prepared by hot-pressing and effects of GNSs on their microstructural, mechanical, thermal, and electrical properties were investigated. At 1.49 vol% GNSs content, the fracture toughness (5.09 MPa m1/2) and flexural strength (441 MPa) of the composite were significantly increased by 30.17% and 17.28%, respectively, compared to monolithic AlN. The electrical conductivity of the composites was effectively enhanced with the addition of GNSs, and showed a typical percolation behavior with a low percolation threshold of 2.50 7 0.4 vol%. The thermal conductivity of the composites decreased with the addition of GNSs. & 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Keywords: C. Electrical properties; C. Mechanical properties; C. Thermal properties; Graphene nanosheets; AlN

1. Introduction Aluminum nitride (AlN) has high thermal conductivity, a low thermal coefficient, good thermal shock resistance, ideal mechanical properties, and excellent electrical properties (dielectric constant, dielectric loss, and volume resistivity) [1]. AlN ceramics have already attracted considerable attention as components of semiconductor manufacturing equipment [2]. In addition, AlN ceramics are generally used as electrostatic chucks, wave-absorbing materials, plasma etching electrodes, EDM-machinable ceramic substrates, and electrical feedthroughs [3–6]. These applications all require different levels of electrical conductivity, thereby making it necessary to fine-tune the electrical conductivity of the respective AlN material. Meanwhile, the expansion of applications of AlN ceramics is restricted because of their low strength [7–9]. Therefore, fillers have been introduced into AlN matrices for a wider range of applications. n Corresponding author at: College of Materials Science and Engineering, Nanjing Tech University, No. 5 Xinmofan Road, Nanjing 210009, China. Tel.: þ 86 25 83587262; fax: þ86 25 83587268. E-mail address: [email protected] (Y. Feng).

http://dx.doi.org/10.1016/j.ceramint.2015.03.075 0272-8842/& 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Graphene, i.e., the 2D carbon lattice, is considered a promising candidate nanofiller material for composites because it has large specific surface area, high charge carrier mobility, and outstanding mechanical properties [10]. By contrast, graphene nanosheets (GNSs) are formed by several layers of graphene with a thickness of up to 100 nm [11,12]. Compared with carbon nanotubes, GNSs have generated considerable interest in the application of composites because of their various potential advantages, including their good dispersibility and they being less prone to damage after exposure to high temperatures [13,14]. To improve the mechanical and electrical properties of ceramic composites, several research groups have investigated GNSs as filler materials [12–18]. GNSs are ideal reinforcing and functionalizing additives to improve the mechanical, electrical, and thermal properties of ceramic composites. Thus far, to the best of our knowledge, no relevant reports exist on GNS/AlN ceramics. The few related studies were devoted to the preparation of AlN/ graphene nanohybrids [19]. Therefore, the tailoring of GNSs into AlN matrix is expected to produce desirable mechanical and electrical properties in AlN composites. In this work, the AlN composites were successfully prepared with different amounts of GNSs by hot-pressing. The effects of

8644

C. Yun et al. / Ceramics International 41 (2015) 8643–8649

GNSs on their microstructural, mechanical, electrical, and thermal properties were investigated. 2. Materials and methods 2.1. Preparation of GNS/AlN composites Appropriate quantities of GNSs (C492%, Oo5%, The Sixth Element, Ltd., China) were initially dispersed in N-methyl-2pyrrolidone (Sinopharm Chemical Reagent Co., Ltd., China) and sonicated for 1.5 h. AlN powders (497.7% purity, 3 mm, AT&M, Ltd., China) with 2 wt% Y2O3 (499.7% purity, 6 mm, Yuelong Co., Ltd., China) were ground for 4 h and subsequently diluted in ethanol with a planetary mill. The mixture of GNSs and N-methyl-2-pyrrolidone was added to the milled slurry mixture and ground for another hour. The milled slurry mixture was then dried at 80 1C in an oven. The dried powder was mixed in a polythene pot for 24 h and sieved through a 60 mesh. Bulk composites were subsequently fabricated via a hotpressing process, i.e., the powders were heated to 1850 1C and then exposed to a pressure of 30 MPa in a N2 atmosphere for 1 h. 2.2. Tests and characterization methods The density of the samples was measured via Archimedes' method. The three-point bending method was applied to measure the flexural strength (3 mm 4 mm 36 mm) using a span of 30 mm with a crossing speed of 0.5 mm/min (Reger-RWT10, Reger Instrument Co., Ltd., Shenzhen). The fracture toughness (2 mm 4 mm 22 mm) was determined using the single-edge notched beam (SENB) method with a span of 16 mm and a crosshead speed of 0.05 mm/min. The notch with a depth of 2 mm and width of approximately 0.26 mm was made by a dicing saw. Vickers' hardness was tested on the polished surfaces by a microhardness tester at a load of 9.8 N with a dwell time of 10 s (HX-1000TM/LCD, Shanghai Taiming Optical Instrument Co., Ltd., Shanghai). Phase composites of the as-prepared samples were characterized by X-ray diffraction (XRD; Smartlab, Tokyo). The microstructure of the fractured surfaces and the crack propagation paths (produced by the Vickers indenter) was observed by field-emission scanning electron microscopy (FESEM; SU8010 microscope, Tokyo). Furthermore, samples for high-resolution transmission electron microscopy (HRTEM; with a Tecnai G2 F30 S-TWIN microscope, FEI) were

prepared for the detailed investigation of their microstructure. Two methods were chosen for the conductivity measurements because of the large differences in conductivity between different samples at room temperature. The electrical conductivity of samples with a GNS content of 0, 0.22, and 1.49 vol% was measured by a high resistance meter (ZC-90E, Probes Tech, Guangzhou), whereas that of the samples with a GNS content of 2.96, 4.41, 7.28, and 10.10 vol% was measured via a four-probe method (RTS-8, Probes Tech, Guangzhou). The thermal diffusivity of the samples (diameter of 10 mm and thickness of 2 mm) was measured via the laser flash analysis method (NanoflashLFA447, Netzsch, Selb). 3. Results and discussion 3.1. Sintering behavior and microstructure The FESEM images of individual GNS are illustrated in Fig. 1. The diameter of a representative nanosheet is approximately 2 mm (Fig. 1a), and its edge thickness is approximately 20 nm (Fig. 1b), whose morphology resembles wrinkled paper. The XRD patterns of the as-prepared samples are shown in Fig. 2. These samples were made of an almost pure AlN phase with traces of the Y3Al5O12 liquid phase. The liquid phases promoted the densification of the GNS/AlN composites [20]. GNSs content up to 4.41 vol% could be detected by XRD measurement, which indicated the preservation of GNSs in the composites. GNSs were not observed when their content was below 4.41 vol% in the composites, which may be attributed to the limitations of the measurement instrument. In addition, the sintering performance results (Table 1) indicated that the monolithic AlN sintered at 1850 1C is fully dense. It was noticed that even if the addition of GNSs was up to 1.49 vol%, the apparent density could still attain 99%, indicating that GNSs content below this amount had no remarkable deleterious effect on the densification process. However, with GNSs greater than 7.28 vol%, the apparent density dropped to below 93%. The FESEM images of the fracture surfaces of the GNS/AlN composites are presented in Fig. 3. The fracture mode of these composites was predominantly intergranular. GNSs are distributed along the grain boundaries, which could prevent grain growth. The AlN grain size obviously decreased as the GNSs content increased, from approximately 6.5 mm for the monolithic AlN to approximately 3.5 mm for the 7.28 vol% GNS/AlN

Fig. 1. FESEM images of the GNSs. (a) The diameter of a nanosheet is about 2 mm. (b) The edge thickness of a nanosheet is about 20 nm.


8645

Fig. 2. X-ray diffraction patterns of as-prepared samples.

Table 1 The sintering performance results and mean grain size of GNS/AlN composites and monolithic AlN. Material

Apparent Bulk density porosity (%) (g/cm3)

Apparent density (%)

Porosity Mean grain (%) size (mm)

Monolithic AlN 0.22 vol% GNS/AlN 1.49 vol% GNS/AlN 2.96 vol% GNS/AlN 4.41 vol% GNS/AlN 7.28 vol% GNS/AlN 10.10 vol% GNS/AlN

3.28

0.05

99.91

0.09

6.5

3.27

0.08

99.61

0.39

5.1

3.25

0.09

99.00

1.00

4.6

3.19

0.16

97.17

2.83

4.3

3.14

0.19

95.65

4.35

4.0

3.04

0.23

92.60

7.40

3.5

2.95

0.29

89.86

10.14

–

composite (Table 1). In addition, several clusters (marked by arrows) could be observed in the composites containing more than 2.96 vol% GNSs (Fig. 3d–f). The TEM and HRTEM images of a composite containing 4.41 vol% GNSs are compared in Fig. 4. Overlapping nanosheets (with a combined thickness of approximately 50 nm) were observed (Fig. 4b), probably because the nanosheets were not ideally dispersed during the fabrication process. The sintering additives were located at the grain boundaries and hardly connected to each other (Fig. 4c). According to the XRD patterns, the grain boundary phase consisted of Y3Al5O12. 3.2. Mechanical properties The mechanical properties of the GNS/AlN composites and monolithic AlN are shown in Fig. 6. With increasing GNSs content, the flexural strength and fracture toughness of the

GNS/AlN composites initially increased and then decreased. Meanwhile, the flexural strength and fracture toughness were significantly improved in the composite with 1.49 vol% GNSs. In addition, the hardness of the GNS/AlN composite almost linearly decreased with increasing GNSs content. Compared with the monolithic AlN, the fracture toughness of the composites increased by 30.18%, i.e., from 3.91 MPa m1/2 for monolithic AlN to 5.09 MPa m1/2 for 1.49 vol% GNS/AlN composites, thereby indicating the good toughening effect of the GNSs. Fig. 5a and b shows the FESEM images of the crack propagation path in the 1.49 vol% GNS/AlN composites produced by Vickers indentation. GNS bridging in the crack propagation path indicated the crack bridging effect of GNSs during crack propagation, which in turn, increased the fracture toughness. Fig. 5c shows that this phenomenon can be viewed as evidence of “sheet pull-out” on the fracture surface. However, when the GNSs content was further increased to 2.96 vol%, the toughness decreased to 3.88 MPa m1/2. The decreased fracture toughness may be ascribed to the poor interfacial bonding between the GNS clusters and AlN matrix (Fig. 3d–f), which considerably weakened the GNS bridging and pull-out effect of the GNSs. The flexural strength of the GNS/AlN composites followed a trend similar to that of the fracture toughness (Fig. 6a). The addition of 1.49 vol% GNSs improved the flexural strength of the AlN-based composite by 17.29%, from 376 MPa (monolithic AlN) to 441 MPa, which indicated the good strengthening effect of the GNSs. The grain growth was inhibited by adding GNSs, thereby producing a fine-grain-size effect, which could cause the increased flexural strength [21–23]. The decreased flexural strength could be ascribed to the poor cohesion force between GNSs and AlN as well as the presence of GNS clusters in the composites. The hardness of GNS/AlN composites decreased almost linearly with increasing GNSs content (Fig. 6b). The hardness of the GNS/ceramic system seems to decrease with the addition of GNSs [12,15]. Some GNSs were pulled out on the fracture surfaces of the GNS/AlN composites, which reflected a certain

8646


Fig. 3. FESEM images of fracture surfaces of GNS/AlN composites: (a) monolithic AlN, (b) 0.22 vol% GNS/AlN, (c) 1.49 vol% GNS/AlN, (d) 2.96 vol% GNS/ AlN, (e) 4.41 vol% GNS/AlN, and (f) 7.28 vol% GNS/AlN.

Fig. 4. (a) TEM and (b) HRTEM images of a GNS/AlN composite containing 4.41 vol% GNSs. (a and b), GNSs dispersed around the grain boundary. (c) The grain boundary phase is disconnected from each other at the grain boundaries.

degree of interfacial bonding between GNSs and the AlN matrix. In addition, the GNS clusters in the intergranular of the composites with more than 2.96 vol% GNSs would decrease the bonding strength of the AlN matrix (Fig. 3d–f).

3.3. Electrical properties The electrical conductivity of the as-prepared samples versus the GNSs content at room temperature is compared in Fig. 7.


8647

Fig. 5. Toughening mechanisms in 1.49 vol% GNS/AlN composites. (a and b), Details of indentation crack propagation with crack deflection and GNS bridging. (c) FESEM image of fracture surface of GNS/AlN after three-point bending tests.

Fig. 6. Mechanical properties of GNS/AlN composites: (a) fracture toughness and flexural strength; (b) Vickers' hardness.

When up to 2.96 vol% GNSs was added, the conductivity was changed by approximately eight orders of magnitude. According to previous reports [24–29], the percolation threshold of the GNS/ AlN composites is generally in the range of 1.49–2.96 vol%. When the conducting load exceeds the percolation threshold, the conductivity of certain composites adheres to the scaling law described by [30–32]: σ dc ¼ σ c ðV V c Þt ; for V 4 V c

ð1Þ

where σdc and σc are the conductivities of the composites and the conducting component, respectively, V is the GNS volume fraction, and Vc denotes the critical volume fraction or percolation threshold. Using Eq. (1), a percolation threshold of Vc ¼ 2.5070.44 vol% and an exponent of t¼ 2.3670.20 were obtained. These values were also fitted to Eq. (1), as shown on

the inset image in Fig. 7. The percolation threshold value of GNS/AlN is similar to the value (VcE3 vol%) of the GNS/ Al2O3 composites and much lower than that of GNS/Si3N4 composites (VcE10 vol%) [13,14]. The different values were probably caused by the different aspect ratios of the geometrical percolation threshold for randomly distributed overlapping ellipsoids [33]. However, our experimental data had a conductivity critical exponent t¼ 2.36, which contradicts the universal conductivity critical exponent for 2D (t¼ 1.3) or 3D (t¼ 2) materials [34]. The non-universality of t may be understood by assuming a mean-field type behavior (t¼ 3) [35], or by the tunneling of charge carriers from one conducting particle to another, which accounts for a broader t range (up to 9) [36]. The sintering aids were located at the grain boundaries and hardly connected to each other (Fig. 4c). The effect of the Y2O3

8648


Although the thermal conductivity of monolayer graphene with a large area is relatively high [40], the thermal conductivity of graphene with fewer layers was notably decreased as the number of atomic planes (n) increased [41]. As the value of n in the GNS increased, the phonon dispersion changed and more phase-space states became available for phonon scattering, thereby decreasing the thermal conductivity and negating the effects of phononboundary or defect scattering. When n48, the GNS performed like regular bulk graphite in terms of its thermal conductivity [30]. However, the thickness of GNS is approximately 20 nm (Fig. 1a), which is detrimental to the thermal conductivity of the AlN matrix. Decreased thermal conductivity was similarly found in the pressing direction of GNS/Si3N4 composites [42]. 4. Conclusions Fig. 7. Electrical conductivity of GNS/AlN composites as a function of the filler volume fraction.

Fig. 8. Thermal conductivity of GNS/AlN composites.

content on the electrical conductivity of the GNS/AlN composites is negligible when the GNSs content exceeds the percolation threshold [4,5]. The increased GNSs content increased the number of possible connections of the GNSs and more conducting paths became available, thereby increasing the availability of a large number of charge carriers that travel through the conductive network. The electrical conductivity still rapidly increased for GNS volume fractions above the percolation threshold. The value of σdc for GNS/AlN was significantly higher than the value estimated for carbon nanofiber/AlN composites with the same content of conductive phase [37]. 3.4. Thermal properties The thermal conductivity of GNS/AlN composites in the pressing direction is shown in Fig. 8. The specific heat of composites were calculated with simply rule of mixture, and the cp values of AlN and GNS were 0.75 J/(g K) and 0.72 J/(g K) [38,39]. The thermal conductivity rapidly decreased with increasing GNSs content (r2.96 vol%) and then slowly reduced.

GNS/AlN composites were successfully prepared via a hotpressing process. The experimental results showed that GNSs have important effects on the microstructure, mechanical, electrical, and thermal properties of the composites. The AlN grain size obviously decreased as the GNSs content increased, which would produce a fine-grain-size effect with little addition of GNSs. The fracture toughness and flexural strength of the composites containing 1.49 vol% GNSs were obviously increased, respectively, compared to monolithic AlN. The improved fracture toughness could be attributed to crack deflection, GNS pull-out, and bridging. With increasing GNSs content above 1.49 vol%, GNS clusters could be observed and adversely affected the flexural strength and fracture toughness. Furthermore, the compositional dependence of the electrical conductivity displayed a percolation-type behavior, with a percolation GNS volume threshold of 2.507 0.4 vol%. GNSs are distributed along the grain boundaries, which would cause phonon scattering. The thermal conductivity of the composites decreased with the addition of more GNSs. Acknowledgments This work was supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions and Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT), IRT1146. References [1] L. Qiao, H. Zhou, R. Fu, Thermal conductivity of AlN ceramics sintered with CaF2 and YF3, Ceram. Int. 29 (2003) 893–896. [2] M. Watanabe, Y. Mori, T. Ishikawa, T. Iida, K. Akiyama, K. Sawabe, K. Shobatake, X-ray photoelectron spectroscopy of polycrystalline AlN surface exposed to the reactive environment of XeF2, Appl. Surf. Sci. 217 (2003) 82–87. [3] W.A. Curtin, B.W. Sheldon, CNT-reinforced ceramics and metals, Mater. Today 7 (2004) 44–49. [4] T. Kusunose, T. Sekino, K. Niihara, Production of a grain boundary phase as conducting pathway in insulating AlN ceramics, Acta Mater. 55 (2007) 6170–6175. [5] H. Sakai, Y. Katsuda, M. Masuda, C. Ihara, T. Kameyama, Effects of adding Y2O3 on the electrical resistivity of aluminum nitride ceramics, J. Ceram. Soc. Jpn. 116 (2008) 566–571.

C. Yun et al. / Ceramics International 41 (2015) 8643–8649 [6] J Yoshikawa, Y Katsuda, N Yamada, C Ihara, M Masuda, H Sakai, Effects of samarium oxide addition on the phase composition, microstructure, and electrical resistivity of aluminum nitride ceramics, J. Am. Ceram. Soc. 88 (2005) 3501–3506. [7] L.M. Sheppard, Aluminum nitride: a versatile but challenging material, J. Am. Ceram. Soc. Bull. 69 (1990) 1801–1812. [8] F.M. Xu, Z.J. Zhang, X.L. Shi, Y Tan, J.M. Yang, Effects of adding yttrium nitrate on the mechanical properties of hot-pressed AlN ceramics, J. Alloy. Compd. 509 (2011) 8688–8691. [9] R. Terao, J. Tatami, T. Meguro, K. Komeya, Fracture behavior of AlN ceramics with rare earth oxides, J. Eur. Ceram. Soc. 22 (2002) 1051–1059. [10] C. Lee, X. Wei, J.W. Kysar, J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science 321 (2008) 385–388. [11] B.Z. Jang, A Zhamu, Processing of nanographene platelets (NGPs) and NGP nanocomposites: a review, J. Mater. Sci. 43 (2008) 5092–5101. [12] J. Dusza, J. Morgiel, A. Duszová, L. Kvetková, M. Nosko, P. Kund, C. Balázsi, Microstructure and fracture toughness of Si3N4 graphene platelet composites, J. Eur. Ceram. Soc. 32 (2012) 3389–3397. [13] Y. Fan, J. Wang, J. Li, J. Li, S. Sun, F. Chen, L. Chen, W. Jiang, Preparation and electrical properties of graphene nanosheet/Al2O3 composites, Carbon 48 (2010) 1743–1749. [14] C. Ramirez, F.M. Figueiredo, P. Miranzo, P. Poza, M.I. Osendi, Graphene nanoplatelet/silicon nitride composites with high electrical conductivity, Carbon 50 (2010) 3607–3615. [15] L.S. Walker, V.R. Marotto, M.A. Rafiee, N. Koratkar, E.L. Corral, Toughening in graphene ceramic composites, ACS Nano 45 (2011) 3182–3190. [16] J. Liu, H. Yan, K Jiang, Mechanical properties of graphene plateletreinforced alumina ceramic composites, Ceram. Int. 39 (2013) 6215–6221. [17] J. Liu, H. Yan, M.J. Reeceb, K. Jiang, Toughening of zirconia/alumina composites by the addition of graphene platelets, J. Eur. Ceram. Soc. 32 (2012) 4185–4193. [18] M. Zhou, H. Bi, T. Lin, X. Lü, F. Huang, J. Lin, Directional architecture of graphene/ceramic composites with improved thermal conduction for thermal applications, J. Mater. Chem. A 2 (2014) 2187–2193. [19] Z. Gao, Y. Wan, H. Luo, An efficient route for the synthesis of aluminum nitride/graphene nanohybrids, J. Am. Ceram. Soc. 97 (2014) 1966–1970. [20] H. Sakai, Y. Katsuda, M. Masuda, C. Ihara, T. Kameyama, Effects of adding Y2O3 on the electrical resistivity of aluminum nitride ceramics, J. Ceram. Soc. Jpn. 116 (2008) 566–571. [21] E.O. Hall, The deformation and ageing of mild steel: III discussion of results, Proc. Phys. Soc. B 64 (1951) 747–753. [22] N.J. Petch, The cleavage strength of polycrystals, J. Iron Steel Inst. 174 (1953) 25–28. [23] L. Yu, J. Yang, T. Qiu, J Zhang, L. Pan, Microstructure, mechanical, and thermal properties of (ZrB2 þZrC)/Zr3[Al(Si)]4C6 composite, J. Am. Ceram. Soc. 97 (2014) 2950–2956. [24] A. Allaoui, S. Bai, H.M. Cheng, J.B. Bai, Mechanical and electrical properties of a MWNT/epoxy composite, Compos. Sci. Technol. 62 (2002) 1993–1998.

8649

[25] M.K. Seo, S. Park, Electrical resistivity and rheological behaviors of carbon nanotubes-filled polypropylene composites, Chem. Phys. Lett. 395 (2004) 44–48. [26] G. Gorrasi, V. Romeo, D. Sannino, M. Sarno, P. Ciambelli, V. Vittoria, B.D. Vivo, V. Tucci, Carbon nanotube induced structural and physical property transitions of syndiotactic polypropylene, Nanotechnology 18 (2007) 275703. [27] Y. Mamunya, A. Boudenne, N. Lebovka, L. Ibos, Y. Candau, M. Lisunova, Electrical and thermophysical behaviour of PVCMWCNT nanocomposites, Compos. Sci. Technol. 68 (2008) 1981–1988. [28] W. Bauhofer, J. Kovacs, A review and analysis of electrical percolation in carbon nanotube polymer composites, Compos. Sci. Technol. 69 (2009) 1486–1498. [29] K. Ahmad, W. Pan, S.L. Shi, Electrical conductivity and dielectric properties of multiwalled carbon nanotube and alumina composites, Appl. Phys. Lett. 89 (2006) 133122. [30] S. Kirkpatrick, Percolation and conduction, Rev. Mod. Phys. 45 (1973) 574–588. [31] D. Stauffer, Scaling theory of percolation clusters, Phys. Rep. 54 (1979) 1–74. [32] H. Scher, R. Zallen, Critical density in percolation processes, J. Chem. Phys. 53 (1973) 3759–3761. [33] E.J. Garboczi, K.A. Snyder, J.F. Douglas, Geometrical percolation threshold of overlapping ellipsoids, Phys. Rev. E 52 (1995) 819–828. [34] D. Stauffer, A. Aharony, in: Introduction to Percolation Theory, 2nd ed., Taylor and Francis, London, 1994, p. 89–113. [35] M.B. Heaney, Measurement and interpretation of nonuniversal critical exponents in disordered conductor–insulator composites, Phys. Rev. B 52 (1995) 12477–12480. [36] M. Jin, T.H. Kim, S.C. Lim, D.L. Duong, H.J. Shin, Y.W. Jo, H.K. Jeong, J. Chang, S. Xie, Y.H. Lee, Facile physical route to highly crystalline graphene, Adv. Funct. Mater. 21 (2011) 3496–3501. [37] Z. Shi, S. Chen, J. Wang, G. Qiao, Z. Jin, Mechanical and electrical properties of carbon nanofibers reinforced aluminum nitride composites prepared by plasma activated sintering, J. Eur. Ceram. Soc. 31 (2011) 2137–2143. [38] N. Takeshi, I. Tadao, Temperature dependence of lattice vibrations and analysis of the specific heat of graphite, Phys. Rev. B 68 (2003) 134305. [39] C. Wang, C. Peng, R. Wang, C. Li, Typical properties and preparation technologies of AlN packing material, Chin. J. Nonferr. Met. 17 (2007) 1729–1736. [40] L.A. Jauregui, Y. Yue, A.N. Sidorov, J. Hu, Q. Yu, G. Lopez, R. Jalilian, D.K. Benjamin, D.A. Delk, W. Wu, Z. Liu, X. Wang, Z. Jiang, X. Ruan, J. Bao, S.S. Pei, Y.P. Chen, Thermal transport in graphene nanostructures: experiments and simulations, ECS Trans. 28 (2010) 73–83. [41] S. Ghosh, W. Bao, D.L. Nika, S. Subrina, E.P. Pokatilov, C.N. Lau, A.A. Balandin, Dimensional crossover of thermal transport in few-layer graphene, Nat. Mater. 9 (2010) 555–558. [42] P. Rutkowski, L. Stobierski, G. Górny, Thermal stability and conductivity of hot-pressed Si3N4-graphene composites, J. Therm. Anal. Calorim. 116 (2011) 321–328.