Samples of graphene composites with a matrix of indium or indium-gallium alloy were prepared in the form of foils using exfoliated graphene dispersions. The thermal conductivity of the composite samples with different thicknesses was determined using the three-omega method. Indium–graphene composite samples with a thickness of 430 μm exhibited a twofold increase in thermal conductivity, whereas indium-gallium–graphene composite samples with a thickness of 330 μm exhibited a threefold improvement in thermal conductivity over that of the matrix at 300 K. The effective medium approximation (EMA) was used to model the thermal conductivity of the composite samples. The graphene platelet size distribution was used to determine the average thermal conductivity of graphene in the composite samples. The interfacial thermal conductance between graphene and indium or indium-gallium alloy determined from EMA was not the limiting factor in the improvement of the thermal conductivity of the composite samples, although the increase in thermal conductivity was found to be slightly lower than predicted theoretically using acoustic and diffuse mismatch models. The smaller size of the graphene platelets obtained by exfoliation prior to dispersion in the matrix appears to be the limiting factor.
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References
A.A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweidebrhan, F. Miao, and C.N. Lau, Nano Lett. 8, 92 (2008).
R. Prasher, Proc. IEEE 94, 1571 (2006).
T. Tao, A. Majumdar, Z. Yang, A. Kashani, L. Delzeit, and M. Meyyappan, Proceedings of the 10th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronics Systems (IEEE Cat. No. 06CH37733C) (2006), p. 6.
J. Xu and T.S. Fisher, The Ninth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, IEEE Cat. No. 04 CH37543, Vol. 2, Piscataway, NJ (2004), p. 549.
E.M. Garmire and M.T. Tavis, IEEE J. Quantum Electron. QE-20, 1277 (1984).
P.G. Klemens, Int. J. Thermophys. 22, 265 (2001).
M. Morooka, T. Yamamoto, and K. Warnabe, Phys. Rev. B 77, 033412 (2008).
K. Saito, J. Nakamura, and A. Natori, Phys. Rev. B 76, 115409 (2007).
M. Trushin and J. Schliemann, Phys. Rev. Lett. 99, 216602 (2007).
M.T. Lusk and L.D. Carr, Phys. Rev. Lett. 100, 175503 (2008).
A. Naga Sruti and K. Jagannadham, J. Electron. Mater. 39, 1268 (2010).
D.G. Cahill, Rev. Sci. Instrum. 61, 802 (1990).
J.H. Kim, A. Feldman, and D. Novotny, J. Appl. Phys. 86, 3959 (1999).
J. Yang, Thermal Conductivity: Theory, Properties, Applications, ed. T.M. Tritt (New York: Kluwer/Plenum, 2004), p. 1.
S. Ghosh, D.L. Nika, E.P. Pokatilov, and A.A. Balandin, New J. Phys. 11, 095012 (2009).
D.G. deGroot, A.B.M. Hoff, and J.H.P. van Weeren, J. Phys. F Met. Phys. 5, 1559 (1975).
N.W. Ashcroft and N.D. Mermin, Solid State Physics (Saunders, 1976).
Data obtained from Indium Corporation of America. http://www.indium.com/products/indiummetal/physicalconstants.php
A. Matthiessen, Philos. Trans. R. Soc. (Lond.) 148, 383 (1858).
A. Yu, P. Ramesh, M.E. Itkis, E. Bekyarova, and R.C. Haddon, J. Phys. Chem. C 111, 7565 (2007).
A.K. Pal and S. Chaudhuri, J. Mater. Sci. 11, 872 (1976).
C.W. Nan, R. Birringer, D.R. Clarke, and H. Gleiter, J. Appl. Phys. 81, 6692 (1997).
A.A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C.N. Lau, Nano Lett. 8, 902 (2008).
S. Ghosh, I. Calizo, D. Teweldebrhan, E.P. Pokatilov, D.L. Nika, A.A. Balandin, W. Bao, F. Miao, and C.N. Lau, Appl. Phys. Lett. 92, 151911 (2008).
D.L. Nika, E.P. Pokatilov, A.S. Askerov, and A.A. Balandin, Phys. Rev. B 79, 155413 (2009).
D.L. Nika, S. Ghosh, E.P. Pokatilov, and A.A. Balandin, Appl. Phys. Lett. 94, 203103 (2009).
Z. Ghuo, D. Zhang, and X.G. Gong, Appl. Phys. Lett. 95, 163103 (2009).
P.G. Klemens and D.F. Pedraza, Carbon 32, 735 (1994).
D.P.H. Hasselman and L.F. Johnson, J. Compos. Mater. 21, 508 (1987).
A.J. Schmidt, X. Chen, and G. Chen, Rev. Sci. Instrum. 79, 114902 (2008).
J.C. Duda, J.L. Smoyer, P.M. Norris, and P.E. Hopkins, Appl. Phys. Lett. 95, 031912 (2009).
A. Majumdar and P. Reddy, Appl. Phys. Lett. 84, 4768 (2004).
M.W. White and D.C. McCollum, Phys. Rev. B 1, 552 (1970).
E.T. Swartz and R.O. Pohl, Rev. Mod. Phys. 61, 605 (1989).
A. Minnich and G. Chen, Appl. Phys. Lett. 91, 073105 (2007).
B.C. Gundrum, D.G. Cahill, and R.S. Averback, Phys. Rev. B 72, 245426 (2005).
R. Viana, H. Godfrin, E. Lerner, and R. Rapp, Phys. Rev. B 50, 4875 (1994).
R.S. Deacon, K.C. Chuang, R.J. Nicholas, K.S. Novoselov, and A.K. Gein, Phys. Rev. B 76, 08140 (2007).
C. Schmidt and E. Umlauf, J. Low Temp. Phys. 22, 597 (1976).
Y.S. Touloukian and E.H. Buyco, Thermophysical Properties of Matter, The TPRC Data Series, Specific Heat of metallic Elements and Alloys, Vol. 4, and Specific Heat of Nonmetallic Solids, Vol. 5 (New York: IFI/Plenum, 1970).
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Jagannadham, K. Thermal Conductivity of Indium–Graphene and Indium-Gallium–Graphene Composites. J. Electron. Mater. 40, 25–34 (2011). https://doi.org/10.1007/s11664-010-1391-1
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DOI: https://doi.org/10.1007/s11664-010-1391-1