Composite films of graphene platelets (GPs) in titanium matrix were prepared on silicon (001) substrates by physical vapor deposition of titanium using magnetron sputtering and dispersion of graphene platelets. The graphene platelets were dispersed six times after each deposition of titanium film to form the composite film. Samples of titanium film and titanium film with a single layer of dispersed graphene platelets were also prepared by the same procedure. The distribution of the graphene platelets in the film was analyzed by scanning electron microscopy. Energy dispersive spectrometry was used to infer the absence of interstitial elements. The thermal conductivity of the composite and the interface thermal conductance between titanium and silicon or titanium and graphene platelets was determined by three-omega and transient thermo reflectance (TTR) techniques, respectively. The results indicate that the thermal conductivity of the composite is isotropic and improved to 40 Wm−1K−1 from 21 Wm−1 K−1 for Ti. The interface thermal conductance between titanium and silicon is found to be 200 MWm−2K−1 and that between titanium and graphene platelets in the C-direction to be 22 MWm−2K−1. Modeling using acoustic and diffuse mismatch models was carried out to infer the magnitude of interface thermal conductance. The results indicate that the higher value of interface thermal conductance between graphene platelets in the ab plane and titanium matrix is responsible for the isotropic and improved thermal conductivity of the composite. Effective mean field analysis showed that the interface thermal conductance in the ab plane is high at 440 MWm−2K−1 when GPs consist of 8 atomic layers of graphene so that it is not a limitation to improve the thermal conductivity of the composites.

References

References
1.
Novoselov
,
K. S.
,
Geim
,
A. K.
,
Morozov
,
S. V.
,
Jiang
,
D.
,
Zhang
,
Y.
,
Dubonos
,
S. V.
,
Grigorieva
,
I. V.
, and
Firsov
,
A. A.
,
2004
, “
Electric Field Effect in Atomically Thin Carbon Films
,”
Science
,
306
, pp.
666
669
.10.1126/science.1102896
2.
Chen
,
J. H.
,
Jang
,
C.
,
Xia
,
S.
,
Ishigami
,
M.
, and
Fuhrer
,
M. S.
,
2008
, “
Intrinsic and Extrinsic Performance Limits of Graphene Devices on SiO2
,”
Nature Nanotechnol.
,
3
, pp.
206
209
.10.1038/nnano.2008.58
3.
Balandin
,
A. A.
,
Ghosh
,
S.
,
Bao
W.
,
Calizo
,
I.
,
Teweldebrahn
,
D.
,
Miao
,
F.
, and
Lau
,
C. N.
,
2008
, “
Superior Thermal Conductivity of Single-Layer Graphene
,”
Nano Lett.
,
8
, pp.
902
907
.10.1021/nl0731872
4.
Saito
,
K.
,
Nakamura
,
J.
, and
Natori
,
A.
,
2007
, “
Ballistic Thermal Conductance of a Graphene Sheet
,”
Phys. Rev. B
,
76
, p.
1154091
.10.1103/PhysRevB.76.115409
5.
Balandin
,
A. A.
,
Ghosh
,
S.
,
Bao
,
W.
,
Calizo
,
I.
,
Teweldebrahn
,
D.
,
Miao
,
F.
, and
Lau
,
C. N.
,
2008
, “
Extremely High Thermal Conductivity of Graphene: Prospects for Thermal Management Applications in Nanoelectronic Circuits
,”
Appl. Phys. Lett.
,
92
, p.
151911
.10.1063/1.2907977
6.
Sruti
,
A. N.
, and
Jagannadham
,
K.
,
2010
, “
Electrical Conductivity of Graphene Composites With In and In-Ga Alloy
,”
J. Electron. Mater.
,
39
, pp.
1268
1276
.10.1007/s11664-010-1208-2
7.
Jagannadham
,
K.
,
2012
, “
Electrical Conductivity of Copper–Graphene Composite Films Synthesized by Electrochemical Deposition With Exfoliated Graphene Platelets
,”
J. Vac. Sci. Technol., B
,
30
, p.
03D109
.10.1116/1.3701701
8.
Ghosh
,
S.
,
Nika
,
D. L.
,
Pokatilov
,
E. P.
, and
Balandin
,
A. A.
,
2009
, “
Heat Conduction in Graphene: Experimental Study and Theoretical Interpretation
,”
New J. Phys.
,
11
, p.
095012
.10.1088/1367-2630/11/9/095012
9.
Ghosh
,
S.
,
Calizo
,
I.
,
Teweldebrahn
,
D.
,
Pokatilov
,
E. P.
,
Nika
,
D. L.
,
Balandin
,
A. A.
,
Bao
,
W.
,
Miao
,
F.
, and
Lau
,
C. N.
,
2008
, “
Extremely High Thermal Conductivity of Graphene: Prospects for Thermal Management Applications in Nanoelectronic Circuits
,”
Appl. Phys. Lett.
,
92
, p.
151911
.10.1063/1.2907977
10.
Nika
,
D. L.
,
Pokatilov
,
E. P.
,
Askerov
,
A. S.
, and
Balandin
,
A. A.
,
2009
, “
Phonon Thermal Conduction in Graphene: Role of Umklapp and Edge Roughness Scattering
,”
Phys. Rev. B
,
79
, p.
155413
.10.1103/PhysRevB.79.155413
11.
Nika
,
D. L.
,
Ghosh
,
S.
,
Pokatilov
,
E. P.
, and
Balandin
A. A.
,
2009
, “
Lattice Thermal Conductivity of Graphene Flakes: Comparison With Bulk Graphite
,”
Appl. Phys. Lett.
,
94
, p.
203103
.10.1063/1.3136860
12.
Slack
,
G. A.
,
1962
, “
Anisotropic Thermal Conductivity of Pyrolytic Graphite
,”
Phys. Rev.
,
127
, pp.
694
701
.10.1103/PhysRev.127.694
13.
Guo
,
Z.
,
Zhang
,
D.
, and
Gong
,
X. G.
,
2009
, “
Thermal Conductivity of Graphene Nanoribbons
,”
Appl. Phys. Lett.
,
95
, p.
163103
.10.1063/1.3246155
14.
Jagannadham
,
K.
,
2011
, “
Thermal Conductivity of Indium–Graphene and Indium-Gallium–Graphene Composites
,”
J. Electron. Mater.
,
40
, pp.
25
34
.10.1007/s11664-010-1391-1
15.
Jagannadham
,
K.
,
2012
, “
Thermal Conductivity of Copper-Graphene Composite Films Synthesized by Electrochemical Deposition With Exfoliated Graphene Platelets
,”
Metall. Mater. Trans. B
,
43
, pp.
316
324
.10.1007/s11663-011-9597-z
16.
Koh
,
Y. K.
,
Bae
,
M. H.
,
Cahill
,
D. G.
, and
Pop
,
E.
,
2010
, “
Heat Conduction Across Monolayer and Few-Layer Graphenes
,”
Nano Lett.
,
10
, pp.
4363
4368
.10.1021/nl101790k
17.
Hopkins
,
P. E.
,
Baraket
,
M.
,
Barnat
,
E. V.
,
Beechem
,
T. E.
,
Kearney
,
S. P.
,
Duda
,
J. C.
,
Robinson
,
J. T.
, and
Walton
,
S. G.
,
2012
, “
Manipulating Thermal Conductance at Metal-Graphene Contacts Via Chemical Functionalization
,”
Nano Lett.
,
12
, pp.
590
595
.10.1021/nl203060j
18.
Chang
,
S. W.
,
Nair
,
A. K.
, and
Buehler
,
M. J.
,
2012
, “
Geometry and Temperature Effects of the Interfacial Thermal Conductance in Copper– and Nickel–Graphene Nanocomposites
,”
J. Phys.: Condens. Matter.
,
24
, p.
245301
.10.1088/0953-8984/24/24/245301
19.
Nguyen
,
S. T.
,
Ruoff
,
R. S.
,
Stankovich
,
S.
,
Dikin
,
D. A.
,
Piner
,
R. D.
,
Kohlhaas
,
K. A.
,
Kleinhammes
,
A.
,
Yuanyuan
,
J.
, and
Yue
,
W.
,
2007
, “
Synthesis of Graphene-Based Nanosheets Via Chemical Reduction of Exfoliated Graphite Oxide
,”
Carbon
,
45
, pp.
1558
1565
.10.1016/j.carbon.2007.02.034
20.
Wang
,
J.
,
Li
,
Z.
,
Fan
,
G.
, and
Huanhuan
,
D.
,
2012
, “
Reinforcement With Graphene Nanosheets in Aluminum Matrix Composites
,”
Scr. Mater.
,
66
, pp.
594
597
.10.1016/j.scriptamat.2012.01.012
21.
Chen
,
L. Y.
,
Konishi
,
H.
,
Fehrenbacher
,
A.
,
Ma
,
C.
,
Xu
,
J. Q.
,
Choi
,
H.
,
Xu
,
H. F.
,
Pfefferkorna
,
F. E.
, and
Lia
,
X. C.
,
2012
, “
Novel Nanoprocessing Route for Bulk Graphene Nanoplatelets Reinforced Metal Matrix Nanocomposites
,”
Scr. Mater.
,
67
, pp.
29
32
.10.1016/j.scriptamat.2012.03.013
22.
Cahill
,
D. G.
,
1990
, “
Thermal Conductivity Measurement From 30 to 750 K: The 3ω Method
,”
Rev. Sci. Instrum.
,
61
, pp.
802
808
.10.1063/1.1141498
23.
Kim
,
J. H.
,
Feldman
,
A.
, and
Novotny
,
D.
,
1999
, “
Application of the Three Omega Thermal Conductivity Measurement Method to a Film on a Substrate of Finite Thickness
,”
J. Appl. Phys.
,
86
, pp.
3959
3963
.10.1063/1.371314
24.
Panzer
,
M. A.
,
Zhang
,
G.
,
Mann
,
D.
,
Hu
,
X.
,
Pop
,
E.
,
Dai
,
H.
, and
Goodson
,
K. E.
,
2008
, “
Thermal Properties of Metal-Coated Vertically Aligned Single-Wall Nanotube Arrays
,”
ASME J. Heat Transfer
,
130
, p.
052401
.10.1115/1.2885159
25.
Clemens
,
B. M.
,
Eesley
,
G. L.
, and
Paddock
,
C. A.
,
1988
, “
Time-Resolved Thermal Transport in Compositionally Modulated Metal Films
,”
Phys. Rev.
,
37
, pp.
1085
1096
.10.1103/PhysRevB.37.1085
26.
Zheng
,
H.
, and
Jagannadham
,
K.
,
2013
, “
Transient Thermo Reflectance From Graphene Composites With Matrix of Indium and Copper
,”
AIP Adv.
,
3
, p.
032111
.10.1063/1.4794801
27.
Borca-Tasciuc
,
T.
,
Kumar
,
A. R.
, and
Chen
,
G.
,
2001
, “
Data Reduction in 3ω Method for Thin-Film Thermal Conductivity Determination
,”
Rev. Sci. Instrum.
,
72
, pp.
2139
2147
.10.1063/1.1353189
28.
Hutchinson
,
J. R.
, and
Percival
,
C. M.
,
1968
Higher Modes of Longitudinal Wave Propagation Thin Rods
,”
J. Acoust. Soc. Am.
,
44
, pp.
1204
1210
.10.1121/1.1911247
29.
Nath
,
P.
, and
Chopra
,
K. L.
,
1974
, “
Thermal Conductivity of Copper Films
,”
Thin Solid Films
,
20
, pp.
53
62
.10.1016/0040-6090(74)90033-9
30.
Seol
,
J. H.
,
Jo
,
I.
,
Moore
,
A. L.
,
Lindsay
,
L.
,
Aitken
,
Z. H.
,
Pettes
,
M. T.
,
Li
,
X.
,
Yao
,
Z.
,
Huang
,
R.
,
Broido
,
D.
,
Mingo
,
N.
,
Ruoff
,
R. S.
, and
Shi
,
L.
,
2010
, “
Two-Dimensional Phonon Transport in Supported Graphene
,”
Science
,
328
, pp.
213
216
.10.1126/science.1184014
31.
Klemens
,
P. G.
,
2001
, “
Theory of Thermal Conduction in Thin Ceramic Films
,”
Int. J. Thermophys.
,
22
, pp.
265
275
.10.1023/A:1006776107140
32.
Klemens
,
P. G.
, and
Pedraza
,
D. F.
,
1994
, “
Thermal Conductivity of Graphite in the Basal Plane
,”
Carbon
,
32
, pp.
735
741
.10.1016/0008-6223(94)90096-5
33.
Ni
,
Z. H.
,
Wang
,
H. M.
,
Ma
,
Y.
,
Kasim
,
J.
,
Wu
,
Y. H.
, and
Shen
,
Z. X.
,
2008
, “
Tunable Stress and Controlled Thickness Modification in Graphene by Annealing
,”
ACS Nano
,
2
, pp.
1033
1039
.10.1021/nn800031m
34.
Jang
,
W.
,
Chen
,
Z.
,
Bao
,
W.
,
Lau
,
C. N.
, and
Dames
,
C.
,
2010
, “
Thickness-Dependent Thermal Conductivity of Encased Graphene and Ultrathin Graphite
,”
Nano Lett.
,
11
, pp.
3909
3913
.10.1021/nl101613u
35.
Swartz
,
E. T.
, and
Pohl
,
R. O.
,
1989
, “
Thermal Boundary Resistance
,”
Rev. Mod. Phys.
,
33
, pp.
605
668
.10.1103/RevModPhys.61.605
36.
Minnich
,
A.
, and
Chen
,
G.
,
2007
, “
Modified Effective Medium Formulation for the Thermal Conductivity of Nanocomposites
,”
Appl. Phys. Lett.
,
91
, p.
073105
.10.1063/1.2771040
37.
Majumdar
,
A.
, and
Reddy
,
P.
,
2004
, “
Role of Electron-Phonon Coupling in Thermal Conductance of Metal-Nonmetal Interfaces
,”
Appl. Phys. Lett.
,
84
, pp.
4768
4771
.10.1063/1.1758301
38.
Aven
,
M. H.
,
Craig
,
R. S.
,
Waite
,
T. R.
, and
Wallace
,
W. E.
,
1956
, “
Heat Capacity of Ti Between 4 and 15 K
,”
Phys. Rev.
,
102
, pp.
1263
1264
.10.1103/PhysRev.102.1263
39.
Hu
,
C. E.
,
Zeng
,
Z. Y.
,
Zhang
,
L.
,
Chen
,
X. R.
,
Cai
,
L. C.
, and
Alfè
,
D.
,
2010
, “
Theoretical Investigation of the High Pressure Structure, Lattice Dynamics, Phase Transition, and Thermal Equation of State of Titanium Metal
,”
J. Appl. Phys.
,
107
, p.
093509
.10.1063/1.3407560
40.
Hirth
,
J. P.
, and
Lothe
,
J.
,
1992
,
Theory of Dislocations
, 2nd ed.,
Krieger
,
Malabar, FL
, p.
837
.
41.
Touloukian
,
Y. S.
, and
Buyco
,
E. H.
,
1970
,
Thermophysical Properties of Matter
, (Vol. 4 of Specific Heat of Metallic Elements and Alloys and Vol. 5 of Specific Heat of Nonmetallic Solids) (The TPRC Data Series)),
IFI
/
Plenum, New York
.
42.
Klett
,
J.
,
Hardy
,
R.
,
Romine
,
E.
,
Walls
,
C.
, and
Tim Burchell
,
T.
,
2000
, “
High-Thermal-Conductivity, Mesophase-Pitch-Derived Carbon Foams: Effect of Precursor on Structure and Properties
,”
Carbon
,
38
, pp.
953
973
.10.1016/S0008-6223(99)00190-6
43.
Yu
,
A.
,
Ramesh
,
P.
,
Itkis
,
M. E.
,
Bekyarova
,
E.
, and
Haddon
,
R. C.
,
2007
, “
Graphite Nanoplatelet-Epoxy Composite Thermal Interface Materials
,”
J. Phys. Chem. C
,
111
, pp.
7565
7569
.10.1021/jp071761s
44.
Pettes
,
M. T.
,
Ji
,
H.
,
Ruoff
,
R. S.
, and
Shi
,
Li.
,
2012
, “
Thermal Transport in Three-Dimensional Foam Architectures of Few-Layer Graphene and Ultrathin Graphite
,”
Nano Lett.
,
12
, pp.
2959
2964
.10.1021/nl300662q
45.
Sadeghi
,
M. M.
,
Jo
,
I.
, and
Shi
,
L.
,
2013
, “
Phonon-Interface Scattering in Multilayer Graphene on an Amorphous Support
,”
Proc. Nat. Acad. Sci.
,
110
, pp.
16321
16326
.10.1073/pnas.1306175110
46.
Zheng
,
H.
, and
Jagannadham
,
K.
,
2013
, “
Influence of Laser Irradiation and Microwave Plasma Treatment on the Thermal Properties of Graphene Platelets
,”
J. Vac. Sci. Technol.
,
31
, p.
041506
.10.1116/1.4809581
You do not currently have access to this content.