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Research Papers: Conduction

Thermal Conductivity and Interface Thermal Conductance in Composites of Titanium With Graphene Platelets

[+] Author and Article Information
H. Zheng

Materials Science and Engineering,
North Carolina State University,
Raleigh, NC 27695

K. Jaganandham

Materials Science and Engineering,
North Carolina State University,
Raleigh, NC 27695
e-mail: jag_kasichainula@ncsu.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 10, 2013; final manuscript received January 10, 2014; published online March 10, 2014. Assoc. Editor: Wilson K. S. Chiu.

J. Heat Transfer 136(6), 061301 (Mar 10, 2014) (9 pages) Paper No: HT-13-1291; doi: 10.1115/1.4026488 History: Received June 10, 2013; Revised January 10, 2014

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.

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Figures

Grahic Jump Location
Fig. 1

Schematic diagram of (a) three layers consisting of Au, GPs, and Ti deposited on Si substrate (Au-GP-Ti-Si), (b) Ti film deposited on Si (Ti-Si), and (c) composite of Ti with dispersion of GPs deposited on Si (Ti-GP-Ti-Si). Dimensions are not to scale. Figures 1(b) and 1(c) represent the sample geometries used for both 3ω and TTR methods. Figure 1(a) represents the sample geometry for TTR method only. The structure of the Ti-GP-Ti composite film is not layered. The structure consists of GPs dispersed in the Ti film to form the composite as shown in Fig. 1(c).

Grahic Jump Location
Fig. 2

(a) SEM image collected using secondary electron mode to reveal the GPs dispersed in the composite. The topological contrast from secondary electrons arose from the GPs on the surface and the weak contrast arose from the GPs underneath the surface. GPs dispersed uniformly were observed between bands of GPs. (b) Cross-section SEM image collected using backscattering mode to reveal the GPs dispersed in the composite. The strong dark contrast arose from the GPs on the surface and the weak dark contrast arose from the GPs underneath the surface. GPs dispersed uniformly were observed. (c) Number fraction shown as a function of size or size distribution of the GPs in the composite is shown. The weighted average thermal conductivity of the GPs is found to be 800 Wm−1K−1.

Grahic Jump Location
Fig. 3

EDS spectrum collected from sample of Ti film deposited on Si substrate. Absence of peaks from O, N, and C is noted. The inset shows the spectrum at lower energy. The Ti peak coincides with 0.45 KeV. The oxygen peak at 0.525 KeV could not be detected.

Grahic Jump Location
Fig. 4

The increment of temperature of the Au heater line per unit power input shown as a function of ln(f) for Ti or composite film present on Si substrate. Both the experimental results (-exp) and the curve fitted values (-sim) using multilayer analysis are shown. Least square curve fitting analysis was used with R2 = 0.995. The values of thermal conductivity of Ti and Ti-GP-Ti are expected to be within ±10%.

Grahic Jump Location
Fig. 5

Normalized TTR signal shown as a function of time in the sample of Au-GP-Ti-Si. In addition to the temperature variation of the sample surface, the acoustic oscillations are also present in the TTR signal.

Grahic Jump Location
Fig. 6

Normalized TTR signal shown as a function of time in the sample of Ti-Si. The TTR signal does not contain any acoustic oscillations.

Grahic Jump Location
Fig. 7

Normalized TTR signal shown as a function of time in the sample of Ti-GP-Ti-Si. In addition to the temperature variation of the sample surface, the acoustic oscillations are also present in the TTR signal. The center points are taken in the acoustic oscillations to curve fit the signal. Least square curve fitting is used to determine the value of h. The upper TTR signal corresponds to K = 21, the one below to K = 40, and the one further below to K = 60, all in Wm−1K−1.

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