Thermal diffusivity of graphite sheet at low temperatures

Transcription

1 High Temperatures ^ High Pressures, 2001, volume 33, pages 253 ^ ECTP Proceedings pages 853 ^ 859 DOI: /htwu128 Thermal diffusivity of graphite sheet at low temperatures Hosei Nagano}, Hideyuki Kato}, Akira Ohnishi#, Yuji Nagasaka} } Department of Mechanical Engineering, Keio University, Hiyoshi, Kohoku-ku, Yokohama , Japan; fax: ; hosei@pub.isas.ac.jp } National Research Laboratory of Metrology, Umezono, Tsukuba, Ibaraki , Japan # Institute of Space and Astronautical Science, Yoshinodai, Sagamihara, Kanagawa , Japan Presented at the 15th European Conference on Thermophysical Properties, Wu«rzburg, Germany, 5 ^ 9 September 1999 Abstract. The temperature dependence of the in-plane thermal diffusivity and the out-of-plane thermal diffusivity for graphite sheet over the temperature range from 30 to 375 K, and the inplane anisotropy at room temperature measured by a laser-heating AC calorimetric method, are reported. It was found that the value of the in-plane thermal diffusivity was significantly greater than that of the out-of-plane direction. It was also found that the in-plane thermal diffusivity did not show any directional dependence. 1 Introduction In the field of space development, the design of lightweight thermal control systems (TCSs) of spacecraft is required. Space radiators, which are mainly made of aluminium alloys, are one of the heaviest components in TCSs. Recently, as a basic material for the radiators, artificial graphites like carbon fibre and carbon composite have been partially replacing aluminium because of their characteristics of light weight and high thermal conductivity (David and Tung 1995). The purpose of the present study is to apply one of the artificial graphites, graphite sheet (GS), developed by Matsushita Electric Industrial Co. Ltd, to the material of space radiators. The GS has characteristics of light weight, high thermal conductivity, and flexibility like a piece of paper (Nagano et al 1998). In addition to these features, heat in the GS can diffuse two-dimensionally whereas heat in a carbon fibre diffuses along the axis because of its axial orientation. The thermal conductivities of artificial graphites can vary considerably depending on their degrees of graphitisation and grain sizes. Additionally for this material, there exists an extreme anisotropy between the in-plane direction and the out-of-plane direction, and also a large temperature dependence. Therefore, it is important to know the value of thermal conductivity in both directions at various temperaturesöespecially for space use. We describe the measurement of the in-plane and the out-of-plane thermal diffusivities of the GS in the temperature range from 30 to 375 K, and the in-plane anisotropy at room temperature, by the use of a laser-heating AC calorimetric method (Hatta et al 1985; Kato et al 1998). 2 Graphite sheet The GS used in the present study has been prepared from aromatic polyimide films by heat treatment at 2600 ^ C in an inert atmosphere (Murakami et al 1986). The process for making highly oriented GSs from polyimide films is as follows: (i) at temperatures between 400 and 600 8C, the thermal decomposition reaction proceeds preferentially on the imide group, and a planar and heterocycle carbon precursor with the nitrogen contained is made. (ii) Carbonisation occurs by denitrification and dehydrogenation, and aromatic rings are developed above C. (iii) At temperatures above

2 254 H Nagano, H Kato, A Ohnishi, Y Nagasaka 15 ECTP Proceedings page C, lamination layers grow and highly oriented graphite films (100 mm in thickness and 0:79 gcm 3 in density) are produced. Figure 1 shows scanning electron microscope (SEM) photographs of (a) the surface and (b) the cross-sectional view of the GS structures. It is remarkable that the GS is organised in different structures between the in-plane and the out-of-plane directions. This difference is attributed to the presence of a covalent bond between the nearest atoms in the in-plane directions, whereas only van der Waals forces bind the basal planes in the out-of-plane direction. In the cross-sectional view of the GS (figure 1b), there are large vacancies between the layers sporadically, and they seem to affect not only the mechanical flexibility but also the thermal conductivity. (a) (b) Figure 1. SEM images of (a) the surface and (b) the cross-section features of the GS. 3 Principle of the laser-heating AC calorimetric method If heat is liberated at the rate rc exp (iot) at a point heat source, where r is the average density of the medium, c is the heat capacity, o is the frequency, and t the time, the propagation of thermal waves in a three-dimensionally infinite region can be written as (Carslaw and Jaeger 1959): T AC ˆ 1 exp kl i ot kl Š, (1) 4pal where T AC is the AC temperature at the detection point, l the distance between the heating point and the detection point, o ˆ 2pf the angular frequency, a the thermal diffusivity, and k the thermal wave number. This is given by: 1=2 pf k ˆ ˆ l 1, (2) a where l is the thermal diffusion length. The detected phase delay, y, of the AC temperature is given by: y ˆ kl. (3)

3 Thermal diffusivity of graphite sheet at low temperatures ECTP Proceedings page 855 Combining equations (2) and (3), we have: 2 l a ˆ pf. (4) y From equation (4), thermal diffusivity is given as the distance or the frequency dependences of the phase delay. 4 Measurement apparatus Figure 2 shows the present laser-heating AC calorimetric measurement apparatus (Kato et al 1998), which consists of an AC laser-heating source, a 4 He gas continuous flow cryostat to cool the sample, and a measuring apparatus. The heat source is a He ^ Ne gas laser whose maximum output power is 10 mw. The intensity modulation of the laser beam at an arbitrary frequency between 1 and 1000 Hz is achieved by the use of an acousto-optic modulator (AOM). The beam diameter is controlled between 1 and 40 mm by a microscope. The beam irradiation position is adjusted by X^Ydual axes translation stages which are set under the cryostat and can move together with the cryostat. A sample is thermally anchored to the copper cold plate by fixing only both edges of the sample. Temperature in the cryostat is controlled with a heater and 4 He gas between 4 and 375 K in a vacuum. Onto the rear face of the sample, a cross-junction of a Chromel ^ Constantan thermocouple (25 mm in diameter) is attached and both DC and AC temperatures are simultaneously measured with its two independent terminals. The DC temperature is a rise of the sample temperature from its background, and the AC temperature gives information on thermal diffusivity in its amplitude and phase delay by means of a lock-in amplifier. The function generator provides the frequency signal of the AOM and the reference frequency of the lock-in amplifier. In the present system, the phase information is mainly used to analyse the thermal diffusivity.the uncertainty of this apparatus is estimated to be within 5% (in-plane) and 30% ^ 50% (out-of-plane) at room temperature with an austenitic stainless steel SRM1461 (Kuroiwa et al 1998), which is one of the standard reference materials of thermal conductivity of solids supplied by the National Institute of Standards (NIST). integrating sphere beam splitter AOM He ^ Ne laser modulating signal power monitor function generator microscope reference signal T DC cryostat sample lock-in amplifier GP ^ IB digital voltmeter X axis translation stage Y axis translation stage thermocouple PC Figure 2. Instrumentation for laser-heating AC calorimetry.

4 256 H Nagano, H Kato, A Ohnishi, Y Nagasaka 15 ECTP Proceedings page Sample configuration and measurement method In the case of isotropic materials, it is possible to measure both the in-plane and the out-of-plane thermal diffusivities with only one sample in this system (Kuroiwa et al 1998). However, in the case of extreme anisotropic materials such as graphite, two types of sample shape are necessary to measure the thermal diffusivities in both directions. Figure 3 shows three different sample configurations with the following beam operations f ˆ 10:3 Hz l ˆ 0 8 mm b ˆ 8 mm (a) ` (b) laser beam d f ˆ 1:1 696 Hz l ˆ d ˆ 0:11 mm b ˆ 40 mm sample thermocouple f ˆ 10:6 Hz l ˆ 0 3 mm b ˆ 40 mm (c) Figure 3. Typical arrangements of sample and laser beam ( f, chopping frequency; l, scanning distance; d, thickness; b, beam diameter). (Nagano et al 1998). 5.1 In-plane thermal diffusivity, a jj A sample (7 40 mm 2 ) was cut from a sheet with parallel slits at a width 1 mm at the centre in order to make a long strip, which can pass the one-dimensional heat flow toward the slit direction. The laser beam spot was scanned along the slit, and the phase delay was measured as a function of the distance ranging from 0 to 8 mm between the heating point and the detection point at a fixed frequency 10.3 Hz in the temperature range from 30 to 375 K. 5.2 Out-of-plane thermal diffusivity, a? A sample (7 40 mm 2 was cut from a sheet without slits. The width of the sample is much larger than the thermal diffusion length, so there is no reflection of the thermal waves from the edges. The laser beam spot was fixed on the rear face of the thermocouple junction. The phase delay was measured as a function of the chopping frequency ranging from 1.1 to 696 Hz at the temperature range from 30 to 375 K. 5.3 In-plane anisotropy The sample was the same as that for the out-of-plane thermal diffusivity measurement. The laser beam was circularly scanned around the detection point in 158 steps and the in-plane angular dependence of the phase delay was measured at room temperature.

5 Thermal diffusivity of graphite sheet at low temperatures ECTP Proceedings page Results and discussion Figure 4a presents the temperature dependence of the in-plane thermal diffusivity, a k,of the GS. Between 100 and 375 K the thermal diffusivity increases from to m 2 s 1 as the temperature decreases. At lower temperatures below 100 K, the thermal diffusivity starts to decrease again. The in-plane thermal diffusivity at room temperature ( m 2 s 1 ) is very high compared to the thermal diffusivity of pure copper ( m 2 s 1 ) (taken from the Thermophysical Properties Handbook, Japan Society of Thermophysical Properties 1990). Figure 4b shows the temperature dependence of the out-of-plane thermal diffusivity, a?, of the GS. It has a maximum value at 80 K. Between 80 and 375 K, the thermal diffusivity increases from 1: to 3: m 2 s 1 as the temperature decreases a=10 6 m 2 s Temperature/K Temperature/K (a) (b) Figure 4. Temperature dependence of (a) the in-plane and (b) the out-of-plane thermal diffusivity, a, of the GS. The temperature dependence of a? for the GS is not so significant as that of a k. Both the in-plane and the out-of-plane thermal diffusivities above the peak temperature change in proportion to T 1. This phenomenon is caused by phonon scattering by lattice vibration and is common to those materials in which the heat is transported by phonons (Hatta et al 1995) rad 1.0 rad 1.2 rad 1.4 rad 1 y=mm x=mm Figure 5. Contour plots of the phase delay as a function of the heating point to confirm the in-plane anisotropy.

6 258 H Nagano, H Kato, A Ohnishi, Y Nagasaka 15 ECTP Proceedings page 858 Contrasting the in-plane thermal diffusivity, a k, and the out-of-plane thermal diffusivity, a?, of the GS, there is an extreme anisotropy. The value of a k is nearly 400 times higher than that of the out-of-plane a? at room temperature, and it reaches up to about 780 times at 125 K. The origin of this extreme anisotropy is the two-dimensional structure of the GS, and such a tendency is a common characteristic of highly oriented graphites. Figure 5 shows the contour plots of phase delay as a function of heating position to confirm the in-plane anisotropy. The contours form circles and their deviations are within 9%, which is very little in comparison with the anisotropy between the in-plane and the out-of-plane directions (> 400 times). From this result, the GS has homogeneous structures in the in-plane directions. 7 Thermal conductivity The thermal conductivity of the GS can be evaluated by means of these relationships: l k ˆ r GS a k c p, l? ˆ r GS a? c p, (5) where l k and l? are the in-plane and the out-of-plane thermal conductivities respectively, c p the specific heat at constant pressure of graphite, and r GS the density of the GS. The specific heat values of graphite are taken from Magnus (1923) and DeSorbo and Tyler (1953). The in-plane and the out-of-plane thermal conductivities of the GS are plotted in figure 6 in comparison with the thermal conductivities of pyrolytic graphite (PG) and pure copper (99.999%). The values of thermal conductivity for the PG and pure copper are taken from the Thermophysical Properties Handbook (Japan Society of Thermophysical Properties 1990). The in-plane thermal conductivity, l k, of the GS has a maximum value at 150 K. The out-of-plane thermal conductivity, l?, does not show a maximum value between 30 and 375 K, and seems to have a peak at much higher temperature. Compared with the PG, the thermal conductivity of the GS is much lower. The reasons for such differences are as follows: Thermal conductivity/w m 1 K GS (in-plane) GS (out-of-plane) PG (in-plane) PG (out-of-plane) Cu (99.999%) Temperature/K Figure 6. Temperature dependence of thermal conductivity of the GS, pyrolytic graphite (PG), and pure copper (Cu).

7 Thermal diffusivity of graphite sheet at low temperatures ECTP Proceedings page 859 (i) they have different densitiesöthe GS is 0:79 gcm 3, while the PG is 2:26 gcm 3 ; (ii) the thermal conductivity of graphite material is strongly dependent on its grain size. The graphite material with its larger grain size has higher thermal conductivity and has a sharper peak of thermal conductivity at lower temperature. Judging from this fact, the PG has larger grain size than that of the GS. Indeed the GS has lower thermal conductivity due to its lower density and smaller grain size, but this GS has advantages as a practical material: it is flexible, easy to handle, and easy to produce. Compared with the pure copper, the value of l k of the GS below 100 K decreases as the temperature decreases while the thermal conductivity of the copper increases. Above 150 K, the in-plane thermal conductivity of the GS is as large as that of the copper. Taking into account the fact that the density of the GS is only one-thirteenth of that of the copper, the GS is a very good thermal conductor with the advantage of light weight. 8 Conclusions The in-plane and out-of-plane thermal diffusivities of the GS were measured by the laser-heating AC calorimetric method at temperatures between 30 and 375 K. The following results were obtained: (i) the value of thermal diffusivity in the in-plane direction is significantly greater than that in the out-of-plane direction; (ii) in-plane anisotropy does not exist, and that shows its homogeneity in the in-plane direction; (iii) the in-plane thermal conductivity of the GS is very high with advantages of flexibility and light weight. From these results, it is clear that this GS is suitable for the thermal control material for spacecraft. Acknowledgements. We would like to thank Mr N Nishiki of Matsushita Electric Industrial Co. Ltd for supplying graphite sheets. We would also like to thank Dr M Okaji of the National Research Laboratory of Metrology and Mr M Kuroiwa for much help during this research. References Carslaw H S, Jaeger J C, 1959 Conduction of Heat in Solids second edition (London: Oxford University Press) pp 255 ^ 281 David G T C, Tung T L, 1995, AIAA paper No presented at the 30th AIAA Thermophysics Conference, San Diego, CA, 19 ^ 22 June DeSorbo W, Tyler W W, 1953 J. Chem. Phys ^1663 Hatta H, Kogo Y, Yoshihara Y, Sawada Y, Takahashi K, Hosono K, Dozono T, 1995 Mater. Sys ^ 24 Hatta I, Sasuga Y, Kato R, Maezono A, 1985 Rev. Sci. Instrum ^ 1647 Japan Society of Thermophysical Properties, 1990 Thermophysical Properties Handbook (Tokyo: Yokendo Press) pp 265 ^ 267 Kato H, Nara K, Okaji M, Rykov A, Tajima S, Koshizuka N, 1998 Advances in Superconductivity X (Tokyo: Springer) pp 139 ^ 142 Kuroiwa M, Kato H, Okaji M, Ishida K, 1998, presented at the 59th Meeting of Cryogenics and Superconductivity 83, Yamaguchi, Japan, 13 ^ 15 October Magnus A, 1923 Ann. Phys ^ 331 Murakami M, Watanabe K, Yoshimura S, 1986 Appl. Phys. Lett ^ 1956 Nagano H, Kato H, Ohnishi A, Nishiki N, Nagasaka Y, 1998, in Proceedings of the 19th Japan Thermophysical Properties Symposium (Fukuoka: JSTP) pp 247 ^ 250

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