Thermal conductivity of W–Cu composites at various temperatures

Thermal conductivity of W–Cu composites at various temperatures

December 2001 Materials Letters 51 Ž2001. 420–424 www.elsevier.comrlocatermatlet Thermal conductivity of W–Cu composites at various temperatures You...

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December 2001

Materials Letters 51 Ž2001. 420–424 www.elsevier.comrlocatermatlet

Thermal conductivity of W–Cu composites at various temperatures Young Do Kim a,) , Nang Lyeom Oh a , Sung-Tag Oh b, In-Hyung Moon a a b

DiÕision of Materials Science and Engineering, Hanyang UniÕersity, Seoul 133-791, South Korea Department of Metallurgy and Materials Science, Hanyang UniÕersity, Ansan 425-791, South Korea Received 9 January 2001; accepted 16 March 2001

Abstract The effect of temperature on the electrical resistivity and thermal conductivity of W–Cu composites had been studied. In case of pure W and Cu, the thermal conductivity decreased with increase in temperature. However, the W–Cu composites showed increased thermal conductivity with increase of temperature up to 5008C, and then the conductivity decreased with increasing temperatures. This increase in thermal conductivity is explained by the increased number and movement of electrons as well as increased conduction paths for the electrons. The scattering of phonons is believed to be responsible for the decrease of thermal conductivity at the temperature of above 5008C. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Nanostructured materials; Sintering; Microstructure; Electrical resistivity; Thermal conductivity

1. Introduction The tungsten–copper ŽW–Cu. composites are promising materials for micro-electronic applications like blocking materials for microwave package, high voltage contact materials, and heat sink materials for high density integrated circuit. In case of heat sink materials, the coefficient of thermal expansion should be coincident with that of IC substrates such as Al 2 O 3 , BeO and AlN, and concurrently, high thermal conductivity must be accomplished. Thus, the design of compositions and microstructural charac-

) Corresponding author. Tel.: q82-2-2290-0408; fax: q82-22282-1976. E-mail address: [email protected] ŽY.D. Kim..

teristics must be considered to fabricate the heat sink materials with optimal thermal properties. Generally, W–Cu materials are produced by liquid phase sintering through infiltration w1x, activated sintering w2x, etc. But it is difficult to fabricate alloy and composites with homogeneous microstructure, because W and Cu have no solubility of each other through the whole composition. With the recent progress in mechanical alloying of powder mixtures of W–Cu w3x, however, it is now possible to obtain fully densified composites with homogeneous microstructure. In this work, the thermal conductivity of W–Cu composites with various Cu contents had been studied. Nanostructured powder mixtures with homogeneous mixing were prepared by mechanical alloying of raw powders. The thermal conductivity of sintered composites was measured at various temperatures,

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and their dependence on temperature was discussed based on the microstructural characteristics and estimation of measured electrical resistivities.

Ar atmosphere. All samples were made into cylindrical shape with radius of 10 mm and height of 1 mm and coated with carbon.

2. Experimental procedure

3. Results and discussion

The elemental W Žparticle size of 4.92 mm. and Cu Ž78.15 mm. powders were used for raw powders in this experiment. They were premixed in a threedimensional mixer. The mixed powders were mechanically alloyed by high-energy ball milling for 50 h in Ar. A stainless steel jar of 1.5 l and balls of 3r16 in. were used as the milling media. The ball to powder ratio was 60:1 and milling velocity was 400 rpm. The 1 wt.% of stearic acid was added as a process control agent to prevent powders from welding with jar and ball and to maintain balance of welding and fracturing. The mechanically alloyed powders were cold compacted to form the cylindrical shape with 40 " 5% of theoretical density. Then, it was sintered at 12008C for 1 h with a heating rate of 58Crmin from room temperature. The relative densities of the sintered specimens were measured by Archimedes’ principle. The microstructures of the specimens were observed by scanning electron microscope ŽSEM.. The electrical resistivities were measured by the Four-Point Probe method as a function of temperature in vacuum. The thermal diffusivities were measured by the Laser Flash method from room temperature to 10008C in

Microstructural observation revealed that the powder mixtures prepared by mechanical alloying showed fine grain sizes of 30–40 nm and high mixing homogeneity between W and Cu powders w4x. The relative densities of sintered W–10 wt.% Cu, W–20 wt.% Cu and W–30 wt.% Cu composites were 95.4%, 97.4% and 98.0%, respectively. Typical fracture surfaces of sintered composites are shown in Fig. 1. It can be seen that W particles are interconnected and form polyhedral shapes called tetrakaidecahedron. The Cu solidified from liquid phase is located around tetrakaidecahedra forming a network structure. Also, increasing Cu contents induced decrease in W size and increase in contacts area between W and Cu, as clearly shown in Fig. 1a–c. Fig. 2 shows the electrical resistivities of W–Cu composites as a function of Cu content and temperature. Increasing Cu content to 30 wt.% caused the electrical resistivity to decrease, which corresponded directly to the addition of Cu having high electrical conductivity. Also, increasing temperature produced an increase of the electrical resistivity, as shown in Fig. 2. Based on the measured electrical resistivity,

Fig. 1. SEM images of sintered composites with various Cu contents; Ža. W–10 wt.% Cu, Žb. W–20 wt.% Cu and Žc. W–30 wt.% Cu.

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Fig. 2. Electrical resistivities of sintered W–Cu composites as a function of temperatures.

the thermal conductivity for the W–Cu composites was theoretically estimated as a function of temperature. From the quantum mechanical consideration, only the electrons with Fermi energy level can participate in thermal conduction. Thus, thermal conductivity can be expressed by the number and effective mass of electrons with Fermi energy level; Qs

p 2 Nf K B2 Tt 3m )

.

Ž 1.

Considering the conduction by electrons with Fermi energy level, the electrical conductivity can be also expressed by Eq. Ž2., and the relation between thermal and electrical conductivities by Eq. Ž3., as derived by Wiedemann and Franz in Ref. w5x;

ss

Nf e 2t m

Q s

sT

1 s

r

)

p 2 k B2 3e

2

,

s L s 2.443 = 10y8 Ž J VrK 2 s .

Ž 2. Ž 3.

where Q is thermal conductivity, s is electrical conductivity, r is electrical resistivity, Nf is the number of free electrons per volume, m ) is effective mass, t is relaxation time, k B is Boltzmann constant and L is Lorentz constant. Thus, thermal conductivity can be calculated from the Eq. Ž3. by substitution of measured electrical resistivities.

Fig. 3 shows the thermal conductivities of composites, pure W and Cu, calculated by Eq. Ž3., also the reported values for pure W and Cu. As the temperature increases, the thermal conductivity decreases for pure elements of Cu Žcurve a. and W Žcurve c., which is in agreement with the reported results for Cu Žcurve b. and W Žcurve d., respectively. However, it is noted that thermal conductivity of the composites increased with increase of temperature, which shows different tendency with pure elements. In order to confirm thermal conductivities calculated from electrical resistivities, thermal diffusivities of composites were measured by the Laser Flash method w6,7x. Thermal conductivities were calculated by the following equation w8x, and the effect of porosity on thermal conductivity in sintered specimens was corrected by considering of reported literature w9x; Q s k Ž r W C W VW q r Cu CCuVCu .

Ž 4.

where k is thermal diffusivity, r is density, C is specific heat and V is volume fraction. Fig. 4 shows the thermal conductivities for the W–Cu composites as a function of Cu content and temperature. The thermal conductivities increased with increase of Cu content and temperatures below 5008C, which were the same tendency with the values calculated from the electrical resistivities as

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Fig. 3. Thermal conductivities for the composites and the pure element of Cu and W, as a function of temperature; Ža. calculated value from electrical resistivity of Cu, Žb. reported value of Cu, Žc. reported value of W and Žd. calculated value of W.

shown in Fig. 3. However, at temperatures above 5008C, the thermal conductivity decreased with increase in temperature. The thermal conductivity of a metal can be approximated by the sum of two terms, i.e. a residual component and a thermal component. Here, the residual component of a metal is caused by structural imperfections such as dislocations, grain boundaries, pores and impurity atoms and is almost independent

of temperature w11x. The movements of electrons are affected by structural imperfections existing in the composites or alloys. If thermal energies are supplied to the composites, jumping probability of electrons through the imperfections and the number of free electrons may be increased by heat. Thus, it can be suggested that effects of electrons on thermal conduction were more dominant than phonons up to 5008C and thermal conductivity of W–Cu compos-

Fig. 4. Thermal conductivities for the composites with various Cu contents, measured by Laser Flash method as a function of temperature.

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ites increases also with increase of temperature. In addition, from the viewpoint of microstructure ŽFig. 1., paths for thermal conduction can be simplified to the three conductors. One path is through the pure Cu consisting of a network structure in the whole specimen. The second path can consist of polyhedral W because of interconnection. Finally, the third path is a layer mixture of first Cu, then W and finally Cu w10x. If thermal energies are supplied to the composites, jumping probability of electrons may be increased through the third path by heat. Thus, it can be considered that the thermal conductivity through the third paths increased with increase of temperature. For higher temperature, it can be considered that the jumping probability of electrons through the imperfections becomes saturated and the effect of thermal component becomes more conspicuous on thermal conductivity. As a result, a large number of thermally excited elastic waves Žcalled phonons. scatter conduction electrons and decrease the relaxation time between collisions w11x. Thus, it can be explained that in temperatures of above 5008C, thermal conductivities of composites decreased with increase of temperatures by the scattering of phonons.

Acknowledgements This work was supported by the Korea Research Foundation ŽKRF..

References w1x K.V. Sebastian, Int. J. Powder Metall. Powder Technol. 17 Ž1981. 297. w2x I.H. Moon, J.S. Lee, Powder Metall. 1 Ž1979. 5. w3x J.C. Kim, S.S. Ryu, Y.D. Kim, I.H. Moon, Scr. Mater. 39 Ž1998. 669. w4x M.J. Suk, N.L. Oh, Y.D. Kim, Y.S. Kwon, I.H. Moon, Proceedings on International Conference On Powder Metallurgy and Particulate Materials, New York, USA. 2000, in press. w5x R.E. Hummel, Electronic Properties of Materials. Springer, Berlin, 1994, p. 354. w6x J. Blumm, J.B. Henderson, O. Nilsson, J. Fricke, High Temp.-High Press. 29 Ž1997. 555. w7x R.E. Taylor, Mater. Sci. Eng. A245 Ž1998. 160. w8x H.J. Lee, R.E. Taylor, J. Appl. Phys. 47 Ž1976. 148. w9x J.C.Y. Koh, A. Fortini, Int. J. Heat Mass Transfer 16 Ž1973. 2013. w10x R.M. German, Metall. Trans. 24A Ž1993. 1745. w11x W.F. Smith, Foundations of Materials Science and Engineering. McGraw-Hill, New York, 1993, p. 720.