Effects of Bimodal and Monomodal SiC Particle on the Thermal Properties of SiC‐Particle‐Dispersed Al

Journal of Metallurgical Engineering (ME) Volume 5, 2016 www.me‐journal.org doi: 10.14355/me.2016.05.001

Effects of Bimodal and Monomodal SiC Particle on the Thermal Properties of SiC‐Particle‐Dispersed Al‐Matrix Composite Fabricated by SPS Kiyoshi MIZUUCHI1, **, Kanryu INOUE2, Yasuyuki AGARI1, Motohiro TANAKA1, Takashi TAKEUCHI1, Jun‐ichi TANI1, Masakazu KAWAHARA3, Yukio MAKINO4 and Mikio ITO5 Osaka Municipal Technical Research Institute, 1‐6‐50, Morinomiya, Joto‐ku, Osaka, 536‐8553 Japan

1

Materials Science & Engineering, University of Washington, 302 Roberts Hall, Box 352120, Seattle, WA 98195‐2120, USA. 2

Kawahara SPS Technical Office, 2‐4‐25, Ohyabe, Yokosuka, 238‐0024, Japan

3

Forum MACKIY, North Bldg., S04, Kyoto University Katsura Venture Plaza, Katsura Innovation Park, 1‐36, Goryou Ohara, Nishikyou‐ku, Kyoto 612‐8245, Japan.

4

Center for Atomic and Molecular Technologies, Graduate School of Engineering, Osaka University, 2‐1, Yamadaoka, Suita, 565‐0871, Japan 5

** Corresponding author. Tel: +81‐6‐6963‐8153; fax: +81‐6‐6963‐8145.

E‐mail address: mizuuchi@omtri.or.jp (K. Mizuuchi)

Abstract Silicon carbide (SiC)‐particle‐dispersed‐aluminum (Al) matrix composites were fabricated in continuous solid‐liquid co‐existent state by spark plasma sintering (SPS) process from the mixture of SiC powders, Al powders and Al‐5mass%Si alloy powders. As the SiC powders, two kinds of powders, monomodal SiC powders of 109.8μm in diameter and a bimodal SiC powder mixture of 109.8μm and 14.3μm in diameter, were used. The microstructures and thermal conductivities of the composites fabricated were examined. These composites were all well consolidated by heating at a temperature range between 798K and 876K for 1.56ks during SPS process. No reaction at the interface between the SiC particle and the Al matrix was observed by scanning electron microscopy for the composites fabricated under the sintering conditions employed in the present study. The relative packing density of the monomodal composite decreased from 99.8% to 95.1% with increasing SiC volume fraction in a range of 55% and 65%, whereas that of the bimodal composite was 97% or higher than that in a SiC volume fraction range up to 70%. The thermal conductivity of the bimodal composite was higher than that of the monomodal composite in a SiC volume fraction range higher than 55%. The coefficient of thermal expansion of the composites falls in the upper line of Kerner’s model, indicating strong bonding between the SiC particle and the Al matrix in the composite.

Keywords Metal‐Matrix Composites; Particle‐Reinforcement; Thermal Properties; Sintering; Silicon Carbide

Introduction High‐performance thermal management materials should have high thermal conductivities1, 2) and low coefficients of thermal expansion (CTEs) for maximizing heat dissipation3) and minimizing thermal stress and distortion, which are critical issues in packaging of microprocessors, power semiconductors, high‐power laser diodes, light‐emitting diodes (LEDs), and micro‐electro‐mechanical systems (MEMS)3‐9). Traditional packaging base materials are Cu‐W10), AlN11), BeO12) and Al/SiC13‐15). Among these materials, particularly, Al‐matrix composites containing dispersed silicon carbide (SiC) particles have received the most attention as potential candidates for a variety of uses in advanced electronic packaging. They are currently competing with established materials such as Cu‐W or Cu‐Mo in the electronic packaging industry16).

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High thermal conductive composites consisting of Al matrix and SiC particles have been reported by Chu et. al, who fabricated a SiC‐particle‐dispersed Al‐matrix composite by a metal infiltration technique and obtained a thermal conductivity of 163~186 W/mK for Al composites containing 50~65 vol.% SiC13, 14). Al‐matrix composites containing SiC particles are to date mainly fabricated by liquid metal infiltration into SiC preforms13, 14). This process often uses Al alloys with Si and/or Mg additions to avoid the formation of interfacial products such as Al4C3, leading to a detrimental effect on the thermo‐mechanical properties of the composites. When Si and Mg dissolve into the Al matrix, on the other hand, the thermal conductivity of the matrix decreases and lowers the thermal conductivity of the composites. In addition, it is difficult to make SiC particles dispersed homogeneously in the Al composite when it is fabricated by a metal infiltration technique. This is especially true when the composite contains a lower volume fraction of SiC, say less than 50 vol. %, because of the difference in packing density between SiC and Al. Spark plasma sintering (SPS)17‐25) applied as a new method for preparing high performance of Al‐matrix composites containing SiC has been presented recently15). The main advantage of the SPS process is to fabricate various materials for relatively short sintering times at low temperatures, leading to the prevention of Al4C3 at the interface between Al and SiC. Chu et. al fabricated SiC‐particle‐dispersed Al‐matrix composites by SPS and obtained a thermal conductivity of 224 W/mK for an Al‐55 vol.% SiC composite15). However, pores always appear in their study as an unavoidable structure in the Al‐matrix composites containing SiC fabricated in solid state by SPS, which leads to insufficient wetting between Al and SiC. This results in weak Al/SiC interfaces, especially, at high volume fractions of SiC particles. Pores considerably make the thermal conductivity of the Al‐matrix composites decrease due to scattering of the heat flow26).

To fabricate high‐performance thermal management materials with ultra‐high thermal conductivities and low CTEs, we have recently initiated a series of investigations, where diamond‐particle‐dispersed metal‐matrix composites27‐31) were fabricated by spark plasma sintering (SPS) process17‐25, 27‐34).

In our previous work, SiC‐particle‐dispersed Al‐matrix composites were fabricated in continuous solid‐liquid co‐existent state by SPS process, and the composites were shown to have high relative packing densities and good bonding between the Al matrix and the SiC particles. It was shown that the thermal conductivity was 252 W/mK at a SiC volume fraction of 50 vol.%32, 33) . It should be mentioned that, however, the thermal conductivity of Al‐matrix composite containing monomodal SiC particles decreases with increasing volume fraction of SiC particles when it is higher than 50 vol.%. This decrease of thermal conductivity is mainly caused by drastic declines of the relative packing density of the composite in a SiC fraction range higher than 50 vol.%.

In order to make Al‐matrix composites having both high thermal conductivity and low CTEs in a SiC fraction range higher than 50 vol.%, in the present work, composites containing bimodal SiC particles (hereafter called bimodal composites) were fabricated along with those composites containing monomodal SiC particles (hereafter called monomodal composites). In the present fabrication, a continuous solid‐liquid co‐existent state29‐33) was created during SPS process. Process temperatures employed were lower than the melting point of Al and SPS process parameters were optimized. Experimental results of thermal properties obtained from the monomodal and bimodal Al‐matrix composites are reported in the present study along with microstructures of the composites fabricated under various process parameters. The packing density, the thermal conductivity and the CTEs of the composites are measured, and the bimodal and monomodal SiC particle effect on the thermal property of the composites is evaluated.

Experimental Procedure According to three‐dimensional Euclidean space, the maximum volume fraction of SiC particles in Al‐matrix composite can ideally be 74 vol.% if SiC particles are spherical and of uniform size. Due to some experimental constraints, Al‐matrix composites are commonly produced with around 50 vol.% of SiC when roughly mono‐sized SiC particles are used. In the present study, two sizes of α‐SiC powders (i.e., GMF‐60FH2 SiCs with a mean particle diameter of 109.8μm and GMF‐800H2 SiCs with a mean particle diameter of 14.3μm, Pacific Rundum Co., Ltd.) were employed as a filler material. As a matrix material, two kinds of metallic powders, Mitsuwa 99.9% purity pure aluminum (Al) powder (150mesh) and Hikari Material Al‐5mass%Si alloy powder (70μm), were employed.

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Scanning electron micrographs of large SiC, small SiC, pure‐Al and Al‐5mass%Si powders used in the present study is shown in Fig. 1. As seen, the shapes of large SiC, small SiC, pure‐Al and Al‐5mass%Si powder provided by the above‐mentioned manufacturers are flat octahedron‐like for SiC, teardrop‐like for pure‐Al and spherical for Al‐5mass%Si powder, respectively. (a)

(b)

(c)

(d)

FIG. 1 SEM MICROGRAPHS OF AS‐RECEIVED (A) SIC (109.8ΜM), (B) SIC (14.3ΜM), (C) PURE AL AND (D) AL‐5MASS%SI POWDERS, SHOWING THE MORPHOLOGY OF THE POWDERS USED IN THE STUDY.

Al‐Si alloy powder is important to use in the present study for creating a solid‐liquid co‐existent state during SPS processing. We have developed unique SPS fabrication techniques to make metal‐matrix composites with or without dispersed SiC particles. The uniqueness is that during SPS process at a low pressure, continuous solid‐liquid co‐existent state of the metal powder mixtures was created by the nature of Al‐Si alloy. It should be pointed out that because of a low thermal conductivity (150 W/mK) of Al‐5mass%Si alloy powder16) and also because of necessity of avoiding drastic decrease in the thermal conductivity of Al matrix, an Al‐based powder mixture composed of 90 vol. % of pure Al powder and 10 vol. % of Al‐5mass%Si alloy powder was chosen in the present study as the matrix material.

The mixing ratio of large and small SiC particles is important in bimodal SiC particle mixture to achieve the high packing density of Al‐matrix composites containing SiC particles. In the present study, the optimum mixing ratio was determined as follows. When one puts a bimodal powder mixture into a container and tap the mixture, its porosity can be evaluated using Furnas model35), which is described here. Assuming (a) large particles are much larger in diameter than small particles, (b) the mass density of large particles is equal to that of small particles, and (c) small particles fill up the gaps between large particles, the porosityεof the bimodal powder mixture can be calculated in the following equation (1)

  1

1  1 (1) v1

where ε1 is the porosity when large particles are tapped into a container and v1 the volume fraction of large

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particles in a bimodal powder mixture composed of large and small particles. Also assuming (d) larger particles are intermingles with small ones, the porosity of the bimodal powder mixture can be calculated in the following equation (2)

  1

1 2 (2) 1  v1   2

where ε2 is the porosity when small particles are tapped into a container.

In Furnas model35) every v1 value is proposed to choose a larger value of porosity between ones calculated in equation (1) and in equation (2). In the present study, experimentally obtained porosities ε1 and ε2 values were 43.29% and 56.63%, respectively, after a hundred times of tapping of each powder mixture. Using these ε1 and ε2 values, the porosity (ε) of a bimodal SiC powder was calculated and the result obtained is shown in Fig. 2 as a function of v1. As seen, when the volume fraction of large SiC particles in the bimodal SiC powder is 75.1%, the porosity of the bimodal SiC powder becomes minimum and it is 24.5%. From this result, in the present study, a bimodal SiC powder mixture composed of 75.1 vol.% of large SiC particles and 24.9 vol.% of small SiC particles was used to try to obtain the high relative packing density of Al‐matrix composites containing SiC. Relative packing density is defined to be the ratio of the density of a material measured experimentally to the density of the material assumed to have no porosity.

60 56.6% 50 43.3%

Porosity, ε (%)

40

30 24.5% 20 75.1% 10

0 0

20

40

60

80

Volume fraction of large SiC particle. v1 (%)

100

FIG．2 CHANGE IN THE POROSITY OF THE SIC POWDER MIXTURE COMPOSED OF LARGE PARTICLES (109.8ΜM IN DIAMETER) AND SMALL PARTICLES (14.3ΜM IN DIAMETER) AS A FUNCTION OF THE VOLUME FRACTION OF LARGE SIC PARTICLES IN THE SIC POWDER MIXTURE.

Powder mixtures composed of four kinds of powders (large SiC, small SiC, Al and Al‐5mass%Si alloy powders) were prepared as starting materials, and these powder mixtures with various volume fractions of SiC were processed to fabricate Al‐matrix composites using an SPS equipment, Fuji Electric Industrial Dr. Sinter 1020. The equipment consists of an electric power source and a pressure system, and the fabrication of composites was carried out after powder mixtures were placed in a die‐set made of Co/WC composite. A side view of our custom‐made cylindrical Co/W composite die‐set used in the present study is depicted schematically in Fig. 3.

For making one disk‐shaped composite specimen with gauge dimensions of 2 mm thick and 10 mm in diameter, about 0.5 g of the powder mixture of SiC, Al and Al‐Si alloy was prepared and such a power mixture was placed carefully in the above described custom‐made die‐set, and consolidation was carried out. The gauge dimensions of the Co/WC composite die used in the present study are 35 mm in outside diameter, 10 mm in inside diameter and 40 mm high. During SPS processing, the die temperature was measured by a thermo‐couple that was placed in a position 5 mm distant from the inside of the die where a thermo‐couple hole was created on the outside surface of

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the die. The hole was 2 mm in diameter and 7.5 mm deep.

Pressure WC/Co punch

Pulsed current

WC/Codie

WC/Codie

Large SiC SiC β-Si particle Al alloy particle

K-Type

Al particle Small SiC particle

thermocouple

WC/Co punch Pressure

β-SiC SiC particle dispersed Al matrix composite

K-Type thermo couple

FIG. 3 PROCESSING OF SIC‐PARTICLE‐DISPERSED AL‐MATRIX COMPOSITE BY SPARK PLASMA SINTERING. PARTICLE,

: SMALL SIC PARTICLE,

: AL PARTICLE,

:LARGE SIC

:AL ALLOY PARTICLE.

The SPS process employed is described in detail as follows. First, the lower punch was inserted into the die from its one end, followed by pouring of 0.5 g of the powder mixture containing SiC particles. Then, the upper punch was placed onto the powder mixture. The powder mixture was pressed at a pressure of 80 MPa through the upper and lower punches, and then spark plasma sintering was performed after evacuation to a vacuum of 2 Pa. Sintering was then carried out at a heating rate of 0.83 K/s in a temperature range between R.T. and 798 K. After reaching 798 K, further sintering was carried out at a low heating rate of 0.05 K/s in a temperature range between 798 K and 876 K. When the temperature reached 876K, pulsed current was shut off and the pressure was immediately increased to 300 MPa. When the pressure reached 300 MPa, the mixed powder was kept for 0.18 ks at 876K and then furnace cooled. To visualize changes in the relative packing density of the Al/SiC composite during the SPS process, longitudinal displacements between the punches were monitored as a function of time and die temperature. The discharged pulsed current used was about 240 A and sparking was generated at a constant separation of time of approximately 2.78×10‐3s.

Disk‐shaped composites thus fabricated were examined by scanning electron microscopy using a JEOL JSM 6460 LA microscope. Al‐matrix composite disks containing SiC were gold‐coated and their thermal diffusivities were measured by a laser flash technique using a Netzsch LFA‐457 thermal constants analyzer. The achieved packing density of the disks was measured in Archimedes method for optimizing process parameters and for calculation of thermal conductivities. Coefficients of the thermal expansion (CTEs) of the composite were investigated on

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column‐shaped specimens, 5 mm in diameter and 15 mm long, fabricated from the powder mixture of SiC, Al and Al‐5mass%Si alloy by SPS under a similar processing condition mentioned above. The thermal expansion of the composite was measured with a Rigaku TMA8310 dilatometer in a N2 flowing atmosphere with a heating ratio of 3 K/min in a temperature range between 243 and 483 K. The CTEs at room temperature were determined from the slope of the thermal expansion against temperature curve in a temperature range between 288 and 298 K. Results and Discussion Relative Packing Density of Composites Fabricated by SPS The relative packing density of the SiC‐particle‐dispersed Al‐matrix composites fabricated was measured by Archimedes method. Figure 4 shows the measured values as a function of SiC volume fractions. The relative packing density of the monomodal composite was higher than 99% in a range of SiC volume fraction between 40% and 55%. However, in a range of SiC volume fraction higher than 55%, the relative packing density of the composite drastically decreases with increasing volume fraction of SiC. The relative packing density of Al‐60vol.% and Al‐65% SiC composite decreased to 98.9% and 95.1%, respectively. On the other hand, the bimodal composite maintained the relative packing density higher than 98% in a range of SiC volume fraction up to 65%. The present result evidently indicates that the consolidation of the composite containing the bimodal SiC particles is very effective in filling up pores present in metal‐matric composite containing SiC particles. In addition, it is suggested that the mixing ratio of large SiC particles to small ones estimated by Furnas model is appropriate for the decrease of the porosity in the SiC powder mixture used in the present study.

Relative packing debsity, Dr (%)

100

99

98

97 Monomodal

96

Bimodal

95 40

50

60

Volume fraction of SiC, Vf (%)

70

FIG. 4 CHANGES IN RELATIVE PACKING DENSITY OF SIC PARTICLE DISPERSED AL MATRIX COMPOSITE FABRICATED BY SPARK PLASMA SINTERING AS A FUNCTION OF THE VOLUME FRACTION OF SIC IN THE COMPOSITE.

Microstructure The mixtures of powders composed of pure Al, Al‐5 mass%Si alloy and SiC were compacted, consolidated and sintered in order to fabricate SiC‐particle‐dispersed Al‐matrix composites by SPS process. The microstructure of as‐sintered monomodal and bimodal composites containing 65 vol.% SiC was investigated by scanning electron microscopy. Figure 5 is scanning electron micrographs taken from cross sections of SiC‐Al composites consolidated in solid‐liquid co‐existent state by SPS. As seen in Fig. 5(a) and (c), there are some cavities in interfacial boundaries between the SiC particle and the Al matrix in the monomodal composite. In addition, some direct contacts between large SiC Particles in the composite are observed. On the other hand, cavities on the interfacial boundaries between the SiC particle and the Al matrix of the bimodal composite considerably decreases and the direct contacts between large SiC particles become negligible as shown in Fig. 5(b) and (d). It should be emphasized that the decrease of

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cavities and the SiC direct contacts in the latter composite is due probably to the effective filling up of gaps between large SiC particles by small SiC particles.

Monomodal

(a)

(b)

(c)

(d)

Bimodal

FIG．5 SEM MICROGRAPHS OF AL‐65VOL.% SIC COMPOSITES FABRICATED BY SPARK PLASMA SINTERING (SPS). (A) AND (C) FOR MONOMODAL; AND (B) AND (D) FOR BIMODAL.

The formation of Al4C3 phase was reported by Chu et al 13, 14) to occur on interfaces between SiC particle and pure‐Al matrix in Al‐SiC composites when fabricated by metal infiltration. In the present study, however, no such aluminum carbides were detected by scanning electron microscope observation, as shown in Fig. 5(b) and (d). To clarify whether or not Al4C3 is formed on such interfaces in the composite fabricated in the present study, further detailed microstructural investigation is underway by scanning transmission electron microscopy (STEM) with EDX analysis. The results will be soon presented elsewhere.

Thermal Conductivity Thermal conductivities were measured for SiC‐particle‐dispersed Al‐matrix composites fabricated by SPS process and the results obtained were plotted in Fig. 6 as a function of the volume fraction of SiC particles. As seen, at 40, 45 and 50 vol.% of the volume fraction of SiC, the thermal conductivity of the monomodal composite was 239, 245 and 252 W/mK, respectively. The thermal conductivity of the composite increased with increasing volume fraction of SiC in the SiC fraction range between 40% and 50%. It should be emphasized that this result indicates that the thermal conductance between SiC particles and the Al matrix is high and also indicates that damages in the surface region of the SiC particles are small or negligible during consolidation under continuous solid‐liquid co‐existent state in SPS processing. Similar results are also found in our previous works32‐34). It also should be pointed out that the thermal conductivity of the monomodal composite drastically decreased with increasing volume fraction of SiC in a fraction range higher than 50% and reached 171W/mK in a SiC fraction of 65%. The decrease in the thermal conductivity of this composite is considered to be caused by reduction in the relative packing density of the

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composite in a SiC fraction range higher than 50 vol.%.

Thermal conductivity, λ/(W/mK)

300

250

200

150

Monomodal Bimodal;

100 40

50

60

Volume fraction of SiC, Vf (%)

70

FIG. 6 CHANGE IN THERMAL CONDUCTIVITY OF SIC‐PARTICLE‐DISPERSED AL‐MATRIX COMPOSITE FABRICATED BY SPARK PLASMA SINTERING (SPS) AS A FUNCTION OF THE VOLUME FRACTION OF SIC PARTICLES IN THE COMPOSITE.

As seen in Fig. 6, at 55, 60, 65 and 70 vol.% of the volume fraction of SiC, on the other hand, the thermal conductivity of the bimodal composites was 243, 239, 226 and 212 W/mK, respectively and it is also decreased with increasing volume fraction of SiC in a SiC fraction range between 55 and 70 vol.%. However, the thermal conductivity of the bimodal composite decreased gradually as compared with that of the monomodal composite, and it should be mentioned that the thermal conductivity higher than 210W/mK was maintained even in a SiC fraction range of 70 vol.%.

The thermal conductivity of the Al‐matrix composite containing dispersed SiC particles fabricated in the present study was compared with those of a similar composite fabricated by Chu et. al using SPS15). The Al‐matrix SiC‐dispersed composite fabricated in the present study showed higher values of thermal conductivity. That is, the thermal conductivity in the present study is 239‐252 W/mK in a volume fraction range of SiC between 40 and 55 %, whereas it was 211‐224 W/mK in a volume fraction range between 50 and 60 % for the case of Chu et. al15). The thermal conductivity difference between these two cases can be explained as follows. <1> Although similar SPS process was used in both studies, the state of composite materials during SPS process was different. That is, SiC particle‐dispersed Al‐matrix composite was fabricated in continuous solid‐liquid co‐existent state by SPS process in the present study, whereas that was fabricated in solid state in the study by Chu et. al 15). The bonding between the SiC particle and the Al matrix in continuous solid‐liquid co‐existent state would be stronger than that between the SiC particle and Al matrix fabricated in solid state. <2> The formation of Al4C3 often occurs by direct contact between molten Al and SiC particles during consolidation, resulting in a detrimental effect on the thermal conductivity of Al‐matrix composites containing dispersed SiC particles 13, 14, 36). In the case of the continuous solid‐liquid co‐existent state during SPS, molten areas in the Al matrix change their locations every moment with increasing the die temperature at a slow heating stage, resulting in no formation of Al4C3 because of a short time of contact between molten Al and SiC particles32‐34). <3> A two‐stage pressing scheme37) from 80 to 300 MPa was employed during SPS consolidation in the present study. This pressing scheme would be effective not only in minimizing pores or porosities but also in making strong bonding between the Al matrix and the SiC particles in Al‐matrix composite containing dispersed SiC particles37).

The thermal conductivity of the Al/SiC composite fabricated in the present study was also compared with those of a similar composite fabricated by Chu et. al using metal infiltration technque13, 14). The Al‐matrix SiC‐dispersed composite fabricated in the present study showed higher values of theral conductivity. The thermal conductivity in the present study is 210‐252 W/mK in a volume fraction range of SiC between 40 and 70 %, whereas it was 145‐186

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W/mK in a volume fraction range between 45 and 65 % for the case of Chu et. al 13, 14).

The lower thermal conductivity for the case of Chu et. al 13, 14) can be explained as follows. Chu et. al 13, 14) fabricated Al/SiC composites by liquid metal infiltration technique using not pure Al but Al alloys with Si and/or Mg additions as a matrix material to avoid the formation of interfacial products such as Al4C3. When Si and Mg dissolve into the Al matrix, the thermal conductivity of the matrix decreases and the low thermal conductivity of the matrix decreases the thermal conductivity of the composites.

Although high thermal conductivity was obtained for Al/SiC composite fabricated in the present study, gradual decrease in the thermal conductivity of Al/SiC compositere with increasing volume fraction of SiC in a SiC fraction range between 55 and 70 vol.% as mentioned above. The gradual decrease in the thermal conductivities of the bimodal composite may be caused by the following two reasons: 1 the thermal conductivity of small SiC particles is lower than that of large SiC particle due to the purity of small SiCs, which is lower than that of large ones; and 2 the thermal conductance between small SiC particles and the Al matrix is lower than that between large SiC particles and the Al matrix, which may be caused by insufficient mixing of small SiC particles with Al matrix particles. That is, higher thermal conductivity may be obtained for SiC‐particle‐dispersed Al‐matrix bimodal composite by using small high‐purity SiC powder, by optimization of the mixing of SiC and Al matrix powders, and by using Al matrix particles much smaller than SiC particles.

Coefficients of Thermal Expansion Two models by Turner38) and by Kerner39) have been proposed to calculate theoretical coefficients of thermal expansion (CTEs) of a composite material37‐41). Kerner model takes shear effects into account at boundaries between particles and the matrix, whereas Turner model does not take such effects into account. Consequently, Kerner model has widely been used for theoretical evaluations of the CTEs of composite material. Hence, we also utilize Kerner model in the present study to evaluate CTEs of the composites fabricated. Kerner model can be expressed in equation (5),

 c   m .Vm   d Vd  Vd Vm ( d   m ) 

Kd  Km (5) Vm K m  Vd K d  (3K d K m / 4Gm )

where αc is the coefficient of thermal expansion of the composite, αd the coefficient of thermal expansion of the dispersions (in this case, SiC, 4.5×10‐6/K), αm the coefficient of thermal expansion of the matrix (in this case, aluminum, 24.0×10‐6/K), Vd the volume fraction of the dispersions in the composites, Vm the volume fraction of the matrix in the composites, Kd the bulk modulus of the dispersions (in this case SiC, 2.2×1011 Pa), Km the bulk modulus of the matrix (in this case, aluminum, 7.6×1010 Pa) and Gm the shear modulus of the matrix (in this case, aluminum, 2.6×1010 Pa), Figure 7 shows the comparison between theoretically predicted and experimentally obtained CTEs for the SiC‐particle‐dispersed Al matrix composites. Kernerʹs upper line is obtained by considering Al as the matrix of the composite, whereas its lower line is obtained by considering the dispersed SiC as the matrix. For comparison, a theoretically‐obtained curve using Turnerʹs model is also shown. Shown in this figure are the two lines obtained by reversing the role of matrix and dispersions in Kerner model. Experimentally obtained CTEs of the composites is seen to fall in the upper line of Kerner model. The CTEs of the Al‐matrix composites containing monomodal SiC particles obtained in the present study are 14.3×10‐6/K at 40 vol.% SiC and 12.5×10‐6/K at 50 vol.% SiC. In addition, the CTEs of Al‐matrix composites containing bimodal SiC particles are 9.88×10‐6/K at 65 vol.% SiC and 9.39×10‐6/K at 70 vol.% SiC. This result indicates that the SiC particles have bonded well to the Al matrix in the composite fabricated by SPS. The CTEs of Al‐matrix composite with SiC obtained in the present study are 14.3 and 12.5×10‐6/K at 42.8 and 51.9 vol.% SiC, respectively. Considering into account 4~8×10‐6/K of the CTEs for some packaging base materials currently in use, it should be appropriate to add more SiC particles to Al‐matrix composites to meet suitable conditions as heat spreaders. In other words, Al‐matrix composites containing SiC higher than 75 vol.% would be more preferable in applications.

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Coefficient of thermal expansion, α(×10-6)

25 Turner line Kerner lower line Kerner upper line

20

Expermental(Monomodal) Experimental(Bimodal)

15

10

5

0 0

20

40

60

80

Volume fraction of SiC, Vf (%)

100

FIG. 7 COMPARISON OF COEFFICIENTS OF THE THERMAL EXPANSION PREDICTED THEORETICALLY USING KERNER MODEL FOR AL AND SIC COMPOSITE AND THOSE OBTAINED EXPERIMENTALLY FOR AL AND SI COMPOSITE CONTAINING 40, 50, 65 AND 70 VOL.% SIC PARTICLES.

Summary Two kinds of SiC‐particle‐dispersed aluminum (Al) matrix composites containing monomodal and bimodal SiC particles were fabricated in a unique fabrication method, where the powder mixture of SiC, pure Al and Al‐5mass% Si alloy was used to form continuous solid‐liquid co‐existent state during spark plasma sintering (SPS) process. Microstructures and thermal properties of the composites fabricated in such a way were investigated and the bimodal and monomodal SiC particle effect on the thermal properties of the composites was evaluated. The composites were well consolidated in the temperature range between 773 K and 878 K and scanning electron microscopy detected no reaction product at the interface between the SiC particle and the Al matrix. The relative packing density of the composite containing monomodal SiC particles decreased from 98.9 to 95.1 % with increasing SiC volume fraction in a volume fraction range between 50 and 60 %. However, the relative packing density of the composite containing bimodal SiC particles became higher than 98% in a SiC volume fraction range up to 65%. The thermal conductivity of this composite was higher than that of the composite containing monomodal SiC particles in a SiC volume fraction range higher than 55%. Although the thermal conductivity of the bimodal composite decreased gradually in a SiC fraction range between 55 and 70%, the thermal conductivity higher than 210W/mK was maintained for the bimodal composite even in a SiC fraction range of 70 vol.%. The coefficients of the thermal expansion, CTEs, of Al‐matrix composites containing SiC particles fell in the upper line of Kerner model, indicating good bonding between the SiC particle and the Al matrix in the composite.

ACKNOWLEDGEMENT

This work was carried out with the support of JSPS KAKENHI Grant Number 26420751. The authors wish to express their appreciation for this support.

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