Microstructure and thermal expansion behavior of ...

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ScienceDirect Journal of the European Ceramic Society 34 (2014) 1139–1147

Microstructure and thermal expansion behavior of diamond/SiC/(Si) composites fabricated by reactive vapor infiltration Zhenliang Yang a,b , Xinbo He a,∗ , Ligen Wang b , Rongjun Liu c , Haifeng Hu c , Limin Wang b , Xuanhui Qu a a

School of Materials Science and Engineering, University of Science & Technology Beijing, Beijing 100083, PR China b Gripm Advanced Materials Co., Ltd, Beijing 101407, PR China c College of Aerospace and Materials Engineering, National University of Defense Technology, Changsha 410073, PR China Received 25 August 2013; received in revised form 22 October 2013; accepted 25 October 2013 Available online 6 December 2013

Abstract Diamond/SiC/(Si) composites were fabricated by Si vapor vacuum reactive infiltration. The coefficient of thermal expansion (CTE) of composites have been measured from 50 to 400 ◦ C. With the diamond content increasing, CTE of composite decreased, simultaneously, the microstructure of the composites changed from core–shell particles embedded in the Si matrix to an interpenetrating network with the matrix. The CTEs of composites versus temperature matched well with those of Si. The Kerner model was modified according to the structural features of the composites, which exhibited more accurate predictions due to considering the core–shell structure of the composites. The thermal expansion behavior of the matrix was constrained by diamond/SiC network during heating. © 2013 Elsevier Ltd. All rights reserved. Keywords: Sintering; Composites; Thermal properties; SiC

1. Introduction With booming development of electronic industry and rapid extension of market demand, miniature and high-power design of electronic devices are continuously adopted. The diamond/SiC/(Si) composites exhibits density of 3.0–3.4 g cm−3 , Vicker’s hardness of 31–100 GPa,1,2 fracture toughness on the order of 7.8 ± 1.3,1 bending strength of 400–750 MPa3 and thermal conductivity up to 600 W m−1 K−1 ,4 which is deemed one of the most potential packaging materials for high-performance electronic equipment. During the last decade there has been an explosion of research on the diamond reinforced SiC or Si.1,3,5–8 However, up to now most of the literatures were related to the preparation techniques and mechanical properties of the diamond/SiC/(Si) composites. Only a limited number of literatures were reported about the thermal properties of the composites, especially the thermal expansion behavior.

∗

Corresponding author. Tel.: +86 10 62332727; fax: +86 10 62334311. E-mail addresses: [email protected] (Z. Yang), xb [email protected] (X. He). 0955-2219/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jeurceramsoc.2013.10.038

In this paper, diamond/SiC/(Si) composites were prepared by reactive vapor infiltration, which is a cost-effective and timesaving process. The CTEs of the diamond/SiC/(Si) composites in the range of 50–400 ◦ C were measured. The experimental results and the theoretical predictions of CTEs were synthetically compared and discussed. The effects of volume fraction, particle size and shape of diamond on the CTEs of the composites were investigated. 2. Experimental 2.1. Preparation The synthetic diamond powders were purchased from Henan Famous Diamond Industries Co., Ltd. Monocrystalline diamond (MCD, MBD-6 grade) with average particle diameter about 55 ␮m, 110 ␮m, and abrasive polycrystalline diamond (PCD) with average particle diameter about 30 ␮m, 55 ␮m and 110 ␮m were used. The PCD particles were not diamond–cobalt. Phenolic resin powder of the type 2123#-1 was supplied by Henan Zhenzhou Hengtong Chemical Co., Ltd. Silicon powders (purity > 99.99%) with average particle diameter about 1–10 ␮m

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3. Results and discussion 3.1. Microstructure

Fig. 1. Processing route of diamond/SiC/(Si) composites by Si-vapor reactive infiltration.

and graphite powders (purity > 99%) with particle diameter below 50 ␮m were used. The fabrication process of the composites was described in ref. [9], as shown schematically in Fig. 1. In brief, diamond particles were purified by acid cleaning, and then mixed with other raw materials in ethanol for 16 h. The mixed powders were pressed into green compacts, and pyrolyzed at 1100 ◦ C with the heating rate of 0.5 ◦ C min−1 in flowing Ar. Subsequently, the preforms were infiltrated by gaseous Si at 1600 ◦ C for 1 h with heating rate of 10 ◦ C min−1 under vacuum (≈1 Pa). 2.2. Characterization Porosity and density of the specimens were measured by Archimedes’ method. The microstructure of diamond/SiC/(Si) composites was observed on the scanning electron microscopy (SEM, LEO1450). The compositions of the samples were analyzed by energy dispersive X-ray (EDX). The CTE at specific temperature was measured on a DIL 402C Dilameter (NETZSCH Corp.) at the temperature range of 50–400 ◦ C with a heating rate of 5 ◦ C min−1 , under an argon atmosphere with flowing rate of 50 ml min−1 . The specimens with the dimension of 25 mm × 4 mm × 3 mm were used. In view of the difficulty of measuring the content of component in the composites directly, the volume of the diamond added in the green compact is assumed to be constant during the pyrolysis and infiltration processes. The volume fraction of SiC and Si in the composites was determined from measurement of the density, which applies the rule of mixture with the determined diamond volume fraction.9 The parameters of the single phase components used for the modeling were listed in Table 1.10–13

Fig. 2 shows the SEM morphology of the diamond used in this work. The abrasive PCD exhibits an irregular shape, and obvious surface defects. The MCD exhibits a cubo-octahedral morphology with smooth surface and few structural defects. The microstructures of the resultant materials with various diamond particles are shown in Fig. 3. It can be clearly seen that the diamond particles are dispersed in the matrix homogeneously (Fig. 3a and b), which follow a transgranular fracture mode. Fully dense composites without pores or cracks, indicates a strong interfacial bonding. There are no evidences of graphitization of diamond which are beneficial to the interfacial bonding and properties of the composites. Fig. 3c–f shows the backscattering electron images of the fractural surface. The dark, gray and light phases were identified as diamond, SiC and Si by EDX analysis, respectively. For the composites with 30 vol.% (Fig. 3c) and 32 vol.% (Fig. 3e) of diamond, it can be clearly observed that diamond particles are coated by reaction formed SiC layer with thickness about 10 ␮m. The core/shell diamond/SiC particles are uniformly distributed in the Si matrix. For the composites with 49 vol.% (Fig. 3d) and 43 vol.% (Fig. 3f) of diamond, the diamond particles are nearly densely packed, and the content of Si decreases sharply. It is noted that the interconnected diamond/SiC core/shell particles form a continuous network structure interpenetrating Si matrix. The structural changes can be explained by the different structure of the preforms and the structural evolution of the specimens. Green compacts with lower volume fraction of diamond results in larger porosity and pore size of the preforms. In the initial stage of infiltration, Si vapor penetrates into the pore channels of the preform, and reacted with the pyrolytic carbon on diamond. Simultaneously, diamond was isolated from Si by the reaction-formed SiC protective layer, and the Si–C reaction on diamond was slowed down gradually. Finally, crevices between the isolated diamond/SiC core/shell particles were filled with the concentrated Si after the infiltration (Fig. 3c and e). On the contrary, the distance between diamond particles in the preform decreased with increasing content of diamond. The interstice between diamond particles was partially filled with graphite and Si powders. As a result, the interconnected SiC reaction layer around diamond formed a network structure. In order to confirm the inference, the composites with 30–50 vol.% diamond were eroded with HF/HNO3 solution (3:1 mole ratio) to remove the free Si. Fig. 4a reveals that diamond particles are coated with SiC layer, and the diamond/SiC particles are isolated with each other. Fig. 4b displays that most of the diamond/SiC particles are interconnected. The interstice between these particles is broad and continuous, indicating an interpenetrating network (IN) structure of the composites. Fig. 4c shows that the diamond/SiC particles are closely packed. The channel pore size is small, and the channels are partly discontinuous. These results are in good agreement with the inference about the microstructural evolution of the composites. The previous studies9 suggest that the graphitization of


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Table 1 The temperature dependence of elastic moduli E (GPa), Poisson’s ratio v, and CTE (×10−6 K−1 ) of diamond, SiC and Si used for the modeling. Ingredients T (◦ C)

E 50 100 150 200 250 300 350 400

SiC

Diamond

895

v

CTE

0.24

1.18 1.52 1.87 2.21 2.54 2.84 3.12 3.37

diamond are avoided during the reactive vapor infiltration process at 1600 ◦ C. These reasons are speculated to be the removal of catalysts on diamond by pickling and the isolation of catalysts from diamond by the protective layers (phenolic resin, pyrolytic carbon and reaction-formed SiC) during the infiltration. Furthermore, growth of SiC surround diamond particles would constrain the expansion behavior of diamond and increase the pressure on diamond.14–16 The graphitization behavior of diamond will be investigated in the subsequent research. 3.2. Thermal expansion behavior of the composites Fig. 5a shows the CTE of the diamond/SiC/(Si) composites versus volume fraction of diamond. The CTE of the composites is lower than that of most of the MMCs, and decreases with increasing the volume fraction of diamond. CTE of the samples are measured to be in the range of 1.81–2.14 × 10−6 K−1

E

475

Si v

CTE

0.18

2.78 3.09 3.63 4.16 4.39 4.62 4.76 4.89

E

113

v

CTE

0.22

2.79 3.11 3.34 3.53 3.67 3.79 3.89 3.98

with diamond content between 31 and 51 vol.%. These values are similar with the results reported by Zhu et al.6 The slightly lower CTE values in this work may be attributed to the stronger interfacial bonding and lower amount of Si. The CTEs of the samples determined by different diamond particle sizes are in the order of 30 ␮m PCD < 55 ␮m MCD < 110 ␮m MCD < 55 ␮m PCD. Higher volume fraction (about 51 vol.%) of diamond is obtained for the MCD-containing samples, resulting in lower CTE of about 1.8 × 10−6 K−1 . It suggests that high content, high grade and small particle size of diamond would lead to low CTE of the composites. This may be attributed to the intrinsic CTE, particle shape and specific surface area of diamond.17 Firstly, due to the much lower intrinsic CTE of diamond particle compared to SiC and Si (Table 1), it impose significant constraint on the matrix, hence the CTE decreases with increasing diamond content.

Fig. 2. SEM images of the diamond particles: (a) 30 ␮m PCD, (b) 55 ␮m PCD, (c) 55 ␮m MCD and (d) 110 ␮m MCD.

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Fig. 3. SEM micrographs of diamond/SiC/(Si) composites with varied diamond: (a) secondary electron image, 48 vol.% 110 ␮m MCD; (b) 44 vol.% 55 ␮m PCD; (c) backscattering electron image, 30 vol.% 110 ␮m MCD; (d) 49 vol.% 110 ␮m MCD; (e) 32 vol.% 55 ␮m PCD; (f) 43 vol.% 55 ␮m PCD.

Secondly, the PCD is irregular, suggesting more defects compared to the spherical MCD. As a result, shear modulus and bulk modulus of PCD are lower than those of the MCD, which results in higher CTE of the PCD. Besides, irregular shape of PCD may introduce more complex stress, which may promote the expansion of the matrix to some extent. Therefore the composites with

55 ␮m PCD show the highest CTE value with a certain volume fraction of diamond. Thirdly, particle sizes obviously affect CTE of the composites. The composites with 30 ␮m PCD exhibit the lowest CTE. Smaller particle size leads to larger specific surface area and greater number of the diamond particles. The total interface

Fig. 4. SEM images of the composites eroded by HF/HNO3 solution: (a) volume fraction of diamond 28 vol.%, (b) volume fraction of diamond 41 vol.% and (c) volume fraction of diamond 51 vol.%.


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Fig. 5. Experimental CTEs of various diamond/SiC/(Si) composites versus: (a) volume fraction of diamond; (b) temperature of the composites, volume fraction of diamond about 32 vol.%.

between diamond and the matrix increases with decreasing size of diamond particle. Therefore, diamond particles with smaller size are more effective in restricting the expansive behavior of the matrix with increasing temperature.17 Fig. 5b depicts the evolution of CTE with increasing temperature for the samples containing about 32 vol.% diamond. As a whole, the CTE value shows a linear growth at temperature range of 50–200 ◦ C, and then the curves are slightly flat during heating up to 400 ◦ C. Identical order of CTE increasing magnitude with Fig. 5a is also observed in Fig. 5b (30 ␮m PCD < 55 ␮m MCD < 110 ␮m MCD < 55 ␮m PCD). Owing to the decreasing of yield strength with increasing temperature, the change in slope of the CTE curves may be attributed to the release of residual and elastic stress of the composites.18,19 At the beginning, there is a relaxation of residual stresses, the CTE curves are commonly steep. With the relaxation of residual stresses, a stress-free state appeared in the composite, resulting in smooth growth of CTE. The CTE curves of the composites with PCD are steeper than those with MCD, indicating more complex stress state in the composites. The disparity of value between the CTE curves indicates that the influence mechanisms of diamond on CTEs at different temperatures are consistent with the analysis mentioned in Fig. 5a. It is worth noting that the CTEs of the diamond/SiC/(Si) composites matches well with that of Si substrate at the temperature of 50–400 ◦ C. Therefore, it is believed that the diamond/SiC/(Si) composites have huge commercial potential.

where αc is the CTE of the composites, αi and Vi are the CTE and volume fraction of the phase i in the composites, respectively. The Turner model21 assumes that the contraction of each particle is the same as the overall contraction and only uniform hydrostatic stresses exist in the composite. Thus the stresses are insufficient to disrupt the composite, and no cracks are developed during heating. Each component in the composite, which is constrained to change dimensions with temperature, changes at the same rate as the composite, and the shear deformation is negligible. Considering a balance of internal average stresses, the CTE of a multiphase composite is given by the following formula:

3.3. Theoretical predictions of CTE

Upper bound :

The influencing factors of plasticity and the internal structure are complicated, hence the CTEs of the CMCs are difficult to be predicted precisely. Several analytical models have been reported to predict the theoretical CTE of multiphase composites. In the case that the modulus of the matrix is much smaller than that of the reinforcement, if the constraint effect of matrix on the particles is ignored, the CTE of the multiphase composite is expressed as rule of mixture (ROM)20 : αc =

αi Vi

α i Ki V i αc = K i Vi

(2)

where Ki is bulk modulus of the phase i in the composites. The Schapery model22 assumes that the Poisson’s ratios of the components are not different. Bounds on effective CTEs of isotropic and anisotropic composites consisting of elastic phases are derived by employing extremum principles of thermo-elasticity combined with the use of Hashin’s bounds for the composite’s bulk modulus. The lower and upper bounds for the CTE of a multiphase composite which have isotropic reinforcement in an isotropic matrix are given by: αuc = α¯ + ·

Lower bound :

(1)

K i αi Vi − α¯ ¯ K

(1/KL ) − (1/Kc ) + αc ¯ (1/KL ) − (1/K)

αlc = α¯ + ·

(3)

K i αi Vi − α¯ ¯ K

(1/KL ) − (1/Kc ) − αc ¯ (1/KL ) − (1/K)

(4)

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αc =

((1/Kc ) − (1/K))1/2 ((1/KL ) − (1/Kc ))1/2 ¯ (1/KL ) − (1/K) 2 2 1/2 K i αi Vi 1 K i α i Vi 1 2 K i αi Vi − − − α¯ − ≥0 ¯ ¯ ¯ K K K KL

where superscripts l and u represent the lower and upper bounds, ¯ KL are volume average of CTE, Voigt bulk ¯ K, respectively. α, modulus and Reuss bulk modulus of the composites, which are expressed as: αi V i (6) α¯ = ¯ = K Ki Vi (7) KL =

Vi Ki

−1 (8)

The bulk modulus Kc of a composite in Eqs. (3)–(5) are derived from the upper and lower bounds of the bulk modulus of composite, which are calculated from Hashin and Shtrikman (H-S) bounding solutions.23 The Kerner model24 assumes that spherical reinforcement is enclosed and wetted by a uniform layer of matrix. The composites are assumed to be macroscopically isotropic and homogeneous. Thus, the CTE of the composite is stated to be identical to that of a volume element composed of a spherical reinforcement particle surrounded by a shell of matrix, and both phases having the volume fraction present in the composite.10 If the normal and shear stress are taken into account, the CTE of a multiphase composite can be expressed as: 4Gc Ki − Kc αc = α i Vi + αi Vi Kc 4Gc + 3Ki Gc αi Vi = 4 +3 (9) Kc 4Gc /Ki + 3 where Kc and Gc represent bulk modulus and shear modulus of the composites. According to the SEM images of the diamond/SiC/(Si) composites (Fig. 3 and Fig. 4), it can be predicted that the Kerner model is the most appropriate analytical model for predicting the effective CTE αc of diamond/SiC/(Si) composites fabricated by reactive vapor infiltration. The CTE αc is calculated from the Kc and Gc of the composites base on Eq. (9). However, it is difficult to accurately measure the elastic modulus of CMCs, especially for the diamond/SiC/(Si) composites. To overcome this problem, three different methods are adopted to calculate the Kc , Gc and αc of diamond/SiC/(Si) composites: (1) Bulk modulus and shear modulus of the composites are calculated based on the simplest rule of mixtures. Then Kerner model for a three-phase system are used to calculate the αc . This method is marked as Kerner-1. (2) The composites are considered as macroscopical isotropy and quasi-homogeneous three-phase. The upper and lower bounds of the bulk modulus and shear modulus of the composites are calculated from H-S model.23 Subsequently, the

(5)

extremum of predicted αc is calculated from Eq. (9). This method is marked as Kerner-2. (3) Assume spherical diamond particle is surrounded by a shell of SiC matrix, the upper and lower bounds of the CTE (αDia|SiC ), bulk modulus (KDia|SiC ) and shear modulus (GDia|SiC ) of the diamond/SiC core/shell particle are calculated based on Kerner and H-S model for a two-phase system. Then the diamond/SiC/(Si) composites are considered as spherical diamond/SiC particles embedded in the Si matrix, and the extremum of αc is derived from Kerner model for a two-phase system. This method is marked as Kerner-3. The experimental data are compared to the calculated CTEs according to above methods using the materials parameters given in Table 1. Fig. 6 compares the experimental and predicted CTEs of the composites (about 40 vol.% 55 ␮m MCD) as a function of temperature. The Kerner-1 curve exhibits an obvious downward deviation from the experimental curve. The experimental curve locates between the bounds of both Kerner-2 and Kerner-3 models in the whole temperature region. The Kerner-3 curves show more accurate upper and lower bounds compared to the Kerner-2 curves, and the CTE of the composites is close to the upper bound of the Kerner-3 model. In view of the fact that ROM does not take into account the mechanical constraint created on the matrix due to particles, the bulk modulus and shear modulus of the diamond/SiC/(Si) composites are overestimated. Thus, the CTE of the composites is underestimated according to the Kerner-1 model. The Kerner-2 and Kerner-3 models are consistent well with the experimental data, suggesting that the H-S bounding solutions are more suit to predict the elastic modulus of the diamond/SiC/(Si) composites. Such good agreement also indicates that the actual stress state and elastic modulus of

Fig. 6. CTEs of diamond/SiC/(Si)composites with about 40 vol.% 55 ␮m MCD and the comparison between various Kerner predictions and experimental data versus temperature.


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Fig. 7. CTEs of diamond/SiC/(Si)composites with about 32 vol.% diamond and the comparison between predictions and experimental data versus temperature.

the composites are closer to the assumption of Kerner-3. The upper and lower bounds of CTE are derived from the upper and lower bounds of H-S model, respectively. The upper bound of H-S model refers to spherical reinforcement with higher elastic modulus distributing in the matrix with lower elastic modulus in a particular way. The lower bound of H-S model refers to spherical reinforcement with lower elastic modulus distributing in the matrix with higher elastic modulus.23,25 Hence, the actual value of CTE of the composites should be closer to the upper bound of Kerner-3 model, which is confirmed in Fig. 6. Further investigation of CTE was applied by comparing the experimental data to the theoretical predictions of Kerner models. For the Kerner model, the resultant materials are assumed as isotropic three-phase composites with special core–shell structure (Kerner-3). Fig. 7 depicts the experimental and predicted CTEs of the composites (about 30 vol.% diamond) as a function of temperature. The Kerner model is superior to the Turner model and Schapery model due to the following reasons. (1) Turner model neglects the interfacial shear stress in the composite, and it estimates the CTE of the composite based on the bulk modulus of particle and matrix. But the bulk modulus of the reinforced particles is much larger than that of the matrix. Thus the calculated CTEs will be lower than the experimental data.

(2) Schapery model assumes that there is perfect bonding between the phases.17 However, the interfacial bonding between the reinforced particles and the matrix exist defect. Beside, Schapery model considers that diamond and SiC particles uniformly distribute in the Si matrix. In fact, diamond is isolated from Si by the reaction-formed SiC layer (Fig. 3 and Fig. 4), and the matrix is reinforced by the particles with core/shell structure. Thus, the measured CTEs of all the composites lie between the lower and upper Schapery bounds at the temperatures between 50 and 400 ◦ C. Hence the extremum of Kerner model are more precise than those of Turner model and Schapery model. The experimental CTE in Fig. 7a and d is consistent well with the upper Kerner bound, which is similar to the thermal behavior described in Fig. 6. The experimental data in Fig. 7b are higher than the predictions of the upper Kerner bound in the temperature of 50–300 ◦ C. Then the CTE curve falls below the predicted curve in the temperature range from 300 to 400 ◦ C. The CTE value is underestimated owing to the assumption that diamond particles are spherical and isotropic. In fact the shape of the 55 ␮m PCD is extremely irregular (Fig. 2), the lower elastic modulus and more complex stress state of the 55 ␮m PCD in the composites would result in the higher CTEs. The CTE curves drop slightly at high temperature, which is explained by the reduction of internal stresses in the matrix. The reduction of internal

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Fig. 8. CTEs of diamond/SiC/(Si)composites with about 50 vol.% diamond and the comparison between predictions and experimental data versus temperature.

stresses is caused by the decreasing mismatch strains and their more uniform redistribution during heating.18 It is observed that the CTE curve of the composites with 30 ␮m PCD (Fig. 7a) is slightly lower than the upper Kerner bound. This is because CTE of the composites with 30 ␮m PCD is much lower than that with 55 ␮m PCD (Fig. 5). The upper and lower bounds are close to each other in Fig. 7c, and the experimental curve is close to the lower Kerner bound. Because more graphite was added in the green body, the content of residual Si in the composites reduced significantly at a low volume fraction of diamond. The reduction of free Si changes the role of the reinforcement from a dispersion phase into a percolating network interpenetrated with the matrix. At the same time, the matrix turns into reinforcement to some extent. Therefore, the lower Kerner bound should represent the elasticity dominated behavior. Fig. 8 shows the experimental and predicted CTEs of the composites (about 50 vol.% diamond) as a function of temperature. Similarly, the Kerner model is more suitable for theoretical predictions comparing with the Turner and Schapery models. With increasing the volume fraction of diamond, CTEs of the composites decrease significantly. Fig. 8b shows that the experimental values of CTEs of composites match well with the predicted values. The experimental curves in Fig. 8a and c exhibit greater deviation from the upper Kerner bound than those of Fig. 8d. These results are ascribed to the formation of the IN structure in the composites (Fig. 4). The interconnected, threedimensional networks of reinforcement are quite stable during

heating. Relative movement of the particles is prevented by the rigid diamond/SiC network, and the matrix expansion is submitted to hydrostatic stress components.26 As a result, the thermal expansion behavior is effectively constrained, which is also confirmed in Fig. 8. The good accordance between the predicted CTEs and the experimental data in Fig. 8b suggests that the expansion behavior caused by the irregular diamond particles is offset by the constraint of the diamond/SiC network. The little deviation in Fig. 8d is explained by the higher content of residual Si. At a volume fraction of about 50 vol.%, the diamond particles are nearly closely packed. Since larger diameter will lead to greater gap for the close packed spherical particles, the amount of residual Si is larger in the composites of 110 ␮m MCD. Besides, larger particle size of diamond results in smaller diamond/SiC interface and higher CTE of the composites. 4. Conclusions Fully densified diamond/SiC/(Si) composites with extremely low CTE values were produced by vacuum reactive vapor infiltration. The influence of diamond with different volume fractions, morphologies, and particle sizes on the microstructure and CTE of the composites were investigated systematically. The main conclusions can be drawn from the experimental results. (1) When volume fraction of diamond is lower than 30 vol.%, the diamond particles were coated by the reaction-formed


(2)

(3)

(4)

(5)

SiC layers. The composites were characterized as diamond/SiC core/shell particles distributed in the Si matrix. When volume fraction of diamond is higher than 40 vol.%, the diamond/SiC core/shell particles were closely packed, and the diamond/SiC/(Si) composites formed an interpenetrating network structure. Due to the low intrinsic CTE of diamond, the CTEs of the composites decreased with increasing the diamond content. The CTEs of 1.81–2.14 × 10−6 K−1 were achieved for the composites with 31–51 vol.% diamond. The irregular shape reduced the elastic modulus of diamond and introduced complex stress state in the composites, resulting in higher CTE of the composites. Smaller particle size of diamond implied larger diamond/SiC interface and lower CTE of the composites. The CTE curves of composite rise with increasing temperature. Due to the relaxation of elastic stresses of the matrix, the growth rate of CTE curves slow down with increasing temperature. The CTE values of the composites matched well with those of Si in the temperature range of 50–400 ◦ C. The modified Kerner analytical model based on the assumption of diamond/SiC particles with core/shell structure and the H-S bounding solutions exhibited higher accuracy than other thermo-elastic models. For the particle reinforced composites, the CTE values of the composites were in good agreement with the upper Kerner bound due to the higher elastic modulus of the reinforcement. For the composites with an interpenetrating network structure, the CTE curves slightly deviated from the upper Kerner bound, which is attributed to the effective constraint by the rigid diamond/SiC network.

Acknowledgments The research was financially supported by the National Natural Science Foundation of China (Grant no. 51274040), National 973 Program (2011CB606306) and the Fundamental Research Funds for the Central Universities (FRF-TP-10-003B). References 1. Voronin G, Zerda T, Qian J, Zhao Y, He D, Dub S. Diamond-SiC nanocomposites sintered from a mixture of diamond and silicon nanopowders. Diamond Relat Mater 2003;12:1477–81. 2. Ekimov E, Gierlotka S, Gromnitskaya E, Kozubowski J, Palosz B, Lojkowski W, et al. Mechanical properties and microstructure of diamondSiC nanocomposites. Inorg Mater 2002;38:1117–22. 3. Shimono M, Kume S. HIP-sintered composites of C (diamond)/SiC. J Am Ceram Soc 2004;87:752–5. 4. Ekimov EA, Suetin NV, Popovich AF, Ralchenko VG. Thermal conductivity of diamond composites sintered under high pressures. Diamond Relat Mater 2008;17:838–43.

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