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Cu composites with chromium carbide coating for structural applications
Materials Science & Engineering A 588 (2013) 221–227
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Enhanced mechanical properties in diamond/Cu composites with chromium carbide coating for structural applications Chao Zhao n, Jun Wang College of Urban Planning and Environment Science, Xuchang University, Xuchang 461000, China
art ic l e i nf o
a b s t r a c t
Article history: Received 20 August 2013 Received in revised form 9 September 2013 Accepted 11 September 2013 Available online 18 September 2013
Cr7C3-coated diamond particles are used to improve the interfacial bonding and mechanical properties of diamond/Cu composites, which are prepared by the pressure infiltration technique. The characteristics of Cr7C3 coating were investigated by Scanning Electron Microscopy (SEM), X-ray Diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). The results show that a Cr7C3 coating layer between the diamond and Cu matrix greatly improves their interfacial bonding, which in turn helps distribute the external load from matrix to diamonds and enhances Young's modulus and tensile strength of the composites. The measured Young's modulus agrees reasonably well with the predictions by a differential effective-medium (DEM) model. & 2013 Elsevier B.V. All rights reserved.
Keywords: Diamond/Cu composites Coating Tensile strength Young's modulus
1. Introduction Diamond-related materials are widely used as heat spreaders or heat sinks because of their excellent thermal conductivity ( 2000 W/m K) and the low coefficient of thermal expansion (CTE) of diamond ( 1.2 10 6/K) [1]. Metal matrix composites reinforced with diamonds, especially diamond reinforced copper matrix (diamond/Cu) composites, receive the most attention and have been considered to be the next generation of thermal management material for electronic packages and heat sink applications [2,3]. Theoretically, it can be expected that diamond/Cu composites may achieve a higher thermal conductivity than that of copper and CTE in the range of 6–8 10 6/K. On the other hand, good mechanical properties are another requirement for the use of diamond/Cu composites as a thermal management material in order to avoid damage from the pressure, shake and impact during the process of assembly and carriage. For instance, in semiconductor–insulator–substrate assemblies with a sandwich structure, warping is usually observed during thermal cycling [4]. Therefore, it is necessary to investigate the mechanical properties of diamond/Cu composites for their actual thermal management applications. Although diamond has an ultra-high Young's modulus ( 1 TPa) and strength ( 100 GPa) [5], diamond/Cu composites with the desired stiffness and strength, however, are not easy to realize due to the poor wettability or weak interfacial bonding
n
Corresponding author. Tel.: þ 86 13937452507; fax: þ86 03742938755. E-mail address: [email protected] (C. Zhao).
0921-5093/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2013.09.034
between diamond and copper [6]. In metal matrix composites, a strong interfacial bonding is critical for effective stress transfer from rigid particles to soft metal matrix, which leads to high composite strength. The load-bearing capacity of diamond/Cu composites is limited by the interfacial strength between matrix and particles. In response to this problem, alloying elements such as strong carbide formers Cr or B capable of establishing chemical interactions with diamond may provide an effective route to improve the diamond–Cu interface [7]. The recent investigation [4], however, demonstrated that the diamond/CuB composites at a boron content of 2.5 at% exhibited a high thermal conductivity but a rather low tensile strength. This disappointing result indicates that the added alloying elements forming an intermediate interface – enabling effective heat transfer between diamond and the Cu matrix – do not act as a load transfer region, resulting in degradation of the overall strength of the composites. In contrast, surface metallization/coating of diamond particles is a direct and more effective method. The coated diamonds could efficiently enhance the interface bonding energy between the matrix and the diamonds; therefore, the bonding strength and whole mechanical properties of the composites can be improved [8]. Recently, a transition of diamond–Al interface from weak to strong bonding utilizing Ti-coated diamonds has been reported [9]. The results show that Ti coating can effectively improve the tensile strength of diamond/Al composites. To date, most of the works have concentrated on improving the thermal properties of diamond/Cu composites. The thermal conductivity of diamond/Cu composites has been widely investigated [7,10,11]; however, only a few authors have reported the mechanical properties of diamond/metal composites [4,9,12]. To the best
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of the authors' knowledge, there is no detailed investigation on the mechanical properties of diamond/Cu composites with high volume fraction of diamond particles ( 450 vol%). Therefore, in this study, we attempt to capture the salient features of experimental as well as analytical characterization of the mechanical behavior of diamond/Cu composites based on the ultimate tensile strength and Young's modulus measurements. The Cr7C3-coated diamond particles are utilized to improve the interfacial bonding between Cu and diamond and composites are prepared by the pressure infiltration technique. The characteristics of Cr7C3 coating were investigated by Scanning Electron Microscopy (SEM), X-ray Diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). It is suggested that a Cr7C3 coating layer present at the Cu–diamond interface in the composites plays an important role in accommodating the load transfer between the diamond and the Cu matrix.
copper left on the surface of the composites. For comparison, the composites with uncoated diamond particles were prepared under the same processing. The weight fractions of particles (Wp) and matrix (Wm) are typically established prior to composite processing, whereas the volume fractions of particles (Vp) and matrix (Vm) cannot be established without the knowledge of the third volume-based part of porosity (ξ) [14]. The weight (W) and volume fractions (V) of the composites are as follows: Wm þWp ¼ 1
Based on the densities of particles (ρp) and matrix (ρm), expressions for the actual volumes of the particle and matrix parts are as follows: Vp ¼
2. Experimental
W p =ρp 1=ρc
Vm ¼
A block of copper (99.99% in purity) was used as the matrix material. A synthetic MBD-4 diamond with an average particle diameter of 67 μm was used as reinforcement. Chromium carbide coating was applied on the surfaces of the diamond particles using the molten salt method following the reported method [13]. The composites with nominal 50–65% volume fraction of coated diamond particles were fabricated by the pressure infiltration technique using a vertical type, high-pressure vacuum furnace, as illustrated in Fig. 1. Infiltration can be readily used to realize the net-shaped fabrication of diamond/Cu because it is difficult to conduct post-mechanization in these materials owing to the ultra-high hardness of diamond. The diamond particles are first produced to a porous preform by pressing a mixture of diamond particles and organic binder in a cylindrical mold, and then heating at 450 1C for 1 h in a hydrogen atmosphere to degrease the binder. The diamond preform positioned within a tool steel die was preheated in a vacuum less than 0.1 Pa to a temperature of 800 1C. Then the Cu block was melted, degassed and cleaned in a graphite crucible and heated to 1200 1C. Subsequently, the molten Cu was poured into the graphite die and a vertical pressure of up to 80 MPa was applied to force the molten Cu to completely infiltrate the diamond preform. The pressure was maintained for 3 min until the solidification was complete. The composite plates were finally obtained after getting rid of the
ð1Þ
Vm þVp þξ ¼ 1
¼ ρρpc W p
ð1 W p Þ=ρm 1=ρc
¼ ρρc ð1 W p Þ
ð2Þ
m
From Eqs. (1) and (2), porosity can be then expressed as follows: ! Wp 1Wp ξ ¼ 1 ρc þ ð3Þ ρp ρm where ρc is the density of the composite. The density of the diamond particles was measured by the He-pycnometry method [15], whereas the densities of the copper block and final composites were measured by the Archimedes principle. Based on the measured values for densities and weight fractions, the actual volume fractions of particles and porosity can be determined by Eqs. (2) and (3), respectively. The microstructures of the coating and composites were investigated by SEM on a Philips XL30-FEG instrument. The phase of coating was characterized by XRD and XPS. XRD analyses were performed on an X'Pert X-ray diffractometer with Cu Kα, operated at 40 kV and 40 mA. XPS measurements were performed using a VG Scientific ESCALAB 220 iXL spectrometer equipped with a hemispherical electron analyzer and an Mg Ka X-ray source. Tensile tests were conducted on an Instron5569 testing machine at ambient temperature, at the crosshead moving rate of 0.5 mm/min. Dog-bone-shaped specimens with a gage length of 20 mm and width of 3 mm were used for tensile test. Each
Fig. 1. Schematic illustration of the pressure-infiltration process.
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Table 1 Measured mechanical properties of the composites. Sample
Nominal diamond fraction (vol%)
Actual diamond fraction (vol%)
Uncoated-diamond/Cu
50 55 60 65
49.5 54.2 57.6 60.5
Coated-diamond/Cu
50 55 60 65
49.8 54.7 58.4 61.8
UTS (MPa)
Ultimate strain (%)
Young's modulus (GPa)
Relative density (%)
62 53 57 38
0.206 0.187 0.138 0.044
134 166 184 208
99.5 99.2 98.6 97.2
134 146 127 113
0.261 0.211 0.123 0.098
218 289 357 383
99.8 99.6 98.9 98.2
Fig. 2. XRD patterns of coated diamond particles at various plating times.
Fig. 3. SEM image of the surface morphology of coated diamond particles.
ultimate tensile strength (UTS) value and Young's modulus value was the average of at least three measurements. All the measurements are listed in Table 1.
Fig. 2 shows the XRD patterns of the coating with two plating times of 60 min and 90 min. The coating plated for 60 min consists of two phases of Cr7C3 and Cr. Cr7C3 is formed by chemical reactions between Cr atoms plated and C atoms from diamond. The residual Cr is thus covered on top of the Cr7C3 layer. By prolonging the plating time to 90 min, only Cr7C3 peaks are detected, and the intensities of Cr7C3 peaks are found to increase, indicating that the coating plated for 90 min has a unique Cr7C3 carbide phase. The morphology of Cr7C3-coated diamond particles shown in Fig. 3 shows a uniform structure and good adhesion with the diamond particles. Since XRD cannot provide valid information about Cr in the asdeposited coating, XPS is used to further characterize the chemical bonding states of Cr and C. Fig. 4 shows the high-resolution XPS spectra with fitting curves relative to the Cr 2p3/2 band. Deconvolution of the Cr 2p3/2 peak shows that the binding energies of Cr atoms involved are 572.4 eV and 583.2 eV, corresponding to the Cr–C bond (Cr7C3) and Cr–O bond (Cr2O3) [16], respectively. The ratio of these two kinds of bonds (Cr–C and Cr–O) is 97.8% and 2.2%, respectively. This indicates the presence of Cr2O3 minor phase in the Cr7C3 coating. Therefore, the oxygen (O)-containing phase of Cr can be detected by a surface-sensitive technique such as XPS, which cannot be detected by XRD. As the content of Cr2O3
Intensity (a.u)
3. Results and discussion
Cr-C bond 572.4 eV
Cr2p3/2
550
Cr-O bond 583.2 eV
560
570
580
590
600
Binding energy (eV) Fig. 4. XPS narrow-scanning spectra and fitted results of Cr 2p3/2 spectra of the coating: Cr–C and Cr–O bonds are identified in Cr 2p3/2 spectra.
minor phase is only about 2.2%, it is reasonably acceptable that the coating consists of mainly the Cr7C3 phase. In the Cr–C binary phase diagram [17,18], there are three thermodynamically stable chromium carbides: Cr3C2, Cr7C3 and Cr23C6. The XRD and XPS results show that the phase of Cr carbide coating is totally Cr7C3 at the present coating temperature (1173 K). This may be a result of the more stable structure of Cr7C3 than Cr3C2 with relatively low Gibbs free energy K 1173 K (ΔG1173 Cr7 C3 ¼ 126:5 kJ=mol, ΔGCr3 C2 ¼ 76:4 kJ=mol) [19]. However, Cr23C6, which has the lowest Gibbs free energy of the K three chromium carbides (ΔG1173 Cr23 C6 ¼ 368:2 kJ=mol) [19], is not
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observed in the present coating. The reason for this is not well understood, but it may be related to the kinetics of the diffusion of the constituents, i.e. the diffusion coefficients and the activity gradients across the phases and the activity of Cr on the diamond surface [20]. Further research is needed to clarify the mechanism of the preferential formation of Cr7C3 over Cr23C6 on the diamond surface. The appearance of the Cr2O3 minor phase can be attributed to the high affinity between Cr and O during and/or after coating, since Cr2O3 is a more stable compound than Cr7C3 owing K to its lower Gibbs free energy ðΔG1173 Cr2 O3 ¼ 758:3 kJ=molÞ [21]. However, the high-purity argon atmosphere used during the coating processing may prevent the severe oxidation of Cr; thus, the detected minor Cr2O3 phase by XPS can be negligible. Fig. 5 shows the SEM image for the interface of the composites with 60 vol% diamond particles. It is seen that a good interfacial bonding is obtained between Cu and diamond particles, where the thin and uniform Cr7C3 interfacial layer tightly connects the diamond particles and the Cu matrix. The inset shows the EDS line-scanning analysis of the element distribution across the Cu– diamond interface. It is obvious that both Cr and C elements are present only in the interfacial layer, which suggests the segregation of C in the form of Cr7C3 at the Cu–diamond interfaces. The average thickness of the interfacial Cr7C3 layer is about 1.5 μm. The content of Cr7C3 in the composites can be estimated by the following equation [13]: 3 1 1 ¼ ð4Þ 1 þ t=d V c =ð1 V c ÞV p where d is the diameter of the diamond particles and t is the average thickness of the interfacial carbide phase. Vp and Vc are
Fig. 5. SEM image of the interface of the composite with 60 vol% diamonds (inset for the EDS line scanning of the element distribution across the Cu–diamond interface).
volume fractions of the diamond particles and carbide phase in the composites, respectively. By taking d ¼67 μm, t¼1.5 μm and Vp ¼0.6 in Eq. (4), the content of interfacial Cr7C3 phase (Vc) in the composites is determined to be about 0.4 vol%. The fracture surfaces of the composites with coated and uncoated diamonds are shown in Fig. 6. It is clear that the diamond particles protrude completely from the fracture surface and some voids or cracks are clearly observed in the uncoateddiamond/Cu composites (Fig. 6(a)), indicating a very weak interfacial bonding between Cu matrix and the diamonds. In contrast, the coated-diamond/Cu composites show a noticeably improved interfacial bonding (Fig. 6(b)), in which the trans-particle fracture of nearly all the diamond particles is presented. This trans-particle fracture only happens when the interfacial bonding strength in the composite is higher than the fracture stress of diamond particles [22]. No evidence of voids or cavities can be found in this case. According to Young's equation (Eq. (5)), where solid, liquid and vapor are in equilibrium, the wettability improves with (i) increase in the surface energy of the solid–vapor, (ii) decrease in the surface tension of the liquid matrix and (iii) decrease in the solid–liquid interfacial free energy [23]: cos θ ¼
sSV sSL sLV
ð5Þ
where θ is the contact angle and sSV , sSL and sLV are the solid– vapor, solid–liquid and liquid–vapor surface energy, respectively. In the Cu–diamond system, an initial contact angle is 145–1501 at the infiltration temperature of 1200 1C [17], which is a typical non-wetting system. In this case, the adhesion of Cu onto the diamond could be attributed only to van der Waals forces. However, in the presence of Cr7C3 coating at the Cu–diamond interface, the wetting surface is transferred from weakly wetted Cu–diamond to well-wetted Cu–Cr7C3, where the contact angle is only 40–451 at 1200 1C [18]. In this case, the adhesion between Cu and diamond can be interpreted in terms of strong chemical interactions, such as a covalent bond. Accordingly, it is concluded that the Cr7C3 coating layer is responsible for the improved wettability and strong interfacial bonding in coated-diamond/Cu composites. Fig. 7 shows Young's modulus (Fig. 7(a)) and UTS (Fig. 7(b)) of uncoated-diamond/Cu and coated-diamond/Cu composites. It is obvious that Cr7C3-coated diamonds greatly enhance the mechanical performance of the composites. For instance, the addition of 61.8 vol% coated diamonds increases Young's modulus and UTS by 84% and 197% relative to those of 60.5 vol% uncoated-diamond/ Cu composites, respectively. It is thus concluded that the particle– matrix interfacial bonding has a prominent effect on the mechanical performance of diamond/Cu composites. For uncoateddiamond/Cu composites, the stress transfer at the diamond–Cu interface is weaker. Discontinuity in the form of interfacial debonding exists because of the weak adherence of diamond to
Fig. 6. SEM fracture images of (a) uncoated-diamond/Cu and (b) coated-diamond/Cu composites with 60 vol% diamond content.
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estimated previously, the influence of Cr7C3 itself as a composite constituent on Young's modulus can be negligible. Nevertheless, unlike Young's modulus where Young's modulus increases with diamond content, UTS decreases with increasing diamond content in both composites. This can be rationalized by the overall low ductility (below 0.2% for the ultimate strain) for the diamond/Cu composites with high diamond loading. Fig. 7 (c) shows that the ultimate strain at break of the composites decreases with diamond loading. Hence, the enhancement in UTS due to the addition of diamond is compromised by the concomitant reduction in total strain to failure with increasing diamond content. This phenomenon is consistent with previous results for the strength behavior of diamond/Ag composites [12]. The interfacial bonding energy ðγÞ of particulate composites can be estimated by a theoretical model given by [24] γ¼
Fig. 7. Measured mechanical properties of uncoated-diamond/Cu and coateddiamond/Cu composites: (a) Young's modulus; (b) ultimate tensile strength (UTS); (c) ultimate strain at composite break.
Cu matrix. Thus, the diamond particles cannot carry any load and the composites show a low Young's modulus and UTS. However, for coated-diamond/Cu composites, the presence of a Cr7C3 coating layer between diamonds and Cu matrix greatly improves the interfacial interaction of Cu–diamond, which in turn helps distribute the external load from matrix to diamonds effectively and further enhances Young's modulus and UTS of the composites. It is noteworthy that since the content of Cr7C3 is only 0.4 vol% as
as2c 12Em ð1=Ec þ νp Þ
ð6Þ
where s and E are UTS and Young's modulus, respectively, ν is Poisson's ratio and a the volume-to-surface area ratio of particles. The subscripts m, p and c refer to the matrix, reinforced particles and composites, respectively. This model accounts for the interfacial bonding energy based on the parameters of modulus and UTS and, thus, realistically reflects the interface load transfer behavior of particulate composites. Using the values measured for s and E in this study (Fig. 6) and using the materials data compiled in Table 2, γ can be calculated as 7.5 10 2 and 3.8 10 1 J/m2 for uncoated-diamond/Cu and coated-diamond/ Cu composites, respectively, indicating that the interfacial bonding energy of coated-diamond/Cu exceeds that achieved in coateddiamond/Cu by one order of magnitude. This implies that the low interfacial bonding energy in uncoated-diamond/Cu composites does not allow the diamond particles to contribute high strength and stiffness to the mechanical performance of the composites. The remarkable strengthening in coated-diamond/Cu composites is due to the high interfacial bonding energy of the composites, which is realized by the improved interfacial bonding between diamonds and the Cu matrix through interfacial Cr7C3 coating. Young's modulus of the composites can be estimated by several analytical models such as Hashin and Shtrikman (H–S) upper and lower bounds [25], the Mori–Tanaka (MT) model [26] and the differential effective-medium (DEM) model [27] (Table 2). All models presented are derived from the load-transfer theory and composite configuration featuring stiff particles in a soft matrix. The comparison between the measured and calculated Young's modulus of uncoated-diamond/Cu and coated-diamond/Cu composites, with increasing volume fraction of diamond, is shown in Fig. 8. As seen, the measured Young's modulus of coated-diamond/ Cu composites agrees reasonably well with the calculated values by the DEM model, whereas the measurements of uncoateddiamond/Cu composites are considerably lower than the DEM predictions and are close to the predictions of the H–S lower bound. This reveals that the stiffening mechanism in diamond/Cu composites can be explained well by the load transfer theory of the DEM model based on a well-bonded interface. This is in agreement with recent results on diamond/Ag–3Si composites with high volume fractions of diamond particles [12], which show that the DEM model provides the best prediction of Young's modulus of the composites with strong interfacial bonding of the Ag3Si–diamond. The good agreement between the estimated and measured values indicates that the stiffening of the present coated-diamond/Cu composites is due mainly to an efficient load transfer from the diamond to the Cu matrix, as realized by interfacial Cr7C3 coating covalently bonding with the Cu matrix and the diamonds.
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Table 2 Models to predict Young's modulus (Ec) of the particulate composites. Model
Expressions
Hashin–Shtrikman (H–S) upper and lower bounds
Eupper ¼ 3K9Kupper þGGupper ; Elower ¼ 9Klower G lower ; 3K þG 1 3V p 1 þ K upper ¼ K p þ ð1 V p Þ K m K p 3K p þ 4Gp 3ð1 V p Þ 1 1 lower K ¼ Km þVp þ K p K m 3K m þ 4Gm 1 6V p ðK p þ 2Gp Þ 1 upper G ¼ Gp þ ð1 V p Þ þ Gm Gp 5Gp ð3K p þ 4Gp Þ 1 6ð1 V p ÞðK m þ 2Gm Þ 1 lower G ¼ Gm þ V p þ Gp Gm 5Gm ð3K m þ 4Gm Þ
upper
Mori–Tanaka (M–T) model
Ref. upper
lower
lower
[25]
Ec ¼ 3K9Kc cþGGc c Kc ¼ Km þ
V p K m ðK p K m Þ K m þ β2 ð1 V p ÞðK p K m Þ
Gc ¼ Gm þ
V p Gm ðGp Gm Þ Gm þ β1 ð1 V p ÞðGp Gm Þ
[28]
2ð4 5νm Þ ; β ¼ 3 5β1 β1 ¼ 15ð1 νm Þ 2 Differential-effective-medium (DEM) model
Ec ¼ 3K9Kc cþGGc c Kp Kc ∂K c ð1 V p Þ ¼ ðK c þ 4=3Gc Þ ∂V p K p þ 4=3Gc ∂Gc Gp Gc ¼ ðK c þ HÞ ð1 V p Þ ∂V p Gp þ H
[29]
Gc ð3=2K c þ 4=3Gc Þ H¼ K c þ 2Gc
K and G are the bulk and shear modulus, respectively. Vp is the particle volume fraction. ν is Poisson's ratio. The superscripts upper, lower refer to the upper and lower bound estimates, and subscripts m and p refer to matrix and reinforced particles, respectively. The calculation parameters are Km ¼107 GPa, Kp ¼ 1055 GPa, Gm ¼ 48.3 GPa, GP ¼478 GPa; νm ¼ 0:35 [4,5].
300
Cu–diamond interface. The experimental Young's modulus is compared with the predictions of the theoretical models. The measured Young's modulus of coated-diamond/Cu composites agrees reasonably well with the calculated values by the DEM model, whereas the measurements of uncoated-diamond/Cu composites are noticeably lower than the DEM predictions and even lower than the perditions of H–S lower bound.
200
References
100
[1] Y. Yamamoto, T. Imai, K. Tanabe, T. Tsuno, Y. Kumazawa, N. Fujimori, Diamond Relat. Mater. 6 (1997) 1057–1061. [2] T. Schubert, L. Ciupinski, W. Zielinski, A. Michalski, T. Weißgärber, B. Kieback, Scr. Mater. 58 (2008) 263–266. [3] K. Chu, Z. Liu, C. Jia, H. Chen, X. Liang, W. Gao, W. Tian, H. Guo, J. Alloys Compd. 490 (2010) 453–458. [4] K. Weidenmann, R. Tavangar, L. Weber, Mater. Sci. Eng. A 523 (2009) 226–234. [5] D.J. Weidner, Y. Wang, M.T. Vaughan, Science 266 (1994) 419–422. [6] K. Yoshida, H. Morigami, Microelectron. Reliab. 44 (2004) 303–308. [7] L. Weber, R. Tavangar, Scr. Mater. 57 (2007) 988–991. [8] K. Chu, C. Jia, H. Guo, W. Li, Mater. Des. 45 (2013) 36–42. [9] J. Wu, H. Zhang, Y. Zhang, J. Li, X. Wang, Mater. Sci. Eng. A 565 (2013) 33–37. [10] T. Schubert, B. Trindade, T. Weißgärber, B. Kieback, Mater. Sci. Eng. A 475 (2008) 39–44. [11] S.V. Kidalov, F.M. Shakhov, Materials 2 (2009) 2467–2495. [12] K. Weidenmann, R. Tavangar, L. Weber, Compos. Sci. Technol. 69 (2009) 1660–1666. [13] S. Ren, X. Shen, C. Guo, N. Liu, J. Zang, X. He, X. Qu, Compos. Sci. Technol. 71 (2011) 1550–1555. [14] K. Chu, C. Jia, W. Tian, X. Liang, H. Chen, H. Guo, Compos. Part A 41 (2010) 161–167. [15] M. Lee, D. Sordelet, Scr. Mater. 55 (2006) 947–950. [16] C.D. Wagner, A.V. Naumkin, A. Kraut-Vass, J.W. Allison, C.J. Powell, J.R. Rumble Jr., NIST XPS Database Version 3 (2003). [17] D. Mortimer, M. Nicholas, J. Mater. Sci. 5 (1970) 149–155. [18] B. Dewar, M. Nicholas, P. Scott, J. Mater. Sci. 11 (1976) 1083–1090. [19] M. Small, E. Ryba, Metall. Trans. A 12 (1981) 1389–1396. [20] A. Van der Ven, H.-C. Yu, G. Ceder, K. Thornton, Prog. Mater. Sci. 55 (2010) 61–105.
Young's modulus / GPa
500
400
Exp. Coated-diamond/Cu M-T Exp. Uncoated-diamond/Cu DEM H-S lower bound H-S upper bound
0 50
55
60
65
Diamond volume fraction / % Fig. 8. Comparison of measured and predicted Young's modulus of uncoateddiamond/Cu and coated-diamond/Cu composites (model expressions and calculation parameters are given in Table 1).
4. Conclusions The results show that Cr7C3 coating has a strong influence on the interfacial bonding and the resulting mechanical properties of diamond/Cu composites. The combined SEM, XRD and XPS analysis confirms that a coating layer consisting of mainly Cr7C3 phase (97.8%) is uniformly formed on the surface of diamond particles. The addition of 65 vol%-coated diamonds causes an increase in Young's modulus and UTS by 84% and 197% compared to those of 65 vol% uncoated-diamond/Cu composites, respectively. This is attributed to the interface modification through the interfacial Cr7C3 coating, which is beneficial for interfacial bonding and load transfer at the
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[21] G. Róg, A. Kozłowska-Róg, M. Dudek, J. Chem. Thermodyn. 39 (2007) 275–278. [22] X.Y. Shen, X.B. He, S.B. Ren, H.M. Zhang, X.H. Qu, J. Alloys Compd. 529 (2012) 134–139. [23] U. Seifert, R. Lipowsky, Phys. Rev. A 42 (1990) 4768. [24] T. Chow, J. Polym. Sci. Polym. Phys. Ed. 20 (1982) 2103–2109.
[25] [26] [27] [28] [29]
Z. Hashin, S. Shtrikman, J. Mech. Phys. Solids. 11 (1963) 127–140. T. Mori, K. Tanaka, Acta Metall. 21 (1973) 571–574. A. Norris, A. Callegari, P. Sheng, J. Mech. Phys. Solids. 33 (1985) 525–544. J. Schjødt-Thomsen, R. Pyrz, Mech. Mater. 33 (2001) 531–544. A. Norris, Mech. Mater. 4 (1985) 1–16.
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Enhanced mechanical properties in diamond/Cu composites with chromium carbide coating for structural applications Chao Zhao n, Jun Wang College of Urban Planning and Environment Science, Xuchang University, Xuchang 461000, China
art ic l e i nf o
a b s t r a c t
Article history: Received 20 August 2013 Received in revised form 9 September 2013 Accepted 11 September 2013 Available online 18 September 2013
Cr7C3-coated diamond particles are used to improve the interfacial bonding and mechanical properties of diamond/Cu composites, which are prepared by the pressure infiltration technique. The characteristics of Cr7C3 coating were investigated by Scanning Electron Microscopy (SEM), X-ray Diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). The results show that a Cr7C3 coating layer between the diamond and Cu matrix greatly improves their interfacial bonding, which in turn helps distribute the external load from matrix to diamonds and enhances Young's modulus and tensile strength of the composites. The measured Young's modulus agrees reasonably well with the predictions by a differential effective-medium (DEM) model. & 2013 Elsevier B.V. All rights reserved.
Keywords: Diamond/Cu composites Coating Tensile strength Young's modulus
1. Introduction Diamond-related materials are widely used as heat spreaders or heat sinks because of their excellent thermal conductivity ( 2000 W/m K) and the low coefficient of thermal expansion (CTE) of diamond ( 1.2 10 6/K) [1]. Metal matrix composites reinforced with diamonds, especially diamond reinforced copper matrix (diamond/Cu) composites, receive the most attention and have been considered to be the next generation of thermal management material for electronic packages and heat sink applications [2,3]. Theoretically, it can be expected that diamond/Cu composites may achieve a higher thermal conductivity than that of copper and CTE in the range of 6–8 10 6/K. On the other hand, good mechanical properties are another requirement for the use of diamond/Cu composites as a thermal management material in order to avoid damage from the pressure, shake and impact during the process of assembly and carriage. For instance, in semiconductor–insulator–substrate assemblies with a sandwich structure, warping is usually observed during thermal cycling [4]. Therefore, it is necessary to investigate the mechanical properties of diamond/Cu composites for their actual thermal management applications. Although diamond has an ultra-high Young's modulus ( 1 TPa) and strength ( 100 GPa) [5], diamond/Cu composites with the desired stiffness and strength, however, are not easy to realize due to the poor wettability or weak interfacial bonding
n
Corresponding author. Tel.: þ 86 13937452507; fax: þ86 03742938755. E-mail address: [email protected] (C. Zhao).
0921-5093/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2013.09.034
between diamond and copper [6]. In metal matrix composites, a strong interfacial bonding is critical for effective stress transfer from rigid particles to soft metal matrix, which leads to high composite strength. The load-bearing capacity of diamond/Cu composites is limited by the interfacial strength between matrix and particles. In response to this problem, alloying elements such as strong carbide formers Cr or B capable of establishing chemical interactions with diamond may provide an effective route to improve the diamond–Cu interface [7]. The recent investigation [4], however, demonstrated that the diamond/CuB composites at a boron content of 2.5 at% exhibited a high thermal conductivity but a rather low tensile strength. This disappointing result indicates that the added alloying elements forming an intermediate interface – enabling effective heat transfer between diamond and the Cu matrix – do not act as a load transfer region, resulting in degradation of the overall strength of the composites. In contrast, surface metallization/coating of diamond particles is a direct and more effective method. The coated diamonds could efficiently enhance the interface bonding energy between the matrix and the diamonds; therefore, the bonding strength and whole mechanical properties of the composites can be improved [8]. Recently, a transition of diamond–Al interface from weak to strong bonding utilizing Ti-coated diamonds has been reported [9]. The results show that Ti coating can effectively improve the tensile strength of diamond/Al composites. To date, most of the works have concentrated on improving the thermal properties of diamond/Cu composites. The thermal conductivity of diamond/Cu composites has been widely investigated [7,10,11]; however, only a few authors have reported the mechanical properties of diamond/metal composites [4,9,12]. To the best
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of the authors' knowledge, there is no detailed investigation on the mechanical properties of diamond/Cu composites with high volume fraction of diamond particles ( 450 vol%). Therefore, in this study, we attempt to capture the salient features of experimental as well as analytical characterization of the mechanical behavior of diamond/Cu composites based on the ultimate tensile strength and Young's modulus measurements. The Cr7C3-coated diamond particles are utilized to improve the interfacial bonding between Cu and diamond and composites are prepared by the pressure infiltration technique. The characteristics of Cr7C3 coating were investigated by Scanning Electron Microscopy (SEM), X-ray Diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). It is suggested that a Cr7C3 coating layer present at the Cu–diamond interface in the composites plays an important role in accommodating the load transfer between the diamond and the Cu matrix.
copper left on the surface of the composites. For comparison, the composites with uncoated diamond particles were prepared under the same processing. The weight fractions of particles (Wp) and matrix (Wm) are typically established prior to composite processing, whereas the volume fractions of particles (Vp) and matrix (Vm) cannot be established without the knowledge of the third volume-based part of porosity (ξ) [14]. The weight (W) and volume fractions (V) of the composites are as follows: Wm þWp ¼ 1
Based on the densities of particles (ρp) and matrix (ρm), expressions for the actual volumes of the particle and matrix parts are as follows: Vp ¼
2. Experimental
W p =ρp 1=ρc
Vm ¼
A block of copper (99.99% in purity) was used as the matrix material. A synthetic MBD-4 diamond with an average particle diameter of 67 μm was used as reinforcement. Chromium carbide coating was applied on the surfaces of the diamond particles using the molten salt method following the reported method [13]. The composites with nominal 50–65% volume fraction of coated diamond particles were fabricated by the pressure infiltration technique using a vertical type, high-pressure vacuum furnace, as illustrated in Fig. 1. Infiltration can be readily used to realize the net-shaped fabrication of diamond/Cu because it is difficult to conduct post-mechanization in these materials owing to the ultra-high hardness of diamond. The diamond particles are first produced to a porous preform by pressing a mixture of diamond particles and organic binder in a cylindrical mold, and then heating at 450 1C for 1 h in a hydrogen atmosphere to degrease the binder. The diamond preform positioned within a tool steel die was preheated in a vacuum less than 0.1 Pa to a temperature of 800 1C. Then the Cu block was melted, degassed and cleaned in a graphite crucible and heated to 1200 1C. Subsequently, the molten Cu was poured into the graphite die and a vertical pressure of up to 80 MPa was applied to force the molten Cu to completely infiltrate the diamond preform. The pressure was maintained for 3 min until the solidification was complete. The composite plates were finally obtained after getting rid of the
ð1Þ
Vm þVp þξ ¼ 1
¼ ρρpc W p
ð1 W p Þ=ρm 1=ρc
¼ ρρc ð1 W p Þ
ð2Þ
m
From Eqs. (1) and (2), porosity can be then expressed as follows: ! Wp 1Wp ξ ¼ 1 ρc þ ð3Þ ρp ρm where ρc is the density of the composite. The density of the diamond particles was measured by the He-pycnometry method [15], whereas the densities of the copper block and final composites were measured by the Archimedes principle. Based on the measured values for densities and weight fractions, the actual volume fractions of particles and porosity can be determined by Eqs. (2) and (3), respectively. The microstructures of the coating and composites were investigated by SEM on a Philips XL30-FEG instrument. The phase of coating was characterized by XRD and XPS. XRD analyses were performed on an X'Pert X-ray diffractometer with Cu Kα, operated at 40 kV and 40 mA. XPS measurements were performed using a VG Scientific ESCALAB 220 iXL spectrometer equipped with a hemispherical electron analyzer and an Mg Ka X-ray source. Tensile tests were conducted on an Instron5569 testing machine at ambient temperature, at the crosshead moving rate of 0.5 mm/min. Dog-bone-shaped specimens with a gage length of 20 mm and width of 3 mm were used for tensile test. Each
Fig. 1. Schematic illustration of the pressure-infiltration process.
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Table 1 Measured mechanical properties of the composites. Sample
Nominal diamond fraction (vol%)
Actual diamond fraction (vol%)
Uncoated-diamond/Cu
50 55 60 65
49.5 54.2 57.6 60.5
Coated-diamond/Cu
50 55 60 65
49.8 54.7 58.4 61.8
UTS (MPa)
Ultimate strain (%)
Young's modulus (GPa)
Relative density (%)
62 53 57 38
0.206 0.187 0.138 0.044
134 166 184 208
99.5 99.2 98.6 97.2
134 146 127 113
0.261 0.211 0.123 0.098
218 289 357 383
99.8 99.6 98.9 98.2
Fig. 2. XRD patterns of coated diamond particles at various plating times.
Fig. 3. SEM image of the surface morphology of coated diamond particles.
ultimate tensile strength (UTS) value and Young's modulus value was the average of at least three measurements. All the measurements are listed in Table 1.
Fig. 2 shows the XRD patterns of the coating with two plating times of 60 min and 90 min. The coating plated for 60 min consists of two phases of Cr7C3 and Cr. Cr7C3 is formed by chemical reactions between Cr atoms plated and C atoms from diamond. The residual Cr is thus covered on top of the Cr7C3 layer. By prolonging the plating time to 90 min, only Cr7C3 peaks are detected, and the intensities of Cr7C3 peaks are found to increase, indicating that the coating plated for 90 min has a unique Cr7C3 carbide phase. The morphology of Cr7C3-coated diamond particles shown in Fig. 3 shows a uniform structure and good adhesion with the diamond particles. Since XRD cannot provide valid information about Cr in the asdeposited coating, XPS is used to further characterize the chemical bonding states of Cr and C. Fig. 4 shows the high-resolution XPS spectra with fitting curves relative to the Cr 2p3/2 band. Deconvolution of the Cr 2p3/2 peak shows that the binding energies of Cr atoms involved are 572.4 eV and 583.2 eV, corresponding to the Cr–C bond (Cr7C3) and Cr–O bond (Cr2O3) [16], respectively. The ratio of these two kinds of bonds (Cr–C and Cr–O) is 97.8% and 2.2%, respectively. This indicates the presence of Cr2O3 minor phase in the Cr7C3 coating. Therefore, the oxygen (O)-containing phase of Cr can be detected by a surface-sensitive technique such as XPS, which cannot be detected by XRD. As the content of Cr2O3
Intensity (a.u)
3. Results and discussion
Cr-C bond 572.4 eV
Cr2p3/2
550
Cr-O bond 583.2 eV
560
570
580
590
600
Binding energy (eV) Fig. 4. XPS narrow-scanning spectra and fitted results of Cr 2p3/2 spectra of the coating: Cr–C and Cr–O bonds are identified in Cr 2p3/2 spectra.
minor phase is only about 2.2%, it is reasonably acceptable that the coating consists of mainly the Cr7C3 phase. In the Cr–C binary phase diagram [17,18], there are three thermodynamically stable chromium carbides: Cr3C2, Cr7C3 and Cr23C6. The XRD and XPS results show that the phase of Cr carbide coating is totally Cr7C3 at the present coating temperature (1173 K). This may be a result of the more stable structure of Cr7C3 than Cr3C2 with relatively low Gibbs free energy K 1173 K (ΔG1173 Cr7 C3 ¼ 126:5 kJ=mol, ΔGCr3 C2 ¼ 76:4 kJ=mol) [19]. However, Cr23C6, which has the lowest Gibbs free energy of the K three chromium carbides (ΔG1173 Cr23 C6 ¼ 368:2 kJ=mol) [19], is not
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observed in the present coating. The reason for this is not well understood, but it may be related to the kinetics of the diffusion of the constituents, i.e. the diffusion coefficients and the activity gradients across the phases and the activity of Cr on the diamond surface [20]. Further research is needed to clarify the mechanism of the preferential formation of Cr7C3 over Cr23C6 on the diamond surface. The appearance of the Cr2O3 minor phase can be attributed to the high affinity between Cr and O during and/or after coating, since Cr2O3 is a more stable compound than Cr7C3 owing K to its lower Gibbs free energy ðΔG1173 Cr2 O3 ¼ 758:3 kJ=molÞ [21]. However, the high-purity argon atmosphere used during the coating processing may prevent the severe oxidation of Cr; thus, the detected minor Cr2O3 phase by XPS can be negligible. Fig. 5 shows the SEM image for the interface of the composites with 60 vol% diamond particles. It is seen that a good interfacial bonding is obtained between Cu and diamond particles, where the thin and uniform Cr7C3 interfacial layer tightly connects the diamond particles and the Cu matrix. The inset shows the EDS line-scanning analysis of the element distribution across the Cu– diamond interface. It is obvious that both Cr and C elements are present only in the interfacial layer, which suggests the segregation of C in the form of Cr7C3 at the Cu–diamond interfaces. The average thickness of the interfacial Cr7C3 layer is about 1.5 μm. The content of Cr7C3 in the composites can be estimated by the following equation [13]: 3 1 1 ¼ ð4Þ 1 þ t=d V c =ð1 V c ÞV p where d is the diameter of the diamond particles and t is the average thickness of the interfacial carbide phase. Vp and Vc are
Fig. 5. SEM image of the interface of the composite with 60 vol% diamonds (inset for the EDS line scanning of the element distribution across the Cu–diamond interface).
volume fractions of the diamond particles and carbide phase in the composites, respectively. By taking d ¼67 μm, t¼1.5 μm and Vp ¼0.6 in Eq. (4), the content of interfacial Cr7C3 phase (Vc) in the composites is determined to be about 0.4 vol%. The fracture surfaces of the composites with coated and uncoated diamonds are shown in Fig. 6. It is clear that the diamond particles protrude completely from the fracture surface and some voids or cracks are clearly observed in the uncoateddiamond/Cu composites (Fig. 6(a)), indicating a very weak interfacial bonding between Cu matrix and the diamonds. In contrast, the coated-diamond/Cu composites show a noticeably improved interfacial bonding (Fig. 6(b)), in which the trans-particle fracture of nearly all the diamond particles is presented. This trans-particle fracture only happens when the interfacial bonding strength in the composite is higher than the fracture stress of diamond particles [22]. No evidence of voids or cavities can be found in this case. According to Young's equation (Eq. (5)), where solid, liquid and vapor are in equilibrium, the wettability improves with (i) increase in the surface energy of the solid–vapor, (ii) decrease in the surface tension of the liquid matrix and (iii) decrease in the solid–liquid interfacial free energy [23]: cos θ ¼
sSV sSL sLV
ð5Þ
where θ is the contact angle and sSV , sSL and sLV are the solid– vapor, solid–liquid and liquid–vapor surface energy, respectively. In the Cu–diamond system, an initial contact angle is 145–1501 at the infiltration temperature of 1200 1C [17], which is a typical non-wetting system. In this case, the adhesion of Cu onto the diamond could be attributed only to van der Waals forces. However, in the presence of Cr7C3 coating at the Cu–diamond interface, the wetting surface is transferred from weakly wetted Cu–diamond to well-wetted Cu–Cr7C3, where the contact angle is only 40–451 at 1200 1C [18]. In this case, the adhesion between Cu and diamond can be interpreted in terms of strong chemical interactions, such as a covalent bond. Accordingly, it is concluded that the Cr7C3 coating layer is responsible for the improved wettability and strong interfacial bonding in coated-diamond/Cu composites. Fig. 7 shows Young's modulus (Fig. 7(a)) and UTS (Fig. 7(b)) of uncoated-diamond/Cu and coated-diamond/Cu composites. It is obvious that Cr7C3-coated diamonds greatly enhance the mechanical performance of the composites. For instance, the addition of 61.8 vol% coated diamonds increases Young's modulus and UTS by 84% and 197% relative to those of 60.5 vol% uncoated-diamond/ Cu composites, respectively. It is thus concluded that the particle– matrix interfacial bonding has a prominent effect on the mechanical performance of diamond/Cu composites. For uncoateddiamond/Cu composites, the stress transfer at the diamond–Cu interface is weaker. Discontinuity in the form of interfacial debonding exists because of the weak adherence of diamond to
Fig. 6. SEM fracture images of (a) uncoated-diamond/Cu and (b) coated-diamond/Cu composites with 60 vol% diamond content.
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estimated previously, the influence of Cr7C3 itself as a composite constituent on Young's modulus can be negligible. Nevertheless, unlike Young's modulus where Young's modulus increases with diamond content, UTS decreases with increasing diamond content in both composites. This can be rationalized by the overall low ductility (below 0.2% for the ultimate strain) for the diamond/Cu composites with high diamond loading. Fig. 7 (c) shows that the ultimate strain at break of the composites decreases with diamond loading. Hence, the enhancement in UTS due to the addition of diamond is compromised by the concomitant reduction in total strain to failure with increasing diamond content. This phenomenon is consistent with previous results for the strength behavior of diamond/Ag composites [12]. The interfacial bonding energy ðγÞ of particulate composites can be estimated by a theoretical model given by [24] γ¼
Fig. 7. Measured mechanical properties of uncoated-diamond/Cu and coateddiamond/Cu composites: (a) Young's modulus; (b) ultimate tensile strength (UTS); (c) ultimate strain at composite break.
Cu matrix. Thus, the diamond particles cannot carry any load and the composites show a low Young's modulus and UTS. However, for coated-diamond/Cu composites, the presence of a Cr7C3 coating layer between diamonds and Cu matrix greatly improves the interfacial interaction of Cu–diamond, which in turn helps distribute the external load from matrix to diamonds effectively and further enhances Young's modulus and UTS of the composites. It is noteworthy that since the content of Cr7C3 is only 0.4 vol% as
as2c 12Em ð1=Ec þ νp Þ
ð6Þ
where s and E are UTS and Young's modulus, respectively, ν is Poisson's ratio and a the volume-to-surface area ratio of particles. The subscripts m, p and c refer to the matrix, reinforced particles and composites, respectively. This model accounts for the interfacial bonding energy based on the parameters of modulus and UTS and, thus, realistically reflects the interface load transfer behavior of particulate composites. Using the values measured for s and E in this study (Fig. 6) and using the materials data compiled in Table 2, γ can be calculated as 7.5 10 2 and 3.8 10 1 J/m2 for uncoated-diamond/Cu and coated-diamond/ Cu composites, respectively, indicating that the interfacial bonding energy of coated-diamond/Cu exceeds that achieved in coateddiamond/Cu by one order of magnitude. This implies that the low interfacial bonding energy in uncoated-diamond/Cu composites does not allow the diamond particles to contribute high strength and stiffness to the mechanical performance of the composites. The remarkable strengthening in coated-diamond/Cu composites is due to the high interfacial bonding energy of the composites, which is realized by the improved interfacial bonding between diamonds and the Cu matrix through interfacial Cr7C3 coating. Young's modulus of the composites can be estimated by several analytical models such as Hashin and Shtrikman (H–S) upper and lower bounds [25], the Mori–Tanaka (MT) model [26] and the differential effective-medium (DEM) model [27] (Table 2). All models presented are derived from the load-transfer theory and composite configuration featuring stiff particles in a soft matrix. The comparison between the measured and calculated Young's modulus of uncoated-diamond/Cu and coated-diamond/Cu composites, with increasing volume fraction of diamond, is shown in Fig. 8. As seen, the measured Young's modulus of coated-diamond/ Cu composites agrees reasonably well with the calculated values by the DEM model, whereas the measurements of uncoateddiamond/Cu composites are considerably lower than the DEM predictions and are close to the predictions of the H–S lower bound. This reveals that the stiffening mechanism in diamond/Cu composites can be explained well by the load transfer theory of the DEM model based on a well-bonded interface. This is in agreement with recent results on diamond/Ag–3Si composites with high volume fractions of diamond particles [12], which show that the DEM model provides the best prediction of Young's modulus of the composites with strong interfacial bonding of the Ag3Si–diamond. The good agreement between the estimated and measured values indicates that the stiffening of the present coated-diamond/Cu composites is due mainly to an efficient load transfer from the diamond to the Cu matrix, as realized by interfacial Cr7C3 coating covalently bonding with the Cu matrix and the diamonds.
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Table 2 Models to predict Young's modulus (Ec) of the particulate composites. Model
Expressions
Hashin–Shtrikman (H–S) upper and lower bounds
Eupper ¼ 3K9Kupper þGGupper ; Elower ¼ 9Klower G lower ; 3K þG 1 3V p 1 þ K upper ¼ K p þ ð1 V p Þ K m K p 3K p þ 4Gp 3ð1 V p Þ 1 1 lower K ¼ Km þVp þ K p K m 3K m þ 4Gm 1 6V p ðK p þ 2Gp Þ 1 upper G ¼ Gp þ ð1 V p Þ þ Gm Gp 5Gp ð3K p þ 4Gp Þ 1 6ð1 V p ÞðK m þ 2Gm Þ 1 lower G ¼ Gm þ V p þ Gp Gm 5Gm ð3K m þ 4Gm Þ
upper
Mori–Tanaka (M–T) model
Ref. upper
lower
lower
[25]
Ec ¼ 3K9Kc cþGGc c Kc ¼ Km þ
V p K m ðK p K m Þ K m þ β2 ð1 V p ÞðK p K m Þ
Gc ¼ Gm þ
V p Gm ðGp Gm Þ Gm þ β1 ð1 V p ÞðGp Gm Þ
[28]
2ð4 5νm Þ ; β ¼ 3 5β1 β1 ¼ 15ð1 νm Þ 2 Differential-effective-medium (DEM) model
Ec ¼ 3K9Kc cþGGc c Kp Kc ∂K c ð1 V p Þ ¼ ðK c þ 4=3Gc Þ ∂V p K p þ 4=3Gc ∂Gc Gp Gc ¼ ðK c þ HÞ ð1 V p Þ ∂V p Gp þ H
[29]
Gc ð3=2K c þ 4=3Gc Þ H¼ K c þ 2Gc
K and G are the bulk and shear modulus, respectively. Vp is the particle volume fraction. ν is Poisson's ratio. The superscripts upper, lower refer to the upper and lower bound estimates, and subscripts m and p refer to matrix and reinforced particles, respectively. The calculation parameters are Km ¼107 GPa, Kp ¼ 1055 GPa, Gm ¼ 48.3 GPa, GP ¼478 GPa; νm ¼ 0:35 [4,5].
300
Cu–diamond interface. The experimental Young's modulus is compared with the predictions of the theoretical models. The measured Young's modulus of coated-diamond/Cu composites agrees reasonably well with the calculated values by the DEM model, whereas the measurements of uncoated-diamond/Cu composites are noticeably lower than the DEM predictions and even lower than the perditions of H–S lower bound.
200
References
100
[1] Y. Yamamoto, T. Imai, K. Tanabe, T. Tsuno, Y. Kumazawa, N. Fujimori, Diamond Relat. Mater. 6 (1997) 1057–1061. [2] T. Schubert, L. Ciupinski, W. Zielinski, A. Michalski, T. Weißgärber, B. Kieback, Scr. Mater. 58 (2008) 263–266. [3] K. Chu, Z. Liu, C. Jia, H. Chen, X. Liang, W. Gao, W. Tian, H. Guo, J. Alloys Compd. 490 (2010) 453–458. [4] K. Weidenmann, R. Tavangar, L. Weber, Mater. Sci. Eng. A 523 (2009) 226–234. [5] D.J. Weidner, Y. Wang, M.T. Vaughan, Science 266 (1994) 419–422. [6] K. Yoshida, H. Morigami, Microelectron. Reliab. 44 (2004) 303–308. [7] L. Weber, R. Tavangar, Scr. Mater. 57 (2007) 988–991. [8] K. Chu, C. Jia, H. Guo, W. Li, Mater. Des. 45 (2013) 36–42. [9] J. Wu, H. Zhang, Y. Zhang, J. Li, X. Wang, Mater. Sci. Eng. A 565 (2013) 33–37. [10] T. Schubert, B. Trindade, T. Weißgärber, B. Kieback, Mater. Sci. Eng. A 475 (2008) 39–44. [11] S.V. Kidalov, F.M. Shakhov, Materials 2 (2009) 2467–2495. [12] K. Weidenmann, R. Tavangar, L. Weber, Compos. Sci. Technol. 69 (2009) 1660–1666. [13] S. Ren, X. Shen, C. Guo, N. Liu, J. Zang, X. He, X. Qu, Compos. Sci. Technol. 71 (2011) 1550–1555. [14] K. Chu, C. Jia, W. Tian, X. Liang, H. Chen, H. Guo, Compos. Part A 41 (2010) 161–167. [15] M. Lee, D. Sordelet, Scr. Mater. 55 (2006) 947–950. [16] C.D. Wagner, A.V. Naumkin, A. Kraut-Vass, J.W. Allison, C.J. Powell, J.R. Rumble Jr., NIST XPS Database Version 3 (2003). [17] D. Mortimer, M. Nicholas, J. Mater. Sci. 5 (1970) 149–155. [18] B. Dewar, M. Nicholas, P. Scott, J. Mater. Sci. 11 (1976) 1083–1090. [19] M. Small, E. Ryba, Metall. Trans. A 12 (1981) 1389–1396. [20] A. Van der Ven, H.-C. Yu, G. Ceder, K. Thornton, Prog. Mater. Sci. 55 (2010) 61–105.
Young's modulus / GPa
500
400
Exp. Coated-diamond/Cu M-T Exp. Uncoated-diamond/Cu DEM H-S lower bound H-S upper bound
0 50
55
60
65
Diamond volume fraction / % Fig. 8. Comparison of measured and predicted Young's modulus of uncoateddiamond/Cu and coated-diamond/Cu composites (model expressions and calculation parameters are given in Table 1).
4. Conclusions The results show that Cr7C3 coating has a strong influence on the interfacial bonding and the resulting mechanical properties of diamond/Cu composites. The combined SEM, XRD and XPS analysis confirms that a coating layer consisting of mainly Cr7C3 phase (97.8%) is uniformly formed on the surface of diamond particles. The addition of 65 vol%-coated diamonds causes an increase in Young's modulus and UTS by 84% and 197% compared to those of 65 vol% uncoated-diamond/Cu composites, respectively. This is attributed to the interface modification through the interfacial Cr7C3 coating, which is beneficial for interfacial bonding and load transfer at the
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[21] G. Róg, A. Kozłowska-Róg, M. Dudek, J. Chem. Thermodyn. 39 (2007) 275–278. [22] X.Y. Shen, X.B. He, S.B. Ren, H.M. Zhang, X.H. Qu, J. Alloys Compd. 529 (2012) 134–139. [23] U. Seifert, R. Lipowsky, Phys. Rev. A 42 (1990) 4768. [24] T. Chow, J. Polym. Sci. Polym. Phys. Ed. 20 (1982) 2103–2109.
[25] [26] [27] [28] [29]
Z. Hashin, S. Shtrikman, J. Mech. Phys. Solids. 11 (1963) 127–140. T. Mori, K. Tanaka, Acta Metall. 21 (1973) 571–574. A. Norris, A. Callegari, P. Sheng, J. Mech. Phys. Solids. 33 (1985) 525–544. J. Schjødt-Thomsen, R. Pyrz, Mech. Mater. 33 (2001) 531–544. A. Norris, Mech. Mater. 4 (1985) 1–16.
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