Ceramics International 45 (2019) 23815–23819
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Short communication
Influence of interface thermal resistance on thermal conductivity of SiC/Al composites
T
Qiuyuan Liua,b, Feng Wangb, Wei Shenb, Xiaopan Qiub, Zhiyong Heb, Qifu Zhangb, Zhipeng Xiea,* a b
State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing, 100084, China China Iron & Steel Research Institute Group, Beijing, 100081, China
ARTICLE INFO
ABSTRACT
Keywords: SiC/Al composite Cerium Thermal conductivity Digital image processing Finite-element grid model
SiC/Al composites were fabricated via a pressureless infiltration process, using SiC powder and aluminum alloy (3% Mg, 3% Mg–Ce) as the main raw materials. The effect of introducing the rare-earth element Ce, on the thermal conductivity (TC) of the SiC/Al composites, was investigated. The results showed that the introduction of Ce improved the TC of the SiC/Al composites; the TC of the composite with 0.5% Ce was as high as 180 W/ (m·K). An analysis of the true microscopic structure of the sample was performed using digital image processing to facilitate finite-element calculation of the TC of the SiC/Al composites. The TC of the composite was analyzed and quantified by comparing the simulated and test results. An equation for calculating the Ce-modified interface thermal resistance influence coefficient was proposed.
1. Introduction With the recent increase in the integration level of semiconductor circuits, the amount of heat generated in the circuits has risen sharply, thus, requiring electronic packaging materials with excellent heat-dissipation and thermal-matching performances. SiC-reinforced Al matrix composites (SiC/Al composites) combine the excellent properties of SiC and Al. They have the advantages of low density and high thermal conductivity (TC), and their thermal expansion coefficient can match that of Si. Thus, they have become the most promising electronic packaging material of the current generation [1–15]. During the manufacture of SiC/Al composites, it is important to improve the compatibility between SiC and Al. Several techniques have been introduced to achieve this—an alloying element [16] can be added into the aluminum matrix, the surfaces of the particles (SiC) can be pretreated [17], or a liquid-phase preparation process can be performed at high temperatures [18,19]. During high-temperature preparation, atomic diffusion, segregation, and mutual reactions between SiC, aluminum, or matrix alloy elements may occur, resulting in the formation of a reaction product or precipitate phase at the interface of the composite. Therefore, the actual interface area of the composite material is an extremely complex and variable “interface phase” or “interface layer” of a certain thickness. TC is an important indicator of the SiC/Al composites. The actual TC of a SiC/Al composite is quite different from its theoretical TC. This is
*
mainly due to the atomic diffusion and mutual reaction of SiC and the alloying elements of the aluminum alloy matrix during the preparation of the SiC/Al composite materials. The factors affecting the TC of SiC/ Al composites are complex, and are related to not only the thermal properties of the particles and aluminum alloy materials but also the interfacial thermal resistance effect [20,21]. The existing researches on the interface have mainly focused on compatibility improvement [22,23], microstructure characterization [24,25], and the influence of interface on the mechanical properties of the SiC/Al composite materials [26,27]. Very few studies have focused on the interface thermophysical properties. Additionally, the commonly used Maxwell [28], Rayleigh [29], and Hasselman and Johnson models [30,31] have certain limitations regarding the TC of composite materials. Therefore, it is necessary to find an appropriate TC prediction model for SiC/Al composites. In this study, a series of SiC/Al composites with added rare-earth Ce was fabricated by a pressureless infiltration process. The influence of Ce content on the TC of the composites was studied. Integrated digital image-processing technology and the finite-element method were used to establish a finite-element model consistent with the true microstructure of the SiC/Al composites. The apparent TC of the SiC/Al composites, without particle interfaces, was calculated using the Fourier heat-conduction equation system. By comparing the calculated and measured TC values, a mathematical model for calculating the TC of the Ce–modified interface thermal resistance has been proposed,
Corresponding author. E-mail address:
[email protected] (Z. Xie).
https://doi.org/10.1016/j.ceramint.2019.07.358 Received 19 July 2019; Received in revised form 30 July 2019; Accepted 31 July 2019 Available online 01 August 2019 0272-8842/ © 2019 Published by Elsevier Ltd.
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which is a new method for evaluating the thermal properties of the SiC/ Al composites. 2. Experimental 2.1. Preparation process The materials used in the experiments were mostly self-prepared aluminum alloys (Al–8.0 wt% Si–3.0 wt% Mg, Al–8.0 wt% Si–3.0 wt% Mg–0–1.0 wt% Ce) and silicon carbide particle powders (Qingzhou Micro Powder, Co., Ltd, Shandong, China; average particle diameters of 10 μm and 90 μm mixed at a weight ratio of 1:3; purity > 99.5%). To prepare the SiC/Al composites via pressureless infiltration, the silicon carbide powder was first pressed uniaxially into cylindrical pellets with diameter 60 mm, at 20 MPa, using polyvinyl alcohol 1750 (Sinopharm Chemical Reagent Co., Ltd., Beijing, China) as a binder. The obtained green bodies were heated at 773 K for 120 min followed by heating at 1373 K for 240 min in air. The infiltration experiment using the aluminum alloys and sintered silicon carbide was conducted in a graphite furnace. A sintering temperature of 1303 K was maintained for 120 min under high-purity (99.99%) nitrogen atmosphere. Raw specimens were taken from the crucible. 2.2. Characterization The densities of the obtained SiC/Al composite specimens were calculated by the Archimedes’ method, using deionized water as the medium. The microstructures of the specimens were characterized using a scanning electron microscope (SEM; FEI Quanta 650, American). The TC (λ) of the specimens was calculated using the equation = Cp , where α is the thermal diffusivity, ρ is the measured density, and Cp is the specific heat. The thermal diffusivity (of a 10 mm × 10 mm × 3 mm specimen) and specific heat (of a 3 mm × 3 mm × 1 mm, < 50 mg specimen) were measured at 298 K using a thermal conductivity device (LFA467, Micro Flash, Netzsch, Germany) and calorimetric meter (PPMS, Quantum Design, American). 3. Results and discussion For a more in-depth study on the influence of the interface thermal resistance on the TC of the SiC/Al composites, the interfaces of the composites were modified with different rare-earth contents, to establish a model of different interface thermal resistances. Fig. 1 shows the TC values of the SiC/Al composites prepared by adding different amounts of Ce. It can be seen clearly that, as the amount of Ce increases, the TC first increases, and then, decreases. The specimen with
0.5% Ce exhibits the highest TC of 180 W/(m·K). It has been reported that [32–35] Ce was enriched easily at the interface during the infiltration because of its slightly solubility in alumina molten. Moreover, Ce would also be reacted with Al2O3 at the interface due to its high affinity to oxygen. These reasons would lead to the interfacial tension decreasing and the wettibility improving. Therefore, more compact samples were obtained, which was beneficial to the TC enhancement. The factors affecting the TC of the SiC/Al composites mainly include two aspects: (1) the content, morphology, and distribution of SiC and (2) the thermal resistance of the SiC/Al interface. To evaluate the influence of the SiC/Al interface thermal resistance on the TC quantitatively, it is important to characterize the effect of the SiC content, morphology, and distribution, on the TC, accurately. At present, the theoretical model for the TC of composite materials simplifies the SiC into an ideal model with uniform distribution state. It is impossible to consider the actual states of the SiC particles according to their various sizes, shapes, and degrees of dispersion in the actual process. Based on this, in this study, digital image processing technology combined with the finite-element method was used to calculate the finite-element TC, based on the microstructures of the real SiC/Al composites. Then, the influence of the SiC content, morphology, and distribution on the TC was calculated accurately. At present, there are three theoretical models for calculating the TC of composite materials: the Maxwell [28], Rayleigh [29], and Hasselman and Johnson models [30,31]. Neither the Maxwell nor Rayleigh model considers the influence of thermal resistance of the surface, and their results are much larger than the actual experimental values. However, none of the three models considers several factors that may have a greater influence on the TC of SiC/Al composites, such as the distribution and shape of the reinforcement particles. The above theoretical models can be used to predict the TC values of the prepared materials. However, both traditional methods and ideal models cannot reflect the influence of the matrix and particle distribution on the TC, accurately. Therefore, it is necessary to optimize the accuracy and application range of the theoretical model further, to characterize the composites accurately. For this reason, this study used SEM images of real structures to calculate the true TC of the composite materials, using the finite-element method. The microstructure of the prepared sample is presented in Fig. 2, in which the light areas represent the Al components and the dark areas represent the SiC components. Equation (1) shows a two-dimensional continuous function. The amplitude of the image is a continuous function of its position. The two-dimensional image is sampled uniformly according to the pixel points, to obtain a discretized digital image about the pixel unit. The digital image consists of pixels in the
Fig. 1. TC of the samples.
Fig. 2. Microstructure of sample. 23816
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Fig. 5. Heat flux distribution of path L. Fig. 3. Binarized image of sample by gray threshold segmentation.
computer, and each pixel at position (x, y) has a corresponding integer value (0–255) that represents the gray level of the pixel. The entire image consists of pixels, each with a different gradation, and each gradation constitutes a discrete function f(x, y) [36,37]. Therefore, the image can be processed by a binarization method. According to Equation (1), a suitable gray threshold, S (S = 125 in Fig. 3), is set, and all the pixels in the image whose value is less than S are assigned the value 0 and appear as pure black; all the pixels whose gray value is greater than S are assigned the value 1 and appear as pure white. The microstructure of the SiC/Al composite material can be seen in Fig. 3 (based on Fig. 2); the lower gray values represent SiC, for which the binarization is 0, and the higher gray values represent Al, for which the binarization is 1. Because the porosity of the composites studied in this paper is lower than 0.2%, the effect of such a low porosity on its TC is extremely limited. Therefore, in order to better study the influence of TC, the defects are ignored in this paper. The gray threshold, S, is obtained by the optimal threshold search method. The binarization of the SEM image in Fig. 2 is shown in Fig. 3. Subsequently, the binarized image is converted into vectorized microstructure data and imported into a finite-element analysis software to generate the corresponding finite-element model. Fig. 4 shows the generated finite-element model of the SiC/Al composite.
g (x , y ) =
1 f (x , y ) 0 f (x , y )
125 125
When the SiC/Al composite material reaches a steady state under a temperature gradient of 25 °C, a path L, perpendicular to the heatconduction direction in the model, is selected, and a heat flux density distribution map of path L is obtained by simulating the heat flux density q, as shown in Fig. 5. Fig. 6 shows a schematic of the corresponding steady-state temperature field distribution when the upper and lower end faces of the SiC/Al composite material are subjected to different temperature loads. The difference in the TC of the SiC and Al, as well as the uneven distribution of the SiC particles, can be observed. Because of this uneven particle distribution, the steady-state temperature field distribution in the SiC/Al composite is uneven and the temperature gradient varies widely, especially at the interface. The different colors in the figure indicate the different states of the temperature-gradient distribution—the darker areas indicate higher temperature gradient changes in the SiC/Al composite. Large temperature gradients occur mainly at the interface, as indicated by the circle A in the figure (where the temperature gradient is the largest in the SiC/Al composite). These areas of the material are the most prone to thermal focusing and, therefore, the most prone to failure. To further understand the variation of the internal temperature field gradient distribution in the SiC/Al composite under external temperature load, the temperature gradient distribution is calculated using ANSYS software, as shown in Fig. 7. The TC of the samples were calculated using the ANSYS finite-element software. Steady-state thermal analyses were performed by
(1)
Fig. 4. Finite-element grid model of sample.
Fig. 6. Thermal gradient distribution under steady-state conditions. 23817
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Fig. 8. Comparison of calculated and experimental TC results of samples.
earth–modified interface thermal resistance.
K c = K 0 (1
Fig. 7. Temperature gradient distribution of sample.
applying temperature loads of T and T + ΔT to the upper and lower end faces, respectively, of the generated finite-element model. The TC of the SiC/Al composite at room temperature, λ0, was 160 W/(m·K). When the SiC/Al composite reaches a steady state within the temperature gradient ΔT, the heat flowing into the composite will be equal to the heat flowing out. The temperature change rate and the cross-sectional area in the direction (unit thickness) are the same in the model of Fig. 4, and the total heat amount q of the arbitrary path L is the same,
q=
K Td
(2)
where ∇T is the temperature gradient vector, Γ is the integral path of K Td is the total heat flux per unit the heat flux density, and thickness at any height of the SiC/Al composite. Under steady-state conditions, the TC of the material in the heat flow direction can be computed by the Fourier's equation, c
=
hq Tl
(3)
where λc is the calculated TC of the SiC/Al composite (apparent TC), h is the height of the composite, l is the width, ΔT is the temperature difference. Fig. 5 indicates that the heat flux density distribution is quite uneven. As the temperature gradient distribution is large at the interface, the heat flux density varies significantly near the interface, which produces the peaks in the figure. By integrating the heat flux density corresponding to path L (Fig. 7), the total heat flowing through the SiC/ Al composite under the temperature gradient can be obtained. According to Formula (2), the TC of the SiC/Al composite microdomain shown in Fig. 2 can be calculated to be 190 W/(m·K). In this study, sixty SEM images of the samples were selected randomly for the TC calculation. Fig. 8 shows the statistically averaged results and compares the calculated and experimental TC results of the SiC/Al composite specimens. The solid line represents the finite-element calculation value and the dash line represents the test values. The difference between the two indicates the influence of the interface thermal resistance on the TC. In this study, based on the measured effective TC and the finiteelement TC calculation of the real SiC topography distribution, a simplified TC calculation model was established, as shown in Equation (4), where Kc is the test value, K0 is the calculated value, and β is denoted as the influence coefficient of the rare-earth Ce–modified interface thermal resistance on the TC of the composite. Thus, Equation (4) gives the mathematical model for calculating the TC of the rare-
)
(4)
The influence coefficient β is calculated by substituting the measured and calculated TC values into Equation (4), and the results are plotted in Fig. 9. The calculated value of β without rare-earth Ce was 18.75%, which decreased significantly after the addition of rare-earth Ce. The calculated value of β with 0.5% Ce was the smallest, at 11.11%—a reduction of 7.64% points. Thus, this paper presents a novel method for evaluating the thermal performance of SiC/Al composites by calculating the value of β quantitatively. 4. Conclusions In this study, interfacial modification of SiC/Al composites was performed by the addition of different amounts of Ce. The influence of the interface thermal resistance on the TC of the SiC/Al composites was studied. The thermal conductivity reached a high value of 180 W/(m·K) when 0.5% Ce was added. This indicated that the introduction of an appropriate amount of Ce could effectively improve the interface conditions, thereby improving the TC of the SiC/Al composites. A finite-element model consistent with the microstructure of the SiC/Al composites was established based on integrated digital image processing technology and the finite-element mesh generation method. The effective thermal conductivities, according to the different Ce contents, were calculated using the Fourier heat-conduction equation, and a mathematical model for calculating the TC of the Ce-modified interface thermal resistance was established. According to the simulations and calculations, the TC of the sample with 0.5% Ce was the best,
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Fig. 9. Influence coefficient β of interface thermal resistance of samples.
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and its influence coefficient of interface thermal resistance was the smallest (β = 11.11%), which was consistent with the measured analysis results. This work provides a novel research method for analyzing the thermal performance of SiC/Al composites.
[16] [17]
Acknowledgments This work was financially supported by the National Science and Technology Major Project (Grant no. 2013ZX02104) and the CAS Key Laboratory of Cryogenics, TIPC (CRYO201804). References
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