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Electrical resistivity and microstructure of pressureless reactive sintered MoSi2–SiC composite
Materials Chemistry and Physics 86 (2004) 16–20
Electrical resistivity and microstructure of pressureless reactive sintered MoSi2 –SiC composite Xiaoli Zhang a,∗ , Zhenlin Lu b , Zhihao Jin a a
State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, PR China b School of Materials Science and Engineering, Xi’an University of Technology, Xi’an 710048, PR China Received 17 September 2003; received in revised form 31 October 2003; accepted 9 January 2004
Abstract The electrical resistivity of MoSi2 –SiC composites containing different SiC contents were measured and formulated by topological method. The theoretical result and the experimental value were in good agreement with each other. It is indicated that the electrical resistivity of the bulk composites can be increased by increasing volume fractions of the higher electrical resistivity of SiC phase and reducing the MoSi2 phase. The best fitting function may predict the SiC volume fractions and microstructures of the electrical resistivity composites, and give a guideline for material design. © 2004 Published by Elsevier B.V. Keywords: MoSi2 –SiC; Composite; Resistivity; Contiguity
1. Introduction Molybdenum disilicide (MoSi2 ) has been used as heating elements at a temperature of as high as 1900 ◦ C in an air atmosphere [1]. Because of its high melting point (2030 ◦ C), excellent oxidation and corrosion resistance, high electrical conductivity, reasonable density (6.31 g cm−3 ), and thermodynamic compatibility with a wide variety of potential ceramic reinforcements [2–4], this intermetallic was recognized as a potential matrix material useful for high-temperature structural ceramic composites. Unfortunately, due to its brittleness at low temperature and lack of creep resistance at high temperature, several extensive efforts have been done to improve the mechanical properties of MoSi2 [2,5–9]. Till now, many elements and compounds have been used to reinforce its mechanical properties, such as the single elements (Al, Ti, Ta, Ni, B, C), oxides (Sc2 O3 , Y2 O3 , Al2 O3 , ZrO2 ), nitrides (Si3 N4 ), carbides (SiC, TiC), etc. [2,7,10–18]. Among them, SiC particles and whiskers show high chemical compatibility with MoSi2 , high strength, high elastic modulus, and excellent corrosion resistance. The addition of SiC into MoSi2 is considered to be the most effective [19,24]. Although many attempts [3,20–24] have been made to improve the mechanical prop∗ Corresponding author. Tel.: +86-29-82667942; fax: +86-29-82665443. E-mail address: [email protected] (X.L. Zhang).
0254-0584/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.matchemphys.2004.01.027
erties of MoSi2 by the addition of second SiC phase, all of these studies were limited to the process preparation and mechanical property evaluation [25]. For a given two-phase composite, prediction of the electrical resistivity, in terms of microstructural parameters and electrical resistivities of the constituent phases, has been one of the important subjects [26]. It was well known that, besides the electrical resistivities and the volume fraction of the constituent phases, the following microstructural parameters are also most important for precise determination of the electrical resistivity of a macroscopically homogeneous and isotropic two-phase composite: (1) the geometrical distribution of the phases; (2) the size and size distribution of the phases; (3) the topological structure of the phases. It was concluded by Fan et al. [27] that the above microstructural parameters can be simply described by the amount of grain and phase boundary areas present in composites. Based on above introduction, we synthesized MoSi2 –SiC two-phase composites by pressureless reactive sintering for the first time, and made a topological analysis about its electrical resistivity in a new way proposed by Fan [28]. By this approach the SiC volume fractions and microstructures of the composites can be predicted from the desired electrical resistivity, and this can provide an instruction for determining the material microstructures of preparing composites, and make the research on the key composite of MoSi2 –SiC to a microstructural planning stage.
X.L. Zhang et al. / Materials Chemistry and Physics 86 (2004) 16–20
17
2. Experimental procedure The raw materials for preparing the MoSi2 –SiC composite were silicon powder, molybdenum powder (used to synthesis MoSi2 ), 5 m SiC powders, and coke powders and MoSi2 powders with an average size of 42 m, respectively. The Si powder, coke powder, and MoSi2 powder were well mixed to synthesis MoSi2 + Si + C system composites by reactive sintering. The SiC powder and MoSi2 were for MoSi2 +SiC system composites. The Mo powder and Si powder were for MoSi2 monolithic materials to get the ρ␣ (electrical resistivity of MoSi2 phase) of reactive sintering process, and the MoSi2 powder was for MoSi2 bulk materials to get the ρ␣ of MoSi2 + SiC system composites. All the mixtures above were in desired phase constituent confirming to form MoSi2 –SiC composite and MoSi2 . As-mixed powders were pressed into 40 mm × 4 mm × 5 mm dies, then sintered in electrical resistance heating furnace at 1600 ◦ C in an argon atmosphere for 40 min. Electrical resistivity was measured by four-probe method to compensate contact resistance [29]. The phase composition was determined using an X-ray diffractometer (XRD) for MoSi2 +Si+C system composites, and 1600 ◦ C dwelling for 40 min was enough for the reaction to be completed. The resultant phases were MoSi2 , SiC, and very little amount of residual silicon. The density and porosity of the as-sintered products were measured by Archimedes method.
3. The topological transformation for microstructural characterization and electrical resistivity MoSi2 –SiC composite (␣-MoSi2 with a volume fraction of f␣ ; -SiC with a volume fraction of f ) with microstructure A illustrated in Fig. 1(a) could be transformed topologically into a 3-E body (microstructure B) with three microstructural elements illustrated in Fig. 1(b). Element I (EI ) consists only ␣-grains with volume fraction f␣c and only contains ␣-grain boundaries; element II (EII ) consists only -grains with volume fraction fc and only contains -grain boundaries. Only EIII consist phase boundaries with a volume fraction fs (fs = 1 − f␣c − fc ) [30] defined as the degree of separation. EI EII and EIII are parallel along a same direction. Both structures A and B own same electrical current I. Then after this topological transformation, the anal-
Fig. 2. Schematic illustration of (a) current (I) direction in unit cubic 3-E body and (b) equivalent circuit.
ysis of the complicated microstructure was replaced by a study of the simpler but equivalent microstructure with three microstructure elements. Fig. 2(a) shows a unit cube of transformed 3-E body being subjected to an electrical field with a current I, and Fig. 2(b) shows the equivalent electrical circuit of Fig. 2(a). Then the electrical resistivity of 3-E body (ρc ) could be expressed as follows [28]: fc f␣c fs 1 = + + c ρ ρI ρII ρ␣ f␣III + ρ fIII
(1)
where ρI and ρII are electrical resistivity of element I and II; respectively, and f␣III and fIII are the volume fractions of the ␣ and  phase in EIII . It is obvious that ρI = ρ␣ and ρII = ρ , where ρ␣ and ρ are the resistivities of ␣ and  phases, respectively. Assuming that f␣c and fc were power functions of their volume fraction, respectively, then f␣c = f␣m and fc = fn ; therefore fs = 1 − f␣c − fc = 1 − f␣m − fn , where m and n were constants which were characteristics of the phase arrangement in the microstructure. The smaller the values of m and n, the more continuous the relevant phases (usually, a certain porosity in the composite made the contiguity of the phase decrease, and therefore m and n values increase). And from the definition of f␣III and fIII , one can get f␣III = (f␣ − f␣m )/fs and fIII = (f − fm )/fs . Then the Eq. (1) would take the following form: fn (1 − f␣m − fn )2 1 f␣m = + + ρc ρ␣ ρ ρ␣ (f␣ − f␣m ) + ρ (f − fn )
(2)
4. Results and discussion MoSi2
SiC
E
E
E
4.1. Up and low bounds of electrical resistivity
Microstructure A (a)
Microstructure B (b)
Fig. 1. Schematic illustration of topological transformation from microstructure A to microstructure B.
If both MoSi2 phase and SiC phase were perfectly aligned along the direction of the current, i.e. f␣c = f␣ , fc = f , fs = 0, Eq. (1) will become f 1 f␣ = + ρc ρ␣ ρ
(3)
18
X.L. Zhang et al. / Materials Chemistry and Physics 86 (2004) 16–20
concluded that the electrical resistivity of MoSi2 –SiC composite of two systems are changing between HUB (line 1) and LLB (line 2), i.e. the microstructure of MoSi2 phase and SiC phase in the two systems lies between the perfectly parallel and completely separated distribution.
Electrical Resistivity (Ωcm)
0. 05 1
MoSi2 +Si +C System
0. 04
3
0. 03
2
4
0. 02 5
0. 01
4.2. Electrical resistivity of MoSi2 + Si + C and MoSi2 + SiC system and their microstructure analysis
0. 00 0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
Volume Fraction of the SiC Phase
Electrical Resistivity (Ωcm)
Fig. 3. The relationship between resistivity and volume fraction of SiC of MoSi2 + Si + C system. Curve 1: HUB; curve 2: m = 7, n = 4; curve 3: m = 4, n = 7; (䊏) experimental data; curve 5: LLB.
1
0.04 M o Si 2 +SiC System
2
3
0.03 0.02 0.01
4 5
0.00 0.0
0.2
0.4
0.6
0.8
1.0
Volume Fraction of SiC Phase
Fig. 4. The relationship between volume fraction of SiC and electrical resistivity of MoSi2 + SiC system. Curve 1: HUB; curve 2: m = 7, n = 3; curve 3: m = 3, n = 7; (䊏) experimental data; curve 5: LLB.
This is the lowest lower bound (LLB) of electrical resistivity of MoSi2 –SiC composite. If both MoSi2 phase and SiC phase are completely separated, i.e. f␣c = fc = 0, fs = 1, Eq. (1) will become ρc = ρ␣ f␣ + ρ f
(4)
This is the highest upper bound (HUB) of electrical resistivity of MoSi2 –SiC composite. Applying the Eqs. (2)–(4) to MoSi2 +Si+C and MoSi2 + SiC systems, respectively, and considering the experimental data that the electrical resistivity of reactive sintered MoSi2 from Mo and Si powder was 0.002 cm, the electrical resistivity of sintered compressed bulk of MoSi2 from MoSi2 powder was 0.00028 cm, and reported electrical resistivity of SiC produced in literature was 0.0487 cm [31], Figs. 3 and 4 could be obtained, respectively. From that it can be
The electrical resistivities of two kinds of MoSi2 –SiC composites with different SiC content are shown in Table 1. And the densities of specimens with 10, 20, 30, 40, and 50 wt.% SiC content were 5.31, 4.89, 4.51, 4.19, and 3.92 g cm−3 , respectively. It is indicated from Table 1 and Figs. 3 and 4 that the electrical resistivity of the MoSi2 + Si + C system is always one magnitude higher than that of the MoSi2 + SiC system. Fitting the electrical resistivity of both MoSi2 + Si + C system and MoSi2 + SiC system as curve 3 in Figs. 3 and 4 respectively by Eq. (2), the values of m = 4, n = 7 and m = 3, n = 7 could be obtained for both systems, respectively. Because n > m, it was confirmed that the SiC phases were dispersed in the MoSi2 matrix, and furthermore, the contiguity of the MoSi2 phase was lower in the MoSi2 + Si + C system than that in the MoSi2 + SiC system. This would be validated by microstructure of both systems shown in Fig. 5. It was reported [28] that the values of m and n are usually in the range 1–4. But in this study the value of n was higher than 4. The reasons may be that: firstly, it was pressureless sintering in this research and the density of samples was low; and secondly, it was difficult for the composite reinforced by SiC particles to get high density instinctively [32]. Therefore, the porosity would make the phase contiguity low. In this study, the porosity of the as-produced product is below 5%, so it is not the major factor of microstructure issue that influences the electric property. When carbon was used, SiO2 which located at grain boundary would be deoxidized to become Si in situ. This could make the electrical resistivity of MoSi2 + Si + C system a little low because Si was an electric phase. Varying the contiguity of MoSi2 and SiC phases in MoSi2 + Si + C and MoSi2 + SiC systems made the values of m and n to be 7, 4 and 7, 3, respectively, and the curve 2 (in Figs. 3 and 4) could be obtained. It was apparent that the electrical resistivity on line 2 was higher than that
Table 1 The electrical resistivity and porosity of MoSi2 − SiC composite with different SiC content SiC content (wt.%)
10 20 30 40 50
Volume fraction
0.2 0.4 0.5 0.6 0.7
The measured electrical resistivity ( cm)
Porosity (%)
MoSi2 + Si + C system
MoSi2 + SiC system
MoSi2 + Si + C system
MoSi2 + Si + C system
0.007 0.0087 0.014 0.021 0.028
0.00048 0.00143 0.0029 0.0035 0.0079
2.83 3.21 3.54 4.13 4.25
1.39 3.39 3.56 3.91 4.52
X.L. Zhang et al. / Materials Chemistry and Physics 86 (2004) 16–20
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For the reactive sintering, as we know from the literature [33], the produced SiC phase was dispersed in the MoSi2 matrix. It pinned the grain boundaries of MoSi2 matrix, and made the MoSi2 grains become fine and be distributed homogeneously. On the other hand, the SiC particles produced by the reaction C(s) + Si(l) → SiC would be fine (in the size of several molecules) [34], so that the electrical resistivity of MoSi2 + Si + C system would be higher than that of MoSi2 + SiC system, i.e. the reactive sintered composite of MoSi2 + Si + C system had the microstructures with a weak contiguity from both MoSi2 and SiC phase. The SEM photographs of MoSi2 + Si + C system and MoSi2 + SiC system were shown in Fig. 5(a) and (b), respectively. The dark phase was MoSi2 and the white one was SiC. For MoSi2 + Si + C system (Fig. 5(a)), the SiC phase was dispersed in MoSi2 phase and the grain size was small, while for MoSi2 + SiC system (Fig. 5(b)), the MoSi2 phase and SiC phase were joined together respectively and piece-like, and the grain size was very large. It indicated that both the MoSi2 and SiC phases were finer in the former than in the latter. Obviously it coincided with the above analysis about the contiguity of the phase.
5. Conclusions
Fig. 5. SEM photograph of MoSi2 +Si+C system and MoSi2 +SiC system: (a) for MoSi2 + Si + C system; (b) for MoSi2 + SiC system (SiC content is 50 wt.%; the black phase was MoSi2 and the white phase was SiC).
on line 3. For example, taking the volume fraction of SiC phase as 0.3, the value of ρc = 0.00636 cm at m = 4 and n = 7, and ρc = 0.010539 cm at m = 7 and n = 4 for the MoSi2 + Si + C system, while for the MoSi2 + SiC system, ρc = 0.000797 cm at m = 3 and n = 7, and ρc = 0.002828 cm at m = 7 and n = 3. Therefore, the more effective way to increase the electrical resistivity of MoSi2 –SiC composite is to decrease the contiguity of the MoSi2 phase instead of SiC phase.
(1) MoSi2 –SiC composites were prepared by pressureless reactive sintering. The electrical resistivity of MoSi2 –SiC composite of the MoSi2 + Si + C system was always one magnitude higher than that of the MoSi2 + SiC system. The electrical resistivity of both system lay between LLB and HUB. (2) The electrical resistivity of MoSi2 –SiC composite with different SiC content was calculated by topological method. The m, n value of MoSi2 + Si + C system and MoSi2 + SiC system was 4, 7 and 3, 7, respectively, which means that the contiguity of the MoSi2 phase was lower in MoSi2 + Si + C system than that in the MoSi2 + SiC system. The theoretical analysis and the experimental results were in good agreement with each other. (3) The electrical resistivity of the bulk composite can be increased by improving the volume fractions of SiC phase, which has the higher electrical resistivity, and by reducing the contiguity of MoSi2 phase which has lower electrical resistivity. (4) The microstructure of MoSi2 –SiC composite of MoSi2 + Si + C system has much finer grain size than MoSi2 + SiC system. This coincided well with the analysis about the contiguity of two systems. References [1] A.A. Vissa, K. Foston, Ceram. Ind. 33 (1999) 22. [2] J.J. Petrovic, Mater. Sci. Eng. A 192/193 (1995) 31. [3] J. Li, G.Y. Yang, J. Zhu, J. Am. Ceram. Soc. 83 (2000) 992.
20
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[4] A.K. Vasudevan, J.J. Petrovic, Mater. Sci. Eng. A 155 (1992) 1. [5] R.M. Aikin, Ceram. Eng. Sci. Proc. 12 (1991) 1643. [6] K. Yanagihara, T. Maruyama, K. Nagata, Intermetallics 3 (1995) 243. [7] A. Costa e silva, M.J. Kaufman, Mater. Sci. Eng. A 195 (1995) 75. [8] J.J. Petrovic, A.K. Vasudevan, Mater. Sci. Eng. A 261 (1999) 1. [9] W.J. Boettinger, J.H. Perepezko, P.S. Frankwicz, Mater. Sci. Eng. A 155 (1992) 33. [10] H. Chen, M. Suzuki, J. Mater. Sci. 36 (2001) 5773. [11] M.K. Vasudevan, A.J. Thom, M. Akinc, Intermetallics 7 (1999) 153. [12] K. Yanagihara, T. Maruyama, K. Nagata, Intermetallics 3 (1995) 243. [13] K. Yanagihara, T. Maruyama, K. Nagata, Intermetallics 5 (1997) 1. [14] J.M. Ting, J. Am. Ceram. Soc. 77 (1994) 2751. [15] Y. Suzuki, P.E.D. Morgan, K. Niihara, J. Am. Ceram. Soc. 81 (1998) 3141. [16] J. Subrahmanyam, R. Mohan Rao, J. Mater. Res. 10 (1995) 1226. [17] H. Kung, Y.C. Lu, A.H. Bartlett, R.G. Castro, J.J. Petrovic, J. Mater. Res. 13 (1998) 1522. [18] K. Tanaka, K. Nawata, H. Inui, M. Yamaguchi, M. Koiwa, Intermetallics 6 (1998) 607. [19] Q. Zhu, K. Shobu, J. Mater. Sci. 35 (2000) 863. [20] M. Ting, J. Mater. Sci. 30 (1995) 4027.
[21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]
[32] [33] [34]
S. Jayashankar, M.J. Kaufman, J. Mater. Res. 8 (1993) 1428. C.H. Henager Jr., J.L. Brimhall, Mater. Sci. Eng. A 155 (1992) 109. J. Ik Lee, N.L. Hecht, J. Am. Ceram. Soc. 81 (1998) 421. Q. Ma, Y.Q. Yang, M.K. Kang, Q.J. Xue, Compos. Sci. Technol. 61 (2001) 963. X.W. Fu, W.Y. Yang, L.Q. Zhang, J. Univ. Sci. Technol. Beijing 23 (2001) 249. F. Lux, J. Mater. Sci. 28 (1993) 285. Z. Fan, A.P. Miodownik, P. Tsakiropoulos, Mater. Sci. Technol. 12 (1993) 1094. Z. Fan, Acta Metall. Mater. 43 (1998) 43. W.X. Zhang, Electrician Measurement, HuaNanLiGong University, Guang Zhou, 1991, p. 2704. Z. Fan, A.P. Miodownik, P. Tsakiropoulos, Mater. Sci. Technol. 9 (1993) 1094. Z.L. Lu, Reactive sintering SiC materials and its electricity, oxidation characteristic, Doctorate Thesis, Xi’an JiaoTong University, 2000, p. 17. X.L. Zhang, Z.L. Lu, Z.H Jin, China Molyb. Ind. 3 (2002) 29. D.G. Morris, Mater. Sci. Eng. A 251 (1998) 262. L.M. Hongmao, Engineering Ceramic, China Science Publisher, 1989, p. 124 (S.-X. Chen, Trans.).
Electrical resistivity and microstructure of pressureless reactive sintered MoSi2 –SiC composite Xiaoli Zhang a,∗ , Zhenlin Lu b , Zhihao Jin a a
State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, PR China b School of Materials Science and Engineering, Xi’an University of Technology, Xi’an 710048, PR China Received 17 September 2003; received in revised form 31 October 2003; accepted 9 January 2004
Abstract The electrical resistivity of MoSi2 –SiC composites containing different SiC contents were measured and formulated by topological method. The theoretical result and the experimental value were in good agreement with each other. It is indicated that the electrical resistivity of the bulk composites can be increased by increasing volume fractions of the higher electrical resistivity of SiC phase and reducing the MoSi2 phase. The best fitting function may predict the SiC volume fractions and microstructures of the electrical resistivity composites, and give a guideline for material design. © 2004 Published by Elsevier B.V. Keywords: MoSi2 –SiC; Composite; Resistivity; Contiguity
1. Introduction Molybdenum disilicide (MoSi2 ) has been used as heating elements at a temperature of as high as 1900 ◦ C in an air atmosphere [1]. Because of its high melting point (2030 ◦ C), excellent oxidation and corrosion resistance, high electrical conductivity, reasonable density (6.31 g cm−3 ), and thermodynamic compatibility with a wide variety of potential ceramic reinforcements [2–4], this intermetallic was recognized as a potential matrix material useful for high-temperature structural ceramic composites. Unfortunately, due to its brittleness at low temperature and lack of creep resistance at high temperature, several extensive efforts have been done to improve the mechanical properties of MoSi2 [2,5–9]. Till now, many elements and compounds have been used to reinforce its mechanical properties, such as the single elements (Al, Ti, Ta, Ni, B, C), oxides (Sc2 O3 , Y2 O3 , Al2 O3 , ZrO2 ), nitrides (Si3 N4 ), carbides (SiC, TiC), etc. [2,7,10–18]. Among them, SiC particles and whiskers show high chemical compatibility with MoSi2 , high strength, high elastic modulus, and excellent corrosion resistance. The addition of SiC into MoSi2 is considered to be the most effective [19,24]. Although many attempts [3,20–24] have been made to improve the mechanical prop∗ Corresponding author. Tel.: +86-29-82667942; fax: +86-29-82665443. E-mail address: [email protected] (X.L. Zhang).
0254-0584/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.matchemphys.2004.01.027
erties of MoSi2 by the addition of second SiC phase, all of these studies were limited to the process preparation and mechanical property evaluation [25]. For a given two-phase composite, prediction of the electrical resistivity, in terms of microstructural parameters and electrical resistivities of the constituent phases, has been one of the important subjects [26]. It was well known that, besides the electrical resistivities and the volume fraction of the constituent phases, the following microstructural parameters are also most important for precise determination of the electrical resistivity of a macroscopically homogeneous and isotropic two-phase composite: (1) the geometrical distribution of the phases; (2) the size and size distribution of the phases; (3) the topological structure of the phases. It was concluded by Fan et al. [27] that the above microstructural parameters can be simply described by the amount of grain and phase boundary areas present in composites. Based on above introduction, we synthesized MoSi2 –SiC two-phase composites by pressureless reactive sintering for the first time, and made a topological analysis about its electrical resistivity in a new way proposed by Fan [28]. By this approach the SiC volume fractions and microstructures of the composites can be predicted from the desired electrical resistivity, and this can provide an instruction for determining the material microstructures of preparing composites, and make the research on the key composite of MoSi2 –SiC to a microstructural planning stage.
X.L. Zhang et al. / Materials Chemistry and Physics 86 (2004) 16–20
17
2. Experimental procedure The raw materials for preparing the MoSi2 –SiC composite were silicon powder, molybdenum powder (used to synthesis MoSi2 ), 5 m SiC powders, and coke powders and MoSi2 powders with an average size of 42 m, respectively. The Si powder, coke powder, and MoSi2 powder were well mixed to synthesis MoSi2 + Si + C system composites by reactive sintering. The SiC powder and MoSi2 were for MoSi2 +SiC system composites. The Mo powder and Si powder were for MoSi2 monolithic materials to get the ρ␣ (electrical resistivity of MoSi2 phase) of reactive sintering process, and the MoSi2 powder was for MoSi2 bulk materials to get the ρ␣ of MoSi2 + SiC system composites. All the mixtures above were in desired phase constituent confirming to form MoSi2 –SiC composite and MoSi2 . As-mixed powders were pressed into 40 mm × 4 mm × 5 mm dies, then sintered in electrical resistance heating furnace at 1600 ◦ C in an argon atmosphere for 40 min. Electrical resistivity was measured by four-probe method to compensate contact resistance [29]. The phase composition was determined using an X-ray diffractometer (XRD) for MoSi2 +Si+C system composites, and 1600 ◦ C dwelling for 40 min was enough for the reaction to be completed. The resultant phases were MoSi2 , SiC, and very little amount of residual silicon. The density and porosity of the as-sintered products were measured by Archimedes method.
3. The topological transformation for microstructural characterization and electrical resistivity MoSi2 –SiC composite (␣-MoSi2 with a volume fraction of f␣ ; -SiC with a volume fraction of f ) with microstructure A illustrated in Fig. 1(a) could be transformed topologically into a 3-E body (microstructure B) with three microstructural elements illustrated in Fig. 1(b). Element I (EI ) consists only ␣-grains with volume fraction f␣c and only contains ␣-grain boundaries; element II (EII ) consists only -grains with volume fraction fc and only contains -grain boundaries. Only EIII consist phase boundaries with a volume fraction fs (fs = 1 − f␣c − fc ) [30] defined as the degree of separation. EI EII and EIII are parallel along a same direction. Both structures A and B own same electrical current I. Then after this topological transformation, the anal-
Fig. 2. Schematic illustration of (a) current (I) direction in unit cubic 3-E body and (b) equivalent circuit.
ysis of the complicated microstructure was replaced by a study of the simpler but equivalent microstructure with three microstructure elements. Fig. 2(a) shows a unit cube of transformed 3-E body being subjected to an electrical field with a current I, and Fig. 2(b) shows the equivalent electrical circuit of Fig. 2(a). Then the electrical resistivity of 3-E body (ρc ) could be expressed as follows [28]: fc f␣c fs 1 = + + c ρ ρI ρII ρ␣ f␣III + ρ fIII
(1)
where ρI and ρII are electrical resistivity of element I and II; respectively, and f␣III and fIII are the volume fractions of the ␣ and  phase in EIII . It is obvious that ρI = ρ␣ and ρII = ρ , where ρ␣ and ρ are the resistivities of ␣ and  phases, respectively. Assuming that f␣c and fc were power functions of their volume fraction, respectively, then f␣c = f␣m and fc = fn ; therefore fs = 1 − f␣c − fc = 1 − f␣m − fn , where m and n were constants which were characteristics of the phase arrangement in the microstructure. The smaller the values of m and n, the more continuous the relevant phases (usually, a certain porosity in the composite made the contiguity of the phase decrease, and therefore m and n values increase). And from the definition of f␣III and fIII , one can get f␣III = (f␣ − f␣m )/fs and fIII = (f − fm )/fs . Then the Eq. (1) would take the following form: fn (1 − f␣m − fn )2 1 f␣m = + + ρc ρ␣ ρ ρ␣ (f␣ − f␣m ) + ρ (f − fn )
(2)
4. Results and discussion MoSi2
SiC
E
E
E
4.1. Up and low bounds of electrical resistivity
Microstructure A (a)
Microstructure B (b)
Fig. 1. Schematic illustration of topological transformation from microstructure A to microstructure B.
If both MoSi2 phase and SiC phase were perfectly aligned along the direction of the current, i.e. f␣c = f␣ , fc = f , fs = 0, Eq. (1) will become f 1 f␣ = + ρc ρ␣ ρ
(3)
18
X.L. Zhang et al. / Materials Chemistry and Physics 86 (2004) 16–20
concluded that the electrical resistivity of MoSi2 –SiC composite of two systems are changing between HUB (line 1) and LLB (line 2), i.e. the microstructure of MoSi2 phase and SiC phase in the two systems lies between the perfectly parallel and completely separated distribution.
Electrical Resistivity (Ωcm)
0. 05 1
MoSi2 +Si +C System
0. 04
3
0. 03
2
4
0. 02 5
0. 01
4.2. Electrical resistivity of MoSi2 + Si + C and MoSi2 + SiC system and their microstructure analysis
0. 00 0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
Volume Fraction of the SiC Phase
Electrical Resistivity (Ωcm)
Fig. 3. The relationship between resistivity and volume fraction of SiC of MoSi2 + Si + C system. Curve 1: HUB; curve 2: m = 7, n = 4; curve 3: m = 4, n = 7; (䊏) experimental data; curve 5: LLB.
1
0.04 M o Si 2 +SiC System
2
3
0.03 0.02 0.01
4 5
0.00 0.0
0.2
0.4
0.6
0.8
1.0
Volume Fraction of SiC Phase
Fig. 4. The relationship between volume fraction of SiC and electrical resistivity of MoSi2 + SiC system. Curve 1: HUB; curve 2: m = 7, n = 3; curve 3: m = 3, n = 7; (䊏) experimental data; curve 5: LLB.
This is the lowest lower bound (LLB) of electrical resistivity of MoSi2 –SiC composite. If both MoSi2 phase and SiC phase are completely separated, i.e. f␣c = fc = 0, fs = 1, Eq. (1) will become ρc = ρ␣ f␣ + ρ f
(4)
This is the highest upper bound (HUB) of electrical resistivity of MoSi2 –SiC composite. Applying the Eqs. (2)–(4) to MoSi2 +Si+C and MoSi2 + SiC systems, respectively, and considering the experimental data that the electrical resistivity of reactive sintered MoSi2 from Mo and Si powder was 0.002 cm, the electrical resistivity of sintered compressed bulk of MoSi2 from MoSi2 powder was 0.00028 cm, and reported electrical resistivity of SiC produced in literature was 0.0487 cm [31], Figs. 3 and 4 could be obtained, respectively. From that it can be
The electrical resistivities of two kinds of MoSi2 –SiC composites with different SiC content are shown in Table 1. And the densities of specimens with 10, 20, 30, 40, and 50 wt.% SiC content were 5.31, 4.89, 4.51, 4.19, and 3.92 g cm−3 , respectively. It is indicated from Table 1 and Figs. 3 and 4 that the electrical resistivity of the MoSi2 + Si + C system is always one magnitude higher than that of the MoSi2 + SiC system. Fitting the electrical resistivity of both MoSi2 + Si + C system and MoSi2 + SiC system as curve 3 in Figs. 3 and 4 respectively by Eq. (2), the values of m = 4, n = 7 and m = 3, n = 7 could be obtained for both systems, respectively. Because n > m, it was confirmed that the SiC phases were dispersed in the MoSi2 matrix, and furthermore, the contiguity of the MoSi2 phase was lower in the MoSi2 + Si + C system than that in the MoSi2 + SiC system. This would be validated by microstructure of both systems shown in Fig. 5. It was reported [28] that the values of m and n are usually in the range 1–4. But in this study the value of n was higher than 4. The reasons may be that: firstly, it was pressureless sintering in this research and the density of samples was low; and secondly, it was difficult for the composite reinforced by SiC particles to get high density instinctively [32]. Therefore, the porosity would make the phase contiguity low. In this study, the porosity of the as-produced product is below 5%, so it is not the major factor of microstructure issue that influences the electric property. When carbon was used, SiO2 which located at grain boundary would be deoxidized to become Si in situ. This could make the electrical resistivity of MoSi2 + Si + C system a little low because Si was an electric phase. Varying the contiguity of MoSi2 and SiC phases in MoSi2 + Si + C and MoSi2 + SiC systems made the values of m and n to be 7, 4 and 7, 3, respectively, and the curve 2 (in Figs. 3 and 4) could be obtained. It was apparent that the electrical resistivity on line 2 was higher than that
Table 1 The electrical resistivity and porosity of MoSi2 − SiC composite with different SiC content SiC content (wt.%)
10 20 30 40 50
Volume fraction
0.2 0.4 0.5 0.6 0.7
The measured electrical resistivity ( cm)
Porosity (%)
MoSi2 + Si + C system
MoSi2 + SiC system
MoSi2 + Si + C system
MoSi2 + Si + C system
0.007 0.0087 0.014 0.021 0.028
0.00048 0.00143 0.0029 0.0035 0.0079
2.83 3.21 3.54 4.13 4.25
1.39 3.39 3.56 3.91 4.52
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For the reactive sintering, as we know from the literature [33], the produced SiC phase was dispersed in the MoSi2 matrix. It pinned the grain boundaries of MoSi2 matrix, and made the MoSi2 grains become fine and be distributed homogeneously. On the other hand, the SiC particles produced by the reaction C(s) + Si(l) → SiC would be fine (in the size of several molecules) [34], so that the electrical resistivity of MoSi2 + Si + C system would be higher than that of MoSi2 + SiC system, i.e. the reactive sintered composite of MoSi2 + Si + C system had the microstructures with a weak contiguity from both MoSi2 and SiC phase. The SEM photographs of MoSi2 + Si + C system and MoSi2 + SiC system were shown in Fig. 5(a) and (b), respectively. The dark phase was MoSi2 and the white one was SiC. For MoSi2 + Si + C system (Fig. 5(a)), the SiC phase was dispersed in MoSi2 phase and the grain size was small, while for MoSi2 + SiC system (Fig. 5(b)), the MoSi2 phase and SiC phase were joined together respectively and piece-like, and the grain size was very large. It indicated that both the MoSi2 and SiC phases were finer in the former than in the latter. Obviously it coincided with the above analysis about the contiguity of the phase.
5. Conclusions
Fig. 5. SEM photograph of MoSi2 +Si+C system and MoSi2 +SiC system: (a) for MoSi2 + Si + C system; (b) for MoSi2 + SiC system (SiC content is 50 wt.%; the black phase was MoSi2 and the white phase was SiC).
on line 3. For example, taking the volume fraction of SiC phase as 0.3, the value of ρc = 0.00636 cm at m = 4 and n = 7, and ρc = 0.010539 cm at m = 7 and n = 4 for the MoSi2 + Si + C system, while for the MoSi2 + SiC system, ρc = 0.000797 cm at m = 3 and n = 7, and ρc = 0.002828 cm at m = 7 and n = 3. Therefore, the more effective way to increase the electrical resistivity of MoSi2 –SiC composite is to decrease the contiguity of the MoSi2 phase instead of SiC phase.
(1) MoSi2 –SiC composites were prepared by pressureless reactive sintering. The electrical resistivity of MoSi2 –SiC composite of the MoSi2 + Si + C system was always one magnitude higher than that of the MoSi2 + SiC system. The electrical resistivity of both system lay between LLB and HUB. (2) The electrical resistivity of MoSi2 –SiC composite with different SiC content was calculated by topological method. The m, n value of MoSi2 + Si + C system and MoSi2 + SiC system was 4, 7 and 3, 7, respectively, which means that the contiguity of the MoSi2 phase was lower in MoSi2 + Si + C system than that in the MoSi2 + SiC system. The theoretical analysis and the experimental results were in good agreement with each other. (3) The electrical resistivity of the bulk composite can be increased by improving the volume fractions of SiC phase, which has the higher electrical resistivity, and by reducing the contiguity of MoSi2 phase which has lower electrical resistivity. (4) The microstructure of MoSi2 –SiC composite of MoSi2 + Si + C system has much finer grain size than MoSi2 + SiC system. This coincided well with the analysis about the contiguity of two systems. References [1] A.A. Vissa, K. Foston, Ceram. Ind. 33 (1999) 22. [2] J.J. Petrovic, Mater. Sci. Eng. A 192/193 (1995) 31. [3] J. Li, G.Y. Yang, J. Zhu, J. Am. Ceram. Soc. 83 (2000) 992.
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