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Investigation of isothermal and no-isothermal oxidation of SiC powder using an analytic kinetic model
Applied Surface Science 257 (2010) 463–467
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Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Investigation of isothermal and no-isothermal oxidation of SiC powder using an analytic kinetic model Yong Li a,b,c , Yun Yang a , Zhi-Ming Lin a , Jiang-Tao Li a,∗ a b c
Technical Institute of Physics and Chemistry, Chinese Academy of Science, Beijing 100101, PR China Graduate School of the Chinese Academy of Science, Beijing 100039, PR China P.O. Box 7220, Beijing 100072, PR China
a r t i c l e
i n f o
Article history: Received 8 May 2010 Received in revised form 2 July 2010 Accepted 6 July 2010 Available online 13 July 2010 Keywords: Oxidation SiC powder Analytic kinetic model Apparent activation energy
a b s t r a c t The oxidation of SiC powder has been investigated under non-isothermal and isothermal conditions. Xray diffraction (XRD) analysis and transmission electron microscopy (TEM) were employed to investigate the morphological development during the oxidation. The results show that the major oxidation product was amorphous silica and the oxidation reaction was mainly diffusion-controlled. Based on limited experimental data, an analytic kinetic model, which expresses the oxidation weight gain as a function of time and temperature explicitly, has been used to predict the oxidation behavior of SiC powder. The comparison between experimental results and theoretical calculation shows that this new model works very well. The activation energy of non-isothermal and isothermal oxidation of SiC powder has been derived to be 226.5 kJ/mol and 187.5 kJ/mol, respectively. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Silicon carbide (SiC) is a material with excellent thermal conductivity, high strength and hardness, good chemical stability. In recent years, SiC based composites have been used in radiant heaters and engine components and electronic device applications demanding high temperature and high power operation [1]. Although SiC powder could be processed into dense SiC ceramics, it is also used as inclusions to fabricate ceramic composites [2]. For example, nanosized silicon carbide has found applications in oxidation coating of carbon composites and bulk composites with enhanced mechanical and tribological properties [3]. Therefore, the oxidation behavior of SiC powder or SiC-containing composites is an important issue for their high temperature applications. Numerous studies have been conducted for the oxidation behavior SiC. It is a general agreement that their oxidation behavior can be divided into passive and active oxidation. In active oxidation, gaseous SiO is formed and escapes away from the surface of SiC. The oxidation process is characterized by the loss in mass. Active oxidation often occurs under low oxygen partial pressures. On the contrary, in the passive oxidation, a coherent and dense SiO2 layer is formed on the surface of SiC, the oxidation rate is greatly reduced [4–7].
∗ Corresponding author. Tel.: +86 10 82543693; fax: +86 10 82543693. E-mail address: [email protected] (J.-T. Li). 0169-4332/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2010.07.012
For most applications, the oxidation of SiC was controlled in the region of passive oxidation. The passive oxidation of SiC has been extensively studied. The classical parabolic equation is intensively used to treat the oxidation behavior when diffusion is the controlling step [8]. Its expression can be written in the following form [9]:
w 2 A
= kt + c
(1)
where w/A is the oxidation mass changes/unit area, k = k0 exp( − Ea /RT) is the parabolic rate constant and c is a numerical constant. Although, the parabolic rate law has been extensively used to investigate the oxidation behavior of SiC, the physical meaning of the parameter k is not clear and this kind of treatment was unable to lead to an explicit analytic expression. Compared with the work of SiC bulk materials, the oxidation behavior of SiC powder is less thoroughly investigated because it is affected by many factors such as particle size, oxygen pressure, and character of the sample. Moreover, weight gain per unit surface area of the samples was often used as the parameter in many studies of SiC oxidation behavior. It is not an easy task to measure the surface area if SiC are powders with a wide range of size distributions. Therefore, there are wide variations in the observed reaction rates and different activation energy has been proposed. In this paper, the oxidation of SiC powder was carried out both in isothermal as well as non-isothermal modes. A new kinetic diffusion control model, which is proposed by Chou [10] was used
464
Y. Li et al. / Applied Surface Science 257 (2010) 463–467
to investigate oxidation kinetic mechanisms of SiC powder. Based on the experimental results, a simple calculation was performed and a simple set of explicit analytic equations were developed, which gives the relation between the reacted fraction of oxidation and temperature and time in the isothermal and non-isothermal oxidation processes. 2. Experimental procedure -SiC powders used in the present study were fabricated by a combustion synthesis (CS) method using silicon powders, carbon black as raw materials in our lab. The fabrication process has been described previously [11]. The as-synthesized powders were fired at 973 K in air for 1 h to remove the excess of carbon. The particle size of the -SiC powders determined by laser scattering method is 0.1–0.3 m. The non-isothermal oxidation experiment was carried out on a Nezsch STA409C thermal analysis system in non-isothermal modes. The balance of the unit had a detection limit of 1 g. The effect of the heating rate was considered. The SiC powders were held in an alumina crucible which was placed in the heating furnace. The sample was heated from 298 K to 1473 K with fixed heating rates (5 K/min, 10 K/min, 15 K/min). Air was introduced into the reaction tube with fixed flow of 60 ml/min. The isothermal oxidation experiments were carried out in the quartz tube in a mafu furnace in air atmosphere at 1223 K. The suitable isothermal oxidation temperature was chosen according to the non-isothermal oxidation results. The following procedure was adopted. The sample about 20.00 g was weighed carefully by an electronic balance with an accuracy of ±0.1 mg. The sample was put in a Al2 O3 crucible. Samples were inserted into a mafu furnace, which was preheated to 1223 K. The SiC powder was withdrawn from the furnace at various intervals in order to measure the weight change. Crucible without SiC powder was also exposed under the same conditions, but their weight changes were negligible. To understand the oxidation process of SiC, X-ray diffraction (XRD) analysis and transmission electron microscopy (TEM) were applied to the samples before and after oxidation treatment. 3. Chou model
=1−
1−
where E represents the apparent activation energy (J/mol), BT =
(2K0 D0 /vm )
3
exp(−E/RT )t BT
(2)
1 PO2 −
eq
PO
2
/R02
eq
PO is oxygen partial pressure equilibrium with oxide (Pa), K0 2 and D0 are equilibrium constant of oxidation reaction and diffusion coefficient of oxygen in dependent of temperature T, vm is a coefficient related to the density of reactant and product, R0 is the radius of the particle. In the present case, it is corresponding to an “effective radius” because of the particle size distribution. If the PO2 eq is constant and the temperature coefficient of PO is very small, the 2 BT can be regarded as constant. When the temperature of furnace is heated up, the sample is in a condition with a certain temperatureincreasing rate ( = dT/dt). If the system is heated from temperature T0 , thus the relation of temperature with time t should be: T = T0 + t
(3)
Thus, Eq. (2) will become
=1−
The oxidation of SiC is a heterogeneous gas–solid reaction, which could include a series of intermediate steps, such as buck diffusion, diffusion within the layer, chemical reaction, and surface penetration. Among all these steps, the oxygen diffusion process in the oxide layer is regarded as rate-controlling step [12–14]. For convenience, the powder of SiC was regarded as spherical balls with the same density and radius. Therefore, the passive oxidation process can be described by the schematic diagram shown in Fig. 1. Where a represented SiC powder with radius of r,  was oxide layer with thickness of x. The whole particle was a ball of radius R0 . Recently, Hou and Chou [15] have developed a new model that can explicitly express the reacted fraction as a function of oxidation time, temperature, particle size, oxygen pressure as well as many other related physical properties. The most attractive point for this model is that one can get a more accurate and simple calculation result in comparison with other method, for example, the parabolic rate law [16]. The analytic kinetic model, Chou model, has been successfully applied to treat the oxidation behavior of –SiAlON, Si3 N4 , AlN, etc. [17–19]. Based on Chou model, the reacted fraction of SiC powder with time t can be described as follows [15]:
Fig. 1. A schematic diagram of oxidation of -SiC particle.
1−
1 E exp − BT RT
T −T
0
3 (4)
Eqs. (2) and (4) are two explicit formulas that describe the reacted fraction as the function of time t, temperature T and other related parameters under condition of diffusion-controlled. The advantage of the above equations is that we can quantitatively investigate the isothermal and non-isothermal passive oxidation behaviors of SiC powders. 4. Results and discussion 4.1. Oxidation products and kinetics Fig. 2 shows the experimental data of the thermo-gravimetric results at different heating rates. The oxidation rate of the sample with the heating rate of 5 K/min was the fasted among the three heating rates. The experimental results also revealed that the weight of SiC powder increased at temperature above 1123 K, indicating the temperature for significant oxidation of the SiC powder was 1123 K. The oxidation behavior followed a parabolic rate law and the weight gain in the oxidation process was attributed to the passive oxidation of SiC [2]. The XRD results of the SiC powders before and after oxidation treatment are shown in Fig. 3. As we can see, the mono-phase of SiC was predominated for the pristine SiC powder. After oxidation for 20 h at 1223 K, the XRD patterns showed a hump around 2 theta
Y. Li et al. / Applied Surface Science 257 (2010) 463–467
465
Fig. 3. XRD patterns of SiC powder oxidized in air.
is that: Fig. 2. The experiment data for non-isothermal oxidation behavior of SiC powder oxidized in air.
equal to 20◦ , indicating that the silica was amorphous. The TEM micrograph of a SiC particle after 20 h oxidation treatment at 1223 K was shown in Fig. 4(a) and the selected electron diffraction (SED) patterns corresponding to the oxide layer and SiC core were shown in Fig. 4(b) and (c). The TEM image and SED patterns show that each SiC particle was surrounded by a layer of amorphous silica. From the above results, we can concluded that the oxidation rate for the SiC powder was controlled by oxygen diffusion through the oxide product layer to the oxide/SiC interface, which is in coincident with the results in literatures [2].
=
m/m0 mmax /m0
(5)
where mmax is the theoretical maximum increment after complete oxidation. Eq. (4) becomes the following:
mmax m = × m0 m0
1−
1−
1 exp BT
εap − RT
(T − T0 )
3 (6)
Now, let us use Eq. (6) to fit our experimental data. The results obtained are plotted in Fig. 5, the corresponding parameters extracted from the fitting are also listed in Fig. 5. Substituting these values into Eq. (6) yields:
3
4.2. Application of Chou model to non-isothermal oxidation of SiC powder
m = 50 × m0
Now we will use Chou model to non-isothermal oxidation of SiC powder. In the present cases, our experimental results represent a relationship between the dimensionless mass change, m/m0 (m0 denotes the sample of original weight and m the increment of sample weight after oxidation at time t) versus temperature, not the reacted fraction , therefore, a transformation of variable is necessary prior to using Chou model. The relation between and m/m0
If the heating rates are taken as = 5 K/min, 10 K/min, 20 K/min we have three theoretical curves. These three are drawn in the same plot for the purpose of comparison. From Fig. 5, we can see that there is a good agreement between the experimental data and theoretical calculation. Some small errors exist in the low temperature, which can be ascribed to particle size distribution, approximation of assumption, etc.
1−
1−
1 2.45 × 10−5
exp
226, 500 − RT
(T − T0 )
(7)
Fig. 4. (a) TEM micrograph of a SiC particle after 1223 K/20 h oxidation. (b) Electron diffraction patterns from the oxide layer. (c) Electron diffraction patterns from the SiC core.
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Y. Li et al. / Applied Surface Science 257 (2010) 463–467
Fig. 5. A comparison of experimental data with model for non-isothermal oxidation of -SiC powder at different temperature-increasing rates.
Fig. 7. A isothermal oxidation of -SiC powder predicted by model at various temperatures.
SiC powders is as follows:
4.3. Application of Chou model to isothermal oxidation process of SiC powder For the isothermal oxidation process, Eq. (2) can be used to investigate the isothermal oxidation process of SiC powder. Similarly, some conversions are also needed before using this formula. After conversion, Eq. (2) can be described as follows:
⎡ m mmax = × ⎣1 − m0 m0
1−
1 exp BT
εap − RT
⎤ 3 ⎦ t
m = 50 × 1− 1− m0
1 1.74 × 10−2
187, 500 3
exp −
RT
t
(9)
Based on Eq. (9), the isothermal oxidation behaviors of SiC powder at temperature from 1100 K to 1300 K with an interval of 50 K can be predicted and they have now been plotted in Fig. 7. 5. Discussion
(8)
Eq. (8) now is used to fit the isothermal oxidation experimental data. The fitting results are shown in Fig. 5. From Fig. 6, it can be seen that Eq. (8) gives a very good fit with the experimental data. The relative coefficient for this curve fitting has reached 0.98. The good fitting between the theoretical prediction and experimental data indicates that Chou model is reasonable. The apparent activation energy can be extracted as 187.5 kJ/mol, and BT = 1.74 × 10−2 . The above εap and BT were substituted into Eq. (8), the model describing the isothermal oxidation behavior of
As mentioned above, the oxidation reaction for SiC powder is a kind of complicated heterogeneous process. It is very difficult for us to give a theoretical description for it. Chou model gives an explicit analytic expression of the oxidation fraction with time and temperature. In this model, all the parameters, for example, temperature T, apparent activation energy εap , diffusion coefficient, etc. have clear physical meanings. Some of the parameters can be combined to construct an auxiliary function like BT . As a result, Chou model will become very simple and easy to use. A good agreement has been reached between experimental data and theoretical model in the isothermal and non-isothermal oxidation process of SiC system when Chou model is applied. The εap for the non-isothermal oxidation of SiC powder, predicted by Chou model, is 226.5 kJ/mol, while for the isothermal oxidation process, the εap is 187.5 kJ/mol. This difference has been regarded as an acceptable value between isothermal and non-isothermal methods in the literatures. Furthermore, we can predict the oxidation behavior within the same oxidation behavior based on limited experimental data, which is very helpful in actual applications. 6. Conclusions
Fig. 6. A comparison of experimental data with model for oxidation of SiC powder at temperature 1173 K and 1223 K.
The oxidation experiments of SiC powders synthesized from a self-propagating method have been performed under both nonisothermal and isothermal conditions. Based on the experimental data and assuming the oxygen diffusion as the controlling step, Chou model was applied to predict the oxidation behavior of SiC powder and worked well. The calculated results showed that both the theoretical calculation and experimental data can reach a good agreement. Two simple and explicit analytic formulas have been proposed to describe the relation between the reacted fraction of oxidation and time and temperature. The activation energy of nonisothermal and isothermal oxidation of SiC powder is obtained to be very close with this model.
Y. Li et al. / Applied Surface Science 257 (2010) 463–467
Acknowledgments The finical support from the following three projects are greatly appreciated: Key Laboratory of Functional Crystals and Laser Technology, TIPC, CAS.; National Natural Science Foundation Key Project, No. 50932006, National Natural Science Foundation Project, No. 50772116. References [1] Y. Lin, L. Chen, Oxidation of SiC powder in SiC/alumina/zirconia compacts, Ceram. Int. 26 (2000) 593–598. [2] P. Mogilevsky, A. Zangvil, Modeling of oxidation behavior of SiC-reinforced ceramic matrix composites, Mater. Sci. Eng. A 262 (1999) 16–24. [3] J.F. Huang, X.R. Zeng, H.J. Li, X.B. Xiong, M. Huang, Carbon 42 (8–9) (2004) 1517–1521. [4] B.E. Deal, A.S. Grove, General relationship for the thermal oxidation of silicon, J. Appl. Phys. 36 (12) (1965) 3770–3778. [5] K.J.D. MacKenzie, S.S. Shimada, T. Aoki, Thermal oxidation of carbothermal  – SiAlON powder: reaction sequence and kinetics, J. Mater. Chem. 7 (3) (1997) 527–530. [6] C.E. Ramberg, G. Cruciani, K.E. Spear, R.E. Tressler, Passive-oxidation kinetics of high-purity silicon carbide from 800◦ to 1100 ◦ C, J. Am. Ceram. Soc. 79 (11) (1996) 2897–2911. [7] L.U.J.T. Ogbuji, Effect of oxide devitrification on oxidation kinetics of SiC, J. Am. Ceram. Soc. 80 (6) (1997) 1544–1550.
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[8] L. Bharadwaj, Y. Fan, L. Zhang, D. Jiang, L. An, Oxidation behavior of a fully dense polymer-derived amorphous silicon carbonitride ceramic, J. Am. Ceram. Soc. 87 (3) (2004) 483–486. [9] J. Quanli, Z. Haijun, L. Suping, J. Xiaolin, Effect of particle size on oxidation of silicon carbide powders, Ceram. Int. 33 (2007) 309–313. [10] K.C. Chou, A kinetic mdel for oxidation of Si–Al–O–N materials, J. Am. Ceram. Soc. 89 (5) (2006) 1568–1576. [11] Y. Yang, K. Yang, Z.M. Lin, J.L. Li, Mechanical-activation-assisted combustion synthesis of SiC, Mater. Lett. 61 (2007) 671–676. [12] K.C. Chou, Q. Li, Q. Lin, L.J. Jiang, K.D. Xu, Kinetics of absorption and desorption of hydrogen in alloy powder, Int. J. Hydrogen Energy 30 (3) (2005) 301–309. [13] X. Hou, G. Zhang, K.-C. Chou, Influence of particle size distribution on oxidation behavior of SiC powder, J. Alloy Compd. 477 (2009) 166–170. [14] X. Hou, K.-C. Chou, Model of oxidation of SiC microparticles at high temperature, Corr. Sci. 50 (2008) 2367–2371. [15] X.-M. Hou, K.-C. Chou, J. Eur. Ceram. Soc. 29 (2006) 517–523. [16] X. Hou, K.-C. Chou, Comparison of the diffusion control models for isothermal oxidation of SiAlON powders, J. Am. Ceram. Soc. 91 (10) (2008) 3315–3319. [17] X. Hou, G. Zhang, K. Chou, A comparison of oxidation kinetics of O – SiAlON and  – SiAlON powders synthesized from bauxite, Int. J. Appl. Ceram. Technol. 5 (5) (2008) 529–536. [18] X. Hou, K.-C. Chou, X. Hu, H. Zhao, A new measurement and treatment for kinetics of isothermal oxidation of Si3 N4 , J. Alloy Compd. 459 (2008) 123–129. [19] X. Hou, K.-C. Chou, Investigation of isothermal oxidation of AlN ceramics using different kinetic model, Corr. Sci. 51 (2009) 556–561.
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Investigation of isothermal and no-isothermal oxidation of SiC powder using an analytic kinetic model Yong Li a,b,c , Yun Yang a , Zhi-Ming Lin a , Jiang-Tao Li a,∗ a b c
Technical Institute of Physics and Chemistry, Chinese Academy of Science, Beijing 100101, PR China Graduate School of the Chinese Academy of Science, Beijing 100039, PR China P.O. Box 7220, Beijing 100072, PR China
a r t i c l e
i n f o
Article history: Received 8 May 2010 Received in revised form 2 July 2010 Accepted 6 July 2010 Available online 13 July 2010 Keywords: Oxidation SiC powder Analytic kinetic model Apparent activation energy
a b s t r a c t The oxidation of SiC powder has been investigated under non-isothermal and isothermal conditions. Xray diffraction (XRD) analysis and transmission electron microscopy (TEM) were employed to investigate the morphological development during the oxidation. The results show that the major oxidation product was amorphous silica and the oxidation reaction was mainly diffusion-controlled. Based on limited experimental data, an analytic kinetic model, which expresses the oxidation weight gain as a function of time and temperature explicitly, has been used to predict the oxidation behavior of SiC powder. The comparison between experimental results and theoretical calculation shows that this new model works very well. The activation energy of non-isothermal and isothermal oxidation of SiC powder has been derived to be 226.5 kJ/mol and 187.5 kJ/mol, respectively. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Silicon carbide (SiC) is a material with excellent thermal conductivity, high strength and hardness, good chemical stability. In recent years, SiC based composites have been used in radiant heaters and engine components and electronic device applications demanding high temperature and high power operation [1]. Although SiC powder could be processed into dense SiC ceramics, it is also used as inclusions to fabricate ceramic composites [2]. For example, nanosized silicon carbide has found applications in oxidation coating of carbon composites and bulk composites with enhanced mechanical and tribological properties [3]. Therefore, the oxidation behavior of SiC powder or SiC-containing composites is an important issue for their high temperature applications. Numerous studies have been conducted for the oxidation behavior SiC. It is a general agreement that their oxidation behavior can be divided into passive and active oxidation. In active oxidation, gaseous SiO is formed and escapes away from the surface of SiC. The oxidation process is characterized by the loss in mass. Active oxidation often occurs under low oxygen partial pressures. On the contrary, in the passive oxidation, a coherent and dense SiO2 layer is formed on the surface of SiC, the oxidation rate is greatly reduced [4–7].
∗ Corresponding author. Tel.: +86 10 82543693; fax: +86 10 82543693. E-mail address: [email protected] (J.-T. Li). 0169-4332/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2010.07.012
For most applications, the oxidation of SiC was controlled in the region of passive oxidation. The passive oxidation of SiC has been extensively studied. The classical parabolic equation is intensively used to treat the oxidation behavior when diffusion is the controlling step [8]. Its expression can be written in the following form [9]:
w 2 A
= kt + c
(1)
where w/A is the oxidation mass changes/unit area, k = k0 exp( − Ea /RT) is the parabolic rate constant and c is a numerical constant. Although, the parabolic rate law has been extensively used to investigate the oxidation behavior of SiC, the physical meaning of the parameter k is not clear and this kind of treatment was unable to lead to an explicit analytic expression. Compared with the work of SiC bulk materials, the oxidation behavior of SiC powder is less thoroughly investigated because it is affected by many factors such as particle size, oxygen pressure, and character of the sample. Moreover, weight gain per unit surface area of the samples was often used as the parameter in many studies of SiC oxidation behavior. It is not an easy task to measure the surface area if SiC are powders with a wide range of size distributions. Therefore, there are wide variations in the observed reaction rates and different activation energy has been proposed. In this paper, the oxidation of SiC powder was carried out both in isothermal as well as non-isothermal modes. A new kinetic diffusion control model, which is proposed by Chou [10] was used
464
Y. Li et al. / Applied Surface Science 257 (2010) 463–467
to investigate oxidation kinetic mechanisms of SiC powder. Based on the experimental results, a simple calculation was performed and a simple set of explicit analytic equations were developed, which gives the relation between the reacted fraction of oxidation and temperature and time in the isothermal and non-isothermal oxidation processes. 2. Experimental procedure -SiC powders used in the present study were fabricated by a combustion synthesis (CS) method using silicon powders, carbon black as raw materials in our lab. The fabrication process has been described previously [11]. The as-synthesized powders were fired at 973 K in air for 1 h to remove the excess of carbon. The particle size of the -SiC powders determined by laser scattering method is 0.1–0.3 m. The non-isothermal oxidation experiment was carried out on a Nezsch STA409C thermal analysis system in non-isothermal modes. The balance of the unit had a detection limit of 1 g. The effect of the heating rate was considered. The SiC powders were held in an alumina crucible which was placed in the heating furnace. The sample was heated from 298 K to 1473 K with fixed heating rates (5 K/min, 10 K/min, 15 K/min). Air was introduced into the reaction tube with fixed flow of 60 ml/min. The isothermal oxidation experiments were carried out in the quartz tube in a mafu furnace in air atmosphere at 1223 K. The suitable isothermal oxidation temperature was chosen according to the non-isothermal oxidation results. The following procedure was adopted. The sample about 20.00 g was weighed carefully by an electronic balance with an accuracy of ±0.1 mg. The sample was put in a Al2 O3 crucible. Samples were inserted into a mafu furnace, which was preheated to 1223 K. The SiC powder was withdrawn from the furnace at various intervals in order to measure the weight change. Crucible without SiC powder was also exposed under the same conditions, but their weight changes were negligible. To understand the oxidation process of SiC, X-ray diffraction (XRD) analysis and transmission electron microscopy (TEM) were applied to the samples before and after oxidation treatment. 3. Chou model
=1−
1−
where E represents the apparent activation energy (J/mol), BT =
(2K0 D0 /vm )
3
exp(−E/RT )t BT
(2)
1 PO2 −
eq
PO
2
/R02
eq
PO is oxygen partial pressure equilibrium with oxide (Pa), K0 2 and D0 are equilibrium constant of oxidation reaction and diffusion coefficient of oxygen in dependent of temperature T, vm is a coefficient related to the density of reactant and product, R0 is the radius of the particle. In the present case, it is corresponding to an “effective radius” because of the particle size distribution. If the PO2 eq is constant and the temperature coefficient of PO is very small, the 2 BT can be regarded as constant. When the temperature of furnace is heated up, the sample is in a condition with a certain temperatureincreasing rate ( = dT/dt). If the system is heated from temperature T0 , thus the relation of temperature with time t should be: T = T0 + t
(3)
Thus, Eq. (2) will become
=1−
The oxidation of SiC is a heterogeneous gas–solid reaction, which could include a series of intermediate steps, such as buck diffusion, diffusion within the layer, chemical reaction, and surface penetration. Among all these steps, the oxygen diffusion process in the oxide layer is regarded as rate-controlling step [12–14]. For convenience, the powder of SiC was regarded as spherical balls with the same density and radius. Therefore, the passive oxidation process can be described by the schematic diagram shown in Fig. 1. Where a represented SiC powder with radius of r,  was oxide layer with thickness of x. The whole particle was a ball of radius R0 . Recently, Hou and Chou [15] have developed a new model that can explicitly express the reacted fraction as a function of oxidation time, temperature, particle size, oxygen pressure as well as many other related physical properties. The most attractive point for this model is that one can get a more accurate and simple calculation result in comparison with other method, for example, the parabolic rate law [16]. The analytic kinetic model, Chou model, has been successfully applied to treat the oxidation behavior of –SiAlON, Si3 N4 , AlN, etc. [17–19]. Based on Chou model, the reacted fraction of SiC powder with time t can be described as follows [15]:
Fig. 1. A schematic diagram of oxidation of -SiC particle.
1−
1 E exp − BT RT
T −T
0
3 (4)
Eqs. (2) and (4) are two explicit formulas that describe the reacted fraction as the function of time t, temperature T and other related parameters under condition of diffusion-controlled. The advantage of the above equations is that we can quantitatively investigate the isothermal and non-isothermal passive oxidation behaviors of SiC powders. 4. Results and discussion 4.1. Oxidation products and kinetics Fig. 2 shows the experimental data of the thermo-gravimetric results at different heating rates. The oxidation rate of the sample with the heating rate of 5 K/min was the fasted among the three heating rates. The experimental results also revealed that the weight of SiC powder increased at temperature above 1123 K, indicating the temperature for significant oxidation of the SiC powder was 1123 K. The oxidation behavior followed a parabolic rate law and the weight gain in the oxidation process was attributed to the passive oxidation of SiC [2]. The XRD results of the SiC powders before and after oxidation treatment are shown in Fig. 3. As we can see, the mono-phase of SiC was predominated for the pristine SiC powder. After oxidation for 20 h at 1223 K, the XRD patterns showed a hump around 2 theta
Y. Li et al. / Applied Surface Science 257 (2010) 463–467
465
Fig. 3. XRD patterns of SiC powder oxidized in air.
is that: Fig. 2. The experiment data for non-isothermal oxidation behavior of SiC powder oxidized in air.
equal to 20◦ , indicating that the silica was amorphous. The TEM micrograph of a SiC particle after 20 h oxidation treatment at 1223 K was shown in Fig. 4(a) and the selected electron diffraction (SED) patterns corresponding to the oxide layer and SiC core were shown in Fig. 4(b) and (c). The TEM image and SED patterns show that each SiC particle was surrounded by a layer of amorphous silica. From the above results, we can concluded that the oxidation rate for the SiC powder was controlled by oxygen diffusion through the oxide product layer to the oxide/SiC interface, which is in coincident with the results in literatures [2].
=
m/m0 mmax /m0
(5)
where mmax is the theoretical maximum increment after complete oxidation. Eq. (4) becomes the following:
mmax m = × m0 m0
1−
1−
1 exp BT
εap − RT
(T − T0 )
3 (6)
Now, let us use Eq. (6) to fit our experimental data. The results obtained are plotted in Fig. 5, the corresponding parameters extracted from the fitting are also listed in Fig. 5. Substituting these values into Eq. (6) yields:
3
4.2. Application of Chou model to non-isothermal oxidation of SiC powder
m = 50 × m0
Now we will use Chou model to non-isothermal oxidation of SiC powder. In the present cases, our experimental results represent a relationship between the dimensionless mass change, m/m0 (m0 denotes the sample of original weight and m the increment of sample weight after oxidation at time t) versus temperature, not the reacted fraction , therefore, a transformation of variable is necessary prior to using Chou model. The relation between and m/m0
If the heating rates are taken as = 5 K/min, 10 K/min, 20 K/min we have three theoretical curves. These three are drawn in the same plot for the purpose of comparison. From Fig. 5, we can see that there is a good agreement between the experimental data and theoretical calculation. Some small errors exist in the low temperature, which can be ascribed to particle size distribution, approximation of assumption, etc.
1−
1−
1 2.45 × 10−5
exp
226, 500 − RT
(T − T0 )
(7)
Fig. 4. (a) TEM micrograph of a SiC particle after 1223 K/20 h oxidation. (b) Electron diffraction patterns from the oxide layer. (c) Electron diffraction patterns from the SiC core.
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Y. Li et al. / Applied Surface Science 257 (2010) 463–467
Fig. 5. A comparison of experimental data with model for non-isothermal oxidation of -SiC powder at different temperature-increasing rates.
Fig. 7. A isothermal oxidation of -SiC powder predicted by model at various temperatures.
SiC powders is as follows:
4.3. Application of Chou model to isothermal oxidation process of SiC powder For the isothermal oxidation process, Eq. (2) can be used to investigate the isothermal oxidation process of SiC powder. Similarly, some conversions are also needed before using this formula. After conversion, Eq. (2) can be described as follows:
⎡ m mmax = × ⎣1 − m0 m0
1−
1 exp BT
εap − RT
⎤ 3 ⎦ t
m = 50 × 1− 1− m0
1 1.74 × 10−2
187, 500 3
exp −
RT
t
(9)
Based on Eq. (9), the isothermal oxidation behaviors of SiC powder at temperature from 1100 K to 1300 K with an interval of 50 K can be predicted and they have now been plotted in Fig. 7. 5. Discussion
(8)
Eq. (8) now is used to fit the isothermal oxidation experimental data. The fitting results are shown in Fig. 5. From Fig. 6, it can be seen that Eq. (8) gives a very good fit with the experimental data. The relative coefficient for this curve fitting has reached 0.98. The good fitting between the theoretical prediction and experimental data indicates that Chou model is reasonable. The apparent activation energy can be extracted as 187.5 kJ/mol, and BT = 1.74 × 10−2 . The above εap and BT were substituted into Eq. (8), the model describing the isothermal oxidation behavior of
As mentioned above, the oxidation reaction for SiC powder is a kind of complicated heterogeneous process. It is very difficult for us to give a theoretical description for it. Chou model gives an explicit analytic expression of the oxidation fraction with time and temperature. In this model, all the parameters, for example, temperature T, apparent activation energy εap , diffusion coefficient, etc. have clear physical meanings. Some of the parameters can be combined to construct an auxiliary function like BT . As a result, Chou model will become very simple and easy to use. A good agreement has been reached between experimental data and theoretical model in the isothermal and non-isothermal oxidation process of SiC system when Chou model is applied. The εap for the non-isothermal oxidation of SiC powder, predicted by Chou model, is 226.5 kJ/mol, while for the isothermal oxidation process, the εap is 187.5 kJ/mol. This difference has been regarded as an acceptable value between isothermal and non-isothermal methods in the literatures. Furthermore, we can predict the oxidation behavior within the same oxidation behavior based on limited experimental data, which is very helpful in actual applications. 6. Conclusions
Fig. 6. A comparison of experimental data with model for oxidation of SiC powder at temperature 1173 K and 1223 K.
The oxidation experiments of SiC powders synthesized from a self-propagating method have been performed under both nonisothermal and isothermal conditions. Based on the experimental data and assuming the oxygen diffusion as the controlling step, Chou model was applied to predict the oxidation behavior of SiC powder and worked well. The calculated results showed that both the theoretical calculation and experimental data can reach a good agreement. Two simple and explicit analytic formulas have been proposed to describe the relation between the reacted fraction of oxidation and time and temperature. The activation energy of nonisothermal and isothermal oxidation of SiC powder is obtained to be very close with this model.
Y. Li et al. / Applied Surface Science 257 (2010) 463–467
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