P. Mogilersky, 4. Zanguil Materials Science and Engineering 4354(2003)58-66 100 the ' parabolic stage. Eq(22) indicates a slight depen dence of the apparent parabolic constant on the size of he reinforcement particles. The dependence in Eq (22) is shown graphically in Fig. 2b for different values of n It Is seen tha deviation from the parabolic kinetics increases with time(as also seen from Fig 2a), and this increase is more profound for smaller particle size and n deviating significantly from 1. This deviation should be -n=1 taken into account if the permeability values are calculated from the apparent parabolic constants Note that the initial value of the apparent parabolic constant does not depend on the reinforcement particle size or rate of the reinforcement oxidation, as is expected ⊥⊥⊥ if the process is entirely controlled by the diffusion through the oxidized layer. If n,=ns=m, then n and bn=an=l [17]. in which case the preceding R equations simplify significantly 2 Time- (24) (o,) For large z the kinetics in this case is true parabolic and the process is entirely controlled by the diffusion through the oxidized layer It is intuitively clear that if there is no reaction 二-:D= between the matrix and the product of the reinforcement oxidation, the oxidation mode I can only occur if Ps is considerably higher than oxygen permeability of the matrix, Pm. In this case, Po can not be greater than Ps and therefore, in normal conditions the value of zc will be of the same order or less as the size of Fig-2. Deviation from the parabolic law(a)and the dependence of the practice it willn es, R(Eq reinforcement particles, R(Eq(21). This means that apparent parabolic constant Kp on the particle size(b)for n+ I stage experimentally. However, a reaction between the matrix and the product of the reinforcement oxidation hay he kinetics of the oxidation process, as is the case for the oxidation of Sic RA1/=p(o,(-b1+b in Al,O3 and mullite/ZrO, matrices. For instance, the new phase can have the permeability value significantly higher than Ps, particularly if it is a glassy phase Substituting Eqs. (14)and(15) into Eq(20)and (aluminosilicate). In such a case, both constantA(21), we obtain for the apparent SiC oxidation and oxygen diffusion through the oxi- dized layer can be considerably accelerated K2=[/R] [8,9, 15, 18, 19](note that in this case Ps in the preceding equations must refer to the permeability not of silica but that of the aluminosilicate glass). In this case, the arly Kp B 2P(Po. )'no[(2-b)(1+bm)7. occur at larger =, and the linear stage can possibly be (23) observed experimentally. On the other hand, in matrices ontaining ZrO2, formation ZrSiO4,can is the apparent parabolic constant in the beginning of occur. This reaction is known to cause a very sharpzc R 1 A1=bn Po Ps (pO2 ) (ns no)=nons
(2  bn)(1 bn) 2an 1=bn (21) Substituting Eqs. (14) and (15) into Eq. (20) and taking note of Eq. (21), we obtain for the apparent parabolic constant Kp: Kp K0 p
z=R A1=bn (1bn) (22) where K0 p B A1=bn 2Po(pO2 ) 1=no aCsfs
(2  bn)(1 bn) 2an 1=bn (23) is the apparent parabolic constant in the beginning of the ‘parabolic’ stage. Eq. (22) indicates a slight depen￾dence of the apparent parabolic constant on the size of the reinforcement particles. The dependence in Eq. (22) is shown graphically in Fig. 2b for different values of n. It is seen that the deviation from the parabolic kinetics increases with time (as also seen from Fig. 2a), and this increase is more profound for smaller particle size and n deviating significantly from 1. This deviation should be taken into account if the permeability values are calculated from the apparent parabolic constants. Note that the initial value of the apparent parabolic constant does not depend on the reinforcement particle size or rate of the reinforcement oxidation, as is expected if the process is entirely controlled by the diffusion through the oxidized layer. If no/ns/m, then n/1 and bn /an /1 [17], in which case the preceding equations simplify significantly: zc RPo Ps (24) and Kp2Po(pO2 ) 1=m aCsfs (25) For large z the kinetics in this case is true parabolic and the process is entirely controlled by the diffusion through the oxidized layer. It is intuitively clear that if there is no reaction between the matrix and the product of the reinforcement oxidation, the oxidation mode I can only occur if Ps is considerably higher than oxygen permeability of the matrix, Pm. In this case, Po can not be greater than Ps, and therefore, in normal conditions the value of zc will be of the same order or less as the size of the reinforcement particles, R (Eq. (21)). This means that in practice it will not be possible to observe the linear stage experimentally. However, a reaction between the matrix and the product of the reinforcement oxidation may have a profound effect on the kinetics of the oxidation process, as is the case for the oxidation of SiC in A12O3 and mullite/ZrO2 matrices. For instance, the new phase can have the permeability value significantly higher than Ps, particularly if it is a glassy phase (aluminosilicate). In such a case, both the process of SiC oxidation and oxygen diffusion through the oxi￾dized layer can be considerably accelerated [8,9,15,18,19] (note that in this case Ps in the preceding equations must refer to the permeability not of silica, but that of the aluminosilicate glass). In this case, the transition from linear to nearly parabolic kinetics will occur at larger z, and the linear stage can possibly be observed experimentally. On the other hand, in matrices containing ZrO2, formation of zircon, ZrSiO4, can occur. This reaction is known to cause a very sharp Fig. 2. Deviation from the parabolic law (a) and the dependence of the apparent parabolic constant Kp on the particle size (b) for n "/1. P. Mogilevsky, A. Zangvil / Materials Science and Engineering A354 (2003) 58
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