P. Mogilensky, 4. Zanguil Materials Science and Engineering 4262(1999)16-24 observed for both considered materials. Taking into Is also clear why mode I was experimentally observed in mullite-SiC composites [101 It should be noted that activation energy for oxygen permeation in such oxides as alumina, and mullite is typically much higher than that for molecular perme- ation of oxygen through silica. Therefore, according to Fig 9. Evaluation of the criterion for oxidation mode I according to the present mode Eqs. (22) and(23), the oxidation of the same material can proceed as mode I at low temperatures, but can change to mode II if the temperature is raised. Also, he oxidation mode I in its pure form cannot take for n+ l the oxidation mode can depend on the exter place: according to Eq (13), some degree of oxidation nal oxygen pressure. Thus, oxidation of a material always takes place even for a particle located at what- proceeding by mode II rding to eq ever large distance below the surface. Therefore, to (22), change to mode I if performed, for example, in introduce the notion of mode i into this model. a practical limit when a particle can be considered not oxidized should be selected, for example when the thickness of the oxide film does not exceed 10% of the 4. Conclusions 9. For this case, the following criterion of mode i can A simple model describing the oxidation mode Il of be evaluated from the present model Sic reinforced oxide CMCs was presented. The model allows a semi-quantitative analysis of the oxidation process and evaluation of the composite parameters <0.1bn (19)(such as matrix oxygen permeability and the rate of the reinforcement oxidation) using experimental mea- where D is the mean particle diameter, and L is the surements of the thickness of the oxide layer on rein- average distance between nearest-neighbor pairs of forcement particles as a function of the depth beneath particles in a volume. The distance L is related to the the composite surface. For systems where permeability mean number of particles per unit volume, Pv, by the values are known or can be assumed with sufficient following expression [32] accuracy, the extent of reinforcement oxidation versus L=0.554P=13 depth can be predicted in a semiquantitative manner. (20) Moreover, the expected mode of oxidation, I or II Defining now the mean particle diameter D as an can be predicted depending on oxygen permeabilities equivalent sphere diameter, we can obtain and volume fraction of the reinforcement phase The model has been applied to the results of the 2_1.1089≈/B (21) microscopic study of the oxidation of Sic reinforced mullite-zirconia CMCs. It was found that the oxygen where fy is the volume fraction of the reinforcement. permeability of the silica layer which grows on SiC Then, Eq(19)becomes particles is significantly higher than that for whiskers As could be expected, it was also found that oxygen permeation through the mullite <0.1 pending on the preparation and processing procedures. (cn) It should be noted that an experimental assembly or, for n= l, simply hich fits best the proposed model is a planar sample such Sic substrate covered with a layer of the 0.2/13 (23) matrix material (a ceramic oxide). It is supposed that application of the proposed model to such planar sam- For typical values fv=l and n=l. the condi ples would allow better evaluation and understanding ion for oxidation mode becomes Pm/P, <0.3- of the mechanisms and rate controlling factors(oxy- corresponds to the gen diffusion through the matrix composites with higher volume fraction of the rein- reaction, evacuation of CO) of the process. This work, forcement Comparing this with the data from as well as further development of the model, are now Table 3, it is clear why mode II was experimentally in progressP. Mogile6sky, A. Zang6il / Materials Science and Engineering A262 (1999) 16–24 23 . Fig. 9. Evaluation of the criterion for oxidation mode I according to the present model. observed for both considered materials. Taking into account very low permeability of pure mullite, it is also clear why mode I was experimentally observed in mullite–SiC composites [10]. It should be noted that activation energy for oxygen permeation in such oxides as alumina, and mullite is typically much higher than that for molecular perme￾ation of oxygen through silica. Therefore, according to Eqs. (22) and (23), the oxidation of the same material can proceed as mode I at low temperatures, but can change to mode II if the temperature is raised. Also, for n"1 the oxidation mode can depend on the exter￾nal oxygen pressure. Thus, oxidation of a material proceeding by mode II in air may, according to Eq. (22), change to mode I if performed, for example, in pure oxygen. 4. Conclusions A simple model describing the oxidation mode II of SiC reinforced oxide CMCs was presented. The model allows a semi-quantitative analysis of the oxidation process and evaluation of the composite parameters (such as matrix oxygen permeability and the rate of the reinforcement oxidation) using experimental mea￾surements of the thickness of the oxide layer on rein￾forcement particles as a function of the depth beneath the composite surface. For systems where permeability values are known or can be assumed with sufficient accuracy, the extent of reinforcement oxidation versus depth can be predicted in a semiquantitative manner. Moreover, the expected mode of oxidation, I or II, can be predicted depending on oxygen permeabilities and volume fraction of the reinforcement phase. The model has been applied to the results of the microscopic study of the oxidation of SiC reinforced mullite–zirconia CMCs. It was found that the oxygen permeability of the silica layer which grows on SiC particles is significantly higher than that for whiskers. As could be expected, it was also found that oxygen permeation through the mullite matrix can vary, de￾pending on the preparation and processing procedures. It should be noted that an experimental assembly which fits best the proposed model is a planar sample such as a SiC substrate covered with a layer of the matrix material (a ceramic oxide). It is supposed that application of the proposed model to such planar sam￾ples would allow better evaluation and understanding of the mechanisms and rate controlling factors (oxy￾gen diffusion through the matrix or silica, chemical reaction, evacuation of CO) of the process. This work, as well as further development of the model, are now in progress. the oxidation mode I in its pure form cannot take place: according to Eq. (13), some degree of oxidation always takes place even for a particle located at what￾ever large distance below the surface. Therefore, to introduce the notion of mode I into this model, a practical limit when a particle can be considered not oxidized should be selected, for example when the thickness of the oxide film does not exceed 10% of the particle size (radius or another typical dimension), Fig. 9. For this case, the following criterion of mode I can be evaluated from the present model: Pm Ps B0.1 2−bn bn < (pO2 ) n−1 n (cn) 1/bn = 2L D (19) where D is the mean particle diameter, and L is the average distance between nearest-neighbor pairs of particles in a volume. The distance L is related to the mean number of particles per unit volume, Pv, by the following expression [32]: L=0.554Pv −1/3 (20) Defining now the mean particle diameter D as an equi6alent sphere diameter, we can obtain 2L D =1.108 3 fv '3 p 6 :f v −1/3 (21) where fv is the volume fraction of the reinforcement. Then, Eq. (19) becomes Pm Ps B0.1 2−bn bn < (pO2 ) n−1 n (cn) 1/bn = f v −1/3 (22) or, for n=1, simply Pm Ps B0.2f v −1/3 (23) For typical values fv=10–40% and n=1, the condi￾tion for oxidation mode I then becomes Pm/PsB0.3– 0.4, where the lower limit corresponds to the composites with higher volume fraction of the rein￾forcement phase. Comparing this with the data from Table 3, it is clear why mode II was experimentally