March 1998 Kinetics of Thermal, Passive Oxidation of Nicalon Fibers Time (hour) Fig 4. Comparison of the present model(Eq(22))and the Deal and Grove(D&G)me the experimental data of Huger fiber radius R of 8 um was used in the calculation. Parameters for Eq(22)are as follows °C:E=50,F=0.8,andG= E=710,F=001,andG=113, and for120cE=110=00andG=380 E=430,F=0.05,andG= the slowing of the oxidation kinetics to the crystallization of the To fully examine the oxidation kinetics of cylindrical fibers orphous oxide film to cristobalite, which has been detected we assume that a fiber with a diameter of 16 um is oxidized at temperatures as low as 1 100C. The diffusion of oxygen with the entire process obeying Eqs. (22)and(25). Assuming through the cristobalite is more difficult than through an amor- values of E 500, F= 0. 1, and G 2, the oxidation kinetics phous SiO2 layer, which will slow the oxidation kinetics. The are calculated as shown in Fig. 6. For comparison, the oxida- ormation of cristobalite renders both the present model and the tion kinetics of a flat plate predicted by the theory of Deal and Deal and Grove model invalid for temperatures >1100oC Note Gro that the present model is in good agreement with the experi mental data at s1000%C. where the cristobalite does not form This observation indicates that the formation of cristobalite at 1 100 and 1200C could be one of the reasons for the discrep. cy between the present model and the experimental data shown in Fig. 4 for the oxidation of Nicalon m fibers at the two temperatures To evaluate the present theory more rigorously, experimen 5 tioned complications. One such experiment could be the oxi- 8 4 need to be performed on fibers that do not have the foremen dation of pure silicon fiber at a temperature <1100C. Despite these complications, however, the present theory agrees quite well with the experimental data Present thoery for fiber(Eq. 22) Deal et al for fate plate (Eq, 38 sE39cL 0500010000150002000025000 Fig. 6. Comparison of the present theory(Eqs. (22)and(25)for the oxidation of cylindrical fibers with the theory of Deal and Grovel (Eqs. (38)and(39)for the oxidation of a flat plate. Equations(22)and Fig. 5. Bubbles form in the oxide layer of a fiber treated at 1200 C(38)use the oxide thickness, whereas Eqs. (25)and(39)use the for 32 h in ygen partial pressure of 0. 14 atm (-0.014 MP fractional reacted volume to describe the oxidation kineticthe slowing of the oxidation kinetics to the crystallization of the amorphous oxide film to cristobalite, which has been detected at temperatures as low as 1100°C.1 The diffusion of oxygen through the cristobalite is more difficult than through an amor￾phous SiO2 layer, which will slow the oxidation kinetics. The formation of cristobalite renders both the present model and the Deal and Grove model invalid for temperatures >1100°C. Note that the present model is in good agreement with the experi￾mental data at #1000°C, where the cristobalite does not form. This observation indicates that the formation of cristobalite at 1100° and 1200°C could be one of the reasons for the discrep￾ancy between the present model and the experimental data shown in Fig. 4 for the oxidation of Nicalon™ fibers at these two temperatures. To evaluate the present theory more rigorously, experiments need to be performed on fibers that do not have the aforemen￾tioned complications. One such experiment could be the oxi￾dation of pure silicon fiber at a temperature <1100°C. Despite these complications, however, the present theory agrees quite well with the experimental data. To fully examine the oxidation kinetics of cylindrical fibers, we assume that a fiber with a diameter of 16 mm is oxidized with the entire process obeying Eqs. (22) and (25). Assuming values of E 4 500, F 4 0.1, and G 4 2, the oxidation kinetics are calculated as shown in Fig. 6. For comparison, the oxida￾tion kinetics of a flat plate predicted by the theory of Deal and Grove10 Fig. 4. Comparison of the present model (Eq. (22)) and the Deal and Grove (D&G) model with the experimental data of Huger et al; 8 an average fiber radius R of 8 mm was used in the calculation. Parameters for Eq. (22) are as follows: for 700°C: E 4 50, F 4 0.8, and G 4 0.085; for 800°C: E 4 100, F 4 0.4, and G 4 0.31; for 900°C: E 4 230, F 4 0.1, and G 4 0.95; for 1000°C: E 4 430, F 4 0.05, and G 4 3.0; for 1100°C: E 4 710, F 4 0.01, and G 4 11.3; and for 1200°C: E 4 1100, F 4 0.001, and G 4 38.0. Fig. 5. Bubbles form in the oxide layer of a fiber treated at 1200°C for 32 h in an oxygen partial pressure of 0.14 atm (∼0.014 MPa). Fig. 6. Comparison of the present theory (Eqs. (22) and (25)) for the oxidation of cylindrical fibers with the theory of Deal and Grove10 (Eqs. (38) and (39)) for the oxidation of a flat plate. Equations (22) and (38) use the oxide thickness, whereas Eqs. (25) and (39) use the fractional reacted volume, to describe the oxidation kinetics. March 1998 Kinetics of Thermal, Passive Oxidation of Nicalon Fibers 659