une 1999 High-Temperature Oxidation of Boron Nitride: Boron Nitride Layers in Composites . Matri Matrix um Fig. 9. Polished longitudinal cross section and associated EDS data for minicomposite to show recession depth after exposure to 10% H,O/O, for 0 h at 700C. Transition from BN to a borosilicate glass is gradual. Also note that this type of as-deposited BN contains some dissolved oxygen. stant, t the time, and T a rrection for very thin oxide Here, d is the width of the annular region. For this approxima layers. For this approximat nore T. At these low tem- tion we have taken the oxidation rate of the fiber and the atures, the linear rate atrix to be equal. At 700 and 800oC, the rate constants SiC are extreme small. The 800%C value is fro ture,2 the 700oC value is extrapolated from this8 and four A(A-+4Bn other higher-temperature measurements. 5 All measurements (15) are in pure oxygen. The lowest linear and parabolic rate con- stants used in Eq(12)are given in Table IV As an approximation, the reduction in area of the annulus n the composite situation, water vapor in the gas stream27, fiber is give and residual boron are expected to enhance the oxidation of the channel walls. Because we do not know exactly how much he parabolic rate constant increases in this situation, we shall treat the parabolic rate constant, B, as an adjustable variable 2-2 and vary it from I to 5000 times its lowest value(Table IV until a good fit to the data is attained. The parameter A is not Note that is a function of time, because x is a function of time Table V(A)lists some calculated times to seal Here, Im is the radius of the matrix opening and rr the radius of nnular regions at 700C, and Table V(B) the fiber(Fig. 11). Also note that x in Eq. (14)is for SiO2 times for a 1 um annular region at 800C whereas x'in Eq. (14)is an x modified to reflect the molar ed oxidation is important in explaining the volume change on conversion from SiC to SiOz. This is sealing gradual cosy o to BN recession roughly a factor of two. Now we can simplify Eq(15)as of the annular channel effectively de- creases the diffusive r=r+dstant, t the time, and t a time correction for very thin oxide layers. For this approximation, we ignore t. At these low tem￾peratures, the linear rate constant is important. Solving for x gives x = −A 2 + ~A2 + 4Bt! 1/2 2 (15) As an approximation, the reduction in area of the annulus around the fiber is given by f = ~rm − x8! 2 − ~rf + x8! 2 rm 2 − rf 2 (16) Note that f is a function of time, because x is a function of time. Here, rm is the radius of the matrix opening and rf the radius of the fiber (Fig. 11). Also note that x in Eq. (14) is for SiO2, whereas x8 in Eq. (14) is an x modified to reflect the molar volume change on conversion from SiC to SiO2. This is roughly a factor of two. Now we can simplify Eq. (15) as follows: rm = rf + d f = 1 − 2x8 d (17) Here, d is the width of the annular region. For this approxima￾tion, we have taken the oxidation rate of the fiber and the matrix to be equal. At 700° and 800°C, the rate constants for SiC are extremely small. The 800°C value is from the litera￾ture;28 the 700°C value is extrapolated from this28 and four other higher-temperature measurements.15 All measurements are in pure oxygen. The lowest linear and parabolic rate con￾stants used in Eq. (12) are given in Table IV. In the composite situation, water vapor in the gas stream27,29 and residual boron5 are expected to enhance the oxidation of the channel walls. Because we do not know exactly how much the parabolic rate constant increases in this situation, we shall treat the parabolic rate constant, B, as an adjustable variable and vary it from 1 to 5000 times its lowest value (Table IV) until a good fit to the data is attained. The parameter A is not varied. Table V(A) lists some calculated times to seal 1.0 and 0.5 mm annular regions at 700°C, and Table V(B) lists the sealing times for a 1 mm annular region at 800°C. Clearly, enhanced oxidation is important in explaining the observed sealing. This gradual closing of the annular channel effectively de￾creases the diffusive flux that leads to BN recession. dyHxByOz dt = − f JHxByOz VBN = f VBN S DHxByOz RT dPHxByOz dyHxByOz D (18) Fig. 9. Polished longitudinal cross section and associated EDS data for minicomposite to show recession depth after exposure to 10% H2O/O2 for 20 h at 700°C. Transition from BN to a borosilicate glass is gradual. Also note that this type of as-deposited BN contains some dissolved oxygen. June 1999 High-Temperature Oxidation of Boron Nitride: Boron Nitride Layers in Composites 1479