Journal of the American Ceramic Society-Zhu et al. Vol 81. No. 3 x+ Ax= Br (38) 4C. vahlas and F. Laanani, " Thermodynamic Study of the Thermal Degra C-Based Fibers: Intluence of sic Grain Size. "' Mater. Sci. Lent 14,1558-61(1995) SPh. Schreck, C. Vix-Guterl, P. Ehrburger, and J. Lahaye, ""Reactivity R2[2-a-2(1-a)12]+AR[1-(1-a)2]=Bt(39) and Molecular Structure of Silicon Carbide Fibers Derived from bosilanes, Part I. Thermal Behavior and Reactivity, J. Mater. Sci., 27 (where A=0. 16774 and B=0.002376 are obtained by fitting (25 Wano F y by x-Ray Photoelectron Spectroscopy, Eq (38)to the curve calculated using Eq (22)for a time range Carbide: Whiskers stud into Eq.(38))are also plotted in Fig. 6. Equation(38)predicts Maniette and A. Oberlin, "TEM Characterization of Some Crude diffusion-controlled oxidation process when the oxide thick ir Heat-Treated SiC Nicalon Fibers, J. Mater. Sci. 24. 3361-70 ess x is large. The present theory(Eqs. (22)and(25)agrees M. Huger, S. Bouchard and C. Gault, ""Oxidation of Nicalon SiC Fibers well with the equation of Deal and Grove o(Eqs. (38)and(39) J Mater. Sci.' Let, 12, 414-16(1993) when x is <2.5 um, and their difference becomes larger as x "T. Shimoo, H. Chen, and K. Okamura,"High-Temperature Stability of increases. The cylindrical geometry of a fiber results in a Nicalon under Ar or O2 Atmosphere, " J Mater. Sct, 29, 456-63(1994) higher oxidation rate than the flat geometry of a plate, which IoB E. Deal and A S. Grove, "General Relationship for the Thermal Oxi- indicates that the effect of the shrinking reaction interface of a dation of Silicon, J. AppL. Phys., 36, 3770-78(1965) IC. Vahlas, P. Bocabois, and C. Bernard, "" Thermal Degradation Mecha cylindrical fiber becomes stronger as the unreacted fiber core nisms of Nicalon Fiber: A Thermodynamic Simulation, "J.Mater. Sci., 29 becomes smaller, so that the reaction kinetics are jointly con- 5839-46(I9 trolled by oxygen diffusion and the shrinking reaction interface 12K. L. Luthra, ""Some New Perspective on Oxidation of Silicon Carbide and Pultz and w. Hertl,"SiO, SiC Re IV. Conclusions tures, Part 1. Kinetics and Mechanism, Trans. Faraday Soc., 62, 2499-504 A general kinetic relationship for the oxidation of cylindrical A. Gulbransen and S.A. Jansson, " The High-Temperature Oxidation, fibers has been derived which can take into account both ox Reduction, and Volatilization Reaction of Silicon and Silicon Carbide, Oxid MeL,4,18l-201(1972) en diffusion and reaction kinetics at the outer fiber surface and K.E. Spear, and R. E. Tressler,""Passive- at the oxide/unoxidized- core interface. Comparison with the de between8o0°Cand experimental data shows good agreement between theory and 2897-911(1996) the observed oxidation kinetics of Nicalon TM fibers at tempera of 7000-1000oC. A cylindrical fiber has an 17RE Adv. Ceran. Mater, 2, 137-41(1987) oxidation rate that is similar to that of a flat plate when the 7R. Bodet, J. Lamon, N. Jia, and R. E. Tressler, " Microstructural Stabili of Si-C-O(Nicalon)F Monoxide and Argon oxide thickness is small: however, the oxidation rate is higher Am. Ceram.Soc,79,2673-86(1996 when the oxide thickness is large. which indicates that the S T. Taylor, Y. T. Zhu, w.R. Blumenthal, M. G. Stout, D. P. Butt, and reaction kinetics are jointly controlled by oxygen diffusion and the shrinking reaction interface Tanaka, and J. Sestak, On the Fractional Conversion a in Kinetic Description of Solid-State Reactions, "J. Therm. AnaL., 38, 2553-57 Referer R. Frade and M. Cable, "Reexamination of the Basic Theoretical Model for the Kinetics of Solid-State Reactions. Am. Ceram. Soc. 75. 1949-57 Fibers": pp 35-46 in Adranced Structural Inorganic Composites. Edited by P. Vincenzini. Elsevier Science Publishers B V, New York, I ea and H. tan Conventional Kinetic Analysis of the Thermo- CT.Ma, N E ec t, E. MeCi.lum, P.R. oenieman. h 1985, dation ot gav.ms 25-26 199 h. Thermal Decomposition of a solid, Thermochem. 223. A. Costello and R.E. Tressler. "Oxidation Kinetics of Silicon Carbide Katz, and H A. Lipsitt,"Thermal Stability of SiC Fibers(Nicalon"), Crystals and Ceramics; Part I. Experimental Studies, J. Am. Ceram. Marer.Sc,19,1191-201(1984). 674-81(1986x2 + Ax = Bt (38) and R2 [2 − a − 2(1 − a) 1/2] + AR[1 − (1 − a) 1/2] 4 Bt (39) (where A 4 0.16774 and B 4 0.002376 are obtained by fitting Eq. (38) to the curve calculated using Eq. (22) for a time range of 0–2000 h, and Eq. (39) is obtained by substituting Eq. (24) into Eq. (38)) are also plotted in Fig. 6. Equation (38) predicts a diffusion-controlled oxidation process when the oxide thick￾ness x is large. The present theory (Eqs. (22) and (25)) agrees well with the equation of Deal and Grove10 (Eqs. (38) and (39)) when x is <2.5 mm, and their difference becomes larger as x increases. The cylindrical geometry of a fiber results in a higher oxidation rate than the flat geometry of a plate, which indicates that the effect of the shrinking reaction interface of a cylindrical fiber becomes stronger as the unreacted fiber core becomes smaller, so that the reaction kinetics are jointly con￾trolled by oxygen diffusion and the shrinking reaction interface. IV. Conclusions A general kinetic relationship for the oxidation of cylindrical fibers has been derived, which can take into account both oxy￾gen diffusion and reaction kinetics at the outer fiber surface and at the oxide/unoxidized-core interface. Comparison with the experimental data shows good agreement between theory and the observed oxidation kinetics of Nicalon™ fibers at tempera￾tures in the range of 700°–1000°C. A cylindrical fiber has an oxidation rate that is similar to that of a flat plate when the oxide thickness is small; however, the oxidation rate is higher when the oxide thickness is large, which indicates that the reaction kinetics are jointly controlled by oxygen diffusion and the shrinking reaction interface. References 1 L. Filipuzzi and R. Naslain, ‘‘Oxidation Kinetics of SiC-Based Ceramic Fibers’’; pp. 35–46 in Advanced Structural Inorganic Composites. Edited by P. Vincenzini. Elsevier Science Publishers B.V., New York, 1991. 2 T. J. Clark, R. M. Arons, and J. B. Stamatoff, ‘‘Thermal Degradation of Nicalon™ SiC Fibers,’’ Ceram. Eng. Sci. Proc., 6, 576–88 (1985). 3 T. Mah, N. L. Hecht, D. E. McCullum, J. R. Hoenigman, H. M. Kim, A. P. Katz, and H. A. Lipsitt, ‘‘Thermal Stability of SiC Fibers (Nicalont),’’ J. Mater. Sci., 19, 1191–201 (1984). 4 C. Vahlas and F. Laanani, ‘‘Thermodynamic Study of the Thermal Degra￾dation of SiC-Based Fibers: Influence of SiC Grain Size,’’ J. Mater. Sci. Lett., 14, 1558–61 (1995). 5 Ph. Schreck, C. Vix-Guterl, P. Ehrburger, and J. Lahaye, ‘‘Reactivity and Molecular Structure of Silicon Carbide Fibers Derived from Polycar￾bosilanes, Part I. Thermal Behavior and Reactivity,’’ J. Mater. Sci., 27, 4237–42 (1992). 6 P. S. Wang, S. M. Hsu, and T. N. Wittberg, ‘‘Oxidation Kinetics of Silicon Carbide Whiskers Studied by X-Ray Photoelectron Spectroscopy,’’ J. Mater. Sci., 26, 1655 (1991). 7 Y. Maniette and A. Oberlin, ‘‘TEM Characterization of Some Crude or Air Heat-Treated SiC Nicalon Fibers,’’ J. Mater. Sci., 24, 3361–70 (1989). 8 M. Huger, S. Souchard, and C. Gault, ‘‘Oxidation of Nicalon SiC Fibers,’’ J. Mater. Sci. Lett., 12, 414–16 (1993). 9 T. Shimoo, H. Chen, and K. Okamura, ‘‘High-Temperature Stability of Nicalon under Ar or O2 Atmosphere,’’ J. Mater. Sci., 29, 456–63 (1994). 10B. E. Deal and A. S. Grove, ‘‘General Relationship for the Thermal Oxi￾dation of Silicon,’’ J. Appl. Phys., 36, 3770–78 (1965). 11C. Vahlas, P. Bocabois, and C. Bernard, ‘‘Thermal Degradation Mecha￾nisms of Nicalon Fiber: A Thermodynamic Simulation,’’ J. Mater. Sci., 29, 5839–46 (1994). 12K. L. Luthra, ‘‘Some New Perspective on Oxidation of Silicon Carbide and Silicon Nitride,’’ J. Am. Ceram. Soc., 74, 1095–103 (1991). 13W. W. Pultz and W. Hertl, ‘‘SiO2 + SiC Reaction at Elevated Tempera￾tures, Part 1. Kinetics and Mechanism,’’ Trans. Faraday Soc., 62, 2499–504 (1966). 14E. A. Gulbransen and S. A. Jansson, ‘‘The High-Temperature Oxidation, Reduction, and Volatilization Reaction of Silicon and Silicon Carbide,’’ Oxid. Met., 4, 181–201 (1972). 15C. E. Ramberg, G. Cruciani, K. E. Spear, and R. E. Tressler, ‘‘Passive￾Oxidation Kinetics of High-Purity Silicon Carbide between 800°C and 1100°C,’’ J. Am. Ceram. Soc., 79, 2897–911 (1996). 16G. H. Schiroky, ‘‘Oxidation Behavior of Chemically Vapor-Deposited Sili￾con Carbide,’’ Adv. Ceram. Mater., 2, 137–41 (1987). 17R. Bodet, J. Lamon, N. Jia, and R. E. Tressler, ‘‘Microstructural Stability and Creep Behavior of Si-C-O (Nicalon) Fibers in Carbon Monoxide and Argon Environments,’’ J. Am. Ceram. Soc., 79, 2673–86 (1996). 18S. T. Taylor, Y. T. Zhu, W. R. Blumenthal, M. G. Stout, D. P. Butt, and T. C. Lowe, ‘‘Characterization of Nicalon Fibers with Varying Diameters. Part I: Strength and Fracture Studies,’’ J. Mater. Sci., in press. 19N. Koga, H. Tanaka, and J. Sestak, ‘‘On the Fractional Conversion a in the Kinetic Description of Solid-State Reactions,’’ J. Therm. Anal., 38, 2553–57 (1992). 20J. R. Frade and M. Cable, ‘‘Reexamination of the Basic Theoretical Model for the Kinetics of Solid-State Reactions,’’ J. Am. Ceram. Soc., 75, 1949–57 (1992). 21N. Koga and H. Tanaka, ‘‘Conventional Kinetic Analysis of the Thermo￾gravimetric Curves for the Thermal Decomposition of a Solid,’’ Thermochem. Acta, 183, 125–26 (1991). 22J. A. Costello and R. E. Tressler, ‘‘Oxidation Kinetics of Silicon Carbide Crystals and Ceramics: Part I. Experimental Studies,’’ J. Am. Ceram. Soc., 69, 674–81 (1986). h 660 Journal of the American Ceramic Society—Zhu et al. Vol. 81, No. 3