K.G. Nickel/Journal of the European Ceramic Sociery 25 (2005)1699-1704 1703 discussed above for the matrix ceramic there is an additional Allowing the linear term in Eq. (9)to become negative it oxidation of the reinforcing phase, in this case to yield TiO handles a great variety of differing mechanisms and processes and an initial amount of this oxide present in the starting ma- and is the preferred tool also for composite corrosion terial. It is highly unlikely that TiO2 is not interacting with the oxides of the matrix system and the newly formed Ox- ides from the matrix oxidation, because there is a solubility for it. TiO2 is also a known opacifier, i. e. an agent to induce Acknowledgements crystallization of silicate glasses. Therefore, it cannot be ex- ed that We gratefully acknowledge funding by the Deutsche which is the base for all the physical models, holds for such Forschungsgemeinschaft (DFG) under contract number Even stronger effects are expected for composites with Corrosion"HPRN-Ct-2000-00044) econd phases, which become volatile upon oxidation. Ex- amples are the boride reinforcement systems. Certainly the paralinear behavior of oxide formation and evaporation can References be handled by physically strict models such as Eqs. (7)and ( 8). But in a reactive matrix with silicate glass and/or borate I. Mogilevsky, P. and Zangvil, A, Kinetics of oxidation in oxide ceramic formation the diffusion coefficients must change with time matrix composites. Mater: Sci. Eng, 2003, A354, 58-66. and temperature. Examples for strongly non-parabolic cor- 2. Maeda, M., Nakamura, K. and Yamada, M., Oxidation resistance of rosion-both in oxidation as well as in liquid corrosion-can silicon nitride ceramics with various additives. J. Mater: Sci., 1990, 5,3790-3794 be found in this volume 3. Hack, K, ChemSage-a computer program for the calculation of As long as such complex changes cannot be treated ad complex chemical equilibria. Met. Trans., 1990, 21B, 1013-1023 equately in a strict physical model, their use is no real ad 4. Chase, M. W, Davies, C. A, Downey, J.R, Frurip, D J, McDonald, vantage over empirical models in those systems. It is thus R. A. and Syverud, A. N, JANAF Thermochemical tables-third dition. J. Phys. Chem. Ref. Data, 1985, 14(Suppl. 1) concluded that Eq. (9)is a simple and robust empirical ap- 5. Deal, B. E. and Grove, A.S., General relationship for the proach to model the corrosion behavior and should be useful mal oxidation of silicon. J. Appl. Phys., 1965, 36(12) for many ceramics and composites thereof The freedom of shapes of corrosion curves implied by 6. Eckel, A J, Cawley, J D and Parthsarathy, T. A, Oxidation kinetics the empirical model necessitates in practice that we need more independent information about the process to be able 7. mogilevsky, P and Zangvil, A, modeling to evaluate it correctly. The translation of mass data into SiC-reinforced ceramic matrix composite er: Sci. Eng, 1999 scale thickness, penetration depths, and component size A262,16-24 ice versa is not straightforward for the 8. Clark, D. E. and Zoitos, B. K, Corrosion of Glass, Ceramics an Each system has to be calibrated by detailed investiga- Ceramic Superconductors. Noyes Publications, ParkRidge, NJ, USA tions using a multiplicity of investigation techniques, aiming 9. Opila, E I and Jacobson, N.S., Sio (g) formation from Sic in mixed for the most important engineering parameter, penetration xidising-reducing gases. Oxid. Metals, 1995, 44(3/4), 1-17 10. Pila, E.J. and Hann Jr, R. E, Paralinear oxidation of CVD SiC in water vapor. J. Am. Ceram. Soc., 1997, 80(1), 197-205 lI J, Smialek, J. L, Robinson, R. C. Fox, D. S and Jacobson N.s., SiC recession caused by Sio scale volatility under combustion 5. Conclusions conditions: Il, thermodynamics and gaseous-diffusion model. J. Am. Ceram soc.,1999,827),1826-1834. Physically strict models for oxidation and corrosion can 12. Filipuzzl, L. and Naslain, R, Oxidation mechanism and kinetics of be successful for simple ceramics and composites. In the ap- D-SiC/C/SiC composite materials: Il, modeling. J Am Ceram Soc. propriate systems they should be used and will allow the best 1994,77(2),467-480 13. Jacobson, N. S, Morscher, G. N, Bryant, D. R. and Tressler, extrapolation outside of the experimental range R. E, High-temperature oxidation of boron nitride: Il, boron ni Complex systems, in particular those involving additive- tride layers in composites. J. Am. Ceram. Soc., 1999, 82(6), 1473 containing matrices, will have transport properties, which 482. change with time. It is a challenge to handle this in phy 14 K. G, Multiple law modelling for the ical models. First results indicate that this is possible with of Adanced Ceramics-Measurement and d. K complex models and a good deal of detailed information on Nickel. Kluwer Academic Pub., Dordrecht, NI For the purpose of describing, comparing, ranking and 15. Nickel,K. G. and Quirmbach, P, Gask developing materials it is often sufficient- and far less ex- keramische Werkstoffe. In Technische K Werkstoffe, ed pensive in terms of time, effort and money-to use empirical J. Kriegesmann. Koln, Deutscher Wirtscha [chapter 5.4.1.1- models. A relatively simple and robust form of such an em- 16. Gogotsi, Y G and Lavrenko, V. A, Corrosion of High-Performance al model is given in Eq (9) Ceramics. Springer Verlag, Berlin, 1992, p. 181K.G. Nickel / Journal of the European Ceramic Society 25 (2005) 1699–1704 1703 discussed above for the matrix ceramic there is an additional oxidation of the reinforcing phase, in this case to yield TiO2, and an initial amount of this oxide present in the starting ma￾terial. It is highly unlikely that TiO2 is not interacting with the oxides of the matrix system and the newly formed ox￾ides from the matrix oxidation, because there is a solubility for it. TiO2 is also a known opacifier, i.e. an agent to induce crystallization of silicate glasses. Therefore, it cannot be ex￾pected that the assumption of constant diffusion coefficients, which is the base for all the physical models, holds for such composites. Even stronger effects are expected for composites with second phases, which become volatile upon oxidation. Ex￾amples are the boride reinforcement systems. Certainly the paralinear behavior of oxide formation and evaporation can be handled by physically strict models such as Eqs. (7) and (8). But in a reactive matrix with silicate glass and/or borate formation the diffusion coefficients must change with time and temperature. Examples for strongly non-parabolic cor￾rosion – both in oxidation as well as in liquid corrosion – can be found in this volume. As long as such complex changes cannot be treated ad￾equately in a strict physical model, their use is no real ad￾vantage over empirical models in those systems. It is thus concluded that Eq. (9) is a simple and robust empirical ap￾proach to model the corrosion behavior and should be useful for many ceramics and composites thereof. The freedom of shapes of corrosion curves implied by the empirical model necessitates in practice that we need more independent information about the process to be able to evaluate it correctly. The translation of mass data into scale thickness, penetration depths, and component size or vice versa is not straightforward for the complex cases. Each system has to be calibrated by detailed investiga￾tions using a multiplicity of investigation techniques, aiming for the most important engineering parameter, penetration depth.25 5. Conclusions Physically strict models for oxidation and corrosion can be successful for simple ceramics and composites. In the ap￾propriate systems they should be used and will allow the best extrapolation outside of the experimental range. Complex systems, in particular those involving additive￾containing matrices, will have transport properties, which change with time. It is a challenge to handle this in phys￾ical models. First results indicate that this is possible with complex models and a good deal of detailed information on the systems. For the purpose of describing, comparing, ranking and developing materials it is often sufficient – and far less ex￾pensive in terms of time, effort and money – to use empirical models. A relatively simple and robust form of such an em￾pirical model is given in Eq. (9). Allowing the linear term in Eq. (9) to become negative it handles a great variety of differing mechanisms and processes and is the preferred tool also for composite corrosion. Acknowledgements We gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) under contract number Ni299/7 and the EU (Research Training Network “Composite Corrosion” HPRN-Ct-2000-00044). References 1. Mogilevsky, P. and Zangvil, A., Kinetics of oxidation in oxide ceramic matrix composites. Mater. Sci. Eng., 2003, A354, 58–66. 2. Maeda, M., Nakamura, K. and Yamada, M., Oxidation resistance of silicon nitride ceramics with various additives. J. Mater. Sci., 1990, 25, 3790–3794. 3. Hack, K., ChemSage—a computer program for the calculation of complex chemical equilibria. Met. Trans., 1990, 21B, 1013–1023. 4. Chase, M. W., Davies, C. A., Downey, J. R., Frurip, D. J., McDonald, R. A. and Syverud, A. N., JANAF Thermochemical tables—third edition. J. Phys. Chem. Ref. Data, 1985, 14(Suppl. 1). 5. Deal, B. E. and Grove, A. S., General relationship for the ther￾mal oxidation of silicon. J. Appl. Phys., 1965, 36(12), 3770– 3778. 6. Eckel, A. J., Cawley, J. D. and Parthsarathy, T. A., Oxidation kinetics of a continuous carbon phase in a nonreactive matrix. J. Am. Ceram. Soc., 1995, 78(4), 972–980. 7. Mogilevsky, P. and Zangvil, A., Modeling of oxidation behavior of SiC-reinforced ceramic matrix composites. Mater. Sci. Eng., 1999, A262, 16–24. 8. Clark, D. E. and Zoitos, B. K., Corrosion of Glass, Ceramics and Ceramic Superconductors. Noyes Publications, ParkRidge, NJ, USA, 1992, 672. 9. Opila, E. J. and Jacobson, N. S., SiO (g) formation from SiC in mixed oxidising-reducing gases. Oxid. Metals, 1995, 44(3/4), 1–17. 10. Opila, E. J. and Hann Jr., R. E., Paralinear oxidation of CVD SiC in water vapor. J. Am. Ceram. Soc., 1997, 80(1), 197–205. 11. Opila, E. J., Smialek, J. L., Robinson, R. C., Fox, D. S. and Jacobson, N. S., SiC recession caused by SiO2 scale volatility under combustion conditions: II, thermodynamics and gaseous-diffusion model. J. Am. Ceram. Soc., 1999, 82(7), 1826–1834. 12. Filipuzzi, L. and Naslain, R., Oxidation mechanism and kinetics of 1D-SiC/C/SiC composite materials: II, modeling. J. Am. Ceram. Soc., 1994, 77(2), 467–480. 13. Jacobson, N. S., Morscher, G. N., Bryant, D. R. and Tressler, R. E., High-temperature oxidation of boron nitride: II, boron ni￾tride layers in composites. J. Am. Ceram. Soc., 1999, 82(6), 1473– 1482. 14. Nickel, K. G., Multiple law modelling for the oxidation of ad￾vanced ceramics and a model-independent figure-of-merit. In Cor￾rosion of Advanced Ceramics—Measurement and Modelling, ed. K. G. Nickel. Kluwer Academic Pub., Dordrecht, NL, 1994, pp. 59– 72. 15. Nickel, K. G. and Quirmbach, P., Gaskorrosion nichtoxidischer keramischer Werkstoffe. In Technische Keramische Werkstoffe, ed. J. Kriegesmann. Koln, Deutscher Wirtschaftsdienst, 1991, pp. 1–76 ¨ [chapter 5.4.1.1]. 16. Gogotsi, Y. G. and Lavrenko, V. A., Corrosion of High-Performance Ceramics. Springer Verlag, Berlin, 1992, p. 181