342 Zhenyu, Wei, and Yedong

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1 Oxidation of Metals, Vol. 5, Nos. /4, 2000 Modeling of Oxidation Kinetics of Y-Doped Fe Cr Al Alloys Zhenyu Liu,* Wei Gao,* and Yedong He Received February 2, 1999; revised June 15, 1999 Studies using advanced analytical techniques indicated that the reactive elements (RE) segregate along the oxide grain boundaries and at the oxide alloy interface during oxidation of α-al 2 O forming alloys. The segregation results in inward oxygen diffusion along the oxide grain boundaries as the predominant transport process in the oxide growth. The present work establishes a mathematical model based on the mechanisms of inward oxygen diffusion along the grain boundaries and oxide grain coarsening. This model has been used to describe the oxidation kinetics of Y-doped Fe Cr Al alloys. The results showed a much better agreement with the experimental data than the parabolic rate law. By using this model, the exponential number for the grain coarsening of alumina scales during oxidation was calculated to be. The activation energy for oxygen diffusing along the grain boundaries was 450 kj/mol. They are also in good agreement with values reported in the literatures. KEY WORDS: oxidation kinetics, α-al 2 O ; Fe Cr Al alloys; RE-doped alloys; grain boundary diffusion. 1. INTRODUCTION The effect of reactive elements (RE) on the oxidation behavior of alloys has been studied since the 1940s. Numerous results showed that small additions of reactive elements such as yttrium (Y), zirconium (Zr) and hafnium (Hf) could significantly change the oxidation behavior of the alloys. Doping with *Department of Chemical and Materials Engineering, School of Engineering, The University of Auckland, New Zealand. z.liu@auckland.ac.nz. University of Science and Technology, Beijing, China X $ Plenum Publishing Corporation

2 42 Zhenyu, Wei, and Yedong reactive elements could, to some extent, reduce the oxidation rates and remarkably improve the adherence of oxide scales to the base alloy. 1 However, the exact mechanisms for the effects of RE on the oxidation behavior, especially for alumina-forming alloys, has been puzzling to most investigators because of the difficulties of tracing the reactive elements during and after oxidation. In the past decade or so, good progress has been made in understanding the effects of RE on oxidation by using advanced analytical techniques, such as high-resolution secondary-ion mass spectroscopy (SIMS) and fieldemission gun scanning transmission electron microscopy (FEG-STEM). Convincing experimental observations on RE in α-alumina-forming alloys indicated that the most important mechanisms include: (1) the segregation of RE ions along the oxide grain boundaries and at the oxide alloy interface, (2) the elimination of the detrimental effect of indigenous sulfur by RE doping, and () the enhancement of inward oxygen diffusion along alumina grain boundaries and the suppression of Al outward cation diffusion through the oxide scale. 4 7 Because the inward transport of oxygen anions along alumina grain boundaries is enhanced and the outward diffusion of Al cations is suppressed, the oxide scales formed on the RE-doped alloys grow mainly inward during oxidation, typically forming columnar oxide grains. The oxide scales formed on the RE-free alloys, on the other hand, grow by simultaneous inward oxygen diffusion and outward Al diffusion through the oxide scale, typically forming equiaxed and or elongated oxide grains. 8,9 Since the growth mechanisms of α-al 2 O scales formed on the RE-doped and RE-free alloys during oxidation are quite different, different oxidation kinetics are expected. Quadakkers and Bennett 10 showed a typical example. In the oxidation of MA956 (Fe 20Cr 4.5Al 0.5Ti 0.4Y 2 O ), the oxidation kinetics followed WGkt 0.5 instead of the traditional parabolic rate law. The reason for it was attributed to the fact that the rate-determining oxide grainboundary density decreased with increasing oxidation time. However, little work has been done to model the effect of the alumina scale-growth mechanism on the oxidation kinetics. The parabolic rate law and its modified form, 11 in which no oxide-growth mechanism has been taken into account, are being used to treat the oxidation kinetics of the alloys with or without RE doping. Y-doped ferritic Fe Cr Al alloys such as Fecralloy (a trademark of UKAEA, Harwell) are important high-temperature materials and used as typical alloys to study the effects of RE on the oxidation behavior. However, most work was focused on the oxide-scale microstructure and adherence to the base alloys. Little work has been done on their oxidation kinetics, especially at elevated temperatures. Studies on the oxidation kinetics of alloys are important to the service-life assessment of alloy components working in high-temperature environments.

3 Modeling of Oxidation Kinetics of Y-Doped Alloys 4 In the present work, isothermal-oxidation tests at temperatures of 1200, 1250, and 100 C were carried out with Fecralloy samples. A mathematical model was established by taking into account the inward oxygen diffusion along the alumina grain boundaries. This model was then used to describe the oxidation kinetics of Fecralloy samples. The mathematical model showed good agreement with the experimental results. 2. EXPERIMENTAL PROCEDURES Commercially available Fecralloy alloy (Fe 22%Cr 5%Al 0.Y wt.%) was used in the present work. The specimens were cut from a cold-rolled sheet of dimensions 15B4.5B2.5 mm. Before oxidation testing, the specimens were mechanically polished down to 20 µm and ultrasonically cleaned in acetone. Isothermal-oxidation tests were performed in a SETARAM thermal-gravimetric analysis (TGA) station. Oxidation tests were performed at temperatures of 1200, 1250, and 100 C in ambient atmosphere for 50 hr. The relatively high temperatures were used to avoid the formation of any metastable Al 2 O phases, which usually form at lower temperatures. During oxidation, the specimen was hung with a piece of fine platinum (Pt) wire into the heating chamber. Evaporation of the Pt wire at high temperatures affects the oxidation mass gains of the samples. Therefore, the linear evaporation kinetics of the Pt wire from 1200 through 100 C were measured and used to correct the oxidation kinetics of the alloy. The evaporation rates are given in Table 1. A Phillips S505 scanning electron microscope (SEM) was used to observe the oxide-surface morphology and the cross-section microstructure of the oxide scale.. MODELING OF OXIDATION KINETICS To establish the kinetics model, the following conditions are assumed on the basis of the experimental conclusions: 1. Only α-alumina formed on Fecralloy samples through the entire oxidation test Table I. Evaporation rate of Pt wire (diameter 0.5B45 mm) Temperature ( C) Evaporation rate (mg hr) 100.4B B B10

4 44 Zhenyu, Wei, and Yedong 2. The alumina scale formed on the RE-doped alloy is dense and contains no microcracks. The growth of the alumina scale is controlled by the inward diffusion of oxygen anions along the oxide grain boundaries; the alumina scale grows inward at the interface of oxide and alloy 4. All oxygen anions are transformed to alumina by reacting with Al ions 5. The diffusion of oxygen anions from the grain boundaries to the grain interiors is ignored because the diffusion along grain boundaries is faster than the diffusion through the lattice by 5 orders of magnitude. Figure 1 shows a schematic drawing of the process of oxygen-anion diffusion and alumina-scale growth. According to Fick s first law, the molar number of oxygen anions passing through the oxide scale per unit area per unit time, J O,is J O G D f c O x D O GD exp Q gb RT where D O is the diffusion coefficient of oxygen anions along the alumina grain boundaries, D is a constant, Q gb is the activation energy for oxygen diffusion along the alumina grain boundaries, R is the gas constant, T is (1) Fig. 1. Schematic drawing of alumina-scale-growth process.

5 Modeling of Oxidation Kinetics of Y-Doped Alloys 45 temperature, and f is the grain-boundary density. f can be calculated by assuming that the oxide grains are square on the top surface, fg 2δ B d Where δ B is the grain boundary width, d is the average width of the columnar oxide grains, or the average size of oxide grains. The volume increase of the oxygen anions at the oxide alloy interface per unit area per unit time, V O,is (2) V O GJ O Ω O () where Ω O is the molar volume of oxygen anions. Since it has been assumed that all oxygen anions are transformed to alumina, the alumina volume increase per unit area per unit time at the interface, V Al2O, can be written as V Al2O G 1 ΩAl 2O Ω O V O (4) where Ω Al2O is the molar volume of alumina. The growth rate of the alumina scale is written as dx dt G V Al2O J O G Ω Al 2O D f c O x According to Smeltzer et al. 12, the gradient of oxygen across the oxide scale can be assumed to be uniform. Then, Eq. (5) can be written as dx dt GΩ Al2O D f c O x where c is the concentration difference of oxygen anions at the two alumina surfaces and x is the thickness of the alumina scale. The alumina scalegrowth kinetics are written as x 2 G Ω Al 2O c D O t 0 fdtg2 ΩAl 2O c D O 2δ B t 0 If the oxide grain coarsening along the y direction can be neglected, it can be seen that the scale growth follows the parabolic rate law x 2 G 4Ω Al 2O dt d (5) (6) (7) δ B cd O t (8) d If oxide grain coarsening along the y direction takes place during oxidation, the oxide scale-growth kinetics are different from the parabolic rate law.

6 46 Zhenyu, Wei, and Yedong The oxide grain coarsening during high-temperature sintering is usually described as 1 d n Gd n 0CKt KGK 0 exp Q g RT where d 0 is the initial oxide grain size, n is the exponential number for grain coarsening, Q g is the activation energy for oxide grain coarsening, K 0 is a constant. Equation (7) is written as x 2 G 4Ω Al 2O GA D O dna1 0 K AG 4Ω Al 2O δ B c The oxidation kinetics are written as dt δ B cd O t n d n 0CKt n 0 (9) na1 1CK t d n 0 (na1)/na1 (10) W 2 GAρ 2 D O dna1 0 K n na1 1CK t d n 0 (na1)/na1 (11) After long oxidation times, Eq. (11) can be simplified as W 2 K P t (na1)/n K (12) P G AD Oρ 2 n K n na1 with the maximum discrepancy of AD d na1 Oρ 2 0 n K n na1 14 (14) 4. ESTIMATION OF THE ACTIVATION ENERGY FOR OXYGEN GRAIN-BOUNDARY DIFFUSION If alumina grain coarsening takes place during oxidation, the linear relationship between 1 (RT) and Ln(K P ) can be derived from Eq. (12) to estimate the oxygen-diffusion activation energy Ln(K P )GLn naρ 2 D K 0 A 1 RT Q gba Q g n (1) The activation energy for grain coarsening, Q g, has been measured to be 640 kj mol by sintering pure-alumina samples. 15,16 Therefore, from the

7 Modeling of Oxidation Kinetics of Y-Doped Alloys 47 Fig. 2. SEM micrographs of (a) surface morphology and (b) fracture cross section of the alumina scale formed after 50 hr isothermal oxidation in air at 100 C. oxidation kinetics data, the activation energy for oxygen diffusion along oxide grain boundaries can be obtained using Eq. (1). 5. RESULTS AND DISCUSSION Figure 2 shows SEM micrographs of the surface morphology and fracture cross-section of the alumina scale formed after oxidation at 100 C.

8 48 Zhenyu, Wei, and Yedong Fig.. Oxidation kinetics of Fecralloy samples in air at 1200, 1250, and 100 C for 50 hr with curve fitting by the parabolic rate law and the grain boundary-diffusion model. An alumina scale with dense microstructure was observed on the specimen after oxidation (Fig. 2a). The fracture cross section of the alumina shows columnar-oxide grains (Fig. 2b). This indicates that oxygen diffusion along grain boundaries is the predominant transport process for the growth of oxide scale formed on the RE-doped alloy. 9 Figure shows the relationships of the square of oxidation mass gains (corrected with the Pt evaporation data) vs. oxidation time. The experimental results (dotted lines) showed great deviations from the parabolic rate law (broken lines) at all temperatures. By using Eq. (12), which was established on the basis of the grain boundary diffusion of anions, curve fitting to the oxidation kinetics was performed, as shown by the solid lines in Fig.. It can be seen that these solid lines fit the experimental data much better than the broken lines, indicating that the new model is better in describing the oxidation kinetics than the parabolic rate law. From the experimental data, the values of n in Eq. (12) were regressed to be and were independent of the oxidation temperatures. The n values were consistent with the experimental value for alumina-grain growth, which had been obtained to be from high-temperature sintering of pure and Y-doped alumina

9 Modeling of Oxidation Kinetics of Y-Doped Alloys 49 Fig. 4. Plot of Ln(K P )vs1 (T) for oxidation of Fecralloy at temperatures ranging from 1200 to 100 C samples The oxidation kinetics can then be written as W 2 K P t 2,in a good agreement with the rate law ( WGkt 0.5 ) for MA956 developed by Quadakkers and Bennett. 10 By using Eq. (1), the activation energy for oxygen diffusion along alumina grain boundaries was calculated. Figure 4 shows the plot of Ln(K P ) vs. reciprocal temperature. It can be seen that the relationships are approximately linear; the value of Q gb is calculated to be 450 kj mol. The activation energy for oxygen diffusion along alumina grain boundaries had been measured using O 18 isotope The values were in the range from 455 to 50 kj mol. The activation energy measured in the present work is in a good agreement with these values. 6. CONCLUSIONS A mathematical model to describe the oxidation kinetics of RE-doped Fe Cr Al alloys has been established. In this model, the diffusion of oxygen anions along alumina grain boundaries and the oxide-grain coarsening during oxidation were considered as the main processes influencing the scalegrowth kinetics. Calculations of the oxidation kinetics indicated that this

10 50 Zhenyu, Wei, and Yedong model fits the experimental results better than the parabolic rate law. It was calculated that the exponential number for alumina grain growth was, and the activation energy for oxygen diffusing along grain boundaries was 450 kj mol. These values are in good agreement with the data given in the literature. The results, therefore, confirmed the validity of the mathematical model. It also showed that the alumina grain coarsening during oxidation annealing has an important effect on the oxidation kinetics. ACKNOWLEDGMENTS This work was supported by a New Zealand FoRST Postdoctoral Fellowship under the contract of UoA815. The authors would like to thank Drs. J. Chen, G. Wright, G. Ferguson, and M. Hyland for various supports, and Dr. M.-S. Li at the Institute of Corrosion and Metal Protection of China for providing Fecralloy samples. REFERENCES 1. F. A. Golightly, F. H. Stott, and G. C. Wood, J. Electrochem. Soc. 126, 105 (1979). 2. J. K. Tien and F. S. Pettit, Metall. Trans., 1587 (1972). B. A. Pint, Oxid. Met. 45, 1 (1986). 4. W. J. Quadakkers, H. Holzbrecher, K. G. Briefs, and H. Beske, Oxid. Met. 2, 67 (1989). 5. B. A. Pint, A. J. Garratt-Reed, and L. W. Hobbs, Mat. High Temp. 1, (1995). 6. R. Prescott and M. J. Graham, Oxid. Met. 8, 2 (1992). 7. C. Mennicke, E. Schumann, M. Ruhle, R. J. Hussey, G. I. Sproule, and M. J. Graham, Oxid. Met. 49, 455 (1998). 8. F. H. Stott and G. C. Woods, Mater. Sci. Eng. 87, 267 (1987). 9. B. A. Pint, in Fundamental Aspects of High Temperature Corrosion VI, D. A. Shores and P. Y. Hou, eds. (The Electrochemical Society, Pennington, NJ, 1996), pp W. J. Quadakkers and M. J. Bennett, Mater. Sci. and Technol. 10, 126 (1994). 11. B. Pieraggi, Oxid. Met. 27, 177 (1987). 12. W. W. Smeltzer, R. R. Haering, and J. S. Kirkaldy, Acta Metall. 9, 880 (1961). 1. W. D. Kingery, Introduction to Ceramics, 4th ed. (Wiley, New York, 1960), pp Z. Liu, W. Gao, K. L. Dahm, and F. Wang, Acta Mater. 46, 1691 (1998) 15. R. L. Coble, J. Appl. Phys. 2, 79 (1961). 16. S. I. Bae and S. Baik, J. Mater. Sci. 28, 4197 (199). 17. J. Fang, A. M. Thompson, M. P. Harmer, and H. M. Chan, J. Amer. Ceram. Soc. 80, 2005 (1997). 18. H. A. Wang and F. A. Kroger, J. Amer. Ceram. Soc. 6, 61 (1980). 19. Y. Oishi and W. D. Kingery, J. Chem. Phys., 480 (1960) 20. R. E. Mistler and R. L. Coble, J. Appl. Phys. 45, 1507 (1974).