Abstract
The effects of steam on the oxidation behavior of model Al2O3-scale forming Ni-base alloys at 1000 °C were studied. This was done by conducting tests using dry air and air +30 % H2O (“wet air” in short) gas environments. It was found that the critical concentration of Al (N *Al ) to form a continuous and protective alumina scale on Ni–Al–Cr alloys is increased when the environment is wet air. Based on a rigorous assessment of the parameters contained in Maak’s modification (Z Met 52:545, 1961) of Wagner’s criterion (Z Elektrochem 63:772, 1959) for the transition from internal oxidation to external scale formation, it was deduced that the factor that can change the critical concentration N *Al to the extent measured is the critical volume fraction f *v .
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Acknowledgments
This research is supported by the U.S. Office of Naval Research, award N000014-09-1-1127 and managed by Dr. David Shifler. The authors wish to thank Professor David Young at the University of New South Wales, Australia, for his constructive suggestions.
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Appendices
Appendix 1
In Wagner’s theory, γ is defined in such a way that the internal oxidation rate of dilute alloy is assumed to follow a parabolic law in the form of:
Based on this definition, Wagner studied the mass balances at the internal oxidation front and found that γ can be calculated by solving the following equation:
where N SO is the oxygen solubility on the alloy surface, G(r) is auxiliary function with the form of \(G(r) = \pi^{1/2} r\exp (r^{2} )erf(r)\) and N oAl is the Al concentration in the alloy.
It is seen that γ is a function of N oAl while the critical concentration N *Al,1 is a function of γ. However, the value of N *Al,1 , which is a unique value for Ni–Al alloy system under a given exposure condition, should have nothing to do with the N oAl . Therefore, there should be an iteration process to determine the N *Al,1 . This iteration process starts with a small N oAl value. Taking this value into Eq. A2 yields a γ value. Then, taking this γ value into Eq. 1 of the main text yields a N *Al,1 . If the N oAl is much smaller than N *Al,1 , N oAl needs to be increased and N *Al,1 is calculated for the new N oAl . The iterations are completed when N oAl equals N *Al,1 .
Appendix 2
Determining the Effective Oxygen Diffusivity DO,eff in the Internal Oxidation Zone
Park and Altstetter [44] measured the oxygen diffusion coefficient in solid γ-Ni by a solid-state electrochemical method. It was found the diffusivity of oxygen in nickel is:
This corresponds to the oxygen diffusivity in a clean bulk nickel matrix. At 1000 °C, D O = 9.1 × 10−9 cm2/s. The effective diffusion coefficient of oxygen in the IOZ should consider the contribution from the internal oxide/alloy matrix interfaces. From a study by Stott et al. [27], the effective diffusion coefficient of oxygen can be calculated by:
where the D O is the oxygen diffusion coefficient in the nickel matrix, D O,i is the interfacial diffusion coefficient, N BOv is the mole fraction of oxide, V ox and V all are the molar volume of the oxide and the alloy, δ i is the width of the interface and r is the radius of the precipitates. From the data used by Stott et al. [27]., V ox = 19.5 cm3, V all = 6.67 cm3, δ i was assumed to be 1 nm, which is typically the width assumed for grain-boundary diffusion study and D O,i/D O was found to be 8.0x103 at 1000 °C. r is measured from Fig. 8 and is determined to be around 0.25 μm. Substituting all these data into Eq. A4, the effective oxygen diffusion coefficient in the internal oxidation zone for Ni-3 at.% Al alloy is calculated to be D O,eff = 1.0x10−7 cm2/s.
Determining the Oxygen Solubility N SO from Thermodynamics
When there is an external NiO scale present, the oxygen solubility N SO is no longer determined by the exterior gas environment, but by the equilibria established at the alloy/scale interface. This equilibrium is not the one for the γ-Ni and NiO. Rather, because of the presence of the Al in the alloy, the equilibria are established by three phases: γ-Ni, NiO and the spinel NiAl2O4. This can be shown by a schematic of an isothermal cross section of the ternary phase diagram for Ni–Al–O at 1000 °C, Fig. 13. The oxygen solubility for our case should correspond to the point B on this ternary phase diagram. Elrefair and Smeltzer [45] determined the oxygen partial pressure corresponding to the three-phase equilibria between 1123 and 1423 K based on electrochemical measurements on a Ni,NiO,NiAl2O4|ZrO2(+CaO)|Ni,NiO cell and it follows the relation:
At 1000 °C, the oxygen pressure corresponding to γ-Ni/NiO/NiAl2O4 coexistence is 4.1 × 10−11atm. This oxygen partial pressure is slightly lower than the one corresponding to point A, 4.5 × 10−11atm, which is the dissociation pressure of oxygen for NiO equilibrated with Ni. Further, the Gibbs free energy change for the reaction:
was found [46] to be:
when O uses 1 at.% standard state, which equals 100 × N SO . Therefore, the oxygen solubility corresponding to the oxygen partial pressure for three-phase equilibria at 1000 °C is determined to be N SO = 4.1 × 10−4.
Determining the Diffusion Coefficient of Aluminum DAl in Nickel
This diffusion coefficient D Al in Ni has been reported in several papers [47–49]. At around 1000 °C, the D Al values from those papers are in fairly good agreement. An accurate temperature dependence is deduced to be [47]:
At 1000 °C, D Al is 2.1 × 10−11 cm2/s.
Determining the Dimensionless Parameter u and γ
The values of u and γ can be determined experimentally from the thickness of the metal recession zone and internal oxidation zone observed on the cross-sectional images. In dry air, by using D O,eff found previously, u dry and γ dry were determined to be u dry = 0.0098 and γ dry = 0.082.
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Zhao, W., Gleeson, B. Assessment of the Detrimental Effects of Steam on Al2O3-Scale Establishment. Oxid Met 83, 607–627 (2015). https://doi.org/10.1007/s11085-015-9541-8
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DOI: https://doi.org/10.1007/s11085-015-9541-8