Assessment of the Detrimental Effects of Steam on Al₂O₃-Scale Establishment

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 .

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:

$$\xi = 2\gamma \sqrt {D_{O} } \cdot t.$$

(A1)

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:

$$\frac{{2N_{O}^{S} }}{{3N_{Al}^{o} }} = \frac{G(\gamma )}{{F(\gamma \varphi^{1/2} )}},$$

(A2)

where N ^S_O 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 ^o_Al is the Al concentration in the alloy.

It is seen that γ is a function of N ^o_Al 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 ^o_Al . Therefore, there should be an iteration process to determine the N ^*_Al,1 . This iteration process starts with a small N ^o_Al 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 ^o_Al is much smaller than N ^*_Al,1 , N ^o_Al needs to be increased and N ^*_Al,1 is calculated for the new N ^o_Al . The iterations are completed when N ^o_Al equals N ^*_Al,1 .

Appendix 2

Determining the Effective Oxygen Diffusivity D_O,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:

$$D_{O} = 4.9 \times 10^{ - 2} \exp \left( { - \frac{{164{\text{kJ/mole}}}}{RT}} \right){\text{cm}}^{ 2} / {\text{s}}\quad (850\,{}^{\circ}{\text{C}}\;\text{to}\;1400\,{}^{\circ}{\text{C}}).$$

(A3)

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:

$$\frac{{D_{O,eff} }}{{D_{O} }} = 1 + \frac{{V_{ox} N_{{BO_{v} }} }}{{V_{all} }}\left[ {\frac{{2\delta_{i} D_{O,i} }}{{rD_{O} }} - 1} \right],$$

(A4)

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 ^S_O from Thermodynamics

When there is an external NiO scale present, the oxygen solubility N ^S_O 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:

$$\log P_{{O_{2} }} ({\text{atm}}) = - \frac{24,478}{T} + 8.804\left( { \pm \frac{60}{T}} \right)\quad (1123 - 1423K).$$

(A5)

Fig. 13

Schematic of the cross-section of Ni–Al–O ternary diagram near the Ni-rich corner at 1000 °C

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:

$$\frac{1}{2}O_{2(g)} = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{O}_{\;(Ni,absorb)} ,$$

(A6)

was found [46] to be:

$$\Delta G_{{}}^{o} = - {179{,}300} + 67.6T\;{\text{J/mol}},$$

(A7)

when O uses 1 at.% standard state, which equals 100 × N ^S_O . Therefore, the oxygen solubility corresponding to the oxygen partial pressure for three-phase equilibria at 1000 °C is determined to be N ^S_O  = 4.1 × 10⁻⁴.

Determining the Diffusion Coefficient of Aluminum D_Al 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]:

$$D_{AlNi} = 1.0\exp \left( {\frac{{ - 260\,{\text{kJ/mol}}}}{RT}} \right){\text{cm}}^{ 2} / {\text{s}}.$$

(A8)

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.