Parabolic internal oxidation

Systematically speaking, so-called internal oxidation reactions of alloys (A,B) are extreme cases of morphological instabilities in oxidation. Internal oxidation occurs if oxygen dissolves in the alloy crystal and the (diffusional) transport of atomic oxygen from the gas/crystal surface into the interior of the alloy is faster than the countertransport of the base metal component (B) from the interior towards the surface. In this case, the oxidation product BO does not form a stable oxide layer on the alloy surface. Rather, BO is internally precipitated in the form of small oxide particles. The internal reaction front moves parabolically ( Vo into the alloy. Examples of internal reactions are discussed quantitatively in Chapter 9. 

These assumptions, however, oversimplify the problem. The parent (A,B)0 phase between the surface and the reaction front coexists with the precipitated (A, B)304 particles. These particles are thus located within the oxygen potential gradient. They vary in composition as a function of ( ) since they coexist with (A,B)0 (AT0<1 see Fig. 9-3). In the Af region, the point defect thermodynamics therefore become very complex [F. Schneider, H. Schmalzried (1990)]. Furthermore, Dv is not constant since it is the chemical diffusion coefficient and as such it contains the thermodynamic factor /v = (0/iV/01ncv). In most cases, one cannot quantify these considerations because the point defect thermodynamics are not available. A parabolic rate law for the internal oxidation processes of oxide solid solutions is expected, however, if the boundary conditions at the surface (reaction front ( F) become time-independent. This expectation is often verified by experimental observations [K. Ostyn, et al. (1984) H. Schmalzried, M. Backhaus-Ricoult (1993)]. 

Important features of the selective oxidation process are shown schematically in Figure 1. The slow growth rates of alumina and silica, illustrated in the plot of parabolic rate constants versus temperature at lower right, makes the formation of one of these oxides as a continuous surface layer necessary for long term oxidation protection. This requires that the protective oxide be more stable thermodynamically than the more rapidly growing oxides. The plot of standard free energy of formation as a function of temperature at lower left shows that the Ni-Al system satisfies this condition. Alumina is stable, relative to NiO, even when the activity of aluminum in the alloy is very low. However, when the Al concentration is low the alumina forms as internal oxide precipitates and is non-protective allowing an external layer of NiO to form (illustrated in the cartoon at top). Therefore, a critical concentration of Al exists above which out-... 

Alloys of Nb with small additions of Zr exhibit internal oxidation of Zr under an external scale of Nb-rich oxides. This class of alloy is somewhat different from those such as dilute Ni-Cr alloys in that the external Nb-rich scale grows at a linear, rather than parabolic rate. The kinetics of this process have been analyzed by Rapp and Colson. The analysis indicates the process should involve a diffusion-controlled internal oxidation coupled with the linear scale growth, i.e., a paralinear process. At steady state, a limiting value for the penetration of the internal zone below the scale-metal interface is predicted. Rapp and Goldberg have verified these predictions for Nb-Zr alloys. 

In Figure 9.27 the parabolic oxidation constant for this alloy at 1100 °C is plotted as a function of the chromium content. Its value decreases sharply as the concentration of chromium reaches 30%. The reason is that at the temperature of the experiments chromium-rich alloys form a compact oxide film, made essentially of Ct203, while low chromium alloys form a number of oxides (Figme 9.28). In low chromium alloys an exterior layer of CoO covers a two-phase layer of CoO and CoCr204. Below, a zone of internal oxidation contains a dispersion of Cr203 within the metal matrix. 

The kinetics of internal oxidation are generally found to be diffusion-controlled. Accordingly, Wagner (1959) assumed that the depth of the internal oxidation zone, obeys the parabolic expression ... 

Figure 6-5. Parabolic rate constants for a-Al203 on various NiAl compositions from 1000-1300 °C. The addition of O.OS at.% Hf reduces the rate constant by an order of magnitude compared with undoped NiAl. The rate at 1100 °C is extremely low because of the initial rapid formation of transient, cubic a-Al203 which then transforms to slow-growing a-Al203. Adding more Hf results in a higher weight gain owing to internal oxidation of Hf.

Oxidation morphology is globally the same for other Cr-rich high-temperature alloys like Alloy 230 and AUoy X exposed to oxidizing helium but for the extent of processes. Fig. 3.13 plots evolution of the above-listed microstructural features with time. All oxidation-induced phenomena visibly follow parabolic laws with specific rate constants. It was shown that surface oxidation is the first contributor to the mass gain, with a measurable part issuing from internal oxidation for AUoy 617. 

In oxidation of this type the oxide is unable to offer a barrier to oxygen coming to the metal surface. If the oxide formed cracks or spalls due to internal stresses a few parabolic weight gain steps might occur which might appear linear overall. 

Fig.l. Important aspects of the selective oxidation process Relative magnitudes of free energies of formation of various oxides, relative magnitudes of the parabolic rate constant for the growth of various oxides, and schematic diagrams showing internal formation of alumina in a dilute Ni-A1 alloy and external alumina on a concentrated alloy such as NiAl. 

Fig. 11.5 Effect of chromium content on the oxidation (parabolic rate constant g /cm /s) of Fe-Cr alloys at 1000 °C and 0.13 atm Oj [19]. Reprinted with permission of ASM International, Materials Park, OH. www.asminternational.org.

G. Borchardt and G. Strehl. On Deviations from Parabolic Growth Kinetics in High Temperature Oxidation. In H. Bode (ed.). Materials Aspects in Automotive Catalytic Converters, pp. 106-116, Weinheim, 2002. DGM - Deutsche Gesellschaft ftir Materialkunde e.V, Wiley-VCH. International Conference Materials Aspects in Automotive Catalytic Converters , 3 October 2001, Munich, Germany. 

An alternative approach to the parabolic kinetics correlations used to simulate U02/cladding and cladding/steam interactions is being developed. In this new model, the diffusion equation of oxygen inside the cladding, due to external oxidation by steam and internal reduction of UO2, will be used in conjimction with oxygen concentrations at the phase boundaries provided by the U-Zr-0 phase diagram. 

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