Parabolic oxidation

Provided the mole fraction of A does not fall below N, then the oxide AO will be formed exclusively. The important criterion is the ratio of the oxidation parabolic rate constant to that of the diffusion coefficient of For A1 in Fe, the parabolic rate constant is very low, whilst the diffusion coefficient is relatively high, whereas the diffusion coefficient of Cr is much lower. Hence, the bulk alloy composition of A1 in iron required for the exclusive formation of AI2O3 at any given temperature is lower than the Cr concentration required for the exclusive formation of CrjOj. 

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.

As regards Zr oxidation, parabolic correlations are used to compute the total o gen mass gain of a stainless steel mesh. The oxide layer is composed of a mixture of iron, chromic and nickel oxides. 

If a compact film growing at a parabolic rate breaks down in some way, which results in a non-protective oxide layer, then the rate of reaction dramatically increases to one which is linear. This combination of parabolic and linear oxidation can be tenned paralinear oxidation. If a non-protective, e.g. porous oxide, is fonned from the start of oxidation, then the rate of oxidation will again be linear, as rapid transport of oxygen tlirough the porous oxide layer to the metal surface occurs. Figure C2.8.7 shows the various growth laws. Parabolic behaviour is desirable whereas linear or breakaway oxidation is often catastrophic for high-temperature materials. 

Figure C2.8.7. Principal oxide growth rate laws for low- and high-temperature oxidation inverse logarithmic, linear, paralinear and parabolic.

This rate expression is known as the parabolic law. It is obeyed by oxidation of Ni, Ti, Cu, and Cr and by halogenation of silver. The product coat retards both diffusion and heat transfer. 

The behavior type may change with temperature range. For instance, oxidation of zinc above 350°C (662°F) obeys the parabolic law, but at lower temperature the product coat seems to develop cracks and the logarithmic law, nw = kt, is obsei ved. 

In part the parabolic law may also apply to multilayer oxide systems where the cation diffusion coefficient is much higher in the lower oxide tlran in the higher oxide, which, growing as a thin layer, undergoes plastic deformation at high temperatures, thus retaining the overall oxide layer as impervious to enuy of tire gas. 

The sulphation of cobalt oxide, CoO, follows the parabolic law up to 700°C and above 850°C, proceeding by outward diffusion of cobalt and oxygen ions through a sulphate layer which is coherent up to about 700°C. The mechanism... 

The second type of oxidation behaviour is parabolic oxidation, with... 

Figure 21.4 illustrates the mechanism of parabolic oxidation. The reaction M + O MO... 

Fig. 21.4. How oxide layers grow to give parabolic oxidation behaviour.

The oxidation of a particular metal in air is limited by the outward diffusion of metallic ions through an unbroken surface film of one species of oxide. Assume that the concentration of metallic ions in the film immediately next to the metal is Cj, and that the concentration of ions in the film immediately next to the air is C2, where and C2 are constants. Use Tick s First Law to show that the oxidation of the metal should satisfy parabolic kinetics, with weight gain Am given by... 

The oxidation of another metal is limited by the outward flow of electrons through a uniform, unbroken oxide film. Assume that the electrical potential in the film immediately next to the metal is Vi, and the potential immediately next to the free surface is Vi, where Vj and Vi are constants. Use Ohm s Law to show that parabolic kinetics should apply in this case also. 

The kinetics of oxidation of mild steel at high temperature are parabolic, with... 

In practice, thermal cycling rather than isothermal conditions more frequently occurs, leading to a deviation from steady state thermodynamic conditions and introducing kinetic modifications. Lattice expansion and contraction, the development of stresses and the production of voids at the alloy-oxide interface, as well as temperature-induced compositional changes, can all give rise to further complications. The resulting loss of scale adhesion and spalling may lead to breakaway oxidation " in which linear oxidation replaces parabolic oxidation (see Section 1.10). 

A protective oxide layer forms a continuous barrier between the reactants (oxygen and metal), which inhibits the reaction. The simplest assumption that can be made about the effectiveness of this barrier is that its protecting power is directly proportional to its thickness. Mathematically, AX/At = k2/X, which on integration gives the parabolic law,... 

If Q is the volume of the oxide per metal atom, the rate of growth, dA /d/, is equal to / Q. Thus from equation 1.179 we derive the parabolic law... 

An important aspect of any theory of the oxidation of a pure metal is that it enables us to see how the protective power of the oxide layer can be altered by the introduction of alloying constituents into the metal. According to Wagner s theory, the parabolic rate constant for the system Ni/NiO for example depends upon the concentration of cation vacancies in the oxide in equilibrium with oxygen gas. If this concentration can be reduced, the oxidation rate is reduced. Now this can be done if cations of lower valency than Ni can be got into the oxide (Fig. 1.77). Suppose, for example, that a little Li is added to the Ni. Each Li ion which replaces Ni is a negative... 

In certain circumstances even the parabolic rate law may be observed under conditions in which the oxide is porous and permeated by the oxidising environment". In these cases it has been shown that it is diffusion of one or other of the reactants through the fluid phase which is rate controlling. More usually however the porous oxide is thought to grow on the surface of a lower oxide which is itself growing at a parabolic rate. The overall rate of growth is then said to be paralinear - and may be described by the sum of linear and parabolic relationships (see equations 1.197 and 1.198). 

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