Wagner’s theory of oxidation

Wagner s theory of oxidation provides a quantitative description of the growth rate of compact oxide layers as a function of the difference in electrochemical potential between the metal-oxide and the oxide-gas interfaces. The following analysis uses concepts developed in Section 4.3 for aqueous electrolytes. This simplifies the theoretical developments proposed by Wagner [4], while yielding the same results. 

In the following, we will develop Wagner s theory of oxidation for divalent oxides with an excess of either cations or anions ... 

An appreciable number of special monographs on metal oxidation are available. These presentations normally start with Wagner s theory of scale formation [C. Wagner (1933), (1951)], which represented the first consistent and quantitative treatment of a solid state reaction model. As Figure 7-1 shows, metal oxidation has quite... 

Wagner s theory of metal oxidation is phenomenological. Many questions concerning atomic aspects of the oxidation process cannot be answered within the frame of this phenomenological theory. Since atomic aspects are important when we analyze the boundary conditions, this will be exemplified by two pertinent problems. Firstly, let us ask about the coherence of the metal/oxide interface during the oxida-... 

In part I above, c. Wagner s theory of mixed conduction was reviewed in terms of an equivalent circuit approach. The implications of mixed conduction theory for parabolic scaling of metals in high temperature atmospheres were also detailed. It was pointed out, however, that current interest in mixed conduction theory is no longer motivated by corrosion considerations because far too few systems of practical interest conform to the conditions required for pareibolic oxidation. 

In many cases, the layer growth can be described by a parabolic rate law x = kpt, where x is the scale thickness at time t and kp is the parabolic rate constant. This law may be derived from Wagner s theory of metal oxidation. The parabolic rate corrstants contain diffusion coefficients which are related to the concentration of the defects responsible for material transport through the layer. In fact, the higher the deviation from stoichiometry, the larger the diffusion coefficient and, consequently, the faster the oxidation rate of a metal at a given temperature. 

On the other hand, from Wagner s theory of metal oxidation it follows that, if the concentration of predominant defects in the growing scale on a given metal is low enough that their mobility is concentration independent, the self-diffusion coefficient of diffusing species depends in the same way on oxidant pressure as the parabolic rate constant of scale growth. Thus, in the case of molybdenum sulfidation should be the following function of sulfur pressure ... 

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... 

Whether the rate of oxidation of an alloy of copper with a baser metal is less or more than that of copper will depend on the concentration of the alloying element and the relative diffusion velocities of metal atoms or ions in the oxide layers. There is extensive literature on the oxidation behaviour of copper alloys According to Wagner s theory the rate of oxida-... 

In addition, the theory predicted that a measurable emf would be established over the tarnishing layer, and moreover, that this voltage could be used to infer the average ionic and electronic transference numbers of the scale. Prior to Wagner s treatment, of course, there had been no reason whatever to think that the electrical properties of the scale compound should bear any relation to oxidation rates, nor was there any reason to think that voltages should appear over these coatings. 

Thus, Wagner s theory can be used to predict how much oxygen will permeate the tube in any given time. If the tube material is predominantly an electronic conductor, this permeability becomes a measure of the chemical dlffuslvity for oxygen in the compound. However, if it is a solid electrolyte material, e.g., doped zirconia or thoria, the permeability is limited by electronic conduction. Thus, some of the best estimates of positive hole conductivity in the oxide solid electrolytes have come from "gas permeability" studies made on tubes of these materials. 

The predichons of Wagner s theory for n-type and p-type oxides in which cations are the mobile species should now be examined. The first class is represented by ZnO which is formed by the oxidahon of zinc. 

One can conclude that for most oxides Wagner s theory is valid for film thicknesses greater than 1 pm at temperatures >500 °C. In oxides with large concentrations of charged defects, Wagner s theory is valid for films greater than 20 nm in thickness, only for thinner films the electric field is too high. 

In Wagner s theory, near-equilibrium is assumed at the metal/oxide interface, that is, the frequency of jumps through the interface is about equal in both directions. The presence of the field, however, decreases the activation energy... 

The two last examples represent the FS intermediate between chemical and electrochemical ones, because the interaction follows the mechanism of electrochemical corrosion overall current is zero, though partial currents flow with opposite sign, typical for corrosion situation. It seems that this kind of systems comprises also the processes of metal oxidation which obey Wagner s theory (see Chap. 4). 

Wagner s oxidation theory assumes that volume diffusion of point defects limits the growth of oxide layers. However, other transport mechanisms are possible, notably grain boundary diffusion. At relatively low temperatures, Tmelting temperature of the oxide, this mechanism contributes considerably to the transport, and the rate of oxidation exceeds that calculated using Wagner s theory. The rate of grain boundary diffusion depends on the microstructure of the oxide films formed, which is difficult to control [8]. For this reason, measured oxidation rates are often not well reproducible. 

---