Wagner metal oxidation theory

According to the Wagner metal oxidation theory, the metal oxidation process is controlled by the crystal lattice diffusion in the oxide phase and by diffusion along the GB. It also conforms to the parabola rule at high temperatures ... 

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-... 

The main difficulty with the first mode of oxidation mentioned above is explaining how the cation vacancies that arrive at the metal/oxide interface are accommodated. This problem has already been addressed in Section 7.2. Distinct patterns of dislocations in the metal near the metal/oxide interface and dislocation climb have been invoked to support the continuous motion of the adherent metal/oxide interface in this case [B. Pieraggi, R. A. Rapp (1988)]. If experimental rate constants are moderately larger than those predicted by the Wagner theory, one may assume that internal surfaces such as dislocations (and possibly grain boundaries) in the oxide layer contribute to the cation transport. This can formally be taken into account by defining an effective diffusion coefficient Del( = (1 -/)-DL+/-DNL, where DL is the lattice diffusion coefficient, DNL is the diffusion coefficient of the internal surfaces, and / is the site fraction of cations located on these internal surfaces. 

Reactions in metal-sulphur systems have been studied, as model systems, to verify mechanisms that are proposed for the high-temperature oxidation processes. The excellent correspondence between the initial theories of Wagner and observation in the case of sulphidation established confidence in the theory, which was then applied widely to the more practically important metal-oxidation processes. 

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 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. 

Chapter 10 deals with high temperature corrosion, in which the thermodynamics and kinetics of metal oxidation are included. The Pilling Bedworth Ratio and Wagner s parabolic rate constant theories are defined as related to formation of metal oxide scales, which are classified as protective or nonprotec-tive. 

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. 

By measuring the cell potential for this ideal case, where the oxide would behave as a tme electrolyte and where no polarization losses at the electrodes would occur, the Gibbs energy of formation for the oxide can be determined. However, for most metal oxides (exceptions would be calcia- or yttria-stabilized zircoiua above 800°C or pure b-BijOj above 650°C) the transport number of the ions is smaller than 1, thus making a direct measurement of the equilibrium cell potential in Figure 15.3 impossible. Alternatively, it could be formulated that the cell is partially short circuited by the electronic current. For oxides growing on a metal substrate under stationary conditions as described by the Wagner theory in Section n, this is the normal situation. 

As mentioned in the previous section, high temperature alloys mainly rely on the formation and maintenance of a protective oxide scale on their external surfaces. This can be achieved if the content of the alloying (or solute) element in the substrate is higher than a critical value. According to the classical selective oxidation theory developed by Wagner (1959), the minimum content of the solute metal, for the formation of an exclusive external oxide scale is estimated as ... 

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 solid state physics, it is well known that many inorganic solids, e.g., the oxides and sulfides, can dissolve metals and nonmetals in excess, and that by this process electron and ion defects in the lattice will be formed. Wagner and co-workers (1) have developed the basic theory of... 

Metals are obtained by the treatment of oxides and sulfide ores found in the earth. However, there is an initial difficulty—the desirable ores are often mixed up with those of little commercial value, and the problem is to obtain the desired ore free from those of lesser worth. For many years now, largely due to the initiative of Australian workers, it has been possible to find organic substances which, when added to a suspension of mixed ores, pick out the desired one, and (when air is bubbled into the system) float it to the surface, from which it can be raked off, i.e., separated and made available for chemical or electrochemical extraction of the metal. It turns out that the basis of this mineral flotation technology involves the Wagner and Traud mixed-potential concept and is thus indirectly related to corrosion theory. 

The preceding theory was used by Wagner to describe oxide film growth on metals [49,50]. The driving force for diffusion is not a concentration gradient. 

Solid materials, in general, are more or less subject to corrosion in the environments where they stand, and materials corrosion is one of the most troublesome problems we have been frequently confronted with in the current industrialized world. In the past decades, corrosion science has steadily contributed to the understanding of materials corrosion and its prevention. Modem corrosion science of materials is rooted in the local cell model of metallic corrosion proposed by Evans [1] and in the mixed electrode potential concept of metallic corrosion proved by Wagner and Traud [2]. These two magnificent achievements have combined into what we call the electrochemical theory of metallic corrosion. It describes metallic corrosion as a coupled reaction of anodic metal dissolution and cathodic oxidant reduction. The electrochemical theory of corrosion can be applied not only to metals but also to other solid materials. 

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. 

---