Wagner theory of oxidation

The Wagner theory [10] for a coupled diffusion and migration (also known as ambipolar diffusion) mass transfer during oxidation of metals and alloys is briefly described. This theory treats the parabolic kinetic behavior of high temperature oxides given by eq. (10.19) with n = 1/2. 

First of aU, combining eqs. (10.31) and (10.41) yields the total ionic flux in the x-direction 

However, if Ae material is an alloy containing at least two elements, then the more active element oxidizes first and its cations react with the gas-phase anions to form the initial oxide, sulfide, carbide, nitride, and so on. Other elements in the alloy may react afterward to form other surface compounds. Consequently, the surface scale may be a combination of phases, which may be identified by X-Ray diffraction and revealed by scanning electron microscopy (SEM). 

This relationship derives directly from the conservation of mass that accompanies the mass transfer and it is suednctly represented in the treatment of ionic flux balance. For ionic electroneutrality, this notation, eq. (10.53), can be further simplified by letting Ja 0 and using eq. (10.52) for both cations and electrons together with (10.53) yields the electrical potential gradient 

Inserting eq. (10.54) into (10.52) and letting Jx,i = Jx,c yields the cation vacancy flux in terms of more easily measurable electrical conductivity 

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Theories of oxidation have been developed by Wagner and by Mott ° . In general the logarithmic rate law applies to very thin oxide layers which form protective coatings and the parabolic rate law to thick oxide layers. More recent reviews of the subject have been given by Grimley , Kubaschewski and Hopkins and by Wyn Roberts . ... 

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 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-... 

The existence of the latter has been recognized for many years, since Wagner (20) applied his thermodynamic theory of defect oxides to the system zinc oxide-oxygen (21). According to this scheme, at sufficiently high temperature an equihbrium sets in between zinc oxide and oxygen in the gas phase, whereby excess zinc (Zn ) can be accommodated in interstitial positions of the lattice ... 

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... 

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. 

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. 

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