Oxidation Wagner theory

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. 

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. 

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. 

The theory for high-temperature oxidation as described under Section II.C can be used also for sulfidation. Because of the high defect concentration in sulfides, the transport of material is mainly governed by lattice diffusion, so that the Wagner theory is probably more appropriate for many sulfides than for oxides, where grain boundary diHusion may be more important The sulfidation of Fe can be described very well with the Wagner theory. Experimental data are in excellent agreement with the partial sulfur pressure dependence (k = k - the reaction... 

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. 

The transport number of the mobile ioiuc species, which is important in the Wagner theory for parabolic oxide growth, can be determined. Eqrration (15.50) thus becomes ... 

Kleitz et al. [Kleitz et al., 1973 Fouletier et al., 1975] were the first to demonstrate that the existence of a nonvanishing semipermeability flux through a solid electrolyte induces a deviation from equilibrium on both sides of the membrane. They expanded the Wagner theory to account for partial control of surface reactions on the transport kinetics through stabilized zirconia. This apvproach has been applied to mixed ionic-electronic oxides [Bouwmeester et al., 1994 Qien et al., 1997 Geffrey et aL, 2011 Xu Thomson, 1999]. 

Determination of hole and electron conductivities and transport numbers of oxide ion in LaGa03-based oxides were performed by the polarization method by Baker et al. [21], Yamajiet al. [35], and Kimand Yoo [36]. Kim et al. reported that Pq2 dependence of hole and electron conductivity is proportional to Pcn and respectively, and well obeys the Hebb-Wagner theory. The results... 

Carl Wagner in association with Schotlky proposed the point defect-mediated mechanism of mass transport in solids, which Wagner extended to the analysis of electronic defects. For these works and Wagner s subsequent research on local equilibrium, his oxidation rate theory and the concept of counter diffusion of cations, he is considered by some to be the father of solid state chemistry . 

As addressed above, a coating with excellent oxidation performance should exhibit a short initial and transient oxidation stage in which continuous chromia- or alumina-TGO scale can form. However, whether the initial and transient stage is short depends on the critical content of chromium or aluminium in the coating, below which less protective oxide scale forms. According to the classical Wagner theory, external scale of chromia or alumina can be exclusively formed if the content of chromium or aluminium of an alloy reaches a critical value, N, ... 

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-... 

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