Oxide films parabolic rate constant

To relate the permeation flux to the parabolic rate constant, Wagner further assumed quasi-steady-state growth conditions. This assumption implies that the flux into the reaction layer is equal to the flux out of it and that there is no accumulation of material in the film. In other words, at any time, the flux was not a function of. r, but was only a function of time. This condition is shown schematically in Fig. 7.18c for various times during scale growth. Mathematically it implies that the flux is inversely proportional to Ax, and hence dx in Eq. (7.73) can be replaced by Ax. Make that substitution, and note that the rate at which the oxide layer is growing is given by... 

In both of these equations, x is the film thickness, t is the time of the oxidation, and k and are experimentally determined constants. The constant fep is called the parabolic rate constant. A linear rate is usually found when the film is porous or cracked. The parabolic equation is found when the film forms a coherent, impenetrable layer. As the rate of film growth, dx/dt, diminishes with time for the parabolic rate law, this equation is associated with protective kinetics. The parabolic rate law arises when the reaction is controlled by diffusion. The species with the lowest diffusion coefficient plays the most important role in this case. 

This parabolic law, which indicates that diffusion is rate-limiting, is of overwhelming importance for scale formation. Wagner (1933) showed that the parabolic scale constant (and hence, rate of oxidation) can be calculated using the enthalpy of formation of the corrosion product, the electrical conductivity of the protective film and the transport number of the ions and electrons in the film. 

The parabolic rate law is applicable when the controlling step is by diffusion of the oxide-forming metal through a barrier such as an oxide or passive film. The oxidation rate is inversely prop)ortional to time and approaches a slow constant rate after finite time. This is the most common type of high-temperature oxidation found on engineering materials. 

The oxidation rate of (OOOl)C is 5-10 times higher than of (OOOl)Si in the temperature range 1000-1300°C in dry and wet hydrogen flow at 15 liters per minute (Fig. 5). The oxidation rate of other facets, for instance, (1120), has an intermediate value compared with 0001 facets. The oxidation process of the (0001)C facet is limited by diffusion of the reaction components through the growing oxide film. Hence the oxidation rate of this facet does not depend on the crystal surface treatment, type and level of doping, or polytype structure. The constants of the linear-parabolic equation for (0001)C oxidation are shown in Table 4. 

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