Paralinear oxidation

If a compact film growing at a parabolic rate breaks down in some way, which results in a non-protective oxide layer, then the rate of reaction dramatically increases to one which is linear. This combination of parabolic and linear oxidation can be tenned paralinear oxidation. If a non-protective, e.g. porous oxide, is fonned from the start of oxidation, then the rate of oxidation will again be linear, as rapid transport of oxygen tlirough the porous oxide layer to the metal surface occurs. Figure C2.8.7 shows the various growth laws. Parabolic behaviour is desirable whereas linear or breakaway oxidation is often catastrophic for high-temperature materials. 

Figure C2.8.7. Principal oxide growth rate laws for low- and high-temperature oxidation inverse logarithmic, linear, paralinear and parabolic.

In certain circumstances even the parabolic rate law may be observed under conditions in which the oxide is porous and permeated by the oxidising environment". In these cases it has been shown that it is diffusion of one or other of the reactants through the fluid phase which is rate controlling. More usually however the porous oxide is thought to grow on the surface of a lower oxide which is itself growing at a parabolic rate. The overall rate of growth is then said to be paralinear - and may be described by the sum of linear and parabolic relationships (see equations 1.197 and 1.198). 

The second type of behaviour (Fig. 1.89) is much closer to that which one might predict from the regular cracking of successive oxide layers, i.e. the rate decreases to a constant value. Often the oxide-metal volume ratio (Table 1.27) is much greater than unity, and oxidation occurs by oxygen transport in the continuous oxide in some examples the data can be fitted by the paralinear rate law, which is considered later. Destructive oxidation of this type is shown by many metals such as molybdenum, tungsten and tantalum which would otherwise have excellent properties for use at high temperatures. 

Fig. 1.90 Kinetic interpertation of paralinear oxidation. Curves a and b correspond to the growth of the inner compact layer and the outer porous layer, respectively curve c represents the total weight and is the algebraic sum of curves a and b. Note that as oxidation proceeds, y tends to a limiting value y, (curve a) and the overall rate of oxidation tends to a constant...

The aforementioned inconsistencies between the paralinear model and actual observations point to the possibility that there is a different mechanism altogether. The common feature of these metals, and their distinction from cerium, is their facility for dissolving oxygen. The relationship between this process and an oxidation rate which changes from parabolic to a linear value was first established by Wallwork and Jenkins from work on the oxidation of titanium. These authors were able to determine the oxygen distribution in the metal phase by microhardness traverses across metallographic sections comparison of the results with the oxidation kinetics showed that the rate became linear when the metal surface reached oxygen... 

In some circumstances, the reaction rates may not be exactly parabolic, and even initially parabolic rates may be influenced by changes within the oxide scale with time. As an oxide scale grows, the build-up of inherent growth stresses, externally applied strains and chemical changes to either oxide scale or metal may all compromise the initial protection offered by the scale, leading to scale breakdown and ultimately partial or complete loss of protection paralinear, or linear kinetics may ensue. In other circumstances, as will be seen later in this chapter, very small additions of contaminants to... 

A system of differential equations of this type appears to have been first proposed by J. Loriers in 1949 (see Ref. 13) to describe paralinear growth kinetics of two oxide layers. The term paralinear growth, being a combination of the words parabolic and linear, means that some initial portion of the time dependence of the total thickness or mass of two compound layers is almost parabolic and then there is a gradual transition to linear kinetics. 

In the oxidation of metals, paralinear growth kinetics of oxide layers are known to be a quite usual phenomenon. Such a dependence is observed much less frequently with metallic systems due to three reasons. Firstly, the duration of investigations of the process of oxidation of metals is far longer than that in examining the solid-state interaction of two metals. Secondly, the minimal measurable thickness (or mass) of compound layers which can be detected using available techniques is in the former case much less than in the latter. Thirdly, since this anomalous dependence has no satisfactory explanation from a diffusional viewpoint, experimentalists investigating metallic systems probably prefer not to accentuate on it. 

Paralinear corrosion (related to dissolution of corrosion product) does not occur for all aluminum alloys in water at all high temperatures. In Figure 13 are plotted data for an alloy (Al, 1% Ni, 0.1% Ti) corroded in water at 350°C (10). The corrosion rate was low and constant, as shown better in other figures in the same publication. For some specimens in the figure 1/3 or 2/3 of the corrosion product was removed mechanically after the first exposure period. There was no discernible effect on subsequent corrosion, indicating that control of corrosion probably resided close to the metal-oxide interface. Similar experiments for the alloys and temperatures where paralinear behavior occurs showed that removing some of the product caused an increase in subsequent corrosion rate. 

Initially, when the diffusion through a thin scale is rapid, the effect of C1O3 volatilization is not significant but, as the scale thickens, the rate of volatilization becomes comparable and then equal to the rate of diffusive growth. This situation, paralinear oxidation, results in a limiting scale thickness, Xq, for which dx/dt = 0, which is shown schematically in Figure 4.11. Setting this condition in Equation (4.25) yields Equation (4.29) ... 

Alloys of Nb with small additions of Zr exhibit internal oxidation of Zr under an external scale of Nb-rich oxides. This class of alloy is somewhat different from those such as dilute Ni-Cr alloys in that the external Nb-rich scale grows at a linear, rather than parabolic rate. The kinetics of this process have been analyzed by Rapp and Colson. The analysis indicates the process should involve a diffusion-controlled internal oxidation coupled with the linear scale growth, i.e., a paralinear process. At steady state, a limiting value for the penetration of the internal zone below the scale-metal interface is predicted. Rapp and Goldberg have verified these predictions for Nb-Zr alloys. 

In common with oxide scales, halide scales can also suffer mechanical damage such as cracks, etc. In addition, the vapour pressure of the halide can be quite high, such that evaporation of the halide from the scale-gas interface can be substanhal. This leads to simultaneous formation and evaporahon of the hahde scale and has also been treated by Daniel and Rapp. The rate of thickening of a scale forming under these conditions then follows paralinear kinehcs" as described for the combined scale growth and evaporahon of chromium oxide in Chapter 4. 

X remains constant because the rate of growth of the scale is then zero. This steady-state thickness, X, becomes smaller as increases with more aggressive erosion. This behaviour has been demonstrated using cobalt and is illustrated in Figure 9.11. This paralinear behaviour is similar to that described in Chapter 4 for the oxidation of chromium under conditions where volatile CrOa evaporates from the scale-gas interface. ... 

The kinetic curves obtained under isothermal conditions (Fig. 13) follow the paralinear law (Fig. 7) with competing B4C oxidation and B2O3 vaporization. 

TiB2 oxidation above 700°C was approximated by the parabolic rate law (9) [190]. Deviations from the parabolic oxidation start at temperatures of 950-1100°C when vaporization of B2O3 becomes noticeable. A cubic law was suggested [191,192], but we assume that a paralinear law (Fig. 7) should better describe the kinetics, similar to the case of BN and B4C. 

Figure 7-19. Paralinear kinetics for SiC oxidized in water vapor. Model results typical of exposures al I200°C in 50% H2O/50% Oj at flow rates of 4.4 cm s. a) oxide growth and matrix recession b) weight change. (Adapted from Opila and Hann, 1997.)...

In some cases, however, these transitory periods carmot be neglected and a kinetic law that does not correspond to the one deduced with the pseudo-steady state is observed for a significant reaction extent, even if the state tends toward a pseudosteady state. We will study the example of the paralinear law, which is sometimes obtained during the oxidation of metal plates. 

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