Oxidation growth law

The critical thickness of the oxide, Xc, can only be obtained experimentally by characterizing the debris. The model is thus not a predictive one. Moreover as pointed out (Smith, 1985) the oxide growth laws based on mass can hardly be used under the conditions of contact characterized by a low air supply, and a poor knowledge of the real contact temperature. In practice, the use of oxidation constants leads to wear rates that are several orders of magnitude different from the experimentally verified ones. 

The above rate law has been observed for many metals and alloys either anodically oxidized or exposed to oxidizing atmospheres at low to moderate temperatures—see e.g. [60]. It should be noted that a variety of different mechanisms of growth have been proposed (see e.g. [61, 62]) but they have in common that they result in either the inverse logaritlnnic or the direct logarithmic growth law. For many systems, the experimental data obtained up to now fit both growth laws equally well, and, hence, it is difficult to distinguish between them. 

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.

If K = 1 K, a = 0.25 nm, and z = 3, X = 30nm at 300 K, so that for a film 1 nm thick, the field increases the rate of growth by a factor of about 10 The term in the growth law due to the field, namely exp (K/X), is large only when X is small. Because of this a thin oxide film can form even at low temperatures where the ordinary rate of entry of ions into the oxide, is negligible. As the film thickens, the factor exp /X) decreases rapidly, and the rate of growth soon falls to such a low value that, for practical purposes, oxidation has ended. 

The volume ratio (see Section 1.9) for cuprous oxide on copper is 1 7, so that an initially protective film is to be expected. Such a film must grow by a diffusion process and should obey a parabolic law. This has been found to apply for copper in many conditions, but other relationships have been noted. Thus in the very early stages of oxidation a linear growth law has been observed (e.g. at 1 000°C) . 

Conway BE, Barnett B, Angerstein-Kozlowska H, Tilak BV. 1990. A surface-electrochemical basis for the direct logarithmic growth law for initial stages of extension of anodic oxide films formed at noble metals. J Chem Phys 93 8361-8373. 

Fig. 18.3 Plots of the growth laws of oxidation a) parabolic, b) rectilinear, c) quasi-rectilinear, d) logarithmic (West, 1980, with permission).

Sometimes crystal growth, dissolution, or oxidation is said to follow a linear growth law or a parabolic growth law. The linear law means that the thickness of the crystal depends linearly on time. 

This completes our development of the thick-film parabolic growth law. This particular theory has been presented in some detail because it is an extremely important domain of metal oxidation. In addition, it provides an excellent example of the way the coupled-currents approach [10,11] can be used to obtain oxide growth kinetics and built-in voltages in thermal oxidation. 

In the case of some metals such as magnesium below a temperature of 200°C, a thin oxide layer is formed, which resists diffusion of oxygen and as a result an initial formation of oxide is followed by practically zero growth of the oxide. The rate law governing this type of oxide growth is logarithmic.75... 

This type of growth law (curve (6), Figure 39) is the most prevalent and is obtain for coherent films in which the rate-determining step is the diffusion of ions through the film. The oxidation of copper, reaction of halogens with silver, and the oxidation of me above 350° C. foUow this law. 

Equation 1.4 directly implies the time behavior (rate) of oxide growth. An inverse logarithmic growth law according to the following expression can be derived to a good approximation (Cabrera and Mott [55]) ... 

Because of different chemical, ionic and electronic properties, the oxide growth on metals, alloys and semiconductors follows different mechanisms and different laws. The most important contribution comes from the migration of ions in electric fields exceeding 5 x 10 V cm . ... 

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