Mott-Cabrera Model

According to the theoretical models of Mott-Cabrera [4.87] and Grimly [4.88], it is expected that the constituent with the largest heat of formation for the corresponding oxide segregates to the surface. This behavior was evidenced experimentally by Walz [4.66], who studied the surface oxidation... 

Numerous other models have been proposed to explain the deviation of dry oxidation from linear-parabolic kinetics. For example, field-assisted oxidant diffiision during the oxidation of metals was proposed by Cabrera and Mott (75) and used by Deal and Grove (69) to explain the results for thin oxides. Ghez and van der Meulen (76) proposed the dissociation of molecular oxygen into atomic oxygen at the Si-Si02 interface and the re-... 

This model locates the rate-determining step within the oxide however, it can also be located at the interfaces without differences in the mathematical description [iii]. Refs. [i] Pringle JPS (1980) Electrochim Acta 25 1423 [ii] VerweyEJW (1935) Physica 2 1059 Lohrengel MM (1993) Mater Sci Eng R11-.243 [iii] Cabrera N, Mott NF (1948-49) Rep Prog Phys 12 163... 

In contrast, Mott [75,76] and Cabrera [15, 48] considered the ITR of metal ions at the interface M/ox, that is. Reaction (15) as rate determining step. Since both models yield the same Eq. (31), a decision is still open. 

One of the first mechanistic models of the kinetics of passive film formation was described by Cabrera and Mott [31]. The passive film thickness in their model is controlled by the transport of the metal cations from the underlying metal to the... 

The model of Cabrera and Mott is also applicable to growth due to the transport of anions. However, under mixed conditions, a more rigorous treatment of the ionic... 

By extension, the model of Cabrera and Mott is often used to describe the growth of nanocrystalline or amorphous oxides by assuming that the potential energy of the mobile ions conserves, on average, a certain periodicity. 

The generally accepted model for passive film growth, illustrated in Fig. 3-14, is of field-assisted film formation, which is essentially a modified Cabrera-Mott model originally established for gaseous oxidation and the formation of thin oxide films in a gas at low temperature (Cabrera and Mott, 1948-1949 Fehlner and Mott, 1970). This classical theory describes the growth, in the direction perpendicular to the surface, of an oxide layer completely covering the substrate surface, by a hopping mechanism. The... 

The rate law derived from the Cabrera-Mott model is as follows... 

The model of Cabrera and Mott is discussed in die book on low-temperature oxidation by Fehiner [5b]. The basis of the model is die quantum mechanical concept of electron tunneling. An electron can penetrate an energy barrier without die requirement for thermal activation. As soon as a three-dimensional oxide forms on a metal, electrons tunneling through the oxide are captured by adsorbed oxygen on die oxide surface. The charge separation thus established between die oxide surfece and the metal sets up an electric field across the oxide. The proposed mechanism is illustrated in Figure 1. 

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