Parabolic rate law for the oxidation of metals

The parabolic rate law, which is named after Tammann [48] and Pilling and Bedworth [11 ], is by 

In order to calculate the practical tarnishing reaction rate constant (Tammann constant) Jc, Wagner assumed that ions and electronic charge carriers are responsible for mass transport through the product layer. This reaction scheme is shown in Fig. 8-1. Local electroneutrality must always be observed, of course. 

The constant Ic can be calculated from the flux equations (5-13), with the condition of electroneutrality being used to eliminate the diffusion potential . The calculation is performed just as in the derivation of the rational rate constant for spinel formation in section 6.2.1. According to eq. (6-22), Tc kv, where n is the increase in volume of the product layer following the passage of one ionic equivalent, k is the rational tarnishing rate constant as introduced by Wagner [12]. It is equal to the flux in equivalents per unit area per unit time for a unit product layer thickness. By the method outlined above, k may be calculated as  

Furthermore, for the tarnishing of divalent transition metals (to form NiO, CoO, FeO, etc.), the electronic transport number can be set equal to one. The practical rate constant is then  

The integration extends from the Me/MeO phase boundary where the chemical potential of the metal is to the phase boundary MeO/02 (g), where the chemical potential of the metal is If the Gibbs free energy of formation of MeO, A is known, then this latter 

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