Parabolic oxidation of metals in homogeneous electric fields

A previously proposed thin film parabolic growth law (Fromhold, 1963) is extended to include film growth due to any number of diffusing defect species of arbitrary valence, and an analysis is made of the effects of applying external electrostatic potentials during oxidation. The total electrical conductivity and the partial conductivities are markedly position-dependent in the protective film, varying by orders of magnitude from one interface to the other. The built in electrostatic potential across the film is independent of thickness of the film and is a function of the partial conductivities of the diffusing ionic and electronic defect species. Effects of electrical shorting of the oxide film by external circuitry are analyzed. Depending on polarity, a constant applied potential can increase or decrease the rate constant but does not alter the kinetics from the parabolic form, in accordance with published experimental data. The net electrostatic potential required to stop metal oxidation is derived for the model in question. For growth by a single ionic species, the stopping potential is that electrostatic potential which gives an equal electrochemical potential at the metal-oxide and the oxideoxygen interfaces. For growth by multiple ionic species, the stopping potential is a function of the ionic partial conductivities.