We use irreversible thermodynamics to formulate a model for the formation of a cation-deficient, p-type oxide on the surface of a pure metal in which local equilibrium is not necessarily maintained at the oxide interfaces and no a priori assumption regarding a rate limiting step is made. The dissipation rate derived here accounts for most of the conceivable processes that can occur during the oxidation of a metal, including bulk diffusion of cations and surface diffusion along the metal-oxide and gas-oxide interfaces. By including capillary effects in the formulation, shape changes in the oxide, which are usually neglected in most theories, can be described. We examine the steady-state solution of the model in one dimension for planar interfaces, and show that the growth law naturally captures the transition from linear to parabolic kinetics as the film thickens. A characteristic lengthscale for the transition is derived and can be obtained from oxide growth curves as a fitting parameter. Wagner's classical oxidation model is obtained as a limiting case of our more general model. We obtain expressions for the interfacial defect concentrations as a function of the departure from local equilibrium at the interfaces. From these expressions, we show that the exponent for the oxygen pressure dependence of the cation vacancy concentration can deviate from the usual values obtained from equilibrium considerations, and thus measuring nonstandard exponents can indicate a nonequilibrium effect. Our analysis serves to clarify the meaning and validity of the local equilibrium assumption in the context of metal oxidation.
ASJC Scopus subject areas
- Materials Science(all)
- Physics and Astronomy (miscellaneous)