Quasi-steady-state growth of layered two-phase oxides on pure metals

Abstract

The kinetic equations for the simultaneous growth of two-layered planar oxide phases on pure metals under electric-field-modified diffusion-controlled conditions have been formulated. These equations enable the determination of quasi-steady-state growth kinetics following step-function changes in the experimental conditions of ambient oxygen partial pressure or temperature. The linked growth equations for the two phases have been numerically evaluated under conditions of single-phase parabolic thermal oxidation to deduce the general predictions of the theory. In the asymptotic limit of a long time lapse following any change in the experimental conditions, the growth rates for the two layers are found to approach a fixed ratio. A simple analytical evaluation of the functional dependence of the rate constant for two-phase growth on the parabolic rate constants for single-phase growth is possible in this limit, the result so obtained for motion of the cation species agreeing with that deduced by Yurek, Hirth, and Rapp assuming a fixed value for the ratio of the layer thicknesses during the entire growth.