Oxide Film Growth Kinetics on Metals and Alloys: II. Numerical Simulation of Transient Behavior

Abstract

A number of passive film growth models have been advanced in the past, each founded on different assumptions and providing different rate laws. A new, generalized growth model has been developed and the numerical simulation of the transient behavior of oxide film growth on metals and alloys is reported here. This model is based on the transport of anions and cations (in a Cr2O3 film for stainless alloy). In contrast to most models up to date, it describes the time-variant behavior of film and film/solution potential differences. Because these potential differences are expressed as exponential functions of film thickness, asymptotic behaviors can be studied and it is shown that a square root law results for very thin and very thick films. Growth rate for intermediate films and during transient periods, on the other hand, is determined by numerical integration. Parameters which were introduced by the model and whose values are unknown are conveniently regrouped into only four lumped parameters, which are easily estimated by numerical optimisation. It is shown that experimental oxide film thickness measurements on stainless alloys in high-temperature aqueous environments can be reproduced. It is further shown that the diffusional rate expressions of all the species contributing to growth are analogous, explaining why it is possible to fit growth kinetics with a single type of point defect.