Impact of Grain Boundary Density on Oxide Scaling Revisited

Journal article, 2019

A straightforward conceptual tool for discriminating between different oxide scaling processes deviating from the parabolic standard model is formulated. Grain boundary diffusion-controlled oxide scaling is generalized to include lateral grains coarsening. Building on traditional Wagner theory, attenuation of rates of inwards growing oxides owing to the gradual loss of grain boundary density is revisited. Two viable cases are identified. One has the rate of grain boundary density loss to be independent of the rate of oxide growth, while the second case takes the two instantaneous rates to be equal. Simple parabolic–logarithmic and superparabolic–cubic expressions are arrived at for the two cases, respectively. Usefulness is demonstrated by applying the models to published experimental data from 1990 to date. Upon arrival at the superparabolic–cubic behaviour, a generic mathematical form analogous to a ‘spring force’ attenuating the scale growth was identified. ‘Parabolic’, ‘cubic’ and ‘logarithmic’ scaling emerges as limiting cases.