Time–Temperature Profiles Resulting in Quasi-constant Oxidation Rates

If a rate of metal oxidation is diffusion-controlled, then a thickness of a scale emerging on its surface at constant temperature is typically a parabolic function of time. If temperature changes, then this inherently parabolic temporal evolution of the thickness may transform into differently shaped functions. By using a concept of equivalent times introduced and elaborated in this work, it is shown how the oxide thickness versus time dependence L(t) can be established for any time–temperature profile T(t). Then, it is explored whether there exists a unique T(t) regime for which a growth rate is constant, i.e., for which L(t) is linear. It is proven that it is possible to design a time–temperature scheme for which the same holding times cause identical thickness changes. Such a growth mode, however, cannot be sustained indefinitely; there is a time threshold beyond which the linear growth of the oxide layer cannot be maintained any longer. Although oxidation is frequently a thermally activated process, mathematical expressions and conclusions remain the same for non-Arrhenius kinetics.