The effect of supersaturation on the parabolic rate constant for internal oxidation with production of a pure oxide: An approximate analytical treatment

Abstract

Internal oxidation in binary alloys leading to the precipitation of a pure oxide is examined, taking into account the finite value of the solubility product of the oxide in the base metal, and approximate analytical expressions for the profiles of the concentrations of oxygen and the less noble component are derived. In contradiction with the original analysis by Wagner, it is found that the knowledge of fundamental parameters like the solubility of oxygen and the diffusivity of oxygen and the oxidized metal in the alloy are not sufficient to calculate the parabolic rate constant for internal oxidation. This in fact depends also on the extent of supersaturation required to nucleate new oxide particles in front of the internally oxidized region. In absence of this information only an upper limiting value for the rate constant may be obtained, corresponding to zero supersaturation, while use of the experimental value of the rate constant enables the critical value of the supersaturation for the system examined to be calculated. In addition, the effect of ternary interactions on the oxygen diffusion in the alloy is examined and it is shown how the apparent product of the solubility and diffusivity of oxygen in the base metal as measured from internal oxidation experiments according to Wagner's formulas may be a function of the alloy composition, a fact which is not predicted by simpler treatments.