Rate Constant
Theoretical growth models for the formation of thick, compact oxide scales on metals at high temperatures assume that the rate is limited by the diffusion of ions or electrons through the layer. Calculation of wagner oxidation kinetics describes a parabolic relationship where the thickness of the scale increases with the square root of time. This model requires that the scale is stoichiometrically uniform and that the interfaces are in local thermodynamic equilibrium.
Transport Logic
Movement of cations outward or anions inward sustains the growth of the oxide at the gas or metal interface. The presence of a chemical potential gradient across the scale provides the driving force for this migration. If the transport of one species is much slower than the others, it becomes the rate determining step for the entire reaction.
Boundary Condition
Accuracy of the model decreases when the scale is very thin or when it develops cracks and pores. In the initial stages of oxidation, surface reaction rates or space charge effects may dominate over bulk diffusion. The transition from linear to parabolic growth marks the point where the wagner model becomes the primary tool for analysis.
Stoichiometric Gradient
Deviations from the ideal chemical ratio influence the concentration of charge carriers within the oxide. This gradient determines the internal electrical field.
