Diffusion- Migration-Reaction-Limited Aggregation of Point Defects: A Model for the Stability of Oxide-layers on Metals and Its Breakdown

TL;DR

This paper develops a mathematical model for the stability and breakdown of oxide layers on metals, incorporating defect diffusion, migration, clustering, and electrochemical reactions to better understand corrosion resistance.

Contribution

It formulates a coupled system of PDEs and ODEs including defect dynamics, advancing the defect model with new equations and clustering mechanisms for oxide-layer stability analysis.

Findings

Initial model results show defect clustering effects.

The model predicts oscillations signaling oxide-layer breakdown.

Framework aims to interpret experimental corrosion data.

Abstract

A thin oxide layer protects metals from electrochemical corrosion and hence the stability of this oxide layer is crucial for corrosion resistance of metals. The dynamics of cationic and anionic point defects which are injected into this oxide layer at the metal-oxide-layer interface and the oxide-layer-environment interface during electrochemical processes determine the stability of this oxide-layer. The point defect model originally advanced by Digby Macdonald and perfected into a correct and complete theory by Bosco Emmanuel provides a concrete basis for investigating this stability question. We have formulated a system of 3 coupled differential equations (2 PDEs and one ODE) with appropriate initial and boundary conditions that include the defect injection reactions. This system of equations recognize the diffusion, migration and clustering of the point defects in the oxide-layer. The defect clustering is modelled using the Avrami Theorem and the area-volume laws for random agglomerates. This research is expected to provide insights into the criticality associated with the oxide-layer breakdown and the periodic, aperiodic and chaotic oscillations in the electrical current / potential which signal the breakdown of the passive oxide-layer. A large body of experimental data is waiting to be understood within a frame-work such as the present. Some initial results from the model are also reported.