On the nature of the electric field within the barrier layer of a passive film

Abstract

In this work, the nature of the electric field (E) in the defective oxide barrier layer on iron has been explored theoretically, within the classical regime, with the goal of ascertaining the validity of the postulates underlying the Point Defect Model (PDM). The analysis shows that if the thickness of the barrier layer under steady-state condition, L, is sufficiently small, the electric field strength and concentrations of point defects are essentially constants in the main part of this layer (with the exceptions in the very thin region near the metal/barrier layer (m/bl) and barrier layer/solution (bl/s) interfaces, depending upon the defect). A quantitative criterion was developed to decide when the barrier layer of the passive film can be considered to be sufficiently thin under these conditions. The potential drops inside the barrier layer and across the m/bl and bl/s interfaces can be represented as linear functions of applied voltage, V. This is the consequence of the change in thickness with applied voltage, with E being approximately (but with high accuracy) independent on the position inside the barrier layer and applied voltage. All conclusions stated above were derived from the solution of the system of mass transport equations for point defects and Poisson equation for the electric potential without applying any additional assumption except the small thickness of the barrier layer and without taking into account quantum (band-to-band) tunneling.