A Model for Coupled Electrical Migration and Stress-Driven Transport in Anodic Oxide Films

Recent experimental evidence suggests that plastic flow of oxide occurs during the growth of anodic oxide films and contributes significantly to ionic mass transport. Skeldon and co-workers used tungsten tracers introduced from the metal to visualize ionic transport within porous anodic alumina films formed in acidic solutions. 1-4 The observed tracer motion deviated strongly from expectations based on electrical migration as the only transport mechanism, the authors attributing the discrepancy to plastic flow in the oxide. The tracer studies supported earlier measurements of the rate of increase in pore wall height relative to stationary reference planes. 5-7 Both experiments revealed plastic flow in the pore walls at typical velocities of 0.1‐1 nm/s. We developed a transport model of porous anodic alumina films, which validated the hypothesis of coupled electrical migration and viscous flow of oxide, through a detailed agreement with the tungsten tracer profiles. 8 The results of this study suggest that the coupled stress and potential distributions in these films regulate the interface motion during the formation of self-ordered pore arrays. The importance of viscous creep may extend beyond porous oxides to planar anodic films typically formed in neutral pH solutions. Evidence for creep in such films is suggested by several experimental studies. Leach and co-workers observed a current-dependent extension of loaded Al wires during anodizing, which they attributed to current-induced plasticity in the anodic film. 9,10 Wuthrich showed that anodic alumina films deform without cracking during anodizing. 11 Zhou et al. attributed the observations of growth and coalescence of oxygen bubbles during the passage of ionic current to the plasticity in the surrounding oxide. 12,13 An additional precedent for creep of amorphous solids at ambient temperatures is found in studies that show that Newtonian viscous flow relieves compressive stresses induced by ion irradiation. 14-17 Like the materials in these experiments, anodic alumina films are amorphous, and stresses large enough to drive significant creep 10‐100 MPa are found during the growth of both porous and planar anodic alumina. 9,11,18-21 Stresses during anodizing may arise from volume constraints at the metal‐ oxide interface, and from electrostatic forces in the oxide dielectric. 22-24 In this paper, we present a model for transport in planar anodic films by coupled electrical migration, plastic flow, and migration in the stress field. Coupling of transport processes results from the constraints of volume and charge conservation. The model is developed for the specific case of barrier-type aluminum oxide films, which have been studied extensively. However, a similar treatment may apply to amorphous anodic oxides formed on a variety of valve metals. The model is adapted from the continuum approach developed by Suo and co-workers to model coupled plastic flow and diffusional transport in metals.