Porous anodic alumina (PAA) films are grown by anodizing in acidic baths. Procedures to grow films with highly ordered geometry have led to the extensive use of PAA films as templates for fabrication of nanostructured devices. The morphology of PAA consists of evenly spaced and mutually parallel pores, oriented perpendicular to the metal/film interface. The ordered PAA morphology has never been fully explained.

A significant body of experimental evidence supports the occurrence of creep of the oxide during anodic film growth. In the present work, we have adapted a continuum theory in which viscous creep is coupled to ion migration through the stress field. The driving force for high-field migration is the gradient of the chemical potential of aluminum and oxygen ions, which includes contributions from stress as well as electric potential. These ions are transported independently, by their generalized migration flux and by convective flow. The model enforces conservation equations for both electrical charge and volume, and the Cauchy momentum equations of fluid flow.

One-dimensional model calculations in a concave spherical shell, simulating the scalloped geometry of the oxide film at the pore base, demonstrate the origin of the experimentally observed flow during growth of PAA. Because of the nonlinearity of high-field migration, metal ions dominate the migration flux where the current density is high (near the solution) while oxygen ion transport is most significant at lower current densities (near the metal). Since metal ions are small compared to oxygen ions, the resulting volume flow due to migration is nonuniform. A stress distribution is produced which generates inward convective flow of oxide near the solution. The flow pattern is very similar to that inferred from recent experimental tracer studies. Further results of two-dimensional calculations will be presented, relating creep directly to the mechanism of ordering during PAA growth.

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