Model for Stress Generation and Flow in Anodic Oxides
Authors: Hebert Kurt , Capraz Omer , Ide Shinsuke , Shrotriya Pranav 
Published: February 2020

Porous anodic oxide (PAO) films are grown by electrochemical polarization of Al, Ti, and other metals in baths that dissolve the oxide. Procedures to grow films with highly ordered and controllable arrangements of nanoscale pores have led to the extensive use of PAO films in nanofunctional devices. Experiments and calculations show that transport in the oxide occurs by electrical migration coupled with oxide flow driven by mechanical stress (1-3). Pores initiate by a morphological instability at the oxide-solution interface when the initially formed barrier oxide reaches a critical thickness (4). In another presentation at this meeting, we showed that this instability is preceded by the buildup of compressive stress due to localized electric field-induced electrolyte anion incorporation at the oxide-solution interface. The instability is modeled by competition between stabilizing oxide formation at the oxide-solution interface and destabilizing oxide flow driven by gradients of anion-induced surface stress. The model predicts important features of self-ordered PAO growth on many metals: the pore separation-voltage scaling ratio, the narrow ranges of anodizing efficiency, and the threshold electric field.
Characteristics of anodic oxides that enable self-organized PAO formation include their ability to flow and to accumulate highly localized stress at interfaces due to electrochemical reactions. Here we report a new model for coupled interfacial reactions, electrochemical transport and mechanics of amorphous anodic oxides. In the model, ionic conduction occurs by high-field electrical migration of oxygen and metal vacancy type defects. In contrast with other point defect models, vacancies are created and destroyed homogeneously within the oxide by electric-field stimulated localized relaxations of the amorphous network. Vacancy creation expands the oxide network generating compressive stress, while vacancy destruction contracts the network producing tensile stress.
Field-stimulated vacancy formation and removal affect the conductance of anodic films and hence may be probed by electrochemical impedance spectroscopy (EIS). Impedance measurements during steady-state Al anodizing in sulfuric and oxalic acids are presented. The spectra reveal inductive loops between 1 and 100 Hz as reported elsewhere (5). The characteristic time constant and resistance of the inductive loop are shown to be determined by the kinetic parameters of the vacancy formation/removal reaction. The values of these parameters are independent of anodizing current density or solution composition.
The kinetic model for vacancy formation/removal identified by EIS was used to simulate evolution of stress distributions in the oxide during Al anodizing in phosphoric acid at a constant current density of 5 mA/cm2 (6). Calculations demonstrate that vacancies are continuously generated at the oxide-solution interface to accommodate incorporation of large electrolyte oxyanions. This process is shown to be quantitatively consistent with localized compressive stress buildup at this interface as revealed by in situ stress measurements, the precursor for oxide flow and pore formation. At the metal interface, vacancies produced by metal oxidation are destroyed continuously at the metal interface, consistent with the buildup of localized tensile stress found experimentally.
Finally we discuss implications of vacancy formation/removal for oxide flow. It is argued that at sufficiently high stress levels, this reaction can account for displacement of oxide volume driven by stress gradients. Such a process is equivalent to vacancy creep and can explain the apparent viscous flow of anodic oxides reported in several papers (1-3,7).
ACKNOWLEDGMENT
This work was supported by the the National Science Foundation through NSF-CMMI-100748.
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