Metal and Oxygen Ion Transport during Ionic Conduction in Amorphous Anodic Oxide Films

Abstract

A mathematical model was developed for ionic conduction in amorphous oxide films. The model is based on a hypothesized "defect cluster" mechanism in which both metal and oxygen ions are involved in transport. Defect clusters are created by inward displacement of oxygen ions around an oxygen vacancy-like defect in response to the vacancy's electric field. Metal ions are assumed to migrate easily in the gap between the first and second layer of oxygen ions around the vacancy. The model includes the polarization of the conductive gap in the applied electric field, the exchange of mobile metal ions in the cluster with stationary metal ions in the surrounding oxide, and space charge generated in the film by clusters and oxide nonstoichiometry. The rate-limiting step is the jump of the oxygen vacancy in the cluster. It was found that polarization of the cluster leads to a stoichiometric excess of metal ions in the cluster and that this excess produces a net transport of metal ions due to the motion of the cluster. The metal ion transport number was found to increase with electric field and to depend on the dielectric constant and cluster size. The field dependence follows that found experimentally. The calculated transport numbers are in quantitative agreement with experimental values for tantalum, niobium, and tungsten oxide but smaller than experimental values for aluminum oxide. The field coefficient in the high-field-conduction-rate expression is also predicted and agrees with experimental values to within 10%.

Growth and field crystallization of anodic films on Ta–Nb alloys

“…Several models of ionic migration have been proposed, ranging from early suggestions of vacancy diffusion and interstitial exchange capture [3] and a place exchange mechanism [8] to a liquid droplet mechanism [10]. A more recent defect cluster mechanism correlates the transport number of cations and field strength [64].…”

Formation of anodic films on sputtering-deposited Al–Hf alloys

“…Various models of ionic migration have been proposed ranging from early suggestions of vacancy diffusion and interstitial exchange capture [24] to a liquid-droplet mechanism [25] that allows for counter-migration of anions and cations with similar transport number. A more recent model links the migration of cations to structural relaxation around oxygen vacancies [26].…”

Kinetics of passivity of NiTi in an acidic solution and the spectroscopic characterization of passive films

“…Models for conduction in amorphous and crystalline oxide films have evolved over time to include new concepts derived from experimental results [21][22][23]. Mathematical model was developed by Wang and Hebert [24] for a cooperative ion conduction mechanism, i.e., for metal and oxygen ion transport in amorphous anodic oxide films on valve metals. Conduction of ionic charge in the oxide films in the model involves jumps of oxygen ions into vacancy together with its associated mobile metal ions (referred to as "defect cluster").…”

“…where H is the electric field strength, z O is the charge number of oxygen ions, e is the electron charge, ε and ε 0 are dielectric constants of oxide film and vacuum, respectively, γ and r 0 are constants defined by "defect cluster" model [24]. According to Eq.…”

“…1. For calculation, the following values were used: (a) experimentally measured electric field strength, H011.7×10 6 V cm −1 ; (b) dielectric constant for amorphous TiO 2 , ε040; (c) the radius of the cluster, r 0 03.57×10 −8 cm; (d) dimensionless constant related to overlap cluster before and after vacancy jump, γ00.2929, defined by "defect cluster" mechanism [24]. Using values (a)-(d), we obtained t M 00.43.…”