Field Dependence of the Tafel Slopes for Formation of Anodic Oxide Films

Abstract

An explanation of the field dependence of Tafel slopes for formation of anodic oxide films is proposed on the basis of an earlier general consideration of charge transfer over potential barriers. An expression for the activation energy as a function of the field strength is derived which contains a quadratic term arising from the shifting of both the barrier top and the equilibrium position of the ion under the influence of the electric field. The treatment includes the usual parabolic approximation of a continuous potential-energy function in the regions of its maximum and minimum. A comparison with the experimental data for anodic oxidation of Ta, Nb, and A1 shows this approximation to be quite satisfactory. The theoretical expression permits the determination of the actual barrier parameters at a given field strength go near the experimental field range, as well as an extrapolation to zero field strength. This theory is applicable equally well to any possible mechanism of the current flow in the anodic formation of oxide layers.The growth of homogeneous oxide layers during anodization of film-forming metals such as A1, Ta, Nb, Zr, etc., in a suitable electrolyte is interpreted by passage of ions across the oxide, surmounting some potential energy barrier in their way. Measurable rates of growth require considerable electric fields (more than 10 6 v/cm)~ so that the ionic transitions can be considered to occur only in the direction of the field.On the basis of elementary kinetic considerations, one obtains the welt-known equation for ionic current densitywith the activation energy being a linear function on the field strengthwhere Wo is the activation energy in the absence of an external field (4 -~ 0), a the activation distance, and q the charge on the moving ion. The pre-exponential factor A has a different meaning depending on the assumptions for the kind and location of the potential barrier. In this respect, the various theories could be classified on the basis of the following three assumptions:(a). Internal control.--According to Verwey's model (1), the limiting factor is the rate at which ions move from one interstitial position to another. It was proposed later (2-4) that the high field produces Frenkel defects (pairs of interstitial cations and cation vacancies) by drawing out metal ions in interstitial positions. Recently, a new theory for the internal control was developed by Dignam (5) on the basis of a dielectric mosaic model of the anodic oxide film.(b). Interlace control.--Mott and Cabrera (6, 7) considered as rate determining the first barrier which metal ions have to surmount to enter the oxide. This was shown to be the case with anodization of sputtered tantalum films (8). Jukova and Odynec (9) assumed that the electrochemical reactions at the oxide/electrolyte interface play a certain role in the growth of nonporous anodic films as well. (c ). Internal-interface control.--That is an extensionof the mentioned models for including effects of space charge due to ions in transit, so tha...

High Field Ionic Conduction in Tantalum Anodic Oxide Films with Incorporated Phosphate

“…One cannot expect an accurate fit for an approximate treatment of a simplified model; the point is whether the fit is accurate enough to suggest that the model contains the essential features of the real system. Further theoretical treatments have been based on the shape of the potential energydistance relation and on dielectric effects treated by transition state theory (13,14). Dreiner and Tripp (15) [cf.…”

High Resistance Anodic Film Formation on Bismuth with or without Appearance of Induction Period

“…which is theoretically a first approximation for not very wide E and T ranges, and is usually observed in formation of insulating anodic films (e.g., [23]). A, B, and a are positive constants.…”

Formation of complex anodic films on porous alumina matrices

“…This dependence has been investigated during anodization of different valve metals including Al (Andreeva and Ikonopisov 1970). The validity of two equations describing the j i (E, T)-dependence has been experimentally proven many times and theoretically interpreted (Christov and Ikonopisov 1969).…”