Transient kinetics of formation of anodic oxide films on tantalum in dilute sulphuric acid

When a high electric field is suddenly applied to a film in which the concentration of Frenkel defects is initially much lower than would be set up at this field in the steady state, the ionic current (which is supposed to be proportional to the concentration of Frenkel defects) builds up slowly at first and then more rapidly (approximately as d i /d t = ki 2 , where k increases with the field) before stabilizing at the steady-state value. This is in contradiction with the theory that Frenkel defects are produced directly by the high electric field which assists the movement of ions from lattice sites into interstitial sites. According to this theory, d i /d t should be greatest at t = 0. The experimental result suggests that mobile ions are produced by a cascade process in which moving ions eject ions from lattice sites into interstitial sites. Experiments in which the electric field in the oxide film is suddenly changed and the ionic current is measured before the concentration of mobile ions has time to change are expected to give f ' 2 ( E ), where the ionic current is determined (for a given concentration of ions) by a Boltzmann factor with activation energy W 2 reduced by the field by an amount f 2 ( E ). The results were consistent with f 2 ( E ) = q ( α 2 E — β 2 E 2 ) where q = charge on ion, α 2 = 2.23 Å and β 2 = 0.106 Å/10 6 V cm -1 . Experiments in which fields were suddenly applied at different temperatures to films in the same initial state gave an estimate of the activation energy for ionic mobility W 2 as 1.28 ± 0.1eV.