On the Mott-Cabrera oxidation rate equation and the inverse-logarithmic law

Abstract

It is shown that the often cited inverse-logarithmic oxidation law, X−1 ∝ −logt, where X is the oxide thickness and t the observation time, is not an asymptotic solution of the rate equation derived by Mott and Cabrera in their theory of low temperature oxidation. Thus whether or not the inverse-logarithmic law is experimentally verified has no bearing on the validity of this theory. A correct solution is presented, and it is shown that for thin oxide films a plot of X−1 vs log(t/X2) should yield straight lines. Vermilyea's data on Ta is reexamined according to this analysis and yields reasonable results for the activation energy of defect solution (1.59 eV) and for the potential across the oxide (1.79 V).

Transient film formation on chalcopyrite in acidic solutions

“…An approximate integration of Eq. 1, valid only for qkE/ kT ) 1, gives the reciprocal logarithmic tarnishing law [49]:…”

Controlled oxidation of aluminum nanoparticles

“…In order to preserve the correct physical characteristics of the phenomena, R. Ghez in [9] explained that the neglected concentration gradients and the space charges in the growing oxide layer have to be taken into account. Hence, the electric field created by the Mott potential cannot be assumed to be uniform or simply proportional to the oxide thickness.…”

Role of Particle Size Distribution on Pt Stability

“…large medium, small, [11] Finally, the current density is ) ( 2 2 1 j j r r aFL i + = [12] where L the thickness of the catalyst layer.…”

“…The MottCabrera model on platinum oxidation was adopted by several groups (5-10) although its functionality for oxide film thicknesses lower than 1 nm was questioned (11). developed the first detailed numerical model for the Pt area loss induced by voltage cycling including potential-dependent dissolution of Pt, chemical dissolution of Pt oxide, and surface tension driven growth of Pt nanoparticles.…”