A Mathematical Model for the Initiation of Aluminum Etch Tunnels

Abstract

A mathematical simulation is presented which predicts the spontaneous shape evolution of cubic etch pits on aluminum as they develop into etch tunnels during anodic etching in chloride solutions. The simulation is based on a model for oxide passivation, according to which the rate of oxide film coverage increases as the potential at the dissolving surface is made more negative than the critical repassivation potential, which depends on the local chloride ion concentration. Mass transport calculations are used to predict the electrolyte concentration and potential in the pit, which in turn determine the rate of oxide advance and hence the shape change of the pit. The model predicts the pit-tunnel transformation, as well as width expansion of tunnels near their mouths. The occurrence of these features is independent of the choice of the passivation rate constant, an adjustable parameter in the simulation. Tunnel width oscillations were found at relatively low values of the rate constant. In the model, the pit-tunnel transformation is produced by rapid pit sidewall passivation, which is due to the relatively slower increase of the pit electrolyte concentration relative to the ohmic drop, during the pit's initial growth. A fully quantitative comparison of the model and experiment is possible with independent experimental information on passivation kinetics. A mathematical simulation is presented which predicts the spontaneous shape evolution of cubic etch pits on aluminum as they develop into etch tunnels during anodic etching in chloride solutions. The simulation is based on a model for oxide passivation, according to which the rate of oxide film coverage increases as the potential at the dissolving surface is made more negative than the critical repassivation potential, which depends on the local chloride ion concentration. Mass transport calculations are used to predict the electrolyte concentration and potential in the pit, which in turn determine the rate of oxide advance and hence the shape change of the pit. The model predicts the pit-tunnel transformation, as well as width expansion of tunnels near their mouths. The occurrence of these features is independent of the choice of the passivation rate constant, an adjustable parameter in the simulation. Tunnel width oscillations were found at relatively low values of the rate constant. In the model, the pit-tunnel transformation is produced by rapid pit sidewall passivation, which is due to the relatively slower increase of the pit electrolyte concentration relative to the ohmic drop, during the pit's initial growth. A fully quantitative comparison of the model and experiment is possible with independent experimental information on passivation kinetics.

Metal Dissolution Kinetics in Aluminum Etch Tunnels

“…Analysis of mass transport in tunnels reveals that as tunnels grow, the potential at the tip decreases and the chloride concentration there increases, such that the tip is continuously maintained very close to E R . 11,12 While the tapered shape of long tunnels has been shown to be consistent with the presence of a nearly saturated AlCl 3 solution at the tip, 11,13 the present work concerns short tunnels (length of 10 m) which have not begun to taper.…”

“…The concentration overpotential was calculated to be 62 mV for all the experiments, using the method of Zhou and Hebert and assuming steady-state diffusion. 12 This assumption is valid because the t L of 12 ms is much smaller than the time constant for diffusion in tunnels of this length. 11 With this additional concentration overpotential correction, the resulting potential is equivalent to the repassivation overpotential defined by Zhou (i.e., the difference between the potential and repassivation potential), augmented with an additive constant.…”

“…Good agreement of the present current-potential relation was obtained with that derived from the measurements of pit currents in thin films by Frankel et S0013-4651(00)02-012-7 CCC: $7.00 © The Electrochemical Society, Inc. drops inside and outside tunnels as well as concentration overpotentials in tunnels, taking advantage of previous measurements of the cell ohmic resistance, 19 as well as model predictions of the internal concentration and potential fields inside tunnels. 12,20 The interpretation of the electrochemical measurements is aided by microscopic observations of the topographic changes on the tip surfaces caused by the anodic current pulses.…”

A Mathematical Model for the Growth of Aluminum Etch Tunnels

“…The failure to predict wall ripples suggests that they do not result from transient diffusion phenomena coupled to passivation kinetics, as was proposed earlier. 10 It is possible that dr/dt in Eq. 4 is not a smooth function of time as the equation indicates, but is, instead, subject to fluctuations.…”

“…Unlike an earlier model of the initial phase of tunnel growth, all phenomena described in the present model are based on independent experimental information, and there are no adjustable parameters. 10 The simulation time was extended so that the lengths of tunnels approached 100 m, and the predicted width profiles are compared with those measured experimentally by Goad. 12 Since the present model does not incorporate a precipitated salt film on the tunnel tip, this comparison tests whether there might be an alternative explanation for tapered tunnel shapes. It is also relevant to the interpretation of near-saturated solutions in pits, as found in a number of other metalelectrolyte systems.…”