A simulation of the growth of pits on aluminum during anodic etching in hot chloride solutions was developed, based on equations for mass transport and for the potential-controlled removal of chloride ions from the dissolving surface. The latter process initiates oxide passivation. Etch pits transform into tunnels which at first maintain parallel sidewalls and then begin to taper. The predicted shapes agree closely with those measured experimentally. Tunnel formation is possible only when the potential during etching is within 20-30 mV of the repassivation potential, so that the dissolving area nearly constant during pit growth. In the tapered-width regime of tunnel growth, the AlCl_3 concentration at the end of the tunnel is near saturation, despite the absence of precipitation from the model equations. The model shows that this condition derives from the low conductivity of the concentrated solution, coupled with the sensitivity of passivation to the potential.
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