Abstract
Random-walk theory has been applied to describe the oxidation of metals. The one-dimensional random-walk problem with a growing site array has, in principle, been solved exactly provided the array is singly occupied and the hop probabilities are independent of site position. This result has been generalized to a pseudo three-dimensional model. The conditions for linear, parabolic and `logarithmic’ growth laws have been delineated. The case where the hop probabilities are different at a boundary has also been treated and it has been shown that, provided this difference is not too great, this leads to a different reaction rate but the same type of rate law. The effect of an electric field on the oxidation has been treated by considering the effect of the field on the hop probabilities, and rate laws for constant field and constant potential situations have been obtained. The way that the surface charge varies during the reaction by virtue of the net difference in rate of arrival of (say) electrons and positive ions at the oxide/ oxygen interface has been investigated numerically and it has been shown that there is often an appreciable region of approximately constant potential. The effect of multiple occupation of the random walk path has been qualitatively discussed.
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Schedule a callMore From: Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
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