Difference-Equation Model for Ionic Conductivity. I. Step Voltage Response

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Abstract
The differential equations for two-carrier charge transport with current blocking electrodes are discussed. An explicit difference equation analog to these quasilinear, parabolic, partial differential equations is obtained. It is shown that such a model is stable over a sufficient time period for a range of input parameters. The initial current obtained when a step voltage is applied to the crystal is shown to be the sum of two exponentials corresponding to the mobilities of the two vacancy species. The dependence of the initial decay constant on various parameters is obtained. In most instances the dependence does not agree with the predictions of a linearized theory. The dependence does agree with experimental results in all cases. The applicability of these results to the problem of electron diffusion is discussed.