Ion Transport In Solids Research Articles

A transport equation is proposed in which the local ion flux density is represented as a function of the local electrostatic potential and concentration gradients and includes the case of high electrostatic potential gradients. The equation is ‘derived’ mainly by recourse to phenomenological considerations, in that it represents the simplest equation which satisfies certain necessary conditions. Previous attempts to extend the ion transport equation to cover the case of concurrent concentration gradients and large electrostatic potential gradients are shown to have led to an incorrect result in that the derived equations failed to satisfy the necessary condition that for zero local electrochemical potential gradient, the local flux density must also be zero. For homogeneous field and steady-state transport conditions, the proposed transport equation leads to a result identical to that obtained by Fromhold and Cook who applied a discrete lattice model to the same conditions. The meaning of effective field strength and effective charge associated with the kinetics of defect migration is examined in some detail. It is concluded that whenever the macroscopic electric field (or Maxwell field) is employed, the charge parameter appropriate for kinetic considerations within the realm of validity of the linear transport equations is simply the charge carried by the defect (i.e. the ‘valence charge’) independent of whether or not bonding is partially covalent and/or extensive dielectric polarization occurs. Even for high field conditions, where the ion flux varies with field strength in a non linear fashion, the so called charge-activation distance product is simply the valence charge times the zero field activation distance, for a symmetrical diffusion barrier. The case of transport in the homogeneous field approximation is considered, particularly in relation to the growth of thin oxide films on metals.

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