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Abstract
In strongly ionic insulating materials, the Nernst–Planck Equation relates the interdiffusion coefficient of the cations (having the same charge) with the corresponding tracer diffusivities and the thermodynamic factor. In this paper, we explore the Nernst–Planck Equation for ionic ternary (quasi-binary) and ionic quaternary (quasi-ternary) systems using the diffusion kinetics formalisms of Darken [Trans. Am. Inst. Min. (Metall.) Eng. 175 184 (1948)], Manning [Phys. Rev. B 4 1111 (1971)] and Moleko, Allnatt and Allnatt [Phil. Mag. A 59 141 (1989)]. It is shown that for the binary system, the Darken and Manning formalisms both give the usual form of the Nernst–Planck Equation. However, the almost exact Moleko, Allnatt and Allnatt formalism (for randomly mixed systems) provides an additional correction factor analogous to the vacancy-wind factor in the well-known Darken–Manning Equation used in binary alloy systems. Nernst–Planck-type equations are also derived for strongly ionic insulating ternary systems and are found to behave similar to the binary case.
Acknowledgements
We thank the Australian Research Council for its support under the Discovery Project Grants Scheme. IVB thanks the Australian Research Council for the award of an Australian Professorial Fellowship.