Multicomponent diffusion in ionic crystals: theoretical model and application to combined tracer- and interdiffusion...

We present a model for multicomponent diffusion in ionic crystals. The model accounts for vacancy-mediated diffusion on a sub-lattice and for diffusion due to binary exchange of different ionic species without involvement of vacancies on the same sub-lattice. The diffusive flux of a specific ionic species depends on the self-diffusion coefficients, on the diffusion coefficients related to the binary exchanges, and on the site fractions of all ionic species. The model delivers explicit expressions for these dependencies, which lead to a set of coupled non-linear diffusion equations. We applied the model to diffusion of ${}^{23}$ Na, ${}^{39}$ K, and ${}^{41}$ K in alkali feldspar. To this end, gem-quality crystals of alkali feldspar were used together with ${}^{41}$ K doped KCl salt as diffusion couples, which were annealed at temperatures between 800 ${}^{\circ }$ and 950 ${}^{\circ }$ C. Concentration-distance data for ${}^{23}$ Na, ${}^{39}$ K, and ${}^{41}$ K were obtained by Time of Flight Secondary Ion Mass Spectrometry. Over the entire investigated temperature range the Na self-diffusion coefficient is by a factor of $\ge 500$ higher than the K self-diffusion coefficient. Diffusion mediated by binary ${}^{39}$ K- ${}^{41}$ K exchange is required for obtaining satisfactory fits of the model curves to the experimental data, and the respective kinetic coefficient is well constrained.