Authors: Elena Petrishcheva | Lisa Tiede | David Heuser | Herbert Hutter | Gerald Giester | Rainer Abart
Source: Physics and Chemistry of Minerals (article, 2020-07-31)
Field: Materials Science — Biomaterials

Multicomponent diffusion in ionic crystals: theoretical model and application to combined tracer- and interdiffusion in alkali feldspar 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow> <mml:mn>23</mml:mn></mml:msup> </mml:math> Na, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow> <mml:mn>39</mml:mn></mml:msup> </mml:math> K, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow> <mml:mn>41</mml:mn></mml:msup> </mml:math> K in alkali feldspar. To this end, gem-quality crystals of alkali feldspar were used together with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow> <mml:mn>41</mml:mn></mml:msup> </mml:math> K doped KCl salt as diffusion couples, which were annealed at temperatures between 800 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow> <mml:mo>∘</mml:mo></mml:msup> </mml:math> and 950 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow> <mml:mo>∘</mml:mo></mml:msup> </mml:math> C. Concentration-distance data for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow> <mml:mn>23</mml:mn></mml:msup> </mml:math> Na, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow> <mml:mn>39</mml:mn></mml:msup> </mml:math> K, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow> <mml:mn>41</mml:mn></mml:msup> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>≥</mml:mo> <mml:mn>500</mml:mn></mml:mrow> </mml:math> higher than the K self-diffusion coefficient. Diffusion mediated by binary <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow> <mml:mn>39</mml:mn></mml:msup> </mml:math> K- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow> <mml:mn>41</mml:mn></mml:msup> </mml:math> K exchange is required for obtaining satisfactory fits of the model curves to the experimental data, and the respective kinetic coefficient is well constrained. Chemistry ; TRACER ; Alkali metal ; Feldspar ; Alkali feldspar ; Diffusion ; Ionic bonding ; Ionic crystal ; Mineralogy ; Chemical physics ; Thermodynamics ; Quartz ; Ion ; Metallurgy ; Organic chemistry Clay minerals and soil interactions ; Geological and Geochemical Analysis ; Soil and Unsaturated Flow