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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{23}$$\end{document}Na, 39\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{39}$$\end{document}K, and 41\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{41}$$\end{document}K in alkali feldspar. To this end, gem-quality crystals of alkali feldspar were used together with 41\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{41}$$\end{document}K doped KCl salt as diffusion couples, which were annealed at temperatures between 800∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ$$\end{document} and 950∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ$$\end{document}C. Concentration-distance data for 23\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{23}$$\end{document}Na, 39\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{39}$$\end{document}K, and 41\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{41}$$\end{document}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 ≥500\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ge 500$$\end{document} higher than the K self-diffusion coefficient. Diffusion mediated by binary 39\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{39}$$\end{document}K–41\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{41}$$\end{document}K exchange is required for obtaining satisfactory fits of the model curves to the experimental data, and the respective kinetic coefficient is well constrained.

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离子晶体中的多组分扩散：碱性长石中示踪剂和相互扩散相结合的理论模型和应用

我们提出了离子晶体中多组分扩散的模型。该模型解释了子晶格上的空位介导的扩散以及由于不同离子种类的二元交换而导致的扩散，而没有涉及同一子晶格上的空位。特定离子种类的扩散通量取决于自扩散系数、与二元交换相关的扩散系数以及所有离子种类的位点分数。该模型为这些依赖关系提供了明确的表达式，这导致了一组耦合的非线性扩散方程。我们将该模型应用于 23\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{23}$$\end{document}Na, 39\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{39}$$\end {document}K 和 41\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{41}$$\end{document}K 在碱长石中。为此，在 800∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek 之间的温度下退火} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ$$\end{document} 和 950∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \ usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ$$\end{document }C。23\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \ 的浓度距离数据setlength{\oddsidemargin}{-69pt} \begin{document}$$^{23}$$\end{document}Na,