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-{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-10-23T16:21:09","documenter_version":"1.7.0"}}
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@@ -17,4 +17,4 @@
 \end{equation}\]</p><p>with <span>$D_i^*$</span> the tracer diffusion coefficient of the <span>$i^{th}$</span> component, <span>$\delta_{ij}$</span> the Kronecker delta, <span>$z$</span> the charge of the species, and <span>$D_n^*$</span> the tracer diffusion coefficient of the dependent molar fraction (here Ca).</p><p>The tracer diffusion coefficient <span>$D_i^*$</span> can be calculated from an Arrhenius relationship:</p><p class="math-container">\[\begin{equation}
   \label{arrhenius}
 D_i^* = D_{0,i} \exp \left( -\frac{E_{a,i} - (P-1)\Delta V^+_i}{RT} \right),
-\end{equation}\]</p><p>with <span>$D_{0,i}$</span> the pre-exponential constant, <span>$E_{a,i}$</span> the activation energy of diffusion, <span>$\Delta V^+_i$</span> the activation volume of diffusion at 1 bar, <span>$R$</span> the universal gas constant, <span>$T$</span> the temperature, and <span>$P$</span> the pressure.</p><p>In DiffusionGarnet.jl, <span>$D_{0,i}$</span>, <span>$E_{a,i}$</span>, and <span>$\Delta V^+_i$</span> are those of Chakraborty &amp; Ganguly (1992) <a href="#refs">[2]</a>. The tracer diffusion coefficient of Ca is defined as <span>$0.5D_{Fe}$</span>, following the approach of Loomis et al. (1985) <a href="#refs">[3]</a>.</p><h3 id="Numerical-approach"><a class="docs-heading-anchor" href="#Numerical-approach">Numerical approach</a><a id="Numerical-approach-1"></a><a class="docs-heading-anchor-permalink" href="#Numerical-approach" title="Permalink"></a></h3><p>By defining the <em>PT</em> conditions of the metamorphic event of interest, (3) can be solved for each component, and the diffusion coefficient tensor can be calculated using (2) from the initial major composition data. In DiffusionGarnet.jl, (1) is then discretised in space using finite differences, and the resulting system of ordinary differential equations is solved with ROCK2, a stabilised explicit method (Abdulle &amp; Medovikov, 2001 <a href="#refs">[4]</a>) using the <a href="https://github.com/SciML/DifferentialEquations.jl">DifferentialEquations.jl</a> ecosystem.</p><h2 id="refs"><a class="docs-heading-anchor" href="#refs">References</a><a id="refs-1"></a><a class="docs-heading-anchor-permalink" href="#refs" title="Permalink"></a></h2><p>[1] Lasaga, A. C. (1979). Multicomponent exchange and diffusion in silicates. Geochimica et Cosmochimica Acta, 43(4), 455-469.</p><p>[2] Chakraborty, S., &amp; Ganguly, J. (1992). Cation diffusion in aluminosilicate garnets: experimental determination in spessartine-almandine diffusion couples, evaluation of effective binary diffusion coefficients, and applications. Contributions to Mineralogy and petrology, 111(1), 74-86.</p><p>[3] Loomis, T. P., Ganguly, J., Elphick, S. C., 1985. Experimental determinations of cation diffusitivities in aluminosilicate garnets. II. Multicomponent simulation and tracer diffusion coefficients. Contributions to Mineralogy and Petrology 90, 45–51.</p><p>[4] Abdulle, A., &amp; Medovikov, A. A. (2001). Second order Chebyshev methods based on orthogonal polynomials. Numerische Mathematik, 90, 1-18.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../diffusion_1D/">Diffusion in 1D Cartesian coordinates »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Wednesday 23 October 2024 16:21">Wednesday 23 October 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+\end{equation}\]</p><p>with <span>$D_{0,i}$</span> the pre-exponential constant, <span>$E_{a,i}$</span> the activation energy of diffusion, <span>$\Delta V^+_i$</span> the activation volume of diffusion at 1 bar, <span>$R$</span> the universal gas constant, <span>$T$</span> the temperature, and <span>$P$</span> the pressure.</p><p>In DiffusionGarnet.jl, <span>$D_{0,i}$</span>, <span>$E_{a,i}$</span>, and <span>$\Delta V^+_i$</span> are those of Chakraborty &amp; Ganguly (1992) <a href="#refs">[2]</a>. The tracer diffusion coefficient of Ca is defined as <span>$0.5D_{Fe}$</span>, following the approach of Loomis et al. (1985) <a href="#refs">[3]</a>.</p><h3 id="Numerical-approach"><a class="docs-heading-anchor" href="#Numerical-approach">Numerical approach</a><a id="Numerical-approach-1"></a><a class="docs-heading-anchor-permalink" href="#Numerical-approach" title="Permalink"></a></h3><p>By defining the <em>PT</em> conditions of the metamorphic event of interest, (3) can be solved for each component, and the diffusion coefficient tensor can be calculated using (2) from the initial major composition data. In DiffusionGarnet.jl, (1) is then discretised in space using finite differences, and the resulting system of ordinary differential equations is solved with ROCK2, a stabilised explicit method (Abdulle &amp; Medovikov, 2001 <a href="#refs">[4]</a>) using the <a href="https://github.com/SciML/DifferentialEquations.jl">DifferentialEquations.jl</a> ecosystem.</p><h2 id="refs"><a class="docs-heading-anchor" href="#refs">References</a><a id="refs-1"></a><a class="docs-heading-anchor-permalink" href="#refs" title="Permalink"></a></h2><p>[1] Lasaga, A. C. (1979). Multicomponent exchange and diffusion in silicates. Geochimica et Cosmochimica Acta, 43(4), 455-469.</p><p>[2] Chakraborty, S., &amp; Ganguly, J. (1992). Cation diffusion in aluminosilicate garnets: experimental determination in spessartine-almandine diffusion couples, evaluation of effective binary diffusion coefficients, and applications. Contributions to Mineralogy and petrology, 111(1), 74-86.</p><p>[3] Loomis, T. P., Ganguly, J., Elphick, S. C., 1985. Experimental determinations of cation diffusitivities in aluminosilicate garnets. II. Multicomponent simulation and tracer diffusion coefficients. Contributions to Mineralogy and Petrology 90, 45–51.</p><p>[4] Abdulle, A., &amp; Medovikov, A. A. (2001). Second order Chebyshev methods based on orthogonal polynomials. Numerische Mathematik, 90, 1-18.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../diffusion_1D/">Diffusion in 1D Cartesian coordinates »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Saturday 11 January 2025 09:48">Saturday 11 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>