Multicomponent diffusion in basaltic melts: A temperature-independent eigenvector matrix, and a multicomponent diffusion calculator

Multicomponent diffusion in natural silicate melts is a fundamental process in magma mixing and evolution. In $N$-component silicate melts, multicomponent diffusion is characterized by an $N-1$ square matrix, termed the diffusion matrix $\left[D\right]$. Eigenvectors of $\left[D\right]$ define $N-1$ eigen-components that diffuse independently of each other. Diffusion eigenvectors in an 8-component SiO₂-TiO₂-Al₂O₃-FeO-MgO-CaO-Na₂O-K₂O basalt appear to be roughly temperature independent (e.g., Guo and Zhang, 2020). For additional verification of the temperature independence and for improving the accuracy of the eigenvector matrix, we use a single eigenvector matrix, $\left[Q\right]$, to simultaneously fit concentration profiles from 26 diffusion couple experiments at three temperatures from Guo and Zhang, (2018, 2020), and one additional experiment conducted in this work. The goodness of fit using one single eigenvector matrix in this work is about the same as that using three different eigenvector matrices in Guo and Zhang (2018, 2020), further supporting the temperature independence of $\left[Q\right]$ in basaltic melts. The eigenvalues (i.e., the diffusion coefficients for individual eigenvector components) follow the Arrhenius relation. Using the extracted eigenvector matrix and eigenvalues, we present an open-access calculator for the community to compute multicomponent diffusion profiles. The calculator is applied to examine multicomponent diffusion in eigen-component space, and minor compositional dependence of eigen-component diffusivities (i.e., eigenvalues) is revealed.