Date: Jul 31, 2024

Dataset Title: Data of the paper "Multicomponent diffusion in natural silicate melts: Toward a universal eigenvector matrix"

Dataset Creators: Bobo Bai and Youxue Zhang

Dataset Contact: bbai@umich.edu(Bobo Bai)

Research Abstract:

Multicomponent diffusion in natural silicate melts is fundamental to understanding igneous processes such as magma mixing. In N-component silicate melts, multicomponent diffusion is characterized by an N-1 square matrix, termed the diffusivity matrix [D]. Eigenvectors of [D] define N-1 eigen-components that diffuse independently of each other. Diffusion eigenvectors in 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, [Q], 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 our fitting further supports the temperature independence of [Q]. Using the extracted eigenvector matrix and eigenvalues, we present an open-access calculator for the community to use to compute multicomponent diffusion profiles.

We further hypothesize that diffusion eigenvectors in natural silicate melts are also roughly compositionally independent. To test this hypothesis, oxide concentrations were converted into eigen-component "concentrations", Z_i, and plotted against distance for both the 27 diffusion experiments in basalt and 133 diffusion experiments from literature in dry rhyolitic to basaltic melts. If [Q] is compositionally invariant, all Z_i profiles should be monotonic. Approximately 98% of  >1000 plots are monotonic, showing that we are getting close to a universal eigenvector matrix. Notably, all Z_i profiles during quartz dissolution in basalt/rhyolite and olivine dissolution in basalt are monotonic. About 1% (9 out of 1120) show clear uphill diffusion, implying the need to further constrain [Q]. The other 1% (16 out of 1120) show complexities but it is less clear whether they reflect uphill diffusion. The test results roughly support the hypothesis of a single diffusion eigenvector matrix for natural silicate melts and show that the eigenvector matrix we extracted from 27 experiments in basalt is close to such a universal eigenvector matrix. 

Once the diffusion eigenvector matrix is shown to be invariant in natural melts and is accurately obtained, we propose to study multicomponent diffusion in eigen-component space through Z_i vs x plots. This approach combines the full rigor of multicomponent treatment with the simplicity of effective binary diffusion treatment. For example, two or three well-designed experiments will suffice to extract all diffusion eigenvalues in a specific 8-component melt composition. Moreover, this approach can treat the compositional dependence of eigenvalues. Lastly, its applicability is self-testable: if there are non-monotonic eigen-component profiles, for example, it would indicate inapplicability of the approach to the system, either because the eigenvector matrix is not accurate enough or because our hypothesis is incorrect.


Methodology:

1. We use the BFGS method in the MatLab program, “BFGS_main.m”, to obtain diffusion eigenvectors and eigenvalues.

2. We used the Newton Method in the MatLab program, “Newton_main.m”, to fit a diffusion profile assuming a diffusivity depending on concentration exponentially.

3. The fitting data for obtaining diffusion eigenvectors and eigenvalues are from 27 diffusion couple experiments from literature and this study. The 27 diffusion couple experiments included in this dataset were conducted in 8-component basaltic melts with similar compositions, but at three different temperatures, 1260 ℃, 1350 ℃ and 1500 ℃.

4. The data used for plotting concentration profiles of oxide components and eigen-components in the file “Bai_Zhang_Multicomponent_diffusion_figure_evaluation.pdf” comes from 160 diffusion experiments from literature and this study.


Summary of open-access data files: 

The open-access data files include the following documents:

1. "MultiComponentDif_calculator_v1.0.xlsx"
A multicomponent diffusion calculator for computing multicomponent diffusion profiles in a diffusion couple.

2. "code_fit_27_exp.zip"
A MatLab program (BFGS_main.m) for obtaining a universal eigenvector matrix and three sets of eigenvalues, with subroutines and diffusion data from 27 diffusion couple experiments used for fitting. For more details about the program, refer to “Readme” in this folder.

3. "code_fit_Z6_vs_x_in_BS13&14C.zip"
A MatLab program (Newton_main.m) for fitting the Z_6 vs x profile, assuming λ_6 to increase exponentially with Z_6, in the experiment BS13&14C. For more details about the program, refer to “Readme” in this folder.
4. "Bai_Zhang_Multicomponent_diffusion_figure_evaluation.pdf"
Concentration profiles of oxide components and eigen-components from 160 diffusion couple or mineral dissolution experiments.

Related publication(s):
Bai, B.. Zhang, Y., 2024. Multicomponent diffusion in natural silicate melts: Toward a universal eigenvector matrix. In progress.

To Cite Data: 
Bai, B., Zhang, Y. Data of the paper "Multicomponent diffusion in natural silicate melts: Toward a universal eigenvector matrix" [Data set], University of Michigan - Deep Blue Data.