Work Description

Date: May 29, 2025

Dataset Title: Data of the paper "Multicomponent diffusion in basaltic melts: A temperature-independent eigenvector matrix, and a multicomponent diffusion calculator"

Dataset Creators: Bobo Bai and Youxue Zhang

Dataset Contact: [email protected](Bobo Bai)

Research Abstract:

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 [D]. Eigenvectors of [D] 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, [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 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 [Q] in basaltic melts. The eigenvalues (i.e., the diffusion coefficients for individual eigenvector components) follows the Arrhenius relation. Using the extracted eigenvector matrix and eigenvalues, we present an open-access calculator for the community to use 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.

Methodology:

1. We use the BFGS method in the MatLab program to obtain diffusion eigenvectors and eigenvalues.

2. 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 ℃.

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

Summary of open-access data files:

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

2. "Bai_and_Zhang_2025_data_in_figures.xlsx":
An excel file provides data that appear in all figures in the paper.

3. "code_global_fit.zip":
A MatLab program (BFGS_main.m) for obtaining a temperature-independent 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.

4. "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.

Related publication(s):
Bai, B.. Zhang, Y., 2025. Multicomponent diffusion in basaltic melts: A temperature-independent eigenvector matrix, and a multicomponent diffusion calculator. In progress.

To Cite Data:
Bai, B., Zhang, Y. Data of the paper "Multicomponent diffusion in basaltic melts: A temperature-independent eigenvector matrix, and a multicomponent diffusion calculator" [Data set], University of Michigan - Deep Blue Data.