Percolation-diffusion model

MATLAB code to compute the diffusional re-equilibration of trace elements (e.g. REE) in a solid matrix of spherical mantle minerals percolated by a melt in a 1D column

The package (tested in Matlab R2021b and R2022b) includes:

• The main percolation-diffusion model (mainPercolationDiffusion.m)
• An input file (input.xlsx) which includes solid, liquid and normalization compositions, and a set of partition and diffusion coefficients for the main mantle minerals
• A user file (initializeAdhoc.m) to load the inputs and set the different percolation-diffusion parameters
• A utils folder that contains all the required dependencies
• An output folder where the models results are saved. This folder currently contains the pre-run model results necessary to reproduce the outputs shown in Tilhac et al. (2023).
• An additional code (plotting.m) to generate plots similar to the figures shown in Tilhac et al. (2023).

Instructions & user changes

The model can be directly launched by running mainPercolationDiffusion.m. There are two main sections that contains parameters that can be safely changed by the user in initializeAdhoc.m (marked as USER CHANGE):

• Firstly, the Main parameters, which include P-T conditions, porosity, melt velocity, time and saving intervals, as well as the proportion of Eu²⁺/Eu³⁺ (to investigate the diffusive fractionation of europium among the REE, as in Tilhac et al., 2023).
• Secondly, the Mineral parameters, which include modal proportions, grain size and the activation of the P and T dependencies on diffusivities. The default mineral allocations are olivine (Oli), clinopyroxene (Cpx), orthopyroxene (Opx), garnet (Grt), spinel (Spl) and plagioclase (Plg).

The partition and diffusion coefficients provided in the input file are taken from Oliveira et al. (2020). They can be changed by the user but it is important that they match the mineral parameters in the user file (e.g. if clinopyroxene, orthopyroxene and olivine are listed in the user file, their respective coefficients must be provided). The input compositions given as example correspond to the data used in Tilhac et al. (2023) (see Reproducibility note below).

Running the model on a desktop computer using the current default settings takes about 1-10 minutes (depending, among others, on the number of time steps required). Do not manually change the number of time steps as it needs to be calculated from the column length and melt velocity based on the number of nodes and particle spacing.

Other parameters such as the size of the column (y2 [m]), the list of elements (TE_list) and minerals (TP_list) can also be changed with caution in mainPercolationDiffusion.m. Please contact me for any specific application.

Reproducibility note

Model outputs as shown in Tilhac et al. (2023) can be reproduced by directly running plotting.m. To reproduce Figure 1 (REE patterns) and Figure 2 (Eu anomalies vs Eu contents), the code reads the output subfolder pre-run. Similar outputs can also directly be obtained by running mainPercolationDiffusion.m as provided, leaving initializeAdhoc.m unchanged.

The benchmark_Eu boolean allows to choose between two diffusivities for Eu²⁺ based on the experimental diffusivities of Sr²⁺ in either synthetic (1 - conservative choice used in Tilhac et al., 2023) or natural (0) diopside.

The benchmark_2Cpx boolean allows to use two different grain-size populations for clinopyroxene only (1 - used in Tilhac et al., 2023) or the default mineral allocations (0).

Credits

By Romain Tilhac, CSIC post-doctoral researcher at the Instituto Andaluz de Ciencias de la Tierra (IACT), Granada, Spain.
Modified from the original MPMCRT code developed by Beñat Oliveira Bravo (Oliveira et al., 2020).
Updated on December 11th, 2022
Contact: [email protected]

References

Tilhac, R., Hidas, K., Oliveira, B., Garrido, C.J. 2023. Evidence of ghost plagioclase signature induced by kinetic fractionation of europium in the Earth’s mantle, Nature Communications, Volume 14, 1099, https://www.nature.com/articles/s41467-023-36753-0

Oliveira, B., Afonso, J.C., Tilhac, R. 2020. A Disequilibrium Reactive Transport Model for Mantle Magmatism, Journal of Petrology, Volume 61, Issue 9, egaa067, https://doi.org/10.1093/petrology/egaa067