Numerical Modelling of Chemical Diffusion in Petrology and Geochemistry
Description
These notes are the pdf slides that were used in the workshop entitled: "Numerical Modelling of Chemical Diffusion in Petrology and Geochemistry" that was held in Mainz in July, 2023. Apart from the lecture material, I have provided code examples that the interested readers can copy and use for their own research. These notes do not cover the diffusion theory extensively, and the interested reader should refer to available textbooks (see the reference list at the end of file). The codes and the rest of the material are provided with no warranty. They are mostly done for educational purposes and assume no programming experience on behalf of the user. Therefore, to more experienced programmers, these codes may look redundant.
Since this is the first version of these notes it is possible that these notes contain errors. Instead of waiting until I complete the 'perfect' notes I decided to proceed with the material that I already have. Any constructive feedback and comments are welcome and should be addressed to evmoulas@uni-mainz.de. I will try to update the notes every year depending on the requests that I get from the workshop participants or other interested readers. In case you find these notes useful, please cite them appropriately (see rules at https://zenodo.org/).
Writing these notes and the organization of the workshop would not have been possible without the support from the German Mineralogical Society (DMG) and the Mainz Institute of Multiscale Modeling (M3ODEL). The institute of Geosciences in Mainz is acknowledged for hosting the workshop and Claudia Scheer is thanked for providing valuable assistance. I would also like to thank Lucie Tajčmanová, Roman Botcharnikov, Sumit Chakraborty and Boris Kaus for encouraging me to organize this workshop. Finally, I would like to thank Simon Boisserée and Annalena Stroh for going through this material and for providing feedback in advance.
Evangelos Moulas
Files
Diffusion_Workshop_1_2.pdf
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(5.5 MB)
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Additional details
Dates
- Updated
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2023-10-30
References
- Balluffi, R.W., Allen, S.M. & Carter, W.C., (2005). Kinetis of Materials. Wiley-Interscience, 645 p.
- Burg, J.-P., & Moulas, E., (2022). Cooling-rate constraints from metapelites across two inverted metamorphic sequences of the Alpine-Himalayan belt; evidence for viscous heating. J. Struct. Geol., 156; https://doi.org/10.1016/j.jsg.2022.104536
- Brady, J. B., & Cherniak, D.J., (2010). Diffusion in Minerals: An Overview of Published Experimental Diffusion Data. Rev. Mineral. Geochem. 72, 899-920; https://doi.org/10.2138/rmg.2010.72.20
- Chakraborty, S., & Ganguly, J. (1992). Cation diffusion in aluminosilicate garnets: experimental determination in spessartine-almandine diffusion couples, evaluation of effective binary diffusion coefficients, and applications. Contrib. Mineral. Petrol. 111, 74–86; https://doi.org/10.1007/BF00296579
- Chakraborty, S., (1994). Relationships between Thermodynamic Mixing and Diffusive Transport in Multicomponent Solutions: Some Constraints and Potential Applications. J. Phys. Chem. 98, 4923 4926; https://doi.org/10.1021/j100069a026
- Cherniak, D.J., & Ryerson, F.J. (1993). A study of strontium diffusion in apatite using Rutherford backscattering spectroscopy and ion implantation. Geochim. Cosmochim. Acta. 125, 4653-4662; https://doi.org/10.1016/0016-7037(93)90190-8
- Crank, J., (1956), The mathematics of diffusion. Oxford University Press, 347 p.
- Cygan, R., & Lasaga, A. (1985). Self-diffusion of magnesium in garnet at 750 degrees to 900 degrees C. Am. J. Sci., 285 (4), 328-350; https://doi.org/10.2475/ajs.285.4.328
- Dohmen, R., & Chakraborty, S. (2007). Fe–Mg diffusion in olivine II: point defect chemistry, change of diffusion mechanisms and a model for calculation of diffusion coefficients in natural olivine. ERRATUM. Phys. Chem. Minerals, 34, 597-598; https://doi.org/10.1007/s00269-007-0185-3
- Lasaga, A. C., (1983), Geospeedometry: An extension to geothermometry, in Saxena, S. K. ed., Kinetics and Equilibrium in Mineral Reactions: Springer New York, p. 81–114
- Moulas E., Brandon M.T. (2022) KADMOS: a Finite Element code for the calculation of apparent K-Ar ages in minerals. Zenodo. doi: 10.5281/zenodo.7358136
- Moulas, E., (2023) GDIFF: a Finite Difference code for the calculation of multicomponent diffusion in garnet. Zenodo. doi:10.5281/zenodo.7805989
- Schwinger, S., Dohmen, R. & Schertl, H.-P. (2016). A combined diffusion and thermal modeling approach to determine peak temperatures of thermal metamorphism experienced by meteorites. Geochim. Cosmochim. Acta, 191, 255-276; http://dx.doi.org/10.1016/j.gca.2016.06.015
- Tajčmanová, L., Podladchikov, Y., Moulas, E.et al.(2021). The choice of a thermodynamic formulation dramatically affects modelled chemical zoning in minerals.Sci. Rep.11, 18740; https://doi.org/10.1038/s41598-021-97568-x
- Toor, H.L. (1964). Solution of the Linearized Equations of Multicomponent Mass Transfer: 11. Matrix Methods. A.I.Ch.E. Journal, 10 (4), 463-465
- Turcotte, D., & Schubert, G. (2014).Geodynamics(3rd ed.). Cambridge University Press. doi:10.1017/CBO9780511843877
- Zhang, Y. (2008).Geochemical Kinetics. Princeton University Press. p.631