Burg, J.-P. and Moulas, E.: Cooling-rate constraints from metapelites across two inverted metamorphic sequences of the Alpine-Himalayan belt; evidence for viscous heating, J. Struct. Geol., 156, 104536, https://doi.org/10.1016/j.jsg.2022.104536, 2022.
Chakraborty, S.: Diffusion modeling as a tool for constraining timescales of evolution of metamorphic rocks, Mineral. Petrol., 88, 7–27, https://doi.org/10.1007/s00710-006-0152-6, 2006.
Chakraborty, S.: Diffusion in Solid Silicates: A Tool to Track Timescales of Processes Comes of Age, Annu. Rev. Earth Planet. Sci., 36, 153–190, https://doi.org/10.1146/annurev.earth.36.031207.124125, 2008.
Chakraborty, S. and Dohmen, R.: Diffusion chronometry of volcanic rocks: looking backward and forward, Bull. Volcanol., 84, 57, https://doi.org/10.1007/s00445-022-01565-5, 2022.
Chakraborty, S. and Ganguly, J.: 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, 1992.
Chen, J., Zou, Y., and Chu, X.: DIFFUSUP: A graphical user interface (GUI) software for diffusion modeling, Appl. Comput. Geosci., 22, 100157, https://doi.org/10.1016/j.acags.2024.100157, 2024.
Chu, X., Ague, J. J., Tian, M., Baxter, E. F., Rumble, D., and Chamberlain, C. P.: Testing for Rapid Thermal Pulses in the Crust by Modeling Garnet Growth–Diffusion–Resorption Profiles in a UHT Metamorphic `Hot Spot', New Hampshire, USA, J. Petrol., 59, 1939–1964, https://doi.org/10.1093/petrology/egy085, 2018.
Connolly, J. A. D.: Computation of phase equilibria by linear programming: A tool for geodynamic modeling and its application to subduction zone decarbonation, Earth Planet. Sc. Lett., 236, 524–541, https://doi.org/10.1016/j.epsl.2005.04.033, 2005.
Costa, F., Dohmen, R., and Chakraborty, S.: Time scales of magmatic processes from modeling the zoning Patterns of crystals, Rev. Mineral. Geochem., 69, 545–594, https://doi.org/10.2138/rmg.2008.69.14, 2008.
Costa, F., Shea, T., and Ubide, T.: Diffusion chronometry and the timescales of magmatic processes, Nat. Rev. Earth Environ., 1, 201–214, https://doi.org/10.1038/s43017-020-0038-x, 2020.
Crank, J.: The mathematics of diffusion, in: 2nd Edn., Clarendon Press, Oxford, England, 414 pp., ISBN 978-0-19-853344-3, 1975.
Dohmen, R. and Chakraborty, S.: Fe–Mg diffusion in olivine II: point defect chemistry, change of diffusion mechanisms and a model for calculation of diffusion coefficients in natural olivine, Phys. Chem. Miner., 34, 409–430, https://doi.org/10.1007/s00269-007-0158-6, 2007a.
Dohmen, R. and Chakraborty, S.: Fe–Mg diffusion in olivine II: point defect chemistry, change of diffusion mechanisms and a model for calculation of diffusion coefficients in natural olivine, Phys. Chem. Miner., 34, 597–598, https://doi.org/10.1007/s00269-007-0185-3, 2007b.
Eiler, J. M., Baumgartner, L. P., and Valley, J. W.: Intercrystalline stable isotope diffusion: a fast grain boundary model, Contrib. Mineral. Petrol., 112, 543–557, https://doi.org/10.1007/BF00310783, 1992.
Fick, A.: Ueber Diffusion, Ann. Phys., 170, 59–86, https://doi.org/10.1002/andp.18551700105, 1855.
Gaidies, F., De Capitani, C., Abart, R., and Schuster, R.: Prograde garnet growth along complex P–T–t paths: results from numerical experiments on polyphase garnet from the Wölz Complex (Austroalpine basement), Contrib. Mineral. Petrol., 155, 673–688, https://doi.org/10.1007/s00410-007-0264-y, 2008.
Garcia, V. H., Scherer, C., and Mors, P. M.: Growth kinetics of phases in solid-state diffusion couples, Phys. Status Solidi A, 152, 385–392, https://doi.org/10.1002/pssa.2211520207, 1995.
Girona, T. and Costa, F.: DIPRA: A user-friendly program to model multi-element diffusion in olivine with applications to timescales of magmatic processes, Geochem. Geophy. Geosy., 14, 422–431, https://doi.org/10.1029/2012GC004427, 2013.
Goldstein, J. I. and Short, J. M.: Cooling rates of 27 iron and stony-iron meteorites, Geochim. Cosmochim. Ac., 31, 1001–1023, https://doi.org/10.1016/0016-7037(67)90076-2, 1967.
Guo, C. and Zhang, Y.: Multicomponent diffusion in silicate melts: SiO
2–TiO
2–Al
2O
3–MgO–CaO–Na
2O–K
2O System, Geochim. Cosmochim. Ac., 195, 126–141, https://doi.org/10.1016/j.gca.2016.09.003, 2016.
Hartley, M. E., Morgan, D. J., Maclennan, J., Edmonds, M., and Thordarson, T.: Tracking timescales of short-term precursors to large basaltic fissure eruptions through Fe–Mg diffusion in olivine, Earth Planet. Sc. Lett., 439, 58–70, https://doi.org/10.1016/j.epsl.2016.01.018, 2016.
Hesse, M. A.: A finite volume method for trace element diffusion and partitioning during crystal growth, Comput. Geosci., 46, 96–106, https://doi.org/10.1016/j.cageo.2012.04.009, 2012.
Hollister, L. S.: Garnet Zoning: An Interpretation Based on the Rayleigh Fractionation Model, Science, 154, 1647–1651, https://doi.org/10.1126/science.154.3757.1647, 1966.
Hughes, T. J. R.: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, New Jersey, 825 pp., ISBN 0-13-317025-X, 1987.
Kahaner, D., Moler, C., and Nash, S.: Numerical Methods and Software, Prentice Hall, New Jersey, 504 pp., ISBN 0-13-645 627258-4, 1989.
Kelly, E. D., Carlson, W. D., and Connelly, J. N.: Implications of garnet resorption for the Lu-Hf garnet geochronometer: an example from the contact aureole of the Makhavinekh Lake Pluton, Labrador: Effects of garnet resorption on LU-HF ages, J. Metamorph. Geol., 29, 901–916, https://doi.org/10.1111/j.1525-1314.2011.00946.x, 2011.
Kittur, M. G. and Huston, R. L.: Finite element mesh refinement criteria for stress analysis, Comput. Struct., 34, 251–255, https://doi.org/10.1016/0045-7949(90)90368-C, 1990.
Kohn, M. J.: Models of garnet differential geochronology, Geochim. Cosmochim. Ac., 73, 170–182, https://doi.org/10.1016/j.gca.2008.10.004, 2009.
Kohn, M. J. and Spear, F.: Retrograde net transfer reaction insurance for pressure-temperature estimates, Geology, 28, 1127–1130, https://doi.org/10.1130/0091-7613(2000)28<1127:RNTRIF>2.0.CO;2, 2000.
Kuiken, G. D. C.: Thermodynamics of irreversible processes – Applications to Diffusion and Rheology, in: 1st Edn., WILEY, England, xxxii
+ 425 pp., ISBN 0 471 94 844 6, 1994.
Lasaga, A. C.: Geospeedometry: An Extension of Geothermometry, in: Kinetics and Equilibrium in Mineral Reactions, edited by: Saxena, S. K., Springer, New York, NY, 81–114, https://doi.org/10.1007/978-1-4612-5587-1_3, 1983.
Lindström, R., Viitanen, M., Juhanoja, J., and Hölttä, P.: Geospeedometry of metamorphic rocks: examples in the Rantasalmi-Sulkava and Kiuruvesi areas, eastern Finland. Biotite–garnet diffusion couples, J. Metamorph. Geol., 9, 181–190, https://doi.org/10.1111/j.1525-1314.1991.tb00513.x, 1991.
Liu, J.-H., Lanari, P., Tamblyn, R., Dominguez, H., Hermann, J., Rubatto, D., Forshaw, J. B., Piccoli, F., Zhang, Q. W. L., Markmann, T. A., Reynes, J., Li, Z. M. G., Jiao, S., and Guo, J.: Ultra-fast metamorphic reaction during regional metamorphism, Geochim. Cosmochim. Ac., 394, 106–125, https://doi.org/10.1016/j.gca.2025.01.036, 2025.
Marschall, H. R., Dohmen, R., and Ludwig, T.: Diffusion-induced fractionation of niobium and tantalum during continental crust formation, Earth Planet. Sc. Lett., 375, 361–371, https://doi.org/10.1016/j.epsl.2013.05.055, 2013.
Moulas, E.: GDIFF: a Finite Difference code for the calculation of multicomponent diffusion in garnet, Zenodo [code], https://doi.org/10.5281/zenodo.8224137, 2023a.
Moulas, E. and Brandon, M. T.: KADMOS: a Finite Element code for the calculation of apparent K-Ar ages in minerals, Zenodo [code], https://doi.org/10.5281/zenodo.7358138, 2023b.
Mutch, E. J. F., Maclennan, J., Shorttle, O., Rudge, J. F., and Neave, D. A.: DFENS: Diffusion Chronometry Using Finite Elements and Nested Sampling, Geochem. Geophys. Geosy., 22, 1–28, https://doi.org/10.1029/2020GC009303, 2021.
Nakamura, M.: Residence time and crystallization history of nickeliferous olivine phenocrysts from the northern Yatsugatake volcanoes, Central Japan: Application of a growth and diffusion model in the system Mg-Fe-Ni, J. Volcanol. Geoth. Res., 66, 81–100, https://doi.org/10.1016/0377-0273(94)00054-K, 1995.
Ozawa, K.: Evaluation of olivine-spinel geothermometry as an indicator of thermal history for peridotites, Contrib. Mineral. Petrol., 82, 52–65, https://doi.org/10.1007/BF00371175, 1983.
Ozawa, K.: Olivine-spinel geospeedometry: Analysis of diffusion-controlled Mg-Fe
2+ exchange, Geochim. Cosmochim. Ac., 48, 2597–2611, https://doi.org/10.1016/0016-7037(84)90308-9, 1984.
Perchuk, A. L. and Philippot, P.: Geospeedometry and Time Scales of High-Pressure Metamorphism, Int. Geol. Rev., 42, 207–223, https://doi.org/10.1080/00206810009465078, 2000.
Rubinsteĭn, L. I.: The Stefan Problem, American Mathematical Soc., Providence, Rhode Island, 432 pp., ISBN 978-0-8218-8656-4, 1971.
Skora, S., Baumgartner, L. P., Mahlen, N. J., Johnson, C. M., Pilet, S., and Hellebrand, E.: Diffusion-limited REE uptake by eclogite garnets and its consequences for Lu–Hf and Sm–Nd geochronology, Contrib. Mineral. Petrol., 152, 703–720, https://doi.org/10.1007/s00410-006-0128-x, 2006.
Smith, V. G., Tiller, W. A., and Rutter, J. W.: A mathematical analysis of solute redistribution during solidification, Can. J. Phys., 33, 723–745, https://doi.org/10.1139/p55-089, 1955.
Spear, F. S.: On the interpretation of peak metamorphic temperatures in light of garnet diffusion during cooling, J. Metamorph. Geol., 9, 379–388, https://doi.org/10.1111/j.1525-1314.1991.tb00533.x, 1991.
Spear, F. S.: The duration of near-peak metamorphism from diffusion modelling of garnet zoning, J. Metamorph. Geol., 32, 903–914, https://doi.org/10.1111/jmg.12099, 2014.
Tajčmanová, L., Podladchikov, Y., Moulas, E., and Khakimova, L.: 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, 2021.
Watson, E. B. and Müller, T.: Non-equilibrium isotopic and elemental fractionation during diffusion-controlled crystal growth under static and dynamic conditions, Chem. Geol., 267, 111–124, https://doi.org/10.1016/j.chemgeo.2008.10.036, 2009.
Zhang, Y., Cherniak, D. J., and Rosso, J. J. (Eds.),: Diffusion in Minerals and Melts, De Gruyter, 1036 pp., ISBN 978-0-939950-86-7, 2010.
Zhong, X., Vrijmoed, J., Moulas, E., and Tajčmanová, L.: A coupled model for intragranular deformation and chemical diffusion, Earth Planet. Sc. Lett., 474, 387–396, https://doi.org/10.1016/j.epsl.2017.07.005, 2017.
