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A Monte Carlo approach to diffusion applied to noble gas/helium thermochronology

Abstract : Knowledge of the diffusion domain is of primary importance for age interpretation in noble gas thermochronometers. We have developed a Monte Carlo method to solve the diffusion equation in three-dimensional space and have used it to examine the effect of realistic crystal geometries and anisotropy on noble gas diffusion. The method is based on the simulation of Brownian motion with a modified distribution of collision distances and with a variable mean free path. This approach drastically reduces calculation time while remaining accurate. This original approach is able to treat isotropic and anisotropic diffusion, any 3D shape, ejection and zonation. A code simulating production, ejection and diffusion from the grain to the external medium has been implemented to compute helium ages of minerals subjected to temperature histories. In parallel, another module has been developed to simulate diffusion experiments and diffusion coefficient determination for all types of He profiles in a grain (homogenous, depleted edge due to ejection, heterogeneous profile due to previous diffusion, etc). Both types of simulations are suitable for isotopic and anisotropic diffusion; we develop examples for apatite and zircon (U–Th)/He thermochronology but the method can be applied to any other noble gas thermochronometer. The Monte Carlo simulation reproduces the He age variation obtained by other calculation methods for simple geometries and for well-known thermal histories, demonstrating the viability of the tool. In the case of isotropic diffusion, we show that generally even for realistic shapes with many ridges the He age resulting from the diffusion can be well calculated by assuming a spherical shape of the same surface/volume (S/V) ratio. The only requirement for adequate representation of grains by spheres is thus accurate knowledge of their true shapes and dimensions. For anisotropic diffusion, we introduce a new concept termed “active radius”, which describes the complex anisotropic diffusion process by isotropic diffusion in a sphere. In this sense, the active radius can be seen as an extension of the sphere-equivalent radius to the anisotropic case. The active radius can be computed for any geometrical shape without Monte Carlo sampling, and a separate simple code is made available for its computation.
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Contributor : Sophie Heurteau <>
Submitted on : Friday, June 18, 2010 - 2:10:10 PM
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C. Gautheron, L. Tassan-Got. A Monte Carlo approach to diffusion applied to noble gas/helium thermochronology. Chemical Geology, Elsevier, 2010, 273, pp.212-224. ⟨10.1016/j.chemgeo.2010.02.023⟩. ⟨in2p3-00492987⟩



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