Numerical modelling of diffusion-limited mineral growth for geospeedometry applications

Abstract. Diffusion and crystal growth are common processes in nature and can be observed in rocks that have experienced relatively high temperatures. Information about these processes is stored in the composition gradients of minerals. Diffusion can either occur within single crystals or across mineral interfaces. In the case of intercrystalline ion exchange, composition profiles across the interfaces are always discontinuous and may exhibit sharp compositional gradients. The compositional discontinuity and the associated gradients require an accurate treatment for the interface boundary condition. Here, we present a software package (MovingBoundaryMinerals.jl) that is openly available. In this package, we use an adaptive finite element method to describe the diffusion-couple equilibrium by taking into account the moving boundary separating the two phases. In addition, we utilize an adaptive grid approach to resolve the compositional gradients accurately at the interface region. This approach allows modelling a wide range of applications from mineral diffusion, simple ion exchange between diffusion couples, and diffusion-limited growth. The package has been tested versus variable available analytical solutions for diffusion and growth, and several benchmark cases are presented. Finally, our package can be used to model compositional gradients in growing/dissolving/diffusing crystals in the framework of diffusion chronometry and geospeedometry. This approach can provide thermal/time constraints in various geologic phenomena.