Numerical modeling of simultaneous diffusion and mineral growth

Compositional concentration profiles across individual crystals or diffusion couples are largely determined by diffusion and growth processes. These two processes are particularly important during the formation of high-temperature rocks such as igneous and metamorphic rocks. The numerical simulation of concentration profiles in crystals is a widely used technique in various fields such as geospeedometry or diffusion chronometry. Compared to single crystals, coupled diffusion pairs yield tighter constraints on the experienced temperature and pressure ranges and thus provide additional information for our models. However, the numerical description of concentration profiles within diffusion couples is challenging due to the sharp compositional gradients. Discontinuities in concentration, which are related to the different mineral properties, commonly occur at the interface of two minerals and lead to technical implementation issues.

To address these issues, we have developed a Finite Element (FE) package in Julia that can calculate the evolution of concentration profiles in diffusion couples with moving interfaces. Both growth and diffusion processes are considered. An adaptive grid enables the accurate reproduction of rapid concentration changes and discontinuities. Our code can be applied to various examples of single crystals or diffusion couples, integrating any combination of growth, diffusion, and temperature dependency. Additionally, it is possible to calculate concentration profiles based on the thermodynamically-constrained, Stefan-Interface condition. Results from our models can be used in petrology and geodynamic applications to provide tighter constraints concerning in the pressure and temperature evolution of magmatic and metamorphic mineral assemblages.