Constraining the rates of olivine crystal growth with diffusion chronometry

Xenocrysts in magmatic rocks are often found having gradients in their composition. These compositional gradients are commonly interpreted as the result of mass fractionation during crystal growth and it is quite common that these gradients are also influenced by intra-crystalline chemical diffusion. Since the interplay between element diffusion and crystal growth in the magma controls the final composition of magmatic minerals, it is not possible to uniquely constrain the high-temperature history of a zoned crystal. To address this problem, we present a numerical model that can be used in an inverse manner to constrain the rate of olivine growth in basaltic magma. The model addresses a classic moving boundary problem, whilst solving the intra-crystalline diffusion of Ca in olivine. Our model is created to account for the growth of a spherical olivine crystal in a finite (or infinite) reservoir. The diffusion equation is solved with a forward Euler scheme and we use a conservative, regridding approach to account for changes in crystal size. The model was tested against experimentally determined olivine growth rates. Our results show that the inferred growth rates agree within an order of magnitude to the results from experiments at fixed pressure, temperature and oxygen-fugacity conditions.