Evolution of crystal sizes in the series of dissolution and precipitation events in open magma systems

We propose a model that describes the evolution of crystal sizes and crystal size distributions (CSD) of igneous phenocrysts in a sequence of dissolution and crystallization events. This model is based on the assumption that crystal dissolution is rate-limited by diffusion in melt while crystal growth is controlled by the slower kinetic of new nucleation and growth. As a result, the dissolution rate is inversely proportional to crystal size coming into effect through the curvature of the crystal's surface, but the growth rate does not depend on the crystal size. Closed-form analytical solution of equation for CSD is obtained. We apply results of modeling to quartz and zircon, two prime minerals in silicic igneous systems that are widely used in geochemical and isotopic investigations. The time-series of multiple solution–reprecipitation episodes generate concave-downward CSDs and this result fits well with experimental and natural observations on the abundant concave-down CSD in silicic igneous rocks. We suggest that maturation of crystal populations with sizes above several micrometers can not be caused by a size effect on the solubility of the crystals (Ostwald ripening), but is rather driven by thermal oscillations in experiments and in nature. The model predicts that mean crystal size increases with time proportionally to ∼ t0.20, which is very close to the published experimental results for quartz maturation with the exponent of 0.19–0.22. Our proposed model gives an opportunity to use natural CSDs for interpretation of pre-eruptive magma history, when solubilities and diffusion data are available for constituent elements of the dissolving mineral. In particular, we present time estimates for maturing zircon populations in large volume ignimbrites and estimate that it takes 100–1000 yrs to mature an initially exponential CSD to a lognormal CSD.