Modeling of zircon nucleation and growth rates using crystal size distributions in a cooling magmatic intrusion

Abstract With a rapid increase in the use of zircons for geochronology and in situ isotopic and chemical analyses it is important to quantify growth rates and nucleation rates of zircons in natural magmatic systems. Here we present a mathematical model of the nucleation and growth of a population of zircon crystals in a cooling magmatic intrusion and apply nucleation laws to derive zircon crystal size distributions (CSD) and particle number density (n per cm 3 of melt) from first principles. The model is based on a numerical solution of the one-dimensional diffusion equation that accounts for the nucleation and growth of individual crystals and the dependence of the equilibrium concentration of Zr on temperature. As experimental studies of zircon nucleation at natural concentration levels of Zr are nearly impossible, we rely on measured CSDs of age-invariant (within error of the method ± 5 ky ) zircon populations in rapidly quenched eruptive products of known crystallization duration to calibrate our model. The CSDs of zircon crystals are calculated at different rates of cooling of the magma chamber and are compared to measurements. The combination of the zircon growth software with measurements of zircon CSDs and particle number density permits direct estimation of the zircon nucleation rates and their evolution with time in cooling magmatic systems. We observe a delayed zircon nucleation of 500–2000 years after the melt becomes zircon saturated. Zr supersaturations that drive grown in simulations range from 1 to ∼ 30 ppm and vary non-monotonically as crystallization proceeds. Initially, the nucleation rates increase exponentially from 10 − 3 to ∼ 1 crystals/cm 3 /yr but then decrease by an order of magnitude as the distance between zircons decreases. Growth rates stay in 10 − 15 cm/s range for the most duration of zircon growth. The ratio of growth to nucleation rates in our model also varies insignificantly and is used to estimate crystallization time based on the CSD slope, which decreases with the increased duration of cooling. Flatter slopes correspond to longer crystallization durations as is also noted for major phases. Due to non-monotonic variations in growth and nucleation rates with time, the observed deficiency of small zircons resulting in concave up CSD shapes can be reproduced from first principles assuming monotonic cooling of the magmatic system. Variations in the mode of cooling from linear to monotonic during conductive heat loss of a cooling intrusion, and minor coeval precipitation ( 10 vol% ) of major phases has little impact on zircon CSD and its evolution. This study has implication to individual zircons IDTIMS dates and demonstrates that most zircons crystallize much later than magma becomes saturated with Zr, despite sometimes having nominally long tail crystallization rate in the inherited cores. For natural CSDs from eight different eruptions randomly selected zircons predate eruption age only by ∼ 300 – 1000 years .