MODELING NUCLEATION DELAY IN IGNEOUS SYSTEMS

Crystal nucleation occurs after a melt reaches supersaturation, but the time between attainment of supersaturation and the first appearance of crystals can vary from less than a second to many years. The duration of the nucleation delay depends upon the extent of supersaturation and the crystal and melt compositions. Differing nucleation delay times of minerals can alter the crystallization sequence of a melt depending upon the rate of cooling. A better understanding of nucleation delay would aid our understanding of the textures of igneous rocks and our modeling of their petrogenesis.

Although classical nucleation theory was developed in the early 20^th century and nucleation delay times of plagioclase and olivine in a few basaltic melts were experimentally determined in the late 20^th century, a quantitative model applicable to magmatic systems remains elusive. Fokin et al. (2006, J. Non-Cryst. Solids 352:2681) propose using the nucleation delay time equation of Collins (1955, Z. Elektrochem. 59:404) for silicate melts. A modification of this equation can be solved with knowledge of the difference in Gibbs free energies between the melt and the crystal, the interfacial energy between the melt and the crystal, the activation energy for transport of nuclei species in the melt, and the size of the structural units creating the nuclei.

Applying thermodynamic data from PhasePlot, activation energies for Si-Al effective binary diffusion, estimated interfacial energies, and the ionic radius of either Al³⁺ or Si⁴⁺, the published experimental nucleation delay times of plagioclase in two basaltic melts and of olivine in another basaltic melt were modeled. The implementation of the Fokin et al. model predicted the nucleation delay of plagioclase and of olivine to within a few hours for most supersaturations, although differences between model and experiment were longer, ~ 10 h, at low supersaturation (undercoolings within 20 °C of the saturation temperature) where the largest nucleation delay times occur. The close agreement between model and experiments suggests that quantitative estimations of nucleation delay times are possible and can be used as an additional tool in the interpretation of magmatic evolution.