Calculation of Time-dependent Nucleation and Growth Rates from Quantitative Textural Data: Inversion of Crystal Size Distribution

Abstract

Magmatictexturesprovideaninsufficientlyexploredtooltointerpretphysical processes and environmental variables that drive differenti-ation and crystallization in magma chambers. We derive a newmethod, which utilizes the crystal size distribution (CSD), to re-trieve the ratesof nucleation and growth from natural igneous rocks.However, a single CSD resultsfrom an arbitrary numberofcombin-ations of nucleation and growth rates; ifadditional parameters suchas crystallinity evolution are employed, the solution for rates becomesunique. Interpretation of representative log^linear CSD trendsshows that the nucleation rates are sensitive to even minor featuresof the CSD, whereas the growth rate functions are mainly related tothe crystallinity evolution. The reconstructed growth rates becomeminimal at intermediate crystallinities but diverge to very highvalues at the beginning and the end of crystallization.This generalresult is related to the small effective area of the solid^liquid inter-face close to the liquidus (few small grains) and near the solidus(largely solidified with diminishing melt pools). Assuming thatgrowth rate is related to environmental variables such as magmaundercooling, these results suggest that the solid fraction in manymagmas increases in a sigmoidal manner over their crystallizationinterval and indicate the tendency for largest undercooling at the be-ginning and at the end of crystallization. For crystallization timesconstrained by conductive cooling models, thegrowth ratescalculatedfor representative CSDs are of the order of10