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

Magmatic textures provide an insufficiently explored tool to interpret physical processes and environmental variables that drive differentiation and crystallization in magma chambers. We derive a new method, which utilizes the crystal size distribution (CSD), to retrieve the rates of nucleation and growth from natural igneous rocks. However, a single CSD results from an arbitrary number of combinations of nucleation and growth rates; if additional parameters such as crystallinity evolution are employed, the solution for rates becomes unique. Interpretation of representative log–linear CSD trends shows that the nucleation rates are sensitive to even minor features of the CSD, whereas the growth rate functions are mainly related to the crystallinity evolution. The reconstructed growth rates become minimal at intermediate crystallinities but diverge to very high values at the beginning and the end of crystallization. This general result is related to the small effective area of the solid–liquid interface close to the liquidus (few small grains) and near the solidus (largely solidified with diminishing melt pools). Assuming that growth rate is related to environmental variables such as magma undercooling, these results suggest that the solid fraction in many magmas increases in a sigmoidal manner over their crystallization interval and indicate the tendency for largest undercooling at the beginning and at the end of crystallization. For crystallization times constrained by conductive cooling models, the growth rates calculated for representative CSDs are of the order of 10⁻¹¹ cm s⁻¹, which is in a good agreement with in situ observations of Hawaiian lava lakes. Calculated growth rates are inversely proportional to the magma body size and increase from the chamber interior to the margins.