A New Model of Crystallization in Magmas: Impact of Pre‐Exponential Factor of Crystal Nucleation Rate on Cooling Rate Exponent and Log‐Linear Crystal Size Distribution

Abstract

AbstractThe processes that control the crystallization of magmas, namely nucleation and growth, remain poorly constrained. Classical nucleation theory (CNT) has so far not provided a unified framework to explain crystal number density in laboratory experiments and the field. We use numerical experiments to study the influence of different cooling rates and CNT parameters on the crystal number density measured under constrained conditions in laboratory experiments. With varying the magnitude of pre‐exponential factor (J0) of nucleation rate, which represents the number of cluster as heterogeneous nucleation sites, we find that the cooling rate exponent (ξ) of the crystal number density varies from 3/2 to −1, depending on the magnitude of J0, cooling rate and surface tension. Using the regime maps of ξ as functions of J0 and surface tension, we can successfully interpret the diversity of cooling rate exponents reported by laboratory experiments in terms of J0 and surface tension. For extreme case of a negative cooling rate exponent ξ = −1, we propose a new crystallization model with constant rates of nucleation and crystallization, which reproduces a log‐linear crystal size distribution. In this condition, it is interesting that the crystal growth rate is inversely proportional to time, even if the diffusion‐limited growth is inversely proportional to the square root of time. For the case study of zoning profiles in microlites formed by decompression‐induced crystallization during the Shinmoedake 2011 subplinian eruptions, the comparison between theoretical predictions and natural volcanic products supports that our model is well applicable to magma ascent processes.