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

The 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 (xi) 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 xi 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 xi = -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. Crystallization of magmas denotes the formation of crystals in cooling magmas owing to heat loss during their ascension to the Earth surface or to the decompression and vesiculation occurring during an eruption. Since it strongly depends on cooling rate, the crystal number density is the most relevant textural index of the final products of the ascending magmas, the erupted rocks. Continuous efforts have been made in theory, laboratory experiments and observation of natural rock samples to understand how the cooling rate of magmas controls the texture of the erupted materials. Yet the role that different factors play on the texture of rocks during crystallization remains poorly constrained. For instance, the crystal number density has been observed to increase with cooling rate in some laboratory experiments and show no dependence or even decrease in others. The model proposed here identifies the nucleation rate as the main parameter controlling the formation of crystals. This study provides a consistent framework to relate the crystal number densities measured in laboratory experiments and observed in natural samples to their cooling conditions. Pre-exponential factor of nucleation rate in classical theory has the greatest effect on number density of crystals formed by coolingThe model can explain the diversity of the experimental and natural dataConstant rates of nucleation and crystallization yield log-linear CSDs

Automated summary

This study investigates the influence of cooling rates and nucleation rate parameters on crystal number density in laboratory experiments using numerical experiments. The results show that the relationship between the nucleation rate's pre-exponential factor and cooling rate and surface tension can explain the diversity in experimental results. A new crystallization model is proposed, which reproduces a log-linear crystal size distribution by assuming constant rates of nucleation and crystallization. The model is also supported by the study of magma ascent processes during volcanic eruptions.