Numerical simulation of the crystallization of multicomponent melts in thin dikes or sills: 1. The liquidus phase

Abstract

Crystal size frequency distributions, crystallization histories, and thermal histories were calculated for the liquidus phase of a two‐component melt to model the crystallization of the liquidus phase of a multicomponent magma injected in a dike or sill. The crystal sizes, the variances of the crystal size frequency distributions, and the crystallization times depend on the competitive rates of crystallization and heat transfer by heat conduction, on the nucleation and growth rate functions, and on the boundary conditions. It is shown that the nucleation and growth rate functions can be parameterized by their maximum amplitudes and by the temperatures of the maxima. The texture of the crystallized intrusion depends on the difference between the initial undercooling and the undercooling of the maximum nucleation rate. The initial undercooling decreases with increasing distance from the margin of the intrusion and with increasing crystallization rate and wall rock temperature. The crystals are moderately sorted if the initial undercooling is larger than the undercooling of the maximum nucleation rate with bimodal and possibly trimodal size distributions. The crystals become increasingly well sorted with decreasing initial undercooling. If the undercooling is smaller than the undercooling of the maximum nucleation rate, the size distributions are unimodal. The unimodal distributions at the central regions of the intrusion typically have positive skewness about the mode and are platykurtic. If crystal embryos and impurities contribute significantly to heterogenous nucleation, the size distributions have a strong negative skewness. The crystal size frequency distributions and the thermal and crystallization histories are systematically different from those of one‐component models, and the solidification times are different from those calculated for purely thermal Stefan models. The analysis can be used to estimate kinetic parameters from the textures of natural intrusions. Peak nucleation and growth rates of plagioclase calculated from the crystal sizes of three dikes are found to be internally consistent and to compare favorably with published laboratory data.