A numerical experiment of crystallization for a binary eutectic system with application to igneous textures

Abstract

Numerical experiments of crystallization in a binary eutectic system were carried out to understand the origin of textural variation in igneous rocks. In this study, the number density of crystals was intensively examined as a parameter of texture. The constant cooling rate experiment (no latent heat release) yields a higher number density of crystals by 1 order of magnitude than the constant heat loss experiment (full latent heat release). Differences in growth mechanism (diffusion‐limited with capillary effect versus reaction‐limited without capillary effect) result in the different dependence of cooling rate on number density of crystals. For diffusion‐limited growth with the capillary effect for spherical crystals the cooling rate dependence of number density of olivine, clinopyroxene, plagioclase, and opaque minerals seems to be consistent with the experimental data with superliquidus initial condition. For plagioclase, experimental data with subliquidus initial temperature and the observational data are not consistent with the present numerical results for both growth processes, suggesting that the plagioclase growth is governed by a different mechanism of nucleation and growth from homogeneous nucleation and both diffusion‐limited growth with capillary effect and simple reaction‐limited growth without capillary effect. Assuming the conductive cooling of a dike, it is predicted that for the diffusion‐limited growth the number density of crystals is proportional to y−3, where y is distance from the cooling boundary. This is in good agreement with some of the observational data by Gray [1978] except for plagioclase. The consistency among numerical, natural, and experimental data highly suggests that at the nucleation stage with superliquidus initial condition, crystals grow by the diffusion‐limited process, taking the spherical shape for olivine, pyroxene, plagioclase, and some oxides. The difference between volcanic and plutonic textures is caused by the difference of cooling rate by 2 orders of magnitude. The variation from intergranular, ophitic to poikilitic textures results from the difference in cooling rate dependence on number density between the plagioclase and the other minerals. The formation of porphyritic texture must satisfy the limited condition: the very small efficiency of latent heat production (nearly constant cooling rate), small values of interfacial energy of the first precipitating phase, and smaller value of interfacial energy of the second phase.