Phase-field simulation for crystallization of a highly supercooled forsterite-chondrule melt droplet

Chondrules are submillimeter-sized and spherical-shaped crystalline grains consisting mainly of silicate material observed in chondritic meteorites. We numerically simulated pattern formation of a forsterite $(Mg2SiO4)$-chondrule in the melt droplet using a phase-field method. Because of the large surface-to-volume ratio, the surface cooling term was introduced in the framework of this method. We reproduced an unique crystal growth pattern inside the droplet composed of two distinguishable parts; the rim that covers whole droplet surface, and dendrite inside the droplet. It was found that the rim was formed when there is a large temperature difference of $∼100K$ between the center and surface of the droplet due to the large cooling flux at the surface. In order to obtain the temperature difference, we derived temperature distribution of the droplet analytically, and concluded that the rim was formed only when the droplet cools rapidly at a rate of $Rcool∼103Ks−1$⁠. However, when the surface cooling was so large as the temperature at the droplet center still remains above the melting point, no dendrite was obtained, though the rim was formed. The double structure captures the distinctive features of barred-olivine textures observed in natural chondrules.