A Semi-empirical Model for the Containerless Solidification of Liquid Carbon

Elemental carbon has important structural diversity, ranging from nanotubes through graphite to diamond. Transmission electron microscope studies of micron-size core/rim carbon spheres suggest that unlayered-graphene composite cores formed from (in some cases “pent-first”) solidification of carbon-vapor droplets condensed in both stellar atmosphere and laboratory settings, followed by gas-to-solid carbon coating to form the graphite rims. In this work, we construct analytical models for 2D reaction-limited nucleation and growth. We then generate an analytical condensation and solidification model to compare with presolar and lab-grown data on graphene sheet size and number density. Unlike 3D metallic elemental liquids’ supercooling thresholds of 30% of the melting temperature, our 2D analysis suggests containerless supercooling thresholds for carbon droplets on the order of 50% of the (inferred) melting temperature.