Abstract.: Liquid salty micro-channels (brine) between growing ice platelets in sea ice are an important habitat for CO2-binding microalgaea with great impact on polar ecosystems. The structure formation of ice platelets is microscopically described and a phase field model is developed. The pattern formation during solidification of the two-dimensional interstitial liquid is considered by two coupled order parameters, the tetrahedricity as structure of ice and the salinity. The coupling and time evolution of these order parameters are described by a consistent set of three model parameters. They determine the velocity of the freezing process and the structure formation, the phase diagram, the super-cooling and super-heating region, and the specific heat. The model is used to calculate the short-time frozen micro-structures. The obtained morphological structure is compared with the vertical brine pore space obtained from X-ray computed tomography. Graphical abstract: [Figure not available: see fulltext.]