An experimental study of solidification is performed for a super-eutectic sodium carbonate solution (Na2CO3-H2O) in a confined cavity with varying initial concentration and temperature. We show important features of transport processes of heat and species during horizontal solidification by quantitative measurements of temperature and concentration. The development of the vertical density stratification that forms as a result of solidification can effectively damp thermal convection in the liquid region, and leads to the establishment of either a stagnant fluid region double-diffusive cells. Initial superheat is found to be responsible for the initiation of the double-diffusive cells. For a higher initial concentration, a larger initial superheat is required for the onset of the double-diffusive cells.